Showing 1–50 of 54 results for author: Kotko, P

TEEC and azimuthal correlations in forward γ-hadron production in proton-proton and proton-lead collisions at LHC

Authors: Ishita Ganguli, Piotr Kotko

Abstract: We investigate photon-hadron Transverse Energy-Energy Correlation (TEEC) and azimuthal correlations in the forward rapidity region for proton-proton and proton-lead collisions within the small $x$ saturation formalism based on the Color Glass Condensate (CGC), supplemented by the initial-state and final-state parton shower simulation and hadronization using CASCADE. The study was performed in ligh… ▽ More We investigate photon-hadron Transverse Energy-Energy Correlation (TEEC) and azimuthal correlations in the forward rapidity region for proton-proton and proton-lead collisions within the small $x$ saturation formalism based on the Color Glass Condensate (CGC), supplemented by the initial-state and final-state parton shower simulation and hadronization using CASCADE. The study was performed in light of the upcoming FoCal detector of ALICE and the ATLAS detector upgrades with the extended pseudorapidity coverage. We predict a significant difference, at hadron-level, between the normalized TEECs in proton-proton and proton-lead collisions. Having a direct access to partonic subprocesses we also directly investigate the impact of the parton shower and hadronization on the TEEC. The ordinary azimuthal $γ$-hadron correlations show substantial suppression for proton-lead collision, as predicted earlier at parton-level. △ Less

Submitted 25 September, 2025; v1 submitted 31 July, 2025; originally announced July 2025.

Comments: Extended framework section and additional references

Polish national input to the 2026 update of the European Strategy for Particle Physics

Authors: K. Adamczyk, B. Badełek, T. Banaszkiewicz, V. Batozskaya, M. Bluj, D. Bocian, P. Bruckman de Renstrom, M. Chorowski, M. Chrząszcz, W. Cichalewski, D. Derendarz, M. Dyndał, J. Gluza, Ł. Graczykowski, K. Grebieszkow, A. Kaczmarska, P. Kalaczyński, A. Kalinowski, J. Kalinowski, M. Konecki, G. Kornakov, P. Kotko, M. Kucharczyk, A. Kupść, A. Kusina , et al. (37 additional authors not shown)

Abstract: The Polish high energy physics (HEP) community fully recognizes the urgent need to host at CERN a flagship project implementing a broad, long-term, and comprehensive vision of particle physics research and pursuing technological advances. Thus, we give preference and declare willingness to actively engage and participate in every aspect of the FCC project (both FCC-ee and FCC-hh), particularly acc… ▽ More The Polish high energy physics (HEP) community fully recognizes the urgent need to host at CERN a flagship project implementing a broad, long-term, and comprehensive vision of particle physics research and pursuing technological advances. Thus, we give preference and declare willingness to actively engage and participate in every aspect of the FCC project (both FCC-ee and FCC-hh), particularly accelerator development, detector construction, theoretical calculations, and physics analyses. As the e+e- Higgs Factory is the top priority for our field, the proposal to build a linear collider facility at CERN, opening up complementary physics prospects, should be considered as the second option. Polish teams declare strong support and are fully committed to contribute to the full exploitation of all aspects of the physics potential of the LHC and the HL-LHC programmes. To ensure the long-term development of particle physics, we also support the continuation of the high-field magnet research programme, as well as investigating other scenarios including, in particular, linear acceleration techniques and new acceleration technologies such as plasma acceleration, the muon collider and Gamma Factory. In addition, CERN should continue to provide support to fixed-target programmes at SPS as well as other non-collider and non-accelerator experiments at CERN. Participation in major projects conducted in and outside Europe should also be fostered. Education, communication, and outreach of particle physics are of paramount importance for the future of our field. An increased effort coordinated at the European level and resources allocated in all Member States are essential to effectively support future large-scale particle physics projects. △ Less

Submitted 28 April, 2025; originally announced April 2025.

Comments: Main (10 page) document combined with the backup document (53 pages with references)

Physics with high-luminosity proton-nucleus collisions at the LHC

Authors: D. d'Enterria, C. A. Flett, I. Grabowska-Bold, C. Hadjidakis, P. Kotko, A. Kusina, J. P. Lansberg, R. McNulty, M. Rinaldi, L. Bonechi, R. Bruce, C. Da Silva, E. G. Ferreiro, S. Fichet, L. Harland-Lang, G. Innocenti, F. Jonas, J. M. Jowett, R. Longo, K. Lynch, C. McGinn, T. Pierog, M. Pitt, S. Redaelli, B. Schenke , et al. (7 additional authors not shown)

Abstract: The physics case for the operation of high-luminosity proton-nucleus ($pA$) collisions during Run 3 and 4 at the LHC is reviewed. The collection of $\mathcal{O}$(1-10 pb$^{-1}$) of proton-lead ($p$Pb) collisions at the LHC will provide unique physics opportunities in a broad range of topics including proton and nuclear parton distribution functions (PDFs and nPDFs), generalised parton distribution… ▽ More The physics case for the operation of high-luminosity proton-nucleus ($pA$) collisions during Run 3 and 4 at the LHC is reviewed. The collection of $\mathcal{O}$(1-10 pb$^{-1}$) of proton-lead ($p$Pb) collisions at the LHC will provide unique physics opportunities in a broad range of topics including proton and nuclear parton distribution functions (PDFs and nPDFs), generalised parton distributions (GPDs), transverse momentum dependent PDFs (TMDs), low-$x$ QCD and parton saturation, hadron spectroscopy, baseline studies for quark-gluon plasma and parton collectivity, double and triple parton scatterings (DPS/TPS), photon-photon collisions, and physics beyond the Standard Model (BSM); which are not otherwise as clearly accessible by exploiting data from any other colliding system at the LHC. This report summarises the accelerator aspects of high-luminosity $pA$ operation at the LHC, as well as each of the physics topics outlined above, including the relevant experimental measurements that motivate -- much -- larger $pA$ datasets. △ Less

Submitted 5 April, 2025; originally announced April 2025.

Comments: 26 pages inc. refs, 1 figure, 3 tables. Slightly expanded version of a contribution submitted for the 2025 European Strategy for Particle Physics

Searching for saturation in forward dijet production at the LHC

Authors: A. van Hameren, H. Kakkad, P. Kotko, K. Kutak, S. Sapeta

Abstract: We review recent results for forward jests at the LHC and EIC as obtained within small-x Improved Transverse Momentum Dependent factorization (ITMD). In addition to elementary overview of various approaches to perturbative QCD at high energy, including High Energy Factorization, Color Glass Condensate and ITMD, we describe the Monte Carlo implementation and discuss the existing and unpublished p… ▽ More We review recent results for forward jests at the LHC and EIC as obtained within small-x Improved Transverse Momentum Dependent factorization (ITMD). In addition to elementary overview of various approaches to perturbative QCD at high energy, including High Energy Factorization, Color Glass Condensate and ITMD, we describe the Monte Carlo implementation and discuss the existing and unpublished phenomenological results for forward dijets. △ Less

Submitted 30 June, 2023; originally announced June 2023.

Comments: 50 pages

Forward $γ$+jet production in proton-proton and proton-lead collisions at LHC within the FoCal calorimeter acceptance

Authors: Ishita Ganguli, Andreas van Hameren, Piotr Kotko, Krzysztof Kutak

Abstract: Using the small-$x$ Improved Transverse Momentum Dependent factorization (ITMD), which, for a general two-to-two massless scattering can be proved within the Color Glass Condensate (CGC) theory for transverse momenta of particles greater than the saturation scale, we provide predictions for isolated forward photon and jet production in proton-proton and proton-nucleus collisions within the planned… ▽ More Using the small-$x$ Improved Transverse Momentum Dependent factorization (ITMD), which, for a general two-to-two massless scattering can be proved within the Color Glass Condensate (CGC) theory for transverse momenta of particles greater than the saturation scale, we provide predictions for isolated forward photon and jet production in proton-proton and proton-nucleus collisions within the planned ALICE FoCal detector acceptance. We study azimuthal correlations, $p_T$ spectra, as well as normalized ratios of proton-proton cross sections for different energies. The only TMD distribution needed for that process is the "dipole" TMD gluon distribution, which in our computations is based on HERA data and undergoes momentum space BK evolution equation with DGLAP corrections and Sudakov resummation. We conclude, that the process provides an excellent probe of the dipole TMD gluon distribution in saturation regime. △ Less

Submitted 20 June, 2023; v1 submitted 7 June, 2023; originally announced June 2023.

Comments: 14 pages, 9 figures, updated references, minor text corrections

Color Reconnection Effects in $J/ψ$ Hadroproduction

Authors: Piotr Kotko, Leszek Motyka, Anna Stasto

Abstract: We investigate production of $J/ψ$ mesons in hadron-hadron collisions, defined as low invariant mass $c\bar{c}$ singlets produced in a mixture of perturbative and nonperturbative mechanisms provided by the PYTHIA Monte Carlo. We find that in this model the color reconnection mechanism, which breaks the factorization, is essential to reasonably describe the experimental data. We investigate production of $J/ψ$ mesons in hadron-hadron collisions, defined as low invariant mass $c\bar{c}$ singlets produced in a mixture of perturbative and nonperturbative mechanisms provided by the PYTHIA Monte Carlo. We find that in this model the color reconnection mechanism, which breaks the factorization, is essential to reasonably describe the experimental data. △ Less

Submitted 11 August, 2023; v1 submitted 23 March, 2023; originally announced March 2023.

Comments: 12 pages, 3 figures, references added, typos corrected

One-loop gauge invariant amplitudes with a space-like gluon

Authors: Etienne Blanco, Alessandro Giachino, Andreas van Hameren, Piotr Kotko

Abstract: Nowadays the particle physics has entered an era where high precision calculations are required in order to compare the theoretical predictions with the experimental data. In this paper, we explicitly compute the virtual contributions for the space-like one-jet processes, $\procgg,\procqq,\procH$ and $\procee$ within the auxiliary parton method. Our results, which are expected to play an important… ▽ More Nowadays the particle physics has entered an era where high precision calculations are required in order to compare the theoretical predictions with the experimental data. In this paper, we explicitly compute the virtual contributions for the space-like one-jet processes, $\procgg,\procqq,\procH$ and $\procee$ within the auxiliary parton method. Our results, which are expected to play an important role in high precision description of small $x$ physics, explicitly confirm the conjecture developed in Ref. \cite{vanHameren:2022mtk}, thus helping to bridge the gap between lowest order calculations and NLO corrections within hybrid $k_T$-factorization scheme. △ Less

Submitted 6 April, 2023; v1 submitted 7 December, 2022; originally announced December 2022.

Report number: IFJPAN-IV-2022-20

Dijet azimuthal correlations in p-p and p-Pb collisions at forward LHC calorimeters

Authors: M. Abdullah Al-Mashad, A. van Hameren, H. Kakkad, P. Kotko, K. Kutak, P. van Mechelen, S. Sapeta

Abstract: We present a state-of-the-art computation for the production of forward dijets in proton-proton and proton-lead collisions at the LHC, in rapidity domains covered by the ATLAS calorimeter and the planned FoCal extension of the ALICE detector. We use the small-x improved TMD (ITMD) formalism, together with collinearly improved TMD gluon distributions and full b-space Sudakov resummation, and discus… ▽ More We present a state-of-the-art computation for the production of forward dijets in proton-proton and proton-lead collisions at the LHC, in rapidity domains covered by the ATLAS calorimeter and the planned FoCal extension of the ALICE detector. We use the small-x improved TMD (ITMD) formalism, together with collinearly improved TMD gluon distributions and full b-space Sudakov resummation, and discuss nonperturbative corrections due to hadronization and showers using the Pythia event generator. We observe that forward dijets in proton-nucleus collisions at moderately low pT are excellent probes of saturation effects, as the Sudakov resummation does not alter the suppression of the cross section. △ Less

Submitted 26 October, 2022; v1 submitted 12 October, 2022; originally announced October 2022.

Comments: 14 pages

Precision QCD, Hadronic Structure & Forward QCD, Heavy Ions: Report of Energy Frontier Topical Groups 5, 6, 7 submitted to Snowmass 2021

Authors: M. Begel, S. Hoeche, M. Schmitt, H. -W. Lin, P. M. Nadolsky, C. Royon, Y-J. Lee, S. Mukherjee, C. Baldenegro, J. Campbell, G. Chachamis, F. G. Celiberto, A. M. Cooper-Sarkar, D. d'Enterria, M. Diefenthaler, M. Fucilla, M. V. Garzelli, M. Guzzi, M. Hentschinski, T. J. Hobbs, J. Huston, J. Isaacson, S. R. Klein, F. Kling, P. Kotko , et al. (25 additional authors not shown)

Abstract: This report was prepared on behalf of three Energy Frontier Topical Groups of the Snowmass 2021 Community Planning Exercise. It summarizes the status and implications of studies of strong interactions in high-energy experiments and QCD theory. We emphasize the rich landscape and broad impact of these studies in the decade ahead. Hadronic interactions play a central role in the high-luminosity Larg… ▽ More This report was prepared on behalf of three Energy Frontier Topical Groups of the Snowmass 2021 Community Planning Exercise. It summarizes the status and implications of studies of strong interactions in high-energy experiments and QCD theory. We emphasize the rich landscape and broad impact of these studies in the decade ahead. Hadronic interactions play a central role in the high-luminosity Large Hadron Collider (LHC) physics program, and strong synergies exist between the (HL-)LHC and planned or proposed experiments at the U.S. Electron-Ion Collider, CERN forward physics experiments, high-intensity facilities, and future TeV-range lepton and hadron colliders. Prospects for precision determinations of the strong coupling and a variety of nonperturbative distribution and fragmentation functions are examined. We also review the potential of envisioned tests of new dynamical regimes of QCD in high-energy and high-density scattering processes with nucleon, ion, and photon initial states. The important role of the high-energy heavy-ion program in studies of nuclear structure and the nuclear medium, and its connections with QCD involving nucleons are summarized. We address ongoing and future theoretical advancements in multi-loop QCD computations, lattice QCD, jet substructure, and event generators. Cross-cutting connections between experimental measurements, theoretical predictions, large-scale data analysis, and high-performance computing are emphasized. △ Less

Submitted 19 November, 2022; v1 submitted 29 September, 2022; originally announced September 2022.

Comments: 95 pages (bibliography 30 pages), 28 figures; v.2: minor changes, authors and references added

Report number: FERMILAB-CONF-22-733-SCD-T, SMU-HEP-22-06

Evolution equation for elastic scattering of hadrons

Authors: Hiren Kakkad, Anderson Kendi Kohara, Piotr Kotko

Abstract: We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which has a form of the complex nonlinear reaction-diffusion equation, with time being played by the logarithm of energy. The initial conditions are provided by the data-driven models for the real and imaginary parts of the amplitude. Numerical calculations o… ▽ More We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which has a form of the complex nonlinear reaction-diffusion equation, with time being played by the logarithm of energy. The initial conditions are provided by the data-driven models for the real and imaginary parts of the amplitude. Numerical calculations of pp differential cross sections and forward quantities for LHC energies agree very well with experimental data extending up to, and including the diffractive cone. Furthermore, we show that at current accessible energies the non-linear effects play an important role, as the impact parameter space profiles approach the unitarity bound. The equation also predicts some other effects discussed in the literature, like the hollowness of nuclear matter or existence of stationary points in momentum transfer t. △ Less

Submitted 4 August, 2022; v1 submitted 31 May, 2022; originally announced May 2022.

Comments: 6 pages, 3 figures and 2 tables

White Paper on Forward Physics, BFKL, Saturation Physics and Diffraction

Authors: Martin Hentschinski, Christophe Royon, Marco Alcazar Peredo, Cristian Baldenegro, Andrea Bellora, Renaud Boussarie, Francesco Giovanni Celiberto, Salim Cerci, Grigorios Chachamis, J. G. Contreras, Sylvain Fichet, Michael Fucilla, Gero von Gersdorff, Pablo González, Andreas van Hameren, Jamal Jalilian-Marian, Mats Kampshoff, Valery Khoze, Michael Klasen, Spencer Robert Klein, Georgios Krintiras, Piotr Kotko, Krzysztof Kutak, Jean-Philippe Lansberg, Emilie Li , et al. (17 additional authors not shown)

Abstract: The goal of this whitepaper is to give a comprehensive overview of the rich field of forward physics. We discuss the occurrences of BFKL resummation effects in special final states, such as Mueller-Navelet jets, jet gap jets, and heavy quarkonium production. It further addresses TMD factorization at low x and the manifestation of a semi-hard saturation scale in (generalized) TMD PDFs. More theoret… ▽ More The goal of this whitepaper is to give a comprehensive overview of the rich field of forward physics. We discuss the occurrences of BFKL resummation effects in special final states, such as Mueller-Navelet jets, jet gap jets, and heavy quarkonium production. It further addresses TMD factorization at low x and the manifestation of a semi-hard saturation scale in (generalized) TMD PDFs. More theoretical aspects of low x physics, probes of the quark gluon plasma, as well as the possibility to use photon-hadron collisions at the LHC to constrain hadronic structure at low x, and the resulting complementarity between LHC and the EIC are also presented. We also briefly discuss diffraction at colliders as well as the possibility to explore further the electroweak theory in central exclusive events using the LHC as a photon-photon collider. △ Less

Submitted 30 March, 2022; v1 submitted 15 March, 2022; originally announced March 2022.

Comments: 77 pages, 27 figures, contribution to Snowmass 2021; contributions updated and authors added

A new Wilson Line-based classical action for gluodynamics

Authors: Hiren Kakkad, Piotr Kotko, Anna Stasto

Abstract: We develop a new classical action that in addition to $\mathrm{MHV}$ vertices contains also $\mathrm{N^kMHV}$ vertices, where $1\leq k \leq n-4$ with $n$ the number of external legs. The lowest order vertex is the four-point MHV vertex -- there is no three point vertex and thus the amplitude calculation involves fewer vertices than in the CSW method and, obviously, considerably fewer than in the s… ▽ More We develop a new classical action that in addition to $\mathrm{MHV}$ vertices contains also $\mathrm{N^kMHV}$ vertices, where $1\leq k \leq n-4$ with $n$ the number of external legs. The lowest order vertex is the four-point MHV vertex -- there is no three point vertex and thus the amplitude calculation involves fewer vertices than in the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action. The action is obtained by a canonical transformation of the Yang-Mills action in the light-cone gauge, where the field transformations are based on the Wilson line functionals. △ Less

Submitted 25 October, 2021; originally announced October 2021.

Comments: Presented at RADCOR-LoopFest 2021. Submitted to SciPost

Probing gluon number density with electron-dijet correlations at EIC

Authors: Andreas van Hameren, Piotr Kotko, Krzysztof Kutak, Sebastian Sapeta, Elżbieta Żarów

Abstract: We propose a novel way of studying the gluon number density (the so-called Weizsäcker-Williams gluon distribution) using the planned Electron Ion Collider. Namely, with the help of the azimuthal correlations between the total transverse momentum of the dijet system and the scattered electron, we examine an interplay between the effect of the soft gluon emissions (the Sudakov form factor) and the g… ▽ More We propose a novel way of studying the gluon number density (the so-called Weizsäcker-Williams gluon distribution) using the planned Electron Ion Collider. Namely, with the help of the azimuthal correlations between the total transverse momentum of the dijet system and the scattered electron, we examine an interplay between the effect of the soft gluon emissions (the Sudakov form factor) and the gluon saturation effects. The kinematic cuts are chosen such that the dijet system is produced in the forward direction in the laboratory frame, which provides an upper bound on the probed longitudinal fractions of the hadron momentum carried by scattered gluons. Further cuts enable us to use the factorization formalism that directly involves the unpolarized Weizsäcker-Williams gluon distribution. We find this observable to be very sensitive to the soft gluon emission and moderately sensitive to the gluon saturation. △ Less

Submitted 12 July, 2021; v1 submitted 26 June, 2021; originally announced June 2021.

Comments: 7 pages, 5 figures. References added

Report number: IFJPAN-IV-2021-10

On systematic effects in the numerical solutions of the JIMWLK equation

Authors: Salvatore Cali, Krzysztof Cichy, Piotr Korcyl, Piotr Kotko, Krzysztof Kutak, Cyrille Marquet

Abstract: In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation… ▽ More In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: "square root" and "noise" prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases. △ Less

Submitted 6 May, 2021; v1 submitted 29 April, 2021; originally announced April 2021.

Comments: 21 pages, 18 figures, references updated

Report number: IFJPAN-IV-2021-7

Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report

Authors: R. Abdul Khalek, A. Accardi, J. Adam, D. Adamiak, W. Akers, M. Albaladejo, A. Al-bataineh, M. G. Alexeev, F. Ameli, P. Antonioli, N. Armesto, W. R. Armstrong, M. Arratia, J. Arrington, A. Asaturyan, M. Asai, E. C. Aschenauer, S. Aune, H. Avagyan, C. Ayerbe Gayoso, B. Azmoun, A. Bacchetta, M. D. Baker, F. Barbosa, L. Barion , et al. (390 additional authors not shown)

Abstract: This report describes the physics case, the resulting detector requirements, and the evolving detector concepts for the experimental program at the Electron-Ion Collider (EIC). The EIC will be a powerful new high-luminosity facility in the United States with the capability to collide high-energy electron beams with high-energy proton and ion beams, providing access to those regions in the nucleon… ▽ More This report describes the physics case, the resulting detector requirements, and the evolving detector concepts for the experimental program at the Electron-Ion Collider (EIC). The EIC will be a powerful new high-luminosity facility in the United States with the capability to collide high-energy electron beams with high-energy proton and ion beams, providing access to those regions in the nucleon and nuclei where their structure is dominated by gluons. Moreover, polarized beams in the EIC will give unprecedented access to the spatial and spin structure of the proton, neutron, and light ions. The studies leading to this document were commissioned and organized by the EIC User Group with the objective of advancing the state and detail of the physics program and developing detector concepts that meet the emerging requirements in preparation for the realization of the EIC. The effort aims to provide the basis for further development of concepts for experimental equipment best suited for the science needs, including the importance of two complementary detectors and interaction regions. This report consists of three volumes. Volume I is an executive summary of our findings and developed concepts. In Volume II we describe studies of a wide range of physics measurements and the emerging requirements on detector acceptance and performance. Volume III discusses general-purpose detector concepts and the underlying technologies to meet the physics requirements. These considerations will form the basis for a world-class experimental program that aims to increase our understanding of the fundamental structure of all visible matter △ Less

Submitted 26 October, 2021; v1 submitted 8 March, 2021; originally announced March 2021.

Comments: 902 pages, 415 authors, 151 institutions

Report number: BNL-220990-2021-FORE, JLAB-PHY-21-3198, LA-UR-21-20953

Journal ref: Nucl. Phys. A 1026 (2022) 122447

A new Wilson line-based action for gluodynamics

Authors: Hiren Kakkad, Piotr Kotko, Anna Stasto

Abstract: We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $\overline{\textrm{MHV}}$ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any… ▽ More We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $\overline{\textrm{MHV}}$ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any $n$-leg vertex has $2\leq m \leq n-2$ negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action. △ Less

Submitted 25 June, 2021; v1 submitted 22 February, 2021; originally announced February 2021.

Comments: Some typos corrected, references updated, 26 pages, 10 figures

Sudakov effects in central-forward dijet production in high energy factorization

Authors: A. van Hameren, P. Kotko, K. Kutak, S. Sapeta

Abstract: We discuss central-forward dijet production at LHC energies within the framework of high energy factorization. In our study, we profit from the recent progress on consistent merging of Sudakov resummation with small-$x$ effects, which allows us to compute two different gluon distributions which depend on longitudinal momentum, transverse momentum and the hard scale of the process: one for the quar… ▽ More We discuss central-forward dijet production at LHC energies within the framework of high energy factorization. In our study, we profit from the recent progress on consistent merging of Sudakov resummation with small-$x$ effects, which allows us to compute two different gluon distributions which depend on longitudinal momentum, transverse momentum and the hard scale of the process: one for the quark channel and one for the gluon channel. The small-$x$ resummation is included by means of the BK equation supplemented with a kinematic constraint and subleading corrections. We test the new gluon distributions against existing CMS data for transverse momentum spectra in forward-central dijet production. We obtain results which are largely consistent with our earlier predictions based on model implementation of Sudakov form factors. In addition, we study dijet azimuthal decorrelations for the forward-central jets, which are known to be sensitive to the modeling of soft radiation. △ Less

Submitted 28 January, 2021; v1 submitted 25 October, 2020; originally announced October 2020.

Comments: 15 pages, 5 figures; v2: extended description of formalism and results, version published by PLB

Report number: IFJPAN-IV-2020-8

All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop

Authors: Etienne Blanco, Andreas van Hameren, Piotr Kotko, Krzysztof Kutak

Abstract: We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell p… ▽ More We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line. △ Less

Submitted 4 March, 2021; v1 submitted 18 August, 2020; originally announced August 2020.

Comments: 20 pages; typos corrected, labels/normalization homogenized

Report number: IFJPAN-IV-2020-6

Journal ref: JHEP 12 (2020) 158

Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians

Authors: Hiren Kakkad, Piotr Kotko, Anna Stasto

Abstract: We investigate the appearance of straight infinite Wilson lines lying on the self-dual plane in the context of the Self Dual sector of the Yang Mills theory and in a connection to the Lagrangian implementing the MHV vertices (MHV Lagrangian) according to the Cachazo-Svrcek-Witten method. It was already recognized in the past by two of the authors, that such Wilson line functional provides the fiel… ▽ More We investigate the appearance of straight infinite Wilson lines lying on the self-dual plane in the context of the Self Dual sector of the Yang Mills theory and in a connection to the Lagrangian implementing the MHV vertices (MHV Lagrangian) according to the Cachazo-Svrcek-Witten method. It was already recognized in the past by two of the authors, that such Wilson line functional provides the field transformation of positive helicity fields between the Yang-Mills theory on the light-cone and the MHV Lagrangian. Here we discuss in detail the connection to the Self Dual sector and we provide a new insight into the solution for the minus helicity field transformation, which can be expressed in terms of a functional derivative of the straight infinite Wilson line on the self-dual plane. △ Less

Submitted 29 June, 2020; originally announced June 2020.

Comments: 26 pages, 3 figures

Forward trijet production in p-p and p-Pb collisions at LHC

Authors: Marcin Bury, Andreas van Hameren, Piotr Kotko, Krzysztof Kutak

Abstract: We calculate various azimuthal angle distributions for three jets produced in the forward rapidity region with transverse momenta $p_T>20\,\mathrm{GeV}$ in proton-proton (p-p) and proton-lead (p-Pb) collisions at center of mass energy $5.02\,\,\mathrm{TeV}$. We use the multi-parton extension of the so-called small-$x$ Improved Transverse Momentum Dependent factorization (ITMD). We study effects re… ▽ More We calculate various azimuthal angle distributions for three jets produced in the forward rapidity region with transverse momenta $p_T>20\,\mathrm{GeV}$ in proton-proton (p-p) and proton-lead (p-Pb) collisions at center of mass energy $5.02\,\,\mathrm{TeV}$. We use the multi-parton extension of the so-called small-$x$ Improved Transverse Momentum Dependent factorization (ITMD). We study effects related to change from the standard $k_T$-factorization to ITMD factorization as well as changes as one goes from p-p collision to p-Pb. We observe rather large differences in the distribution when we change the factorization approach, which allows to both improve the small-$x$ TMD gluon distributions as well as validate and improve the factorization approach. We also see significant depletion of the nuclear modification ratio, indicating a possibility of searches for saturation effects using trijet final states in a more exclusive way than for dijets. △ Less

Submitted 10 September, 2020; v1 submitted 23 June, 2020; originally announced June 2020.

Comments: References added. To appear in JHEP

Trijets in kt-factorisation: matrix elements vs parton shower

Authors: H. Van Haevermaet, A. Van Hameren, P. Kotko, K. Kutak, P. Van Mechelen

Abstract: We study 3-jet event topologies in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13 {\rm\ TeV}$ in a configuration, where one jet is present in the central pseudorapidity region ($|η| < 2.0$) while two other jets are in a more forward (same hemisphere) area ($|η| > 2.0$). We compare various parton level predictions using: collinear factorisation, $\KT{}$-factorisation with ful… ▽ More We study 3-jet event topologies in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13 {\rm\ TeV}$ in a configuration, where one jet is present in the central pseudorapidity region ($|η| < 2.0$) while two other jets are in a more forward (same hemisphere) area ($|η| > 2.0$). We compare various parton level predictions using: collinear factorisation, $\KT{}$-factorisation with fully off-shell matrix elements and the hybrid framework. We study the influence of different parton distribution functions, initial state radiation, final state radiation, and hadronisation. We focus on differential cross sections as a function of azimuthal angle difference between the leading dijet system and the third jet, which is found to have excellent sensitivity to the physical effects under study. △ Less

Submitted 30 July, 2020; v1 submitted 16 April, 2020; originally announced April 2020.

Comments: 10 pages. Published version

BFKL Pomeron loop contribution in diffractive photoproduction and inclusive hadroproduction of $J/ψ$ and $Υ$

Authors: Piotr Kotko, Leszek Motyka, Mariusz Sadzikowski, Anna M. Stasto

Abstract: We analyze contributions to the heavy vector meson production with large transverse momentum in proton--proton and diffractive photon--proton scattering driven by an exchange of two Balitsky--Fadin--Kuraev--Lipatov Pomerons in the squared amplitudes. The Pomerons couple to a single parton and form a Pomeron loop closed by the vector meson impact factors. For the photon--proton case the diffractive… ▽ More We analyze contributions to the heavy vector meson production with large transverse momentum in proton--proton and diffractive photon--proton scattering driven by an exchange of two Balitsky--Fadin--Kuraev--Lipatov Pomerons in the squared amplitudes. The Pomerons couple to a single parton and form a Pomeron loop closed by the vector meson impact factors. For the photon--proton case the diffractive cut of the Pomeron loop contributes, and for the inclusive hadroproduction one finds the loop with two cut Pomerons. We compute both of these Pomeron loop contributions and study in detail their properties. The results are then used to calculate the cross sections for diffractive $J/ψ$ photoproduction with large transverse momentum at HERA and the correlated two Pomeron contribution for inclusive $J/ψ$ and $Υ$ production cross sections at the LHC. Within a unified approach a good description of the photoproduction data is found, but correlated two Pomeron mechanism gives only a small contribution to hadroproduction of the vector mesons at the LHC. △ Less

Submitted 30 April, 2019; originally announced May 2019.

Comments: 34 pages, 16 figures

Broadening and saturation effects in dijet azimuthal correlations in p-p and p-Pb collisions at $\mathbf{\sqrt{s_{NN}}} = $ 5.02 TeV

Authors: Andreas van Hameren, Piotr Kotko, Krzysztof Kutak, Sebastian Sapeta

Abstract: We demonstrate that the recent forward-forward dijet correlation data measured by the ATLAS collaboration for proton-proton and proton-lead collisions are consistent with the broadening effects due to both the gluon saturation and the resummation of large logarithms of the hard scale (the so-called Sudakov logarithms). We find that both effects are necessary to describe the experimental results. We demonstrate that the recent forward-forward dijet correlation data measured by the ATLAS collaboration for proton-proton and proton-lead collisions are consistent with the broadening effects due to both the gluon saturation and the resummation of large logarithms of the hard scale (the so-called Sudakov logarithms). We find that both effects are necessary to describe the experimental results. △ Less

Submitted 30 June, 2019; v1 submitted 4 March, 2019; originally announced March 2019.

Comments: 5 pages. New figure added. To appear in PLB

Report number: IFJPAN-IV-2019-3

Interplay of the CGC and TMD frameworks to all orders in kinematic twist

Authors: Tolga Altinoluk, Renaud Boussarie, Piotr Kotko

Abstract: A framework for an improved TMD (iTMD) factorization scheme at small $x$, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD $k_t \ll Q$ regime and the BFKL $k_t \sim Q$ regime. In this article, we study the relation between CGC and iTMD amplitudes. We first show how the dipole-size expansion of CGC amplitudes resembles the twist expansion of… ▽ More A framework for an improved TMD (iTMD) factorization scheme at small $x$, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD $k_t \ll Q$ regime and the BFKL $k_t \sim Q$ regime. In this article, we study the relation between CGC and iTMD amplitudes. We first show how the dipole-size expansion of CGC amplitudes resembles the twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy by simply getting rid of all genuine twist contributions in a CGC amplitude. Finally we compare the amplitudes obtained via a proper kinematic twist expansion to those obtained via a more standard dilute expansion to show the relation between the iTMD framework and the dilute low $x$ framework. △ Less

Submitted 29 January, 2019; v1 submitted 4 January, 2019; originally announced January 2019.

Comments: 42 pages, 7 figures, 1 table

PHOTON-2017 conference proceedings

Authors: David d'Enterria, Albert de Roeck, Michelangelo Mangano, Jaroslav Adam, Massimiliano Alvioli, Christopher D. Anson, Hamed Bakhshiansohi, Cristian Baldenegro, Valerio Bertone, Stanley J. Brodsky, Peter J. Bussey, Chav Chhiv Chau, Weiren Chou, Ruchi Chudasama, Fernando Cornet, David d'Enterria, Stefan Dittmaier, Babette Dobrich, Dipanwita Dutta, John Ellis, Sylvain Fichet, Leonid Frankfurt, Carlos Garcia-Canal, Rohini M. Godbole, Agnes Grau , et al. (56 additional authors not shown)

Abstract: This document collects the proceedings of the PHOTON 2017 conference ("International Conference on the Structure and the Interactions of the Photon", including the 22th "International Workshop on Photon-Photon Collisions", and the "International Workshop on High Energy Photon Colliders") held at CERN (Geneva) in May 2017. The latest experimental and theoretical developments on the topics of the PH… ▽ More This document collects the proceedings of the PHOTON 2017 conference ("International Conference on the Structure and the Interactions of the Photon", including the 22th "International Workshop on Photon-Photon Collisions", and the "International Workshop on High Energy Photon Colliders") held at CERN (Geneva) in May 2017. The latest experimental and theoretical developments on the topics of the PHOTON conference series are covered: (i) $γ\,γ$ processes in e$^+$e$^-$, proton-proton (pp) and nucleus-nucleus (AA) collisions at current and future colliders, (ii) $γ$-hadron interactions in e$^\pm$p, pp, and AA collisions, (iii) final-state photon production (including Standard Model studies and searches beyond it) in pp and AA collisions, and (iv) high-energy $γ$-ray astrophysics. These proceedings are dedicated to the memory of Maria Krawczyk. △ Less

Submitted 19 December, 2018; originally announced December 2018.

Comments: 296 pages. CERN-Proceedings-2018-001 (CERN, Geneva, 2018), to appear. arXiv admin note: substantial text overlap with arXiv:1804.05614, arXiv:1708.06683, arXiv:1709.09044, arXiv:1708.00912, arXiv:1708.07173, arXiv:1709.02985, arXiv:1709.00176, arXiv:1709.05167, arXiv:1708.05756, arXiv:1708.09759, arXiv:1708.07531, arXiv:1703.08450, arXiv:1711.02551, arXiv:1511.07794, arXiv:1712.10104, arXiv:1708.05776, arXiv:1712.10202, arXiv:1709.07110, arXiv:1702.08730, arXiv:1709.02648, arXiv:1411.6397

TMD gluon distributions for multiparton processes

Authors: Marcin Bury, Piotr Kotko, Krzysztof Kutak

Abstract: We derive gauge invariant operators entering definitions of the Transverse Momentum Dependent (TMD) gluon distributions, for all five and six parton processes. Our calculations utilize color decomposition of amplitudes in the color flow basis. In addition, we find the general result for multi-gluon process (with arbitrary number of gluons) at large $N_{c}$. On phenomenological ground our results m… ▽ More We derive gauge invariant operators entering definitions of the Transverse Momentum Dependent (TMD) gluon distributions, for all five and six parton processes. Our calculations utilize color decomposition of amplitudes in the color flow basis. In addition, we find the general result for multi-gluon process (with arbitrary number of gluons) at large $N_{c}$. On phenomenological ground our results may be used for multi-jet production in the small-$x$ regime, where the TMD gluon distributions can be derived from the Color Glass Condensate effective theory. △ Less

Submitted 21 July, 2020; v1 submitted 24 September, 2018; originally announced September 2018.

Comments: 46 pages, numerical factors corrected. Conclusions unchanged

Report number: IFJPAN-IV-2018-17, CERN-TH-2018-208

Journal ref: Eur.Phys.J.C 79 (2019) 2, 152

Studying minijets and MPI with rapidity correlations

Authors: Maxim Azarkin, Piotr Kotko, Andrzej Siodmok, Mark Strikman

Abstract: We propose and carry a detailed study of an observable sensitive to different mechanisms of minijet production. The class of observables measures how the transverse momenta of hadrons produced in association with various trigger objects are balanced as a function of rapidity. It is shown that the observables are sensitive to the model parameters relevant to the minijet production mechanisms: low-… ▽ More We propose and carry a detailed study of an observable sensitive to different mechanisms of minijet production. The class of observables measures how the transverse momenta of hadrons produced in association with various trigger objects are balanced as a function of rapidity. It is shown that the observables are sensitive to the model parameters relevant to the minijet production mechanisms: low-$p_{\rm T}$ cut-off regulating jet cross-section, transverse distribution of partons in protons, and parton distribution functions. We perform our test at different charge-particle multiplicities and collision energies. The MC models, which describe many features of the LHC data, are found to predict quite different results demonstrating high discriminating power of the proposed observables. We also review mechanisms and components of \sc{Herwig}, \sc{Pythia}, and \sc{Sherpa} Monte Carlo models relevant to the minijet production. △ Less

Submitted 13 February, 2019; v1 submitted 23 June, 2018; originally announced June 2018.

Comments: 27 pages, 16 figures

Predictions for Cold Nuclear Matter Effects in $p+$Pb Collisions at $\sqrt{s_{_{NN}}} = 8.16$ TeV

Authors: J. L. Albacete, F. Arleo, G. G. Barnaföldi, G. Bíró, D. d'Enterria, B. Ducloué, K. J. Eskola, E. G. Ferreiro, M. Gyulassy, S. M. Harangozó, I. Helenius, Z. -B. Kang, P. Kotko, S. A. Kulagin, K. Kutak, J. P. Lansberg, T. Lappi, P. Lévai, Z. W. Lin, G. Ma, Y. -Q. Ma, H. Mäntysaari, H. Paukkunen, G. Papp, R. Petti , et al. (17 additional authors not shown)

Abstract: Predictions for cold nuclear matter effects on charged hadrons, identified light hadrons, quarkonium and heavy flavor hadrons, Drell-Yan dileptons, jets, photons, gauge bosons and top quarks produced in $p+$Pb collisions at $\sqrt{s_{_{NN}}} = 8.16$ TeV are compiled and, where possible, compared to each other. Predictions of the normalized ratios of $p+$Pb to $p+p$ cross sections are also presente… ▽ More Predictions for cold nuclear matter effects on charged hadrons, identified light hadrons, quarkonium and heavy flavor hadrons, Drell-Yan dileptons, jets, photons, gauge bosons and top quarks produced in $p+$Pb collisions at $\sqrt{s_{_{NN}}} = 8.16$ TeV are compiled and, where possible, compared to each other. Predictions of the normalized ratios of $p+$Pb to $p+p$ cross sections are also presented for most of the observables, providing new insights into the expected role of cold nuclear matter effects. In particular, the role of nuclear parton distribution functions on particle production can now be probed over a wider range of phase space than ever before. △ Less

Submitted 7 December, 2017; v1 submitted 31 July, 2017; originally announced July 2017.

Comments: 84 pages, 44 figures, version accepted for publication in Nuclear Physics A

Wilson lines in the MHV action

Authors: P. Kotko, A. M. Stasto

Abstract: The MHV action is the Yang-Mills action quantized on the light-front, where the two explicit physical gluonic degrees of freedom have been canonically transformed to a new set of fields. This transformation leads to the action with vertices being off-shell continuations of the MHV amplitudes. We show that the solution to the field transformation expressing one of the new fields in terms of the Yan… ▽ More The MHV action is the Yang-Mills action quantized on the light-front, where the two explicit physical gluonic degrees of freedom have been canonically transformed to a new set of fields. This transformation leads to the action with vertices being off-shell continuations of the MHV amplitudes. We show that the solution to the field transformation expressing one of the new fields in terms of the Yang-Mills field is a certain type of the Wilson line. More precisely, it is a straight infinite gauge link with a slope extending to the light-cone minus and the transverse direction. One of the consequences of that fact is that certain MHV vertices reduced partially on-shell are gauge invariant -- a fact discovered before using conventional light-front perturbation theory. We also analyze the diagrammatic content of the field transformations leading to the MHV action. We found that the diagrams for the solution to the transformation (given by the Wilson line) and its inverse differ only by light-front energy denominators. Further, we investigate the coordinate space version of the inverse solution to the one given by the Wilson line. We find an explicit expression given by a power series in fields. We also give a geometric interpretation to it by means of a specially defined vector field. Finally, we discuss the fact that the Wilson line solution to the transformation is directly related to the all-like helicity gluon wave function, while the inverse functional is a generating functional for solutions of self-dual Yang-Mills equations. △ Less

Submitted 31 May, 2017; originally announced June 2017.

Comments: 44 pages, a few figures

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC

Authors: P. Kotko, K. Kutak, S. Sapeta, A. M. Stasto, M. Strikman

Abstract: Using the framework that interpolates between the leading power limit of the Color Glass Condensate and the High Energy (or $k_{T}$) factorization we calculate the direct component of the forward dijet production in ultra-peripheral $\mathrm{Pb}$-$\mathrm{Pb}$ collisions at CM energy $5.1\,\mathrm{TeV}$ per nucleon pair. The formalism is applicable when the average transverse momentum of the dijet… ▽ More Using the framework that interpolates between the leading power limit of the Color Glass Condensate and the High Energy (or $k_{T}$) factorization we calculate the direct component of the forward dijet production in ultra-peripheral $\mathrm{Pb}$-$\mathrm{Pb}$ collisions at CM energy $5.1\,\mathrm{TeV}$ per nucleon pair. The formalism is applicable when the average transverse momentum of the dijet system $P_{T}$ is much bigger than the saturation scale $Q_{s}$, $P_{T}\gg Q_{s}$, while the imbalance of the dijet system can be arbitrary. The cross section is uniquely sensitive to the Weizsäcker-Williams (WW) unintegrated gluon distribution, which is far less known from experimental data than the most common dipole gluon distribution appearing in inclusive small-$x$ processes. We have calculated cross sections and nuclear modification ratios using WW gluon distribution obtained from the dipole gluon density through the Gaussian approximation. The dipole gluon distribution used to get WW was fitted to the inclusive HERA data with the nonlinear extension of unified BFKL+DGLAP evolution equation. The saturation effects are visible but rather weak for realistic $p_{T}$ cut on the dijet system, reaching about $20\%$ with the cut as low as $6\,\mathrm{GeV}$. We find that the LO collinear factorization with nuclear leading twist shadowing predicts quite similar effects. △ Less

Submitted 9 February, 2017; originally announced February 2017.

Comments: 20 pages, 9 figures

Report number: IFJPAN-IV-2017-3

Exploring minijets beyond the leading power

Authors: P. Kotko, A. M. Stasto, M. Strikman

Abstract: The crucial parameter of the current Monte Carlo models of high energy hadron-hadron interaction is the transverse momentum cutoff $p_{T0}$ for parton-parton interactions which slowly grows with energy and regularizes the cross section. This modification of the collinear factorization formula goes beyond the leading power and thus a natural question arises if such cutoff can be extracted from a fo… ▽ More The crucial parameter of the current Monte Carlo models of high energy hadron-hadron interaction is the transverse momentum cutoff $p_{T0}$ for parton-parton interactions which slowly grows with energy and regularizes the cross section. This modification of the collinear factorization formula goes beyond the leading power and thus a natural question arises if such cutoff can be extracted from a formalism which takes into account power corrections. In this work, we consider the High Energy Factorization (HEF) valid at small $x$ and a new model, based on a similar principle to HEF, which in addition has a limit respecting the Dokshitzer-Dyakonov-Troyan formula for the dijet momentum disbalance spectrum. Minijet cross section and its suppression is then analyzed in two ways. First, we study minijets directly in the low-$p_T$ region, and demonstrate that higher twist corrections do generate suppression of the inclusive jet production cross section though these effects are not leading to the increase of the cutoff with incident energy. Second, we consider hard inclusive dijet production where Multi Parton Interactions (MPIs) with minijets produce power corrections. We introduce an observable constructed from differential cross section in the ratio $τ$ of dijet disbalance to the average dijet $p_T$ and demonstrate that the $τ>1$ region is sensitive to the cutoff $p_{T0}$ in the MPI minijet models. The energy dependence of the cutoff is reflected in the energy dependence of the bimodality coefficient $b$ of the $τ$ distribution. We compare $b$ calculated from $\mathsf{pythia}$, where one can conveniently control MPIs by the program parameters, and HEF for a few unintegrated gluon distributions (UGDs). We find that the energy dependence of $b$ is very sensitive to the particular choice of UGD and in some models it resembles predictions of the Monte Carlo models. △ Less

Submitted 1 August, 2016; originally announced August 2016.

Comments: 35 pages, 15 figures

Journal ref: Phys. Rev. D 95, 054009 (2017)

Forward di-jet production in p+Pb collisions in the small-x improved TMD factorization framework

Authors: A. van Hameren, P. Kotko, K. Kutak, C. Marquet, E. Petreska, S. Sapeta

Abstract: We study the production of forward di-jets in proton-lead and proton-proton collisions at the Large Hadron Collider. Such configurations, with both jets produced in the forward direction, impose a dilute-dense asymmetry which allows to probe the gluon density of the lead or proton target at small longitudinal momentum fractions. Even though the jet momenta are always much bigger than the saturatio… ▽ More We study the production of forward di-jets in proton-lead and proton-proton collisions at the Large Hadron Collider. Such configurations, with both jets produced in the forward direction, impose a dilute-dense asymmetry which allows to probe the gluon density of the lead or proton target at small longitudinal momentum fractions. Even though the jet momenta are always much bigger than the saturation scale of the target, $Q_s$, the transverse momentum imbalance of the di-jet system may be either also much larger than $Q_s$, or of the order $Q_s$, implying that the small-$x$ QCD dynamics involved is either linear or non-linear, respectively. The small-$x$ improved TMD factorization framework deals with both situation in the same formalism. In the latter case, which corresponds to nearly back-to-back jets, we find that saturation effects induce a significant suppression of the forward di-jet azimuthal correlations in proton-lead versus proton-proton collisions. △ Less

Submitted 11 July, 2016; originally announced July 2016.

Comments: 6 figures

Report number: CERN-TH-2016-XXX, CPHT-RR036.072016, IFJPAN-IV-2016-X

Predictions for $p+$Pb Collisions at $\sqrt{s_{NN}} = 5$ TeV: Comparison with Data

Authors: J. L. Albacete, F. Arleo, G. G. Barnafoldi, J. Barrette, W. -T. Deng, A. Dumitru, K. J. Eskola, E. G. Ferreiro, F. Fleuret, H. Fujii, M. Gyulassy, S. M. Harangozi, I. Helenius, Z. Kang, P. Kotko, K. Kutak, J. -P. Lansberg, P. Levai, Z. -W. Lin, Y. Nara, A. Rakotozafindrabe, G. Papp, H. Paukkunen, S. Peigne, M. Petrovici , et al. (13 additional authors not shown)

Abstract: Predictions made in Albacete {\it et al} prior to the LHC $p+$Pb run at $\sqrt{s_{NN}} = 5$ TeV are compared to currently available data. Some predictions shown here have been updated by including the same experimental cuts as the data. Some additional predictions are also presented, especially for quarkonia, that were provided to the experiments before the data were made public but were too late… ▽ More Predictions made in Albacete {\it et al} prior to the LHC $p+$Pb run at $\sqrt{s_{NN}} = 5$ TeV are compared to currently available data. Some predictions shown here have been updated by including the same experimental cuts as the data. Some additional predictions are also presented, especially for quarkonia, that were provided to the experiments before the data were made public but were too late for the original publication are also shown here. △ Less

Submitted 30 May, 2016; originally announced May 2016.

Comments: 55 pages 35 figures

Heavy ions at the Future Circular Collider

Authors: A. Dainese, U. A. Wiedemann, N. Armesto, D. d'Enterria, J. M. Jowett, J. -P. Lansberg, J. G. Milhano, C. A. Salgado, M. Schaumann, M. van Leeuwen, J. L. Albacete, A. Andronic, P. Antonioli, L. Apolinario, S. Bass, A. Beraudo, A. Bilandzic, S. Borsanyi, P. Braun-Munzinger, Z. Chen, L. Cunqueiro Mendez, G. S. Denicol, K. J. Eskola, S. Floerchinger, H. Fujii , et al. (38 additional authors not shown)

Abstract: The Future Circular Collider (FCC) Study is aimed at assessing the physics potential and the technical feasibility of a new collider with centre-of-mass energies, in the hadron-hadron collision mode, seven times larger than the nominal LHC energies. Operating such machine with heavy ions is an option that is being considered in the accelerator design studies. It would provide, for example, Pb-Pb a… ▽ More The Future Circular Collider (FCC) Study is aimed at assessing the physics potential and the technical feasibility of a new collider with centre-of-mass energies, in the hadron-hadron collision mode, seven times larger than the nominal LHC energies. Operating such machine with heavy ions is an option that is being considered in the accelerator design studies. It would provide, for example, Pb-Pb and p-Pb collisions at sqrt{s_NN} = 39 and 63 TeV, respectively, per nucleon-nucleon collision, with integrated luminosities above 30 nb^-1 per month for Pb-Pb. This is a report by the working group on heavy-ion physics of the FCC Study. First ideas on the physics opportunities with heavy ions at the FCC are presented, covering the physics of the Quark-Gluon Plasma, of gluon saturation, of photon-induced collisions, as well as connections with other fields of high-energy physics. △ Less

Submitted 12 October, 2016; v1 submitted 4 May, 2016; originally announced May 2016.

Comments: 57 pages, 28 figures. This document will be part of a CERN Yellow Report on Physics at FCC-hh

Report number: CERN-TH-2016-107

Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope

Authors: Piotr Kotko, Mirko Serino, Anna M. Stasto

Abstract: One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works using the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for som… ▽ More One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes, if working in the light cone gauge. As shown in recent works using the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for some helicity configurations. In this work, we show that such structure is helicity independent and emerges from analytic properties of matrix elements of Wilson line operators, where the slope of the straight gauge path is shifted in a certain complex direction. This is similar to the procedure leading to the Britto-Cachazo-Feng-Witten (BCFW) recursion, however we apply a complex shift to the Wilson line slope instead of the external momenta. While in the original BCFW procedure the boundary integrals over the complex shift vanish for certain deformations, here they are non-zero and are equal to the off-shell amplitudes. The main result can thus be summarized as follows: we derive a decomposition of a helicity-fixed off-shell current into gauge invariant component given by a matrix element of a straight Wilson line plus a reminder given by a sum of products of gauge invariant and gauge dependent quantities. We give several examples realizing this relation, including the five-point next-to-MHV helicity configuration. △ Less

Submitted 1 August, 2016; v1 submitted 12 January, 2016; originally announced January 2016.

Comments: 23 pages, version accepted for JHEP

Proceedings of the Sixth International Workshop on Multiple Partonic Interactions at the Large Hadron Collider

Authors: R. Astalos, S. Baranov, P. Bartalini, I. Belyaev, Ch. Bierlich, B. Blok, A. Buckley, F. A. Ceccopieri, I. Cherednikov, J. R. Christiansen, D. Ciangottini, M. Deak, B. Ducloue, R. Field, J. R. Gaunt, K. Golec-Biernat, L. Goerlich, A. Grebenyuk, O. Gueta, P. Gunnellini, I. Helenius, H. Jung, D. Kar, O. Kepka, M. Klusek-Gawenda , et al. (32 additional authors not shown)

Abstract: Multiple Partonic Interactions are often crucial for interpreting results obtained at the Large Hadron Collider (LHC). The quest for a sound understanding of the dynamics behind MPI - particularly at this time when the LHC is due to start its "Run II" operations - has focused the aim of this workshop. MPI@LHC2014 concentrated mainly on the phenomenology of LHC measurements whilst keeping in perspe… ▽ More Multiple Partonic Interactions are often crucial for interpreting results obtained at the Large Hadron Collider (LHC). The quest for a sound understanding of the dynamics behind MPI - particularly at this time when the LHC is due to start its "Run II" operations - has focused the aim of this workshop. MPI@LHC2014 concentrated mainly on the phenomenology of LHC measurements whilst keeping in perspective those results obtained at previous hadron colliders. The workshop has also debated some of the state-of-the-art theoretical considerations and the modeling of MPI in Monte Carlo event generators. The topics debated in the workshop included: Phenomenology of MPI processes and multiparton distributions; Considerations for the description of MPI in Quantum Chromodynamics (QCD); Measuring multiple partonic interactions; Experimental results on inelastic hadronic collisions: underlying event, minimum bias, forward energy flow; Monte Carlo generator development and tuning; Connections with low-x phenomena, diffraction, heavy-ion physics and cosmic rays. In a total of 57 plenary talks the workshop covered a wide range of experimental results, Monte Carlo development and tuning, phenomenology and dedicated measurements of MPI which were produced with data from the LHC's Run I. Recent progress of theoretical understanding of MPI in pp, pA and AA collisions as well as the role of MPI in diffraction and small-x physics were also covered. The workshop forstered close contact between the experimental and theoretical communities. It provided a setting to discuss many of the different aspects of MPI, eventually identifying them as a unifying concept between apparently different lines of research and evaluating their impact on the LHC physics programme. △ Less

Submitted 18 June, 2015; originally announced June 2015.

Comments: MPI@LHC 2014, 3 - 7 November 2014, Krakow, Poland, 81 pages

Resummation effects in forward production of Z0+jet at LHC

Authors: A. van Hameren, P. Kotko, K. Kutak

Abstract: We calculate several differential cross sections for Z0 and high-pT jet production in the forward rapidity region at the LHC using the hybrid High Energy Factorization. We test various unintegrated gluon distributions involving subleading BFKL effects (such as kinematic constraint, running strong coupling and DGLAP correction) and compare the results with experimental data obtained by the LHCb exp… ▽ More We calculate several differential cross sections for Z0 and high-pT jet production in the forward rapidity region at the LHC using the hybrid High Energy Factorization. We test various unintegrated gluon distributions involving subleading BFKL effects (such as kinematic constraint, running strong coupling and DGLAP correction) and compare the results with experimental data obtained by the LHCb experiment. We find that the hard scale dependence of unintegrated gluon distributions, which effectively resums the Sudakov-type logarithms on the top of the resummation of the small x logarithms, is essential to describe the normalized azimuthal decorrelations between the Z0-boson and the jet. △ Less

Submitted 20 May, 2015; v1 submitted 11 May, 2015; originally announced May 2015.

Comments: 16 pages

Report number: IFJPAN-IV-2015-8

Journal ref: Phys. Rev. D 92, 054007 (2015)

Unintegrated gluon distributions for forward jets at LHC

Authors: Piotr Kotko, Wojciech Slominski, Dawid Toton

Abstract: We test several BFKL-like evolution equations for unintegrated gluon distributions against forward-central dijet production at LHC. Our study is based on fitting the evolution scenarios to the LHC data using the high energy factorization approach. Thus, as a by-product, we obtain a set of LHC-motivated unintegrated gluon distributions ready to use. We utilize this application by calculating azimut… ▽ More We test several BFKL-like evolution equations for unintegrated gluon distributions against forward-central dijet production at LHC. Our study is based on fitting the evolution scenarios to the LHC data using the high energy factorization approach. Thus, as a by-product, we obtain a set of LHC-motivated unintegrated gluon distributions ready to use. We utilize this application by calculating azimuthal decorrelations for forward-central dijet production and compare with existing data. △ Less

Submitted 26 May, 2015; v1 submitted 3 April, 2015; originally announced April 2015.

Comments: 18 pages, 6 figures; small corrections in the text and references

Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions

Authors: P. Kotko, K. Kutak, C. Marquet, E. Petreska, S. Sapeta, A. van Hameren

Abstract: We study forward dijet production in dilute-dense hadronic collisions. By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum imbalance of the dijet system, $k_t$, is of the order of either the saturat… ▽ More We study forward dijet production in dilute-dense hadronic collisions. By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum imbalance of the dijet system, $k_t$, is of the order of either the saturation scale, or the hard jet momenta, the former being always much smaller than the latter. We propose a new formula for forward dijets that encompasses both situations and is therefore applicable regardless of the magnitude of $k_t$. That involves generalizing the TMD factorization formula for dijet production to the case where the incoming small-$x$ gluon is off-shell. The derivation is performed in two independent ways, using either Feynman diagram techniques, or color-ordered amplitudes. △ Less

Submitted 28 September, 2015; v1 submitted 11 March, 2015; originally announced March 2015.

Comments: The improved version of the manuscript. 37 pages, 8 figures, several tables

Report number: CERN-PH-TH-2015-045, CPHT-RR005.0315, IFJPAN-IV-2015-2

Journal ref: JHEP 1509 (2015) 106

Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines

Authors: C. Cruz-Santiago, P. Kotko, A. Stasto

Abstract: We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell ampl… ▽ More We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the gauge invariance of light-front amplitudes, it is demonstrated that the Ward identities in this framework need additional instantaneous terms in the light-front graphs. △ Less

Submitted 6 March, 2015; originally announced March 2015.

Comments: 26 pages, a few figures

Small-$x$ dynamics in forward-central dijet decorrelations at the LHC

Authors: A. van Hameren, P. Kotko, K. Kutak, S. Sapeta

Abstract: We provide a description, within the High Energy Factorization formalism, of central-forward dijet decorrelation data measured by the CMS experiment and the predictions for nuclear modification ratio~$R_{pA}$ in p+Pb collisions. In our study, we use the unintegrated gluon density derived from the BFKL and BK equations supplemented with subleading corrections and a hard scale dependence. The latter… ▽ More We provide a description, within the High Energy Factorization formalism, of central-forward dijet decorrelation data measured by the CMS experiment and the predictions for nuclear modification ratio~$R_{pA}$ in p+Pb collisions. In our study, we use the unintegrated gluon density derived from the BFKL and BK equations supplemented with subleading corrections and a hard scale dependence. The latter is introduced at the final step of the calculation by reweighting the Monte Carlo generated events using suitable Sudakov form factors, without changing the total cross section. We achieve a good description of data in the whole region of the azimuthal angle. △ Less

Submitted 7 May, 2014; v1 submitted 24 April, 2014; originally announced April 2014.

Comments: 10 pages, 4 figures; legends of the plots corrected, references added, minor refinements

Report number: IFJPAN-IV-2014-6, CERN-PH-TH-2014-070

Wilson lines and gauge invariant off-shell amplitudes

Authors: Piotr Kotko

Abstract: We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned "polarization vectors" which (in the Feynman gauge) are transverse to their off-shell momenta and define the direction of the corresponding Wilson line operators. The infinite Wilson lines are first regul… ▽ More We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned "polarization vectors" which (in the Feynman gauge) are transverse to their off-shell momenta and define the direction of the corresponding Wilson line operators. The infinite Wilson lines are first regularized to prove the correctness of the method. We have implemented the method in a computer FORM program that can calculate gluonic matrix elements of Wilson line operators automatically. In addition we formulate the Feynman rules that are convenient in certain applications, e.g. proving the Ward identities. Using both the program and the Feynman rules we calculate a few examples, in particular the matrix elements corresponding to gauge invariant $g^{*}g^{*}g^{*}g$ and $g^{*}g^{*}g^{*}g^{*}g$ processes. An immediate application of the approach is in the high energy scattering, as in a special kinematic setup our results reduce to the form directly related to Lipatov's vertices. Thus the results we present can be directly transformed into Lipatov's vertices, in particular into $RRRP$ and $RRRRP$ vertices with arbitrary "orientation" of reggeized gluons. Since the formulation itself is not restricted to high-energy scattering, we also apply the method to a decomposition of an ordinary on-shell amplitude into a set of gauge invariant objects. △ Less

Submitted 24 April, 2014; v1 submitted 19 March, 2014; originally announced March 2014.

Comments: 30 pages, quite a few figures. Minor corrections, references updated. Submitted to JHEP

Report number: IFJPAN-IV-2014-3

Saturation effects in forward-forward dijet production in p+Pb collisions

Authors: A. van Hameren, P. Kotko, K. Kutak, C. Marquet, S. Sapeta

Abstract: We study saturation effects in the production of forward dijets in proton-lead collisions at the Large Hadron Collider, using the framework of High Energy Factorization. Such configurations, with both jets produced in the forward direction, probe the gluon density of the lead nucleus at small longitudinal momentum fraction, and also limit the phase space for emissions of additional jets. We find s… ▽ More We study saturation effects in the production of forward dijets in proton-lead collisions at the Large Hadron Collider, using the framework of High Energy Factorization. Such configurations, with both jets produced in the forward direction, probe the gluon density of the lead nucleus at small longitudinal momentum fraction, and also limit the phase space for emissions of additional jets. We find significant suppression of the forward dijet azimuthal correlations in proton-lead versus proton-proton collisions, which we attribute to stronger saturation of the gluon density in the nucleus than in the proton. In order to minimize model dependence of our predictions, we use two different extensions of the Balitsky-Kovchegov equation for evolution of the gluon density with sub-leading corrections. △ Less

Submitted 18 June, 2014; v1 submitted 20 February, 2014; originally announced February 2014.

Comments: 13 pages, 4 figures; v2: added figure 4, several clarifying sentences and a reference; version accepted by PRD

Report number: CERN-PH-TH/2014-029, CPHT-RR005.0214, IFJPAN-IV-2014-2

Journal ref: Phys. Rev. D 89, 094014 (2014)

Off-shell helicity amplitudes in high-energy factorization

Authors: Piotr Kotko

Abstract: In the Catani-Ciafaloni-Hautmann high-energy factorization approach a cross section is expressed as a convolution of unintegrated gluon densities and a gauge-invariant hard process, in which two incoming gluons are off-shell with momenta satisfying certain high-energy kinematics. We present two methods of evaluating the tree-level hard process with multiple final states. The first one assumes that… ▽ More In the Catani-Ciafaloni-Hautmann high-energy factorization approach a cross section is expressed as a convolution of unintegrated gluon densities and a gauge-invariant hard process, in which two incoming gluons are off-shell with momenta satisfying certain high-energy kinematics. We present two methods of evaluating the tree-level hard process with multiple final states. The first one assumes that only one of the gluons is off-shell and relies on the Slavnov-Taylor identities. Such asymmetric configuration of incoming gluons is phenomenologically important in small x probing by forward processes. The second method deals also with two off-shell gluons and is based on the analytic continuation of the off-shell gluons momenta to the complex space. The methods were implemented into Monte Carlo computer programs and used in phenomenological applications. The results of both methods are straightforwardly related to Lipatov's effective vertices in quasi-multi-regge kinematics. △ Less

Submitted 20 September, 2013; v1 submitted 19 September, 2013; originally announced September 2013.

Comments: Presented at the Low x workshop, May 30 - June 4 2013, Rehovot and Eilat, Israel

Three jet production and gluon saturation effects in p-p and p-Pb collisions within high-energy factorization

Authors: Andreas van Hameren, Piotr Kotko, Krzysztof Kutak

Abstract: We analyze three jet production in the central-forward and forward rapidity regions in proton-proton and proton-lead collisions at LHC energies. Our calculation relies on high-energy factorization with a single off-shell gluon obeying small x evolution equation which includes saturation. The calculations are made using two independent Monte Carlo codes implementing tree-level gauge invariant off-s… ▽ More We analyze three jet production in the central-forward and forward rapidity regions in proton-proton and proton-lead collisions at LHC energies. Our calculation relies on high-energy factorization with a single off-shell gluon obeying small x evolution equation which includes saturation. The calculations are made using two independent Monte Carlo codes implementing tree-level gauge invariant off-shell matrix elements. We calculate differential cross sections for azimuthal decorrelations and unbalanced jet transverse momenta and discuss them in the context of differences in the evolution of the unintegrated gluon densities. △ Less

Submitted 10 July, 2014; v1 submitted 2 August, 2013; originally announced August 2013.

Comments: We append an erratum with certain differential distributions recalculated in terms of a modified variable

Report number: IFJPAN-IV-2013-14

Journal ref: Phys. Rev. D 88, 094001 (2013)

Helicity amplitudes for high-energy scattering

Authors: A. van Hameren, P. Kotko, K. Kutak

Abstract: We present a prescription to calculate manifestly gauge invariant tree-level helicity amplitudes for arbitrary scattering processes with off-shell initial-state gluons within the kinematics of high-energy scattering. We show that it is equivalent to Lipatov's effective action approach, and show its computational potential through numerical calculations for scattering processes with several particl… ▽ More We present a prescription to calculate manifestly gauge invariant tree-level helicity amplitudes for arbitrary scattering processes with off-shell initial-state gluons within the kinematics of high-energy scattering. We show that it is equivalent to Lipatov's effective action approach, and show its computational potential through numerical calculations for scattering processes with several particles in the final state. △ Less

Submitted 10 January, 2013; v1 submitted 5 November, 2012; originally announced November 2012.

Comments: 27 pages, reference added

Report number: IFJPAN-IV-2012-12

Journal ref: JHEP 1301 (2013) 078

Multi-gluon helicity amplitudes with one off-shell leg within high energy factorization

Authors: Andreas van Hameren, Piotr Kotko, Krzysztof Kutak

Abstract: Basing on the Slavnov-Taylor identities, we derive a new prescription to obtain gauge invariant tree-level scattering amplitudes for the process g*g->Ng within high energy factorization. Using the helicity method, we check the formalism up to several final state gluons, and we present analytical formulas for the the helicity amplitudes for N=2. We also compare the method with Lipatov's effective a… ▽ More Basing on the Slavnov-Taylor identities, we derive a new prescription to obtain gauge invariant tree-level scattering amplitudes for the process g*g->Ng within high energy factorization. Using the helicity method, we check the formalism up to several final state gluons, and we present analytical formulas for the the helicity amplitudes for N=2. We also compare the method with Lipatov's effective action approach. △ Less

Submitted 23 October, 2012; v1 submitted 13 July, 2012; originally announced July 2012.

Comments: 25 pages, quite a few figures, an appendix added, typos corrected

Report number: IFJPAN-IV-2012-5

Journal ref: JHEP 1212 (2012) 029

General Mass Scheme for Jet Production in DIS

Authors: Piotr Kotko, Wojciech Slominski

Abstract: We propose a method for calculating DIS jet production cross sections in QCD at NLO accuracy with consistent treatment of heavy quarks. The scheme relies on the dipole subtraction method for jets, which we extend to all possible initial state splittings with heavy partons, so that the Aivazis-Collins-Olness-Tung massive collinear factorization scheme (ACOT) can be applied. As a first check of the… ▽ More We propose a method for calculating DIS jet production cross sections in QCD at NLO accuracy with consistent treatment of heavy quarks. The scheme relies on the dipole subtraction method for jets, which we extend to all possible initial state splittings with heavy partons, so that the Aivazis-Collins-Olness-Tung massive collinear factorization scheme (ACOT) can be applied. As a first check of the formalism we recover the ACOT result for the heavy quark structure function using a dedicated Monte Carlo program. △ Less

Submitted 18 June, 2012; originally announced June 2012.

Comments: 6 pages, 2 figures

Fully massive Scheme for Jet Production in DIS

Authors: Piotr Kotko, Wojciech Slominski

Abstract: We present a consistent treatment of heavy quarks for jet production in DIS at NLO accuracy. The method is based on the ACOT massive factorization scheme and dipole subtraction method for jets. The last had to be however extended in order to take into account initial state splittings with heavy quarks. We constructed relevant kinematics and dipole splitting functions together with their integrals.… ▽ More We present a consistent treatment of heavy quarks for jet production in DIS at NLO accuracy. The method is based on the ACOT massive factorization scheme and dipole subtraction method for jets. The last had to be however extended in order to take into account initial state splittings with heavy quarks. We constructed relevant kinematics and dipole splitting functions together with their integrals. We partially implemented the method in a MC program and checked against the known inclusive result for charm structure function. △ Less

Submitted 15 June, 2012; originally announced June 2012.

Comments: 4 pages, 1 figure. Presented at DIS 2012

Photon Distribution Amplitudes in nonlocal chiral quark model

Authors: Piotr Kotko, Michal Praszalowicz

Abstract: Photon distribution amplitudes up to twist four are calculated within the nonlocal chiral quark model with a simple pole ansatz for momentum dependence of the constituent quark mass. Calculations are performed using modified electromagnetic vector current in order to satisfy Ward identities. Quark condensate and magnetic susceptibility of the QCD vacuum entering definitions of the distribution a… ▽ More Photon distribution amplitudes up to twist four are calculated within the nonlocal chiral quark model with a simple pole ansatz for momentum dependence of the constituent quark mass. Calculations are performed using modified electromagnetic vector current in order to satisfy Ward identities. Quark condensate and magnetic susceptibility of the QCD vacuum entering definitions of the distribution amplitudes are computed and compared with existing phenomenological estimates. Both real and off-shell photons are considered and relevant form factors are calculated. Our results are analytical up to the numerical solution of certain algebraic equation. △ Less

Submitted 7 December, 2009; v1 submitted 30 November, 2009; originally announced December 2009.

Comments: 38 pages, 9 figures. Refs. added

Report number: TPJU-3/2009

Journal ref: Phys.Rev.D81:034019,2010