Showing 1–50 of 158 results for author: Manohar, A

Darkly Charged ALPs

Authors: Nicolás M. Arenaza, Enrique Fernández-Martínez, Belén Gavela, Elizabeth E. Jenkins, Aneesh V. Manohar, Pablo Quílez, Thomas Steingasser

Abstract: The established $d=5$ ALP effective Lagrangian describes the interaction of scalars with approximate shift-symmetry which carry no Standard Model (SM) charges with SM fields. It implicitly assumes that ALPs are not charged under any symmetries of the dark sector. In this paper, we remove this assumption. For ALPs carrying conserved dark charges, no $d=5$ ALP effective interaction to SM particles i… ▽ More The established $d=5$ ALP effective Lagrangian describes the interaction of scalars with approximate shift-symmetry which carry no Standard Model (SM) charges with SM fields. It implicitly assumes that ALPs are not charged under any symmetries of the dark sector. In this paper, we remove this assumption. For ALPs carrying conserved dark charges, no $d=5$ ALP effective interaction to SM particles is possible. We build the effective Lagrangian for these darkly charged ALPs stemming from a general breaking pattern, and we show that the lowest-order shift-symmetric effective Lagrangian contains just two $d=6$ operators coupling ALPs to SM particles. We explore the model-independent phenomenological implications of these interactions, as well as the question of whether the dark matter observed in the Universe may consist of darkly charged ALPs. We identify higher order operators of the effective field theory, and determine which types of dark symmetry groups can seed darkly charged ALPs. Illustrative examples of ultraviolet completions which result in darkly charged ALPs at low-energies are provided as well. The darkly-charged ALP scenario can be generalized by including dark gauge interactions. In this paper, we have considered only the case with no such interactions. △ Less

Submitted 10 July, 2026; originally announced July 2026.

Comments: 47 pages, 13 figures

Report number: IFT-UAM/CSIC-15-116, CERN-TH-2026-122

Updated Simulation of GRETA Detector Response and Exploration of Temperature Sensitivity

Authors: Arin Manohar, Mario Cromaz, Christopher Campbell, Heather Crawford, Marco Salathe

Abstract: The Gamma-Ray Energy Tracking Array (GRETA) is a next-generation gamma-ray spectrometer designed to push the frontiers of nuclear structure and astrophysics experiment. Its high sensitivity is enabled by high-precision localization of gamma-ray interactions within its active detector volume, and the subsequent tracking of gamma-ray scattering sequences. In order to perform gamma-ray tracking, we n… ▽ More The Gamma-Ray Energy Tracking Array (GRETA) is a next-generation gamma-ray spectrometer designed to push the frontiers of nuclear structure and astrophysics experiment. Its high sensitivity is enabled by high-precision localization of gamma-ray interactions within its active detector volume, and the subsequent tracking of gamma-ray scattering sequences. In order to perform gamma-ray tracking, we need to simulate signal generation in the detectors accurately. This requires both accurate calculations of charge movement in the semiconductor volume, as well as a faithful reproduction of real-world experimental effects such as the electronics response. This work addresses the fidelity of the calculated signals for GRETA in two ways. An updated approach has been applied to find an optimized parameterization of the electronics response, while the impact of the detector temperature was also explored to best reproduce experimental signals and improve the position localization performance for GRETA. The results suggest that the electronics response can be simplified without impacting performance, and that the response correction parameters can effectively compensate for the changes in signal which arise due to the crystal temperature, resulting in minimal sensitivity of the position resolution to the assumed temperature. △ Less

Submitted 13 December, 2025; originally announced December 2025.

Comments: Keywords: GRETA, HPGe detectors, electronics response, signal decomposition, semiconductor temperature

Polarized Deep Inelastic Scattering as $x \to 1$ using Soft Collinear Effective Theory

Authors: Jaipratap Singh Grewal, Aneesh V. Manohar, Jyotirmoy Roy

Abstract: We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions $g_1(x)$ and $g_2(x)$, and to sum Sudakov double logarithms of $1-x$. The analysis is done both in terms of lightcone parton distributions and their moments. Computing $g_2$ requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficie… ▽ More We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions $g_1(x)$ and $g_2(x)$, and to sum Sudakov double logarithms of $1-x$. The analysis is done both in terms of lightcone parton distributions and their moments. Computing $g_2$ requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the parton distribution function (PDF). The PDF in SCET is given by a bilocal operator, rather than the trilocal operator used in the QCD analysis of $g_2$ for generic $x$. We compute the one-loop anomalous dimension of the PDF operator for any $x$, and show that as $x \to 1$, it factors into a single-variable evolution. We comment on the QCD anomalous dimensions of twist-three operators, their equation-of-motion relation, and connection to the SCET analysis. We briefly discuss the definition of axial operators in the BMHV scheme. As a side result, we derive the $1/N$ dependence of the QCD coefficient functions for $F_1$, $F_L$ and $g_1$ in the $N \to \infty$ limit, where $N$ is the moment, which is expected to hold to all orders in $α_s$. △ Less

Submitted 19 April, 2026; v1 submitted 9 July, 2025; originally announced July 2025.

Comments: 47 Pages. v3: journal version - includes footnote 11 and appendix F

The Robot of Theseus: A modular robotic testbed for legged locomotion

Authors: Karthik Urs, Jessica Carlson, Aditya Srinivas Manohar, Michael Rakowiecki, Abdulhadi Alkayyali, John E. Saunders, Faris Tulbah, Talia Y. Moore

Abstract: Robotic models are useful for independently varying specific features, but most quadrupedal robots differ so greatly from animal morphologies that they have minimal biomechanical relevance. Commercially available quadrupedal robots are also prohibitively expensive for biological research programs and difficult to customize. Here, we present a low-cost quadrupedal robot with modular legs that can m… ▽ More Robotic models are useful for independently varying specific features, but most quadrupedal robots differ so greatly from animal morphologies that they have minimal biomechanical relevance. Commercially available quadrupedal robots are also prohibitively expensive for biological research programs and difficult to customize. Here, we present a low-cost quadrupedal robot with modular legs that can match a wide range of animal morphologies for biomechanical hypothesis testing. The Robot Of Theseus (TROT) costs approximately $4000 to build out of 3D printed parts and standard off-the-shelf supplies. Each limb consists of 2 or 3 rigid links; the proximal joint can be rotated to become a knee or elbow. Telescoping mechanisms vary the length of each limb link. The open-source software accommodates user-defined gaits and morphology changes. Effective leg length, or crouch, is determined by the four-bar linkage actuating each joint. The backdrivable motors can vary virtual spring stiffness and range of motion. Full descriptions of the TROT hardware and software are freely available online. We demonstrate the use of TROT to compare locomotion among extant, extinct, and theoretical morphologies. In addition to biomechanical hypothesis testing, we envision a variety of different applications for this low-cost, modular, legged robotic platform, including developing novel control strategies, clearing land mines, or remote exploration. All CAD and code is available for download on the TROT project page. △ Less

Submitted 18 May, 2025; originally announced May 2025.

The photon parton distribution function: updates and applications

Authors: Aneesh Manohar, Paolo Nason, Gavin Salam, Giulia Zanderighi

Abstract: The photon parton distribution function (PDF) of the proton is crucial for precise comparisons of LHC cross sections with theoretical predictions. However, it was previously affected by very large uncertainties of around ${\cal O}(100\%)$ or dependent upon phenomenologically inspired models. In the paper~\cite{Manohar:2016nzj}, we demonstrated how the photon PDF could be determined using the proto… ▽ More The photon parton distribution function (PDF) of the proton is crucial for precise comparisons of LHC cross sections with theoretical predictions. However, it was previously affected by very large uncertainties of around ${\cal O}(100\%)$ or dependent upon phenomenologically inspired models. In the paper~\cite{Manohar:2016nzj}, we demonstrated how the photon PDF could be determined using the proton structure functions $F_2$ and $F_L$ measured in electron--proton scattering experiments. We provided an explicit formula for the PDF, which can be systematically improved order by order in perturbation theory. We obtained a photon PDF with errors $\lesssim 2$\% for $10^{-4} < x < 0.1$. Here, we recall the underlying idea and method used to obtain this result, as well as the progress made since then. △ Less

Submitted 22 August, 2024; originally announced August 2024.

Comments: Conference proceedings of the 2nd International Conference of Basics Science, 13 pages , 6 figures

Protocol Optimization for Functional Cardiac CT Imaging Using Noise Emulation in the Raw Data Domain

Authors: Zhye Yin, Pengwei Wu, Ashish Manohar, Elliot R. McVeigh, Jed D. Pack

Abstract: Four-dimensional (4D) wide coverage computed tomography (CT) is an effective imaging modality for measuring the mechanical function of the myocardium. However, repeated CT measurement across several heartbeats is still a concern. A projection-domain noise emulation method is presented to generate accurate low-dose (mA modulated) 4D cardiac CT scans from high-dose scans, enabling protocol optimizat… ▽ More Four-dimensional (4D) wide coverage computed tomography (CT) is an effective imaging modality for measuring the mechanical function of the myocardium. However, repeated CT measurement across several heartbeats is still a concern. A projection-domain noise emulation method is presented to generate accurate low-dose (mA modulated) 4D cardiac CT scans from high-dose scans, enabling protocol optimization to deliver sufficient image quality for functional cardiac analysis while using a dose level that is as low as reasonably achievable. Given a targeted low-dose mA modulation curve, the proposed noise emulation method injects both quantum and electronic noise of proper magnitude and correlation to the high-dose data in projection domain. A spatially varying detector gain term as well as its calibration method were proposed to further improve the noise emulation accuracy. To determine the low dose threshold, a projection domain image quality (IQ) metric was proposed that is based on the number of projection rays that do not fall under the non-linear region of the detector. Experiments were performed to validate the noise emulation method with both phantom and clinical data. For both phantom and clinical data, the low-dose emulated images exhibited similar noise magnitude, artifacts, and texture to that of the real low-dose images. The proposed channel-dependent detector gain term resulted in additional increase in emulation accuracy. Using the proposed IQ metric, recommended kVp and mA settings were calculated for low dose 4D Cardiac CT acquisitions for patients of different sizes. In conclusion, a detailed method to estimate system-dependent parameters for a raw-data based low dose emulation framework was described. The proposed low-dose emulation method can be used to prospectively select patient-specific minimal-dose protocols for functional cardiac CT. △ Less

Submitted 13 March, 2024; originally announced March 2024.

Comments: First two authors contributed equally

Field Redefinitions and Infinite Field Anomalous Dimensions

Authors: Aneesh V. Manohar, Julie Pagès, Jasper Roosmale Nepveu

Abstract: Field redefinitions are commonly used to reduce the number of operators in the Lagrangian by removing redundant operators and transforming to a minimal operator basis. We give a general argument that such field redefinitions, while leaving the $S$-matrix invariant and consequently finite, lead not only to infinite Green's functions, but also to infinite field anomalous dimensions $γ_φ$. These dive… ▽ More Field redefinitions are commonly used to reduce the number of operators in the Lagrangian by removing redundant operators and transforming to a minimal operator basis. We give a general argument that such field redefinitions, while leaving the $S$-matrix invariant and consequently finite, lead not only to infinite Green's functions, but also to infinite field anomalous dimensions $γ_φ$. These divergences cannot be removed by counterterms without reintroducing redundant operators. △ Less

Submitted 13 February, 2024; originally announced February 2024.

Comments: 10+6 pages, 2 figures

Report number: DESY-24-020, HU-EP-24/04-RTG

Two Loop Renormalization of Scalar Theories using a Geometric Approach

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Luca Naterop, Julie Pagès

Abstract: We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our… ▽ More We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order $p^6$. △ Less

Submitted 9 November, 2023; v1 submitted 30 October, 2023; originally announced October 2023.

Comments: ChPT results to O($p^6$) now agree with Bijnens, Colangelo, and Ecker, hep-ph/9907333

Report number: ZU-TH 69/23, PSI-PR-23-39

An Algebraic Formula for Two Loop Renormalization of Scalar Quantum Field Theory

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Luca Naterop, Julie Pagès

Abstract: We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizabl… ▽ More We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order. △ Less

Submitted 30 October, 2023; v1 submitted 11 August, 2023; originally announced August 2023.

Comments: 25 pages, 8 figures, 6 tables

Report number: ZU-TH 45/23, PSI-PR-23-29

Fermion Geometry and the Renormalization of the Standard Model Effective Field Theory

Authors: Benoît Assi, Andreas Helset, Aneesh V. Manohar, Julie Pagès, Chia-Hsien Shen

Abstract: The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalizatio… ▽ More The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight. △ Less

Submitted 6 July, 2023; originally announced July 2023.

Comments: 28 pages

Report number: CALT-TH-2023-024, FERMILAB-PUB-23-362-T

Renormalization of the Standard Model Effective Field Theory from Geometry

Authors: Andreas Helset, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: $S… ▽ More $S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature $R_{ijkl}$ of this combined space, with indices $i,j,k,l$ chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight. △ Less

Submitted 6 December, 2022; originally announced December 2022.

Comments: 40 pages, 8 tables, 1 figure

Report number: CALT-TH-2022-041

Geometry in Scattering Amplitudes

Authors: Andreas Helset, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: We formulate the field-space geometry for an effective field theory of scalars and gauge bosons. Geometric invariants such as the field-space curvature enter in both scattering amplitudes and the renormalization group equations, with the scalar and gauge results unified in a single expression. We formulate the field-space geometry for an effective field theory of scalars and gauge bosons. Geometric invariants such as the field-space curvature enter in both scattering amplitudes and the renormalization group equations, with the scalar and gauge results unified in a single expression. △ Less

Submitted 20 March, 2024; v1 submitted 14 October, 2022; originally announced October 2022.

Comments: 7 pages. Updated references and corrected typo

Report number: CALT-TH-2022-036

Radiated Angular Momentum and Dissipative Effects in Classical Scattering

Authors: Aneesh V. Manohar, Alexander K. Ridgway, Chia-Hsien Shen

Abstract: We present a new formula for the angular momentum $J^{μν}$ carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum $P^μ$, completes the set of radiated Poincare charges due to scattering. We parametrize $P^μ$ and $J^{μν}$ by non-perturbative form factors and derive exact relations using the Poincare algebra.… ▽ More We present a new formula for the angular momentum $J^{μν}$ carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum $P^μ$, completes the set of radiated Poincare charges due to scattering. We parametrize $P^μ$ and $J^{μν}$ by non-perturbative form factors and derive exact relations using the Poincare algebra. There is a contribution to $J^{μν}$ due to static (zero-frequency) modes, which can be derived from Weinberg's soft theorem. Using tools from scattering amplitudes and effective field theory, we calculate the radiated $J^{μν}$ due to the scattering of two spinless particles to third order in Newton's constant $G$, but to all orders in velocity. Our form-factor analysis elucidates a novel relation found by Bini, Damour, and Geralico between energy and angular momentum loss at $\mathcal{O}(G^3)$. Our new results have several nontrivial implications for binary scattering at $\mathcal{O}(G^4)$. We give a procedure to bootstrap an effective radiation reaction force from the loss of Poincare charges due to scattering. △ Less

Submitted 7 October, 2022; v1 submitted 8 March, 2022; originally announced March 2022.

Comments: 5 pages +refs, two figures and one Mathematica ancillary file for table I; minor revision and fixed a typo in the definition of Δb, matched to PRL version in v2

Journal ref: Phys. Rev. Lett. 129, 121601, 2022

Dark Matter Effective Field Theory and an Application to Vector Dark Matter

Authors: Jason Aebischer, Wolfgang Altmannshofer, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: The Standard Model Effective Field Theory (SMEFT) and the Low Energy Effective Field Theory (LEFT) can be extended by adding additional spin 0, 1/2 and 1 dark matter particles which are singlets under the Standard Model (SM) gauge group. We classify all gauge invariant interactions in the Lagrangian up to terms of dimension six, and present the tree-level matching conditions between the two theori… ▽ More The Standard Model Effective Field Theory (SMEFT) and the Low Energy Effective Field Theory (LEFT) can be extended by adding additional spin 0, 1/2 and 1 dark matter particles which are singlets under the Standard Model (SM) gauge group. We classify all gauge invariant interactions in the Lagrangian up to terms of dimension six, and present the tree-level matching conditions between the two theories at the electroweak scale. The most widely studied dark matter models, such as those based on the Higgs portal or on kinetic mixing between the photon and a dark photon, are based on dimension-four interactions with the SM sector. We consider a model with dark vector particles with a $\mathbb{Z}_2$ symmetry, so that the lightest dark matter particle is stable. The leading interaction with the SM is through dimension-six operators involving two dark vector field-strength tensors and the electromagnetic field-strength tensor. This model is a viable dark matter model in the freeze-in scenario for a wide range of parameters. △ Less

Submitted 12 October, 2022; v1 submitted 14 February, 2022; originally announced February 2022.

Comments: 50 pages, 3 figures, matches published version

Quark-Gluon Backscattering in the Regge Limit at One-Loop

Authors: Arindam Bhattacharya, Aneesh V. Manohar, Matthew D. Schwartz

Abstract: At small momentum transfer, the quark-gluon scattering cross section dσ/dt has a power-law divergence in the backward scattering region where the outgoing quark is nearly collinear to the incoming gluon. In this Regge limit |t|<< s, the leading behavior of the 2 2 amplitude can be described by the exchange of Glauber quarks. In Soft-Collinear Effective Theory (SCET) at leading power, Glauber quark… ▽ More At small momentum transfer, the quark-gluon scattering cross section dσ/dt has a power-law divergence in the backward scattering region where the outgoing quark is nearly collinear to the incoming gluon. In this Regge limit |t|<< s, the leading behavior of the 2 2 amplitude can be described by the exchange of Glauber quarks. In Soft-Collinear Effective Theory (SCET) at leading power, Glauber quark exchange is given by five non-local Glauber quark operators, of which only one is generated at tree-level. We show that at leading power the QCD amplitude for quark-gluon backscattering at one-loop can be exactly reproduced by SCET using the tree-level Glauber operator. The agreement between QCD and SCET of the ultraviolet, infrared, and rapidity divergences as well as all logarithms, Glauber phases and finite parts for all polarizations of the external gluons is a strong check on the effective theory. We find that the entire one-loop matching vanishes -- there is no correction to the operator generated at tree-level, and the coefficients of the other four operators remain zero at one-loop. This suggests that SCET with Glauber operators may be useful for uncovering new aspects of Regge physics in a systematically improveable way. △ Less

Submitted 6 October, 2021; originally announced October 2021.

Comments: 39 pages

Effective field theory interpretation of lepton magnetic and electric dipole moments

Authors: Jason Aebischer, Wouter Dekens, Elizabeth E. Jenkins, Aneesh V. Manohar, Dipan Sengupta, Peter Stoffer

Abstract: We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT… ▽ More We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation. △ Less

Submitted 11 November, 2021; v1 submitted 17 February, 2021; originally announced February 2021.

Comments: 34 pages, 7 figures; v2: numbers updated to new experimental value for g-2; version published in JHEP

Report number: UWThPh 2021-2

Journal ref: JHEP 07 (2021) 107

Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops

Authors: Christian W. Bauer, Aneesh V. Manohar, Pier Francesco Monni

Abstract: The resummation of radiative corrections to collider jet observables using soft collinear effective theory is encoded in differential renormalization group equations (RGEs), with anomalous dimensions depending on the observable under consideration. This observable dependence arises from the ultraviolet (UV) singular structure of real phase space integrals in the effective field theory. We show tha… ▽ More The resummation of radiative corrections to collider jet observables using soft collinear effective theory is encoded in differential renormalization group equations (RGEs), with anomalous dimensions depending on the observable under consideration. This observable dependence arises from the ultraviolet (UV) singular structure of real phase space integrals in the effective field theory. We show that the observable dependence of anomalous dimensions in SCETI problems can be disentangled by introducing a suitable UV regulator in real radiation integrals. Resummation in the presence of the new regulator can be performed by solving a two-dimensional system of RGEs in the collinear and soft sectors, and resembles many features of resummation in SCETII theories by means of the rapidity renormalization group. We study the properties of SCETI with the additional regulator and explore the connection with the system of RGEs in SCETII theories, highlighting some universal patterns that can be exploited in perturbative calculations. As an application, we compute the two-loop soft and jet anomalous dimensions for a family of recoil-free angularities and give new analytic results. This allows us to study the relations between the SCETI and SCETII limits for these observables. We also discuss how the extra UV regulator can be exploited to calculate anomalous dimensions numerically, and the prospects for numerical resummation. △ Less

Submitted 21 December, 2020; v1 submitted 16 December, 2020; originally announced December 2020.

Comments: Fixing an incorrect statement in the first version of the paper, results and conclusions are unaffected

Report number: CERN-TH-2020-189

Renormalization Group Improvement of the Effective Potential: an EFT Approach

Authors: Aneesh V. Manohar, Emily Nardoni

Abstract: We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-par… ▽ More We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the $O(N)$ model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop $β$-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem. △ Less

Submitted 16 March, 2021; v1 submitted 29 October, 2020; originally announced October 2020.

Comments: Added a section explaining why the EFT method does not suffer from the Goldstone boson infrared divergence problem. Typos fixed

Axion strings are superconducting

Authors: Hajime Fukuda, Aneesh V. Manohar, Hitoshi Murayama, Ofri Telem

Abstract: We explore the cosmological consequences of the superconductivity of QCD axion strings. Axion strings can support a sizeable chiral electric current and charge, which alters their early universe dynamics. Shrinking axion string loops can become effectively stable remnants called vortons, supported by the electromagnetic force of the string current. Generically, vortons produced by axion strings ov… ▽ More We explore the cosmological consequences of the superconductivity of QCD axion strings. Axion strings can support a sizeable chiral electric current and charge, which alters their early universe dynamics. Shrinking axion string loops can become effectively stable remnants called vortons, supported by the electromagnetic force of the string current. Generically, vortons produced by axion strings overclose the universe, unless there are efficient current leakage processes. Furthermore, if a primordial magnetic field (PMF) exists in the early universe, a large current is induced on axion strings, creating a significant drag force from interactions with the surrounding plasma. As a result, the strings are slowed down, which leads to an orders of magnitude enhancement in the number of strings per Hubble volume. Finally, we study the implications for the QCD axion relic abundance. The QCD axion window is shifted by orders of magnitude in some parts of our parameter space. △ Less

Submitted 29 June, 2021; v1 submitted 6 October, 2020; originally announced October 2020.

Comments: 40 pages, 11 figures

TAPESTRY: A Blockchain based Service for Trusted Interaction Online

Authors: Yifan Yang, Daniel Cooper, John Collomosse, Constantin C. Drăgan, Mark Manulis, Jamie Steane, Arthi Manohar, Jo Briggs, Helen Jones, Wendy Moncur

Abstract: We present a novel blockchain based service for proving the provenance of online digital identity, exposed as an assistive tool to help non-expert users make better decisions about whom to trust online. Our service harnesses the digital personhood (DP); the longitudinal and multi-modal signals created through users' lifelong digital interactions, as a basis for evidencing the provenance of identit… ▽ More We present a novel blockchain based service for proving the provenance of online digital identity, exposed as an assistive tool to help non-expert users make better decisions about whom to trust online. Our service harnesses the digital personhood (DP); the longitudinal and multi-modal signals created through users' lifelong digital interactions, as a basis for evidencing the provenance of identity. We describe how users may exchange trust evidence derived from their DP, in a granular and privacy-preserving manner, with other users in order to demonstrate coherence and longevity in their behaviour online. This is enabled through a novel secure infrastructure combining hybrid on- and off-chain storage combined with deep learning for DP analytics and visualization. We show how our tools enable users to make more effective decisions on whether to trust unknown third parties online, and also to spot behavioural deviations in their own social media footprints indicative of account hijacking. △ Less

Submitted 15 May, 2019; originally announced May 2019.

Comments: Submitted to IEEE TSC Special Issue on Blockchain Services, May 2019

Non-Perturbative Effects in $μ\to e γ$

Authors: Wouter Dekens, Elizabeth E. Jenkins, Aneesh V. Manohar, Peter Stoffer

Abstract: We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q σ^{μν} q)(\bar \ell σ_{μν} \ell)$ to the purely leptonic process $μ\to e γ$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons.… ▽ More We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q σ^{μν} q)(\bar \ell σ_{μν} \ell)$ to the purely leptonic process $μ\to e γ$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $μ\to e $ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $Λ_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions. △ Less

Submitted 24 January, 2019; v1 submitted 12 October, 2018; originally announced October 2018.

Comments: 21 pages, 1 figure; version published in JHEP

Journal ref: JHEP 1901 (2019) 088

Introduction to Effective Field Theories

Authors: Aneesh V. Manohar

Abstract: Lecture notes from the 2017 Les Houches Summer School on Effective Field Theories. The lectures covered introductory material on EFTs as used in high energy physics to compute experimentally observable quantities. Other lectures at the school covered a wide range of applications in greater depth. Lecture notes from the 2017 Les Houches Summer School on Effective Field Theories. The lectures covered introductory material on EFTs as used in high energy physics to compute experimentally observable quantities. Other lectures at the school covered a wide range of applications in greater depth. △ Less

Submitted 16 April, 2018; originally announced April 2018.

Comments: 94 pages

Electroweak Gauge Boson Parton Distribution Functions

Authors: Bartosz Fornal, Aneesh V. Manohar, Wouter J. Waalewijn

Abstract: Transverse and longitudinal electroweak gauge boson parton distribution functions (PDFs) are computed in terms of deep-inelastic scattering structure functions, following the recently developed method to determine the photon PDF. The calculation provides initial conditions at the electroweak scale for PDF evolution to higher energies. Numerical results for the $W^\pm$ and $Z$ transverse, longitudi… ▽ More Transverse and longitudinal electroweak gauge boson parton distribution functions (PDFs) are computed in terms of deep-inelastic scattering structure functions, following the recently developed method to determine the photon PDF. The calculation provides initial conditions at the electroweak scale for PDF evolution to higher energies. Numerical results for the $W^\pm$ and $Z$ transverse, longitudinal and polarized PDFs, as well as the $γZ$ transverse and polarized PDFs are presented. △ Less

Submitted 17 May, 2018; v1 submitted 16 March, 2018; originally announced March 2018.

Comments: 24 pages, 7 figures; v2: journal version

Report number: Nikhef 2018-011

Journal ref: JHEP 1805 (2018) 106

Electroweak Logarithms in Inclusive Cross Sections

Authors: Aneesh V. Manohar, Wouter J. Waalewijn

Abstract: We develop the framework to perform all-orders resummation of electroweak logarithms of Q/M for inclusive scattering processes at energies Q much above the electroweak scale M. We calculate all ingredients needed at next-to-leading logarithmic (NLL) order and provide an explicit recipe to implement this for 2 $\to$ 2 processes. PDF evolution including electroweak corrections, which lead to Sudakov… ▽ More We develop the framework to perform all-orders resummation of electroweak logarithms of Q/M for inclusive scattering processes at energies Q much above the electroweak scale M. We calculate all ingredients needed at next-to-leading logarithmic (NLL) order and provide an explicit recipe to implement this for 2 $\to$ 2 processes. PDF evolution including electroweak corrections, which lead to Sudakov double logarithms, is computed. If only the invariant mass of the final state is measured, all electroweak logarithms can be resummed by the PDF evolution, at least to LL. However, simply identifying a lepton in the final state requires the corresponding fragmentation function and introduces angular dependence through the exchange of soft gauge bosons. Furthermore, we show the importance of polarization effects for gauge bosons, due to the chiral nature of SU(2) - even the gluon distribution in an unpolarized proton becomes polarized at high scales due to electroweak effects. We justify our approach with a factorization analysis, finding that the objects entering the factorization theorem do not need to be SU(2) $\times$ U(1) gauge singlets, even though we perform the factorization and resummation in the symmetric phase. We also discuss a range of extensions, including jets and how to calculate the EW logarithms when you are fully exclusive in the central (detector) region and fully inclusive in the forward (beam) regions. △ Less

Submitted 11 September, 2018; v1 submitted 23 February, 2018; originally announced February 2018.

Comments: 55 pages, 3 figures, 9 tables, v2: includes polarization effects, v3: journal version

Report number: Nikhef 2017-067

Neutrino Oscillation Measurements Computed in Quantum Field Theory

Authors: Andrew Kobach, Aneesh V. Manohar, John McGreevy

Abstract: We perform a calculation in quantum field theory of neutrino oscillation probabilities, where we include simultaneously the source, detector, and neutrino fields in the Hamiltonian. Within the appropriate limits associated with current neutrino oscillation experiments, we recover the standard oscillation formula. On the other hand, we find that the dominant contributions to the amplitude are assoc… ▽ More We perform a calculation in quantum field theory of neutrino oscillation probabilities, where we include simultaneously the source, detector, and neutrino fields in the Hamiltonian. Within the appropriate limits associated with current neutrino oscillation experiments, we recover the standard oscillation formula. On the other hand, we find that the dominant contributions to the amplitude are associated with different neutrino mass eigenstates being emitted at different times, such that they arrive at the detector at the same time. This is contrary to the neutrino wave packet picture, where they are emitted simultaneously and separate as they travel to the detector. This has direct consequences regarding the mechanisms that lead to a damping of neutrino oscillations for very long baselines. Our analysis also provides a pedagogical example of a measurement process in quantum mechanics. △ Less

Submitted 16 July, 2018; v1 submitted 20 November, 2017; originally announced November 2017.

Comments: 12+12 pages, 3 figures; v2: improved appendix B, added refs, close to published version

Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Peter Stoffer

Abstract: We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton ma… ▽ More We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. The use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions. △ Less

Submitted 20 March, 2024; v1 submitted 14 November, 2017; originally announced November 2017.

Comments: 50 pages, 2 tables, 144 diagrams; version published in JHEP; includes erratum JHEP 12 (2023) 042

Journal ref: JHEP 01 (2018) 084

Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Peter Stoffer

Abstract: The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $ΔB= \pm ΔL = \pm 1$, $ΔL=\pm 2$, and $ΔL=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field… ▽ More The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $ΔB= \pm ΔL = \pm 1$, $ΔL=\pm 2$, and $ΔL=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order $1/Λ^2$ is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints. △ Less

Submitted 20 March, 2024; v1 submitted 13 September, 2017; originally announced September 2017.

Comments: 46 pages, 22 tables; version published in JHEP; includes erratum JHEP 12 (2023) 043

Journal ref: JHEP 03 (2018) 016

The Photon Content of the Proton

Authors: Aneesh V. Manohar, Paolo Nason, Gavin P. Salam, Giulia Zanderighi

Abstract: The photon PDF of the proton is needed for precision comparisons of LHC cross sections with theoretical predictions. In a recent paper, we showed how the photon PDF could be determined in terms of the electromagnetic proton structure functions $F_2$ and $F_L$ measured in electron-proton scattering experiments, and gave an explicit formula for the PDF including all terms up to next-to-leading order… ▽ More The photon PDF of the proton is needed for precision comparisons of LHC cross sections with theoretical predictions. In a recent paper, we showed how the photon PDF could be determined in terms of the electromagnetic proton structure functions $F_2$ and $F_L$ measured in electron-proton scattering experiments, and gave an explicit formula for the PDF including all terms up to next-to-leading order. In this paper we give details of the derivation. We obtain the photon PDF using the factorisation theorem and applying it to suitable BSM hard scattering processes. We also obtain the same PDF in a process-independent manner using the usual definition of PDFs in terms of light-cone Fourier transforms of products of operators. We show how our method gives an exact representation for the photon PDF in terms of $F_2$ and $F_L$, valid to all orders in QED and QCD, and including all non-perturbative corrections. This representation is then used to give an explicit formula for the photon PDF to one order higher than our previous result. We also generalise our results to obtain formulæ for the polarised photon PDF, as well as the photon TMDPDF. Using our formula, we derive the $P_{γi}$ subset of DGLAP splitting functions to order $αα_s$ and $α^2$, which agree with known results. We give a detailed explanation of the approach that we follow to determine a photon PDF and its uncertainty within the above framework. △ Less

Submitted 18 August, 2017; v1 submitted 3 August, 2017; originally announced August 2017.

Comments: 75 pages, 25 figures, data files corresponding to the figures available at http://doi.org/10.5281/zenodo.837233, LUXqed17 PDF files available in LHAPDF, references added in v2

How bright is the proton? A precise determination of the photon parton distribution function

Authors: Aneesh Manohar, Paolo Nason, Gavin P. Salam, Giulia Zanderighi

Abstract: It has become apparent in recent years that it is important, notably for a range of physics studies at the Large Hadron Collider, to have accurate knowledge on the distribution of photons in the proton. We show how the photon parton distribution function (PDF) can be determined in a model-independent manner, using electron-proton ($ep$) scattering data, in effect viewing the $ep\to e+X$ process as… ▽ More It has become apparent in recent years that it is important, notably for a range of physics studies at the Large Hadron Collider, to have accurate knowledge on the distribution of photons in the proton. We show how the photon parton distribution function (PDF) can be determined in a model-independent manner, using electron-proton ($ep$) scattering data, in effect viewing the $ep\to e+X$ process as an electron scattering off the photon field of the proton. To this end, we consider an imaginary, beyond Standard Model process with a flavour changing photon-lepton vertex. We write its cross section in two ways, one in terms of proton structure functions, the other in terms of a photon distribution. Requiring their equivalence yields the photon distribution as an integral over proton structure functions. As a result of the good precision of $ep$ data, we constrain the photon PDF at the level of 1-2% over a wide range of momentum fractions. △ Less

Submitted 16 December, 2016; v1 submitted 14 July, 2016; originally announced July 2016.

Comments: 6 pages, 5 figures; v3 includes small textual changes and an updated CT14 comparison in Fig. 4, as published. LUXqed_PDF4LHC15_nnlo_100 set available from LHAPDF, further information at http://cern.ch/luxqed/

Report number: CERN-TH/2016-155

Journal ref: Phys. Rev. Lett. 117, 242002 (2016)

Geometry of the Scalar Sector

Authors: Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renorm… ▽ More The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold ${\mathcal M}$ is flat. We explicitly compute the one-loop correction to scalar scattering in the SM written in non-linear Callan-Coleman-Wess-Zumino (CCWZ) form, where it has an infinite series of higher dimensional operators, and show that the $S$-matrix is finite. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved ${\mathcal M}$, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only if ${\cal M}$ has a $SU(2)_L \times U(1)_Y$ invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of ${\mathcal M}$ such as sectional curvatures, which are of order $1/Λ^2$, where $Λ$ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general $\mathcal G \to \mathcal H$ symmetry breaking pattern. (Full abstract in pdf) △ Less

Submitted 11 May, 2016; originally announced May 2016.

Sigma Models with Negative Curvature

Authors: Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n,1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-p… ▽ More We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n,1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values. △ Less

Submitted 1 February, 2016; originally announced February 2016.

Report number: CERN-TH-2016-024

Analysis of General Power Counting Rules in Effective Field Theory

Authors: M. B. Gavela, E. E. Jenkins, A. V. Manohar, L. Merlo

Abstract: We derive the general counting rules for a quantum effective field theory (EFT) in $\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of cross sections is cont… ▽ More We derive the general counting rules for a quantum effective field theory (EFT) in $\mathsf{d}$ dimensions. The rules are valid for strongly and weakly coupled theories, and predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of cross sections is controlled by the $Λ$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ($χ$PT). The relation between $Λ$ and $f$ is generalized to $\mathsf{d}$ dimensions. We show that the naive dimensional analysis $4π$ counting is related to $\hbar$ counting. The EFT counting rules are applied to $χ$PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT. △ Less

Submitted 9 September, 2016; v1 submitted 27 January, 2016; originally announced January 2016.

Comments: V2: more details and examples added; version published in journal. 17 pages, 4 figures, 2 tables

Report number: CERN-TH-2016-015, FTUAM-16-2, IFT-UAM/CSIC-16-006

Journal ref: Eur. Phys. J. C (2016) 76:485

A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space

Authors: Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold $\mathcal M$. We show how the curvature can be measured experimentally via Higgs cross-sections, $W_L$ scattering, and the $S$ parameter. The one-loop action of HEFT is gi… ▽ More A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms of geometric invariants of the scalar sigma model sector such as the curvature of the scalar field manifold $\mathcal M$. We show how the curvature can be measured experimentally via Higgs cross-sections, $W_L$ scattering, and the $S$ parameter. The one-loop action of HEFT is given in terms of geometric invariants of $\mathcal M$. The distinction between the Standard Model (SM) and HEFT is whether $\mathcal M$ is flat or curved, not whether the scalars transform linearly or non-linearly under the electroweak group. △ Less

Submitted 3 February, 2016; v1 submitted 2 November, 2015; originally announced November 2015.

Comments: Journal version. The introduction has been rewritten to make clearer the distinction between SM, SMEFT and HEFT. A slight change of notation has been introduced to connect observables with sectional curvature

Non-cancellation of electroweak logarithms in high-energy scattering

Authors: Aneesh V. Manohar, Brian Shotwell, Christian W. Bauer, Sascha Turczyk

Abstract: We study electroweak Sudakov corrections in high energy scattering, and the cancellation between real and virtual Sudakov corrections. Numerical results are given for the case of heavy quark production by gluon collisions involving the rates $gg \to t \bar t, b \bar b, t \bar b W, t \bar t Z, b \bar b Z, t \bar t H, b \bar b H$. Gauge boson virtual corrections are related to real transverse gauge… ▽ More We study electroweak Sudakov corrections in high energy scattering, and the cancellation between real and virtual Sudakov corrections. Numerical results are given for the case of heavy quark production by gluon collisions involving the rates $gg \to t \bar t, b \bar b, t \bar b W, t \bar t Z, b \bar b Z, t \bar t H, b \bar b H$. Gauge boson virtual corrections are related to real transverse gauge boson emission, and Higgs virtual corrections to Higgs and longitudinal gauge boson emission. At the LHC, electroweak corrections become important in the TeV regime. At the proposed 100 TeV collider, electroweak interactions enter a new regime, where the corrections are very large and need to be resummed. △ Less

Submitted 9 December, 2014; v1 submitted 5 September, 2014; originally announced September 2014.

Comments: 11 pages, 12 figures, 1 table. v2: Journal version

Journal ref: Physics Letters B 740 (2015) 179

Holomorphy without Supersymmetry in the Standard Model Effective Field Theory

Authors: Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar

Abstract: The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a supersymmetric theory. The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. The holomorphy conditions are reminiscent of supersymmetry, even though the SMEFT is not a supersymmetric theory. △ Less

Submitted 30 July, 2015; v1 submitted 2 September, 2014; originally announced September 2014.

Comments: Minor corrections in Table I, see note added at end of paper. The complete SMEFT RGE will be maintained at http://einstein.ucsd.edu/smeft

Renormalization group evolution of dimension-six baryon number violating operators

Authors: Rodrigo Alonso, Hsi-Ming Chang, Elizabeth E. Jenkins, Aneesh V. Manohar, Brian Shotwell

Abstract: We calculate the one-loop anomalous dimension matrix for the dimension-six baryon number violating operators of the Standard Model effective field theory, including right-handed neutrino fields. We discuss the flavor structure of the renormalization group evolution in the contexts of minimal flavor violation and unification. We calculate the one-loop anomalous dimension matrix for the dimension-six baryon number violating operators of the Standard Model effective field theory, including right-handed neutrino fields. We discuss the flavor structure of the renormalization group evolution in the contexts of minimal flavor violation and unification. △ Less

Submitted 25 June, 2014; v1 submitted 2 May, 2014; originally announced May 2014.

Comments: 7 pages, 1 figure, 1 table. v2: Journal version

Journal ref: Physics Letters B 734 (2014) 302

Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Wouter J. Waalewijn, Amit P. S. Yadav

Abstract: We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O(φ^4) in the len… ▽ More We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O(φ^4) in the lensing potential $φ$. We consider both the diagonal noise TTTT, EBEB, etc. and, for the first time, the off-diagonal noise TTTE, TBEB, etc. The previously noted large O(φ^4) term in the second order noise is identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the $φ$ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one $B$ component of the CMB, such as EEEB. △ Less

Submitted 18 March, 2014; originally announced March 2014.

Comments: 17 pages, 17 figures

Report number: NIKHEF 2014-007

Gravitational Lensing of the CMB: a Feynman Diagram Approach

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Wouter J. Waalewijn, Amit P. S. Yadav

Abstract: We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to ${\mathcal O}(φ^4)$ in the l… ▽ More We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to ${\mathcal O}(φ^4)$ in the lensing potential $φ$. The previously noted large ${\mathcal O}(φ^4)$ term can be significantly reduced by a reorganization of the $φ$ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields. △ Less

Submitted 11 July, 2014; v1 submitted 10 March, 2014; originally announced March 2014.

Comments: 5 pages, 8 figures, v2: journal version

Report number: NIKHEF 2014-003

Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology

Authors: Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

Abstract: We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $λ$ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 $CP$-even and $1149$ $CP$-odd parame… ▽ More We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $λ$ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 $CP$-even and $1149$ $CP$-odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire $2499 \times 2499$ anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension $d \le 4$ terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as $gg \to h$, $h \to γγ$ and $h \to Z γ$, for Higgs couplings to fermions, for the precision electroweak parameters $S$ and $T$, and for the operators that modify important processes in precision electroweak phenomenology, such as the three-body Higgs boson decay $h \rightarrow Z \, \ell^+ \, \ell^-$ and triple gauge boson couplings. We discuss how the renormalization group improved results can be used to study the flavor problem in the SM EFT, and to test the minimal flavor violation (MFV) hypothesis. We briefly discuss the renormalization effects on the dipole coefficient $C_{eγ}$ which contributes to $μ\to e γ$ and to the muon and electron magnetic and electric dipole moments. △ Less

Submitted 13 June, 2024; v1 submitted 6 December, 2013; originally announced December 2013.

Comments: 28 pages + appendices v5: Minor corrections. The complete SMEFT RGE will be maintained at http://einstein.ucsd.edu/smeft/

Report number: CERN-PH-TH/2013-305

Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

Abstract: We calculate the complete order y^2 and y^4 terms of the 59 x 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order lambda, lambda^2 and lambda y^2 depending on the Standard Model Higgs self-coupling lambda which were calculated in a previous work, yiel… ▽ More We calculate the complete order y^2 and y^4 terms of the 59 x 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order lambda, lambda^2 and lambda y^2 depending on the Standard Model Higgs self-coupling lambda which were calculated in a previous work, yield the complete one-loop anomalous dimension matrix in the limit of vanishing gauge couplings. The Yukawa contributions result in non-trivial flavor mixing in the various operator sectors of the Standard Model effective theory. △ Less

Submitted 15 July, 2020; v1 submitted 17 October, 2013; originally announced October 2013.

Comments: 23 pp, 1 figure, v3: minor corrections. The complete SMEFT RGE will be maintained at http://einstein.ucsd.edu/smeft/

Report number: CERN-PH-TH/2015-247

Journal ref: JHEP 01 (2014) 035

Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

Abstract: We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dime… ▽ More We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this paper are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory. △ Less

Submitted 3 September, 2013; originally announced September 2013.

Comments: 10 pages, 1 fig

Report number: CERN-PH-TH/2013-213

Journal ref: Phys.Lett. B726 (2013) 697 - 702

Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

Abstract: We calculate the order λ, λ^2 and λy^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where λand y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixin… ▽ More We calculate the order λ, λ^2 and λy^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where λand y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion. △ Less

Submitted 15 July, 2020; v1 submitted 12 August, 2013; originally announced August 2013.

Comments: 19 pages, 4 fig, v4: minor corrections, the complete SMEFT RGE will be maintained at http://einstein.ucsd.edu/smeft/

Journal ref: JHEP 1310 (2013) 087

An Exactly Solvable Model for Dimension Six Higgs Operators and $h \to γγ$

Authors: Aneesh V. Manohar

Abstract: An exactly solvable large $N$ model is constructed which reduces at low energies to the Standard Model plus the dimension six Higgs-gauge operators $g_1^2 H^\dagger H B_{μν} B^{μν}$, $g_2^2 H^\dagger H W^a_{μν} W^{aμν}$, $g_1 g_2 H^\dagger τ^a H W^a_{μν} B^{μν}$, and $ε^{abc} W^a_μ{}^νW^b_ν{}^ρW^c_ρ{}^μ$. All other dimension six operators are suppressed by powers of $1/N$. The Higgs-gauge operator… ▽ More An exactly solvable large $N$ model is constructed which reduces at low energies to the Standard Model plus the dimension six Higgs-gauge operators $g_1^2 H^\dagger H B_{μν} B^{μν}$, $g_2^2 H^\dagger H W^a_{μν} W^{aμν}$, $g_1 g_2 H^\dagger τ^a H W^a_{μν} B^{μν}$, and $ε^{abc} W^a_μ{}^νW^b_ν{}^ρW^c_ρ{}^μ$. All other dimension six operators are suppressed by powers of $1/N$. The Higgs-gauge operators lead to deviations from the Standard Model $h \to γγ$ and $h \to γZ$ rates. A simple variant of the model can be used to also generate the Higgs-gluon operator $g_3^2 H^\dagger H G^A_{μν} G^{Aμν}$ which contributes to the Higgs production rate via gluon fusion. △ Less

Submitted 16 May, 2013; originally announced May 2013.

Probing the nature of the Higgs-like Boson via h -> VF decays

Authors: Gino Isidori, Aneesh V. Manohar, Michael Trott

Abstract: We give a general decomposition of the h -> VF amplitude where V={W,Z} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=l^+l^-, l nu (l =e, mu) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracte… ▽ More We give a general decomposition of the h -> VF amplitude where V={W,Z} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=l^+l^-, l nu (l =e, mu) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracted from a global fit to Higgs signal strengths. We also demonstrate how rare h -> VP decays, where P is a single hadron, with SM rates in the 10^{-5} range, can be used to provide complementary information on the couplings of the newly discovered Higgs-like scalar and are an interesting probe of the vacuum structure of the theory. △ Less

Submitted 28 November, 2013; v1 submitted 3 May, 2013; originally announced May 2013.

Comments: 5 pages, 4 figures [v3: numerics updated, refs added, accepted PLB version]

Report number: CERN-PH-TH-159

Journal ref: Physics Letters B 728C (2014), pp. 131-135

On Gauge Invariance and Minimal Coupling

Authors: Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

Abstract: The principle of minimal coupling has been used in the study of Higgs boson interactions to argue that certain higher dimensional operators in the low-energy effective theory generalization of the Standard Model are suppressed by loop factors, and thus smaller than others. It also has been extensively used to analyze beyond-the-standard-model theories. We show that in field theory, and even in qua… ▽ More The principle of minimal coupling has been used in the study of Higgs boson interactions to argue that certain higher dimensional operators in the low-energy effective theory generalization of the Standard Model are suppressed by loop factors, and thus smaller than others. It also has been extensively used to analyze beyond-the-standard-model theories. We show that in field theory, and even in quantum mechanics, the concept of minimal coupling is ill-defined and inapplicable as a general principle, and give many pedagogical examples which illustrate this fact. We also clarify some related misconceptions about the dynamics of strongly coupled gauge theories. Many arguments in the literature on Higgs boson interactions that use minimal coupling, particularly in pseudo-Goldstone Higgs theories, are inherently flawed. △ Less

Submitted 13 September, 2013; v1 submitted 30 April, 2013; originally announced May 2013.

Comments: 25 pp, 2 figures v2: refs added, JHEP version, conclusions unchanged

Report number: CERN-PH-TH-160

Journal ref: JHEP 1309 (2013) 063

The Topology and Size of the Universe from CMB Temperature and Polarization Data

Authors: Grigor Aslanyan, Aneesh V. Manohar, Amit P. S. Yadav

Abstract: We analyze seven year and nine year WMAP temperature maps for signatures of three finite flat topologies M_0=T^3, M_1=T^2 x R^1, and M_2=S^1 x R^2. We use Monte-Carlo simulations with the Feldman-Cousins method to obtain confidence intervals for the size of the topologies considered. We analyze the V, W, and Q frequency bands along with the ILC map and find no significant difference in the results… ▽ More We analyze seven year and nine year WMAP temperature maps for signatures of three finite flat topologies M_0=T^3, M_1=T^2 x R^1, and M_2=S^1 x R^2. We use Monte-Carlo simulations with the Feldman-Cousins method to obtain confidence intervals for the size of the topologies considered. We analyze the V, W, and Q frequency bands along with the ILC map and find no significant difference in the results. The 95.5% confidence level lower bound on the size of the topology is 1.5L_0 for M_0, 1.4L_0 for M_1, and 1.1L_0 for M_2, where L_0 is the radius of the last scattering surface. Our results agree very well with the recently released results from the Planck temperature data. We show that the likelihood function is not Gaussian in the size, and therefore simulations are important for obtaining accurate bounds on the size. We then introduce the formalism for including polarization data in the analysis. The improvement that we find from WMAP polarization maps is small because of the high level of instrumental noise, but our forecast for Planck maps shows a much better improvement on the lower bound for L. For the M_0 topology we expect an improvement on the lower bound of L from 1.7L_0 to 1.9L_0 at 95.5% confidence level. Using both polarization and temperature data is important because it tests the hypothesis that deviations in the TT spectrum at small l originate in the primordial perturbation spectrum. △ Less

Submitted 8 August, 2013; v1 submitted 5 April, 2013; originally announced April 2013.

Comments: Updated to match the published version

Journal ref: JCAP 08 (2013) 009

Limits on Semiclassical Fluctuations in the Primordial Universe

Authors: Grigor Aslanyan, Aneesh V. Manohar, Amit P. S. Yadav

Abstract: We place limits on semiclassical fluctuations that might be present in the primordial perturbation spectrum. These can arise if some signatures of pre-inflationary features survive the expansion, or could be created by whatever mechanism ends inflation. We study two possible models for such remnant fluctuations, both of which break the isotropy of CMB on large scales. We first consider a semiclass… ▽ More We place limits on semiclassical fluctuations that might be present in the primordial perturbation spectrum. These can arise if some signatures of pre-inflationary features survive the expansion, or could be created by whatever mechanism ends inflation. We study two possible models for such remnant fluctuations, both of which break the isotropy of CMB on large scales. We first consider a semiclassical fluctuation in one Fourier mode of primordial perturbations. The second scenario we analyze is a semiclassical Gaussian bump somewhere in space. These models are tested with the seven-year WMAP data using a Markov Chain Monte Carlo Bayesian analysis, and we place limits on these fluctuations. The upper bound for the amplitude of a fluctuation in a single Fourier mode is a<=10^(-4), while for the Gaussian bump a<=10^(-3). △ Less

Submitted 27 February, 2013; v1 submitted 23 January, 2013; originally announced January 2013.

Comments: Minor changes to match the published version

Journal ref: JCAP 02 (2013) 040

Renormalization Group Scaling of Higgs Operators and Γ(h -> γγ)

Authors: Christophe Grojean, Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

Abstract: We compute the renormalization of dimension six Higgs-gauge boson operators that can modify Γ(h -> γγ) at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consist… ▽ More We compute the renormalization of dimension six Higgs-gauge boson operators that can modify Γ(h -> γγ) at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consistent with renormalization group evolution. We study the implications of our results for Higgs phenomenology and for new physics models which attempt to explain a deviation in Γ(h -> γγ). We derive a new relation between the S parameter and the Γ(h -> γγ) and Γ(h ->Z γ) decay rates. △ Less

Submitted 11 January, 2013; originally announced January 2013.

Comments: 20 pp. 2 fig

Report number: CERN-PH-TH/2013-008

Double Parton Correlations in the Bag Model

Authors: Hsi-Ming Chang, Aneesh V. Manohar, Wouter J. Waalewijn

Abstract: Double parton scattering is sensitive to correlations between the two partons in the hadron, including correlations in flavor, spin, color, momentum fractions and transverse separation. We obtain a first estimate of the size of these correlations by calculating the corresponding double parton distribution functions in a bag model of the proton. We find significant correlations between momentum fra… ▽ More Double parton scattering is sensitive to correlations between the two partons in the hadron, including correlations in flavor, spin, color, momentum fractions and transverse separation. We obtain a first estimate of the size of these correlations by calculating the corresponding double parton distribution functions in a bag model of the proton. We find significant correlations between momentum fractions, spin and flavor, but negligible correlations with transverse separation. The model estimates of the relative importance of these correlations will help experimental studies disentangle them. △ Less

Submitted 11 February, 2013; v1 submitted 13 November, 2012; originally announced November 2012.

Comments: 9 pages, 7 figures

Journal ref: Phys. Rev. D 87, 034009 (2013)

Closing the Window on Strongly Interacting Dark Matter

Authors: Gregory D. Mack, Adithya Manohar

Abstract: Constraints are placed on the spin-independent interaction cross section of dark matter with regular matter by refining two methods. First, dark matter--cosmic ray interactions are considered, wherein cosmic ray protons collide with dark matter to contribute to the gamma ray sky. This constraint is developed using the NFW and Moore dark matter density profiles and new data from the Fermi gamma ray… ▽ More Constraints are placed on the spin-independent interaction cross section of dark matter with regular matter by refining two methods. First, dark matter--cosmic ray interactions are considered, wherein cosmic ray protons collide with dark matter to contribute to the gamma ray sky. This constraint is developed using the NFW and Moore dark matter density profiles and new data from the Fermi gamma ray space telescope. Second, the Earth capture scenario is considered, wherein particles that are captured self-annihilate at Earth's center, thus adding to its internal heat flow. The constraint presented here is developed based on analysis of the drift time of dark matter particles through Earth, modeled as a core composed of iron and a mantle composed of oxygen with linear density gradients between layers. An analysis of the cosmic ray constraint (which rules out dark matter--regular matter interaction cross sections greater than its value) shows that it overlaps significantly with the Earth drift time constraint (which rules out cross sections smaller than its value), closing the window on strongly interacting dark matter particles up to a mass of about 10^{17} GeV when combined with other exclusions. △ Less

Submitted 8 November, 2012; originally announced November 2012.

Comments: 5 pages, 2 figures, Submitted to Phys Rev. D