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Partial wave analysis of reactions with four meson final states
Authors:
M. A. Matveev,
A. T. Sitnikov,
A. V. Sarantsev
Abstract:
We construct a formalism which describes the resonances decaying into four pseudoscalar meson final states. This method is fully covariant and can be directly applied for the partial-wave analysis of high statistical data. Two topologies of the process are considered: two intermediate resonances each decaying into two final mesons and cascade decay via three meson intermediate states. In particula…
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We construct a formalism which describes the resonances decaying into four pseudoscalar meson final states. This method is fully covariant and can be directly applied for the partial-wave analysis of high statistical data. Two topologies of the process are considered: two intermediate resonances each decaying into two final mesons and cascade decay via three meson intermediate states. In particular, we consider the production of such states in the central collision reactions and in radiative $J/Ψ$ decay.
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Submitted 22 May, 2025;
originally announced May 2025.
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Differential technique for the covariant orbital angular momentum operators
Authors:
M. A. Matveev,
A. V. Sarantsev,
K. M. Semenov-Tian-Shansky,
A. N. Semenova
Abstract:
The orbital angular momentum operator expansion turns to be a powerful tool to construct the fully covariant partial wave amplitudes of hadron decay reactions and hadron photo- and electroproduction processes. In this paper we consider a useful development of the orbital angular momentum operator expansion method. We present the differential technique allowing the direct calculation of convolution…
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The orbital angular momentum operator expansion turns to be a powerful tool to construct the fully covariant partial wave amplitudes of hadron decay reactions and hadron photo- and electroproduction processes. In this paper we consider a useful development of the orbital angular momentum operator expansion method. We present the differential technique allowing the direct calculation of convolutions of two orbital angular momentum operators with an arbitrary number of open Lorentz indices. This differential technique greatly simplifies calculations when the reaction subject to the partial wave analysis involves high spin particles in the initial and/or final states. We also present a useful generalization of the orbital angular momentum operators.
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Submitted 22 February, 2018;
originally announced February 2018.
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Diquark-diquark-antiquark model for pentaquarks with hidden charm: current status and problems
Authors:
V. V. Anisovich,
M. A. Matveev,
J. Nyiri,
A. V. Sarantsev,
A. N. Semenova
Abstract:
The $J/ψp$ signals at 4380 MeV and 4450 MeV which were seen by the LHCb collaboration in the decay $Λ^0_b\to K^-J/ψp$ are discussed following the hypothesis of the existence of diquark-diquark-antiquark composite states. The discussed problems concern: (i) estimation of masses and mass splittings for low-lying states, (ii) determination of decay modes in the quark recombination scheme, (iii) unita…
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The $J/ψp$ signals at 4380 MeV and 4450 MeV which were seen by the LHCb collaboration in the decay $Λ^0_b\to K^-J/ψp$ are discussed following the hypothesis of the existence of diquark-diquark-antiquark composite states. The discussed problems concern: (i) estimation of masses and mass splittings for low-lying states, (ii) determination of decay modes in the quark recombination scheme, (iii) unitarity and analyticity constrains for pentaquark propagators, (iv) hadronic deuteron-like components in the diquark-diquark-antiquark multiplet.
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Submitted 29 November, 2017;
originally announced November 2017.
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Narrow pentaquarks as diquark-diquark-antiquark systems
Authors:
V. V. Anisovich,
M. A. Matveev,
J. Nyiri,
A. N. Semenova
Abstract:
The diquark-diquark-antiquark model describes pentaquark states both in terms of quarks and hadrons. The latest LHCb data for pentaquarks with open charm emphasize the importance of hadron components in the structure of pentaquarks. We discuss pentaquark states with hidden charm $P(\bar c cuud)$ and those with open charm $P(\bar uussc)$ which were discovered recently in LHCb data ($J/Ψp$ and…
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The diquark-diquark-antiquark model describes pentaquark states both in terms of quarks and hadrons. The latest LHCb data for pentaquarks with open charm emphasize the importance of hadron components in the structure of pentaquarks. We discuss pentaquark states with hidden charm $P(\bar c cuud)$ and those with open charm $P(\bar uussc)$ which were discovered recently in LHCb data ($J/Ψp$ and $Ξ_c^+ K^-$ spectra correspondingly). Considering the observed states as members of the lowest (s-wave) multiplet we discuss the mass splitting of states and the dumping of their widths.
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Submitted 31 August, 2017; v1 submitted 5 June, 2017;
originally announced June 2017.
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Propagators of resonances and rescatterings of the decay products
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
A. V. Sarantsev,
A. N. Semenova,
J. Nyiri
Abstract:
Hadronic resonance propagators which take into account the analytical properties of decay processes are built in terms of the dispersion relation technique. Such propagators can describe multi-component systems, for example, those when quark degrees of freedom create a resonance state, and decay products correct the corresponding pole by adding hadronic deuteron-like components. Meson and baryon s…
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Hadronic resonance propagators which take into account the analytical properties of decay processes are built in terms of the dispersion relation technique. Such propagators can describe multi-component systems, for example, those when quark degrees of freedom create a resonance state, and decay products correct the corresponding pole by adding hadronic deuteron-like components. Meson and baryon states are considered, examples of particles with different spins are presented.
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Submitted 9 August, 2016; v1 submitted 21 May, 2016;
originally announced May 2016.
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Non-strange and strange pentaquarks with hidden charm
Authors:
V. V. Anisovich,
M. A. Matveev,
J. Nyiri,
A. V. Sarantsev,
A. N. Semenova
Abstract:
Non-strange and strange pentaquaks with hidden charm are considered as diquark-diquark-antiquark composite systems. Spin and isospin content of such exotic states is discussed and masses are evaluated.
Non-strange and strange pentaquaks with hidden charm are considered as diquark-diquark-antiquark composite systems. Spin and isospin content of such exotic states is discussed and masses are evaluated.
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Submitted 16 September, 2015;
originally announced September 2015.
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Pentaquarks and strange tetraquark mesons
Authors:
V. V. Anisovich,
M. A. Matveev,
A. V. Sarantsev,
A. N. Semenova
Abstract:
We consider the interplay of the pentaquark states and strange tetraquark states in the decay $Λ^0_b\to K^-J/ψp$. Possible existence of ($cs\bar c\bar u$)-states is taken up and their manifestation in the $K^-J/ψ$-channel is discussed. It is emphasised that these exotic mesons can imitate broad bumps in the in the $pJ/ψ$-channel.
We consider the interplay of the pentaquark states and strange tetraquark states in the decay $Λ^0_b\to K^-J/ψp$. Possible existence of ($cs\bar c\bar u$)-states is taken up and their manifestation in the $K^-J/ψ$-channel is discussed. It is emphasised that these exotic mesons can imitate broad bumps in the in the $pJ/ψ$-channel.
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Submitted 16 September, 2015; v1 submitted 10 September, 2015;
originally announced September 2015.
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Pentaquarks and resonances in the $pJ/ψ$ spectrum
Authors:
V. V. Anisovich,
M. A. Matveev,
J. Nyiri,
A. V. Sarantsev,
A. N. Semenova
Abstract:
We consider exotic baryons with hidden charm as antiquark-diquark-diquark composite systems. Spin and isospin structure of such exotic states is given and masses are estimated. The data for production of pentaquarks in the reaction $Λ_b\to K^-p J/ψ$ are discussed. We suggest that the narrow peak in $pJ/ψ$ spectra at 4450 MeV is antiquark-diquark-diquark state with negative parity, $5/2^{-}(4450)$,…
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We consider exotic baryons with hidden charm as antiquark-diquark-diquark composite systems. Spin and isospin structure of such exotic states is given and masses are estimated. The data for production of pentaquarks in the reaction $Λ_b\to K^-p J/ψ$ are discussed. We suggest that the narrow peak in $pJ/ψ$ spectra at 4450 MeV is antiquark-diquark-diquark state with negative parity, $5/2^{-}(4450)$, while the broad bump $3/2^{+}(4380)$ is the result of rescatterings in the ($pJ/ψ$)-channel. Positions of other pentaquarks with negative parity are estimated.
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Submitted 28 July, 2015;
originally announced July 2015.
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Exotic mesons with hidden charm as diquark-antidiquark states
Authors:
V. V. Anisovich,
M. A. Matveev,
A. V. Sarantsev,
A. N. Semenova
Abstract:
Exotic mesons with hidden strange ($s\bar s$) and heavy quark pairs ($Q\bar Q$), where $Q=c,b$, are considered as diquark-antidiquark systems, $(Qs)(\bar Q\bar s)$. Taking into account that these states can recombinate into two-meson ones, we study the interplay of these states in terms of the dispersion relation D-function technique. The classification of exotic mesons is discussed, coefficients…
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Exotic mesons with hidden strange ($s\bar s$) and heavy quark pairs ($Q\bar Q$), where $Q=c,b$, are considered as diquark-antidiquark systems, $(Qs)(\bar Q\bar s)$. Taking into account that these states can recombinate into two-meson ones, we study the interplay of these states in terms of the dispersion relation D-function technique. The classification of exotic mesons is discussed, coefficients for decay modes are given, predictions for new states are presented. The nonet structure for $((Qq)(\bar Q \bar q)$, ($(Qs)(\bar Q\bar s$)), ($(Qq)(\bar Q\bar s))$- states ($q=u,d$) is suggested.
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Submitted 26 July, 2015;
originally announced July 2015.
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Central production of lepton-antilepton pairs and heavy quark composite states in hadron diffractive collisions at ultrahigh energies
Authors:
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov,
J. Nyiri
Abstract:
Central production of lepton-lepton pairs ($e^+e^-$ and $μ^+μ^-$) and heavy quark composite states (charmonia and bottomonia) in diffractive proton collisions (proton momenta transferred ${|\bf q_\perp}|\sim m/\ln s$) are studied at ultrahigh energies ($\ln{s}>>1$), where $σ_{tot}(pp^\pm)\sim\ln^N s$ with $1\la N\la 2$. The $pp^\pm$-rescattering corrections, which are not small, are calculated in…
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Central production of lepton-lepton pairs ($e^+e^-$ and $μ^+μ^-$) and heavy quark composite states (charmonia and bottomonia) in diffractive proton collisions (proton momenta transferred ${|\bf q_\perp}|\sim m/\ln s$) are studied at ultrahigh energies ($\ln{s}>>1$), where $σ_{tot}(pp^\pm)\sim\ln^N s$ with $1\la N\la 2$. The $pp^\pm$-rescattering corrections, which are not small, are calculated in terms of the $K$-matrix approach modified for ultrahigh energies. Two versions of hadron interactions are considered in detail: the growth (i) $σ_{tot}(pp^\pm)\sim\ln^2 s$, $σ_{inel}(pp^\pm)\sim\ln^2 s$ within the black disk mode and (ii) $σ_{tot}(pp^\pm)\sim\ln^2 s$, $σ_{inel}(pp^\pm)\sim\ln s$ within the resonant disk mode. The energy behavior of the diffractive production processes differs strongly for these modes, thus giving a possibility to distinguish between the versions of the ultrahigh energy interactions.
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Submitted 20 August, 2014;
originally announced August 2014.
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Hadron diffractive production at ultrahigh energies
Authors:
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov
Abstract:
Diffractive production is considered in the ultrahigh energy region where pomeron exchange amplitudes are transformed into black disk ones due to rescattering corrections. The corresponding corrections in hadron reactions $h_1+h_3\to h_1+h_2+h_3$ with small momenta transferred ($q^2_{1\to 1}\sim m^2/\ln^2s$, $q^2_{3\to 3}\sim m^2/\ln^2s$) are calculated in terms of the $K$-matrix technique modifie…
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Diffractive production is considered in the ultrahigh energy region where pomeron exchange amplitudes are transformed into black disk ones due to rescattering corrections. The corresponding corrections in hadron reactions $h_1+h_3\to h_1+h_2+h_3$ with small momenta transferred ($q^2_{1\to 1}\sim m^2/\ln^2s$, $q^2_{3\to 3}\sim m^2/\ln^2s$) are calculated in terms of the $K$-matrix technique modified for ultrahigh energies. Small values of the momenta transferred are crucial for introducing equations for amplitudes. The three-body equation for hadron diffractive production reaction $h_1+h_3\to h_1+h_2+h_3$ is written and solved precisely in the eikonal approach. In the black disk regime final state scattering processes do not change the shapes of amplitudes principally but dump amplitudes in a factor $\sim\frac 14$.
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Submitted 17 July, 2014;
originally announced July 2014.
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Dependence of nucleon mass on parameters of instanton medium
Authors:
E. G. Drukarev,
E. L. Kryshen,
M. A. Matveev,
M. G. Ryskin,
V. A. Sadovnikova
Abstract:
We trace the dependence of the nucleon mass and of the effective size of the nucleon on the characteristics of the instanton medium, which are the average instanton size $ρ$ and the distance between the instantons in instanton medium R. We consider several scenario for variation of the values of $ρ$ and R.
We trace the dependence of the nucleon mass and of the effective size of the nucleon on the characteristics of the instanton medium, which are the average instanton size $ρ$ and the distance between the instantons in instanton medium R. We consider several scenario for variation of the values of $ρ$ and R.
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Submitted 12 December, 2013;
originally announced December 2013.
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Sigma-Meson and Confinement Singularity
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
K. V. Nikonov,
V. A. Nikonov,
J. Nyiri,
A. V. Sarantsev,
T. O. Vulfs
Abstract:
We describe the meson-meson data for the ($IJ^{PC}=00^{++}$) wave at $280\leq\sqrt s\leq 1900$ MeV in two approaches: (i) the K-matrix approach and (ii) the dispersion relation D-matrix method. With a good description of low energy data (at $280\leq\sqrt s\leq 900$ MeV) as well as the data of two-meson transition amplitudes and antiproton-proton annihilation into three pseudoscalar meson states (a…
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We describe the meson-meson data for the ($IJ^{PC}=00^{++}$) wave at $280\leq\sqrt s\leq 1900$ MeV in two approaches: (i) the K-matrix approach and (ii) the dispersion relation D-matrix method. With a good description of low energy data (at $280\leq\sqrt s\leq 900$ MeV) as well as the data of two-meson transition amplitudes and antiproton-proton annihilation into three pseudoscalar meson states (at $450\leq\sqrt s\leq 1950$ MeV) we have found the positions of the resonance poles: (i) for the $σ$ meson pole: $M_σ= (390\pm 35)-i(235\pm 50)$ MeV; (ii) two poles for the $f_0(980)$, on the second sheet (under the $ππ$ cut): $M_{I} = (1011\pm 5)-i(35\pm 5)$ MeV, and on the third sheet (under the $ππ$ and $K\bar K$ cuts), $M_{II} = (1035\pm 50)-i(460\pm 50)$ MeV; for the $f_0(1370)$ meson, $M= (1285\pm 30)-i(160\pm 20)$ MeV; for the $f_0(1500)$ meson, $M = (1488\pm 4)-i(53\pm 5)$ MeV; for the $f_0(1790)$ meson, $M = (1775\pm 25)-i(140\pm 15)$ MeV and for the broad state $f_0(1200-1600)$ $M=(1540\pm 120)-i(550\pm 70)$ MeV. Our estimation of the scalar-isoscalar scattering length obtained under different parameterizations and assumptions about the quality of low energy $ππ$ scattering data is $a^0_0=(0.215\pm 0.040)μ^{-1}_π$. We also discuss the idea according to which the $σ$-meson could be a remnant of the confinement singularity, $1/s^2$, in a white channel.
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Submitted 30 May, 2011;
originally announced May 2011.
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Quasi-diffraction production of white quark--gluon clusters at superhigh-energy hadron collisions
Authors:
V. V. Anisovich,
L. G. Dakhno,
M. A. Matveev,
V. A. Nikonov
Abstract:
We discuss a collective effect, which can be possible in hadron--hadron collisions at superhigh energies, that is, a quasi-diffraction production of several white clusters of quarks and gluons. Being transformed into hadrons, such clusters are sources of the fastest particles, which move forward nearly parallel to each other.
We discuss a collective effect, which can be possible in hadron--hadron collisions at superhigh energies, that is, a quasi-diffraction production of several white clusters of quarks and gluons. Being transformed into hadrons, such clusters are sources of the fastest particles, which move forward nearly parallel to each other.
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Submitted 3 November, 2010;
originally announced November 2010.
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Quark-diquark Systematics of Baryons: Spectral Integral Equations for Systems Composed by Light Quarks
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev,
T. O. Vulfs
Abstract:
For baryons composed by the light quarks ($q=u,d$) we write spectral integral equation using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We present spectral integral equations for the $qD^{0}_{0}$ and $qD^{1}_{1}$ states taking into account quark--diquark con…
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For baryons composed by the light quarks ($q=u,d$) we write spectral integral equation using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We present spectral integral equations for the $qD^{0}_{0}$ and $qD^{1}_{1}$ states taking into account quark--diquark confinement interaction.
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Submitted 8 May, 2010;
originally announced May 2010.
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Quark--Diquark Systematics of Baryons and the SU(6)SYMMETRY for Light States
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev,
T. O. Vulfs
Abstract:
We continue our attempts to systematize baryons, which are composed of light quarks ($q=u,d$), as quark--diquark systems. The notion of two diquarks is used: (i) $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) $D^{0}_{0}$, with $S_D=0$ and $I_D=0$. Here we try to resolve the problem of the low-lying $Δ(\frac 52^-)$ states: in the last experiments the lightest state is observed at…
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We continue our attempts to systematize baryons, which are composed of light quarks ($q=u,d$), as quark--diquark systems. The notion of two diquarks is used: (i) $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) $D^{0}_{0}$, with $S_D=0$ and $I_D=0$. Here we try to resolve the problem of the low-lying $Δ(\frac 52^-)$ states: in the last experiments the lightest state is observed at $\ga 2200$ MeV, not at $1900 - 2000$ MeV as it has been stated 20 years ago. We are looking for different systematization variants with the forbidden low-lying $Δ(\frac 52^-)$ states in the mass region $\la 2000$ MeV. We see that the inclusion of the SU(6) constraints on $qD^{1}_{1}$ states with angular momentum L=1 results in a shift of the lightest $Δ(\frac 52^-)$ isobar to $\sim 2300$ MeV. The scheme with the SU(6) constraints for low-lying $qD^{1}_{1}$ and $qD^{0}_{0}$ states (with $L=0,1$) is presented in detail here.
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Submitted 8 February, 2010;
originally announced February 2010.
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Searching for the quark--diquark systematics of baryons composed by light quarks $q=u,d$
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev,
T. O. Vulfs
Abstract:
Supposing quark--diquark structure of baryons, we look for systematics of baryons composed of light quarks ($q=u,d$). We systematize baryons using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We consider several schemes for the composed baryons: (1) with dif…
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Supposing quark--diquark structure of baryons, we look for systematics of baryons composed of light quarks ($q=u,d$). We systematize baryons using the notion of two diquarks: (i) axial--vector state, $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii) scalar one, $D^{0}_{0}$, with the spin $S_D=0$ and isospin $I_D=0$. We consider several schemes for the composed baryons: (1) with different diquark masses, $M_{D^0_0} \ne M_{D^1_1}$, (2) with $M_{D^0_0} = M_{D^1_1}$ and overlapping $qD^0_0$ and $qD^1_1$ states (resonances), (3) with/without SU(6) constraints for low-lying states (with quark--diquark orbital momenta L=0). In the high-mass region the model predicts several baryon resonances at $M\sim 2.0-2.9$ GeV. Moreover, the model gives us the double pole structure (i.e. two poles with the same Re$M$ but different Im$M$) in many amplitudes at masses $M\ga 2.0$ GeV. We see also that for description of low-lying baryons (with L=0), the SU(6) constraint is needed.
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Submitted 8 January, 2010;
originally announced January 2010.
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Photoproduction of pions and properties of baryon resonances from a Bonn-Gatchina partial wave analysis
Authors:
A. V. Anisovich,
E. Klempt,
V. A. Nikonov,
M. A. Matveev,
A. V. Sarantsev,
U. Thoma
Abstract:
Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for $γp\to pπ^0$ and $γp\to nπ^+$ are given and compared to results from other…
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Masses, widths and photocouplings of baryon resonances are determined in a coupled-channel partial wave analysis of a large variety of data. The Bonn-Gatchina partial wave formalism is extended to include a decomposition of t- and u-exchange amplitudes into individual partial waves. The multipole transition amplitudes for $γp\to pπ^0$ and $γp\to nπ^+$ are given and compared to results from other analyses.
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Submitted 22 February, 2010; v1 submitted 27 November, 2009;
originally announced November 2009.
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Two-pion decays of mesons and confinement singularities
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov,
J. Nyiri,
A. V. Sarantsev
Abstract:
We consider the two-pion decay of the $ρ$-meson, the $^3S_1q\bar q$-state of the constituent quarks -- the decay being determined by the transition $q\bar q\to ππ$ contains information about confinement interactions. One can specify in this decay two types of transitions: ({\bf i}) the bremsstrahlung radiation of a pion $q\to q+π$ (or $\bar q\to\bar q+π$) with the subsequent fusion…
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We consider the two-pion decay of the $ρ$-meson, the $^3S_1q\bar q$-state of the constituent quarks -- the decay being determined by the transition $q\bar q\to ππ$ contains information about confinement interactions. One can specify in this decay two types of transitions: ({\bf i}) the bremsstrahlung radiation of a pion $q\to q+π$ (or $\bar q\to\bar q+π$) with the subsequent fusion $q\bar q\to π$, and ({\bf ii}) the direct transition $q\bar q\to ππ$. We demonstrate how in the amplitudes of the corresponding transitions the quark singularities have to disappear, {\it i.e.} what is the way the quark confinement at relatively short distances can be realized. We calculate and estimate the contributions of processes with bremsstrahlung radiation of the pion and of the direct transition $q\bar q\to ππ$. The estimates demonstrate that the processes involving the direct transition $q\bar q\to ππ$ are necessary, but they cannot be determined unambiguously by the decay $ρ(775)\to ππ$. We conclude that for the determination of the $q\bar q\to ππ$ transition more complete data on the resonance decays into the $ππ$ channels are required than those available at the moment.
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Submitted 3 March, 2009;
originally announced March 2009.
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The rho -> gamma pi and omega -> gamma pi decays in quark-model approach and estimation of coupling for pion emission by quark
Authors:
A. V. Anisovich,
V. V. Anisovich,
L. G. Dakhno,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev
Abstract:
In the framework of the relativistic and gauge invariant spectral integral technique, we calculate radiative decays rho(770)-> gamma pi(140) and omega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to be quark-antiquark states. The q anti-q wave functions found for mesons and photon lead to a reasonably good description of data ($Γ^{(exp)}_{ρ^{\pm} \toγπ^{\pm}}=68\pm 30$ keV,…
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In the framework of the relativistic and gauge invariant spectral integral technique, we calculate radiative decays rho(770)-> gamma pi(140) and omega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to be quark-antiquark states. The q anti-q wave functions found for mesons and photon lead to a reasonably good description of data ($Γ^{(exp)}_{ρ^{\pm} \toγπ^{\pm}}=68\pm 30$ keV, $Γ^{(exp)}_{ρ^{0}\toγπ^0}=77\pm 28$ keV, $Γ^{(exp)}_{ω\toγπ^0}=776\pm 45$ keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks $g_π\equiv g_π(u\to d π)$. We have found two values for the pion bremsstrahlung coupling: $|g_π|=16.7 \pm 0.3 ^{+0.1}_{-2.3}$ (Solution I) and $|g_π|=3.0 \pm 0.3 ^{+0.1}_{-2.1}$ (Solution II). Within SU(6)-symmetry for nucleons, Solution I gives us for pi NN coupling the value $16.4 \le g_{πNN}^2/(4π) \le 23.2$ that is in qualitative agreement with the pi N scattering data, $g_{πNN}^2/(4π)\simeq 14$. For excited states, we have estimated the partial widths in Solution I as follows: $Γ(ρ_{2S}^\pm\to γπ)\simeq 10 - 130$ keV, $Γ(ρ_{2S}^0\to γπ)\simeq 10 -130$ keV, $Γ(ω_{2S}\to γπ)\simeq 60 - 1080$ keV. The large uncertainties emphasise the necessity to carry out measurements of the meson radiative processes in the region of large masses.
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Submitted 30 January, 2009;
originally announced January 2009.
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Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge III.} Light mesons
Authors:
V. V. Anisovich,
L. G. Dakhno,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev
Abstract:
We continue the investigation of mesons in terms of the spectral integral equation initiated before [hep-ph/0510410, hep-ph/0511005] for the $b\bar b$ and $c\bar c$ systems: in this paper we consider the light-quark ($u, d,s$) mesons with masses $M\le 3$ GeV. The calculations have been performed for the mesons lying on linear trajectories in the $(n,M^2)$-planes, where $n$ is the radial quantum…
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We continue the investigation of mesons in terms of the spectral integral equation initiated before [hep-ph/0510410, hep-ph/0511005] for the $b\bar b$ and $c\bar c$ systems: in this paper we consider the light-quark ($u, d,s$) mesons with masses $M\le 3$ GeV. The calculations have been performed for the mesons lying on linear trajectories in the $(n,M^2)$-planes, where $n$ is the radial quantum number. Our consideration relates to the $q\bar q$ states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as $π(0^{-+})$, $ρ(1^{--})$, $ω(1^{--})$, $φ(1^{--})$, $a_0(0^{++})$, $a_1(1^{++})$, $a_2(2^{++})$, $b_1(1^{+-})$, $f_2(2^{++})$, $π_2(2^{-+})$, $ρ_3(3^{--})$, $ω_3(3^{--})$, $φ_3(3^{--})$, $π_4(4^{-+})$ at $n\le 6$. We obtained the wave functions and mass values of mesons lying on these trajectories. The corresponding trajectories are linear, in agreement with data. We have calculated the two-photon decays $π\to γγ$, $a_0(980)\to γγ$, $a_2(1320)\to γγ$, $f_2(1285)\to γγ$, $f_2(1525)\to γγ$ and radiative transitions $ρ\toγπ$, $ω\toγπ$, that agree qualitatively with the experiment. On this basis, we extract the singular part of the interaction amplitude, which corresponds to the so-called "confinement interaction". The description of the data requires the presence of the strong $t$-channel singularities for both scalar and vector exchanges.
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Submitted 9 November, 2005;
originally announced November 2005.
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Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge II.} Charmonia
Authors:
V. V. Anisovich,
L. G. Dakhno,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev
Abstract:
In the precedent paper of the authors (hep-ph/0510410), the $b\bar b$ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium $(c\bar c)$ states. We reconstruct the interaction in the $c\bar c$-sector on the basis of data f…
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In the precedent paper of the authors (hep-ph/0510410), the $b\bar b$ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium $(c\bar c)$ states. We reconstruct the interaction in the $c\bar c$-sector on the basis of data for the charmonium levels with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$, $1^{+-}$ and radiative transitions $ψ(2S)\toγχ_{c0}(1P)$, $γχ_{c1}(1P)$, $γχ_{c2}(1P)$, $γη_{c}(1S)$ and $χ_{c0}(1P)$, $χ_{c1}(1P)$, $χ_{c2}(1P)\toγJ/ψ$. The $c\bar c$ levels and their wave functions are calculated for the radial excitations with $n\le 6$. Also, we determine the $c\bar c$ component of the photon wave function using the $e^+e^-$ annihilation data: $e^+e^- \to J/ψ(3097)$, $ψ(3686)$, $ψ(3770)$, $ψ(4040)$, $ ψ(4160)$, $ψ(4415)$ and perform the calculations of the partial widths of the two-photon decays for the $n=1$ states: $η_{c0}(1S)$, $χ_{c0}(1P)$, $χ_{c2}(1P)\toγγ$, and $n=2$ states: $η_{c0}(2S)\toγγ$, $χ_{c0}(2P)$, $χ_{c2}(2P)\to γγ$. We discuss the status of the recently observed $c\bar c$ states X(3872) and Y(3941): according to our results, the X(3872) can be either $χ_{c1}(2P)$ or $η_{c2}(1D)$, while Y(3941) is $χ_{c2}(2P)$.
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Submitted 9 November, 2005; v1 submitted 1 November, 2005;
originally announced November 2005.
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Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge I.} Bottomonia
Authors:
V. V. Anisovich,
L. G. Dakhno,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev
Abstract:
In the framework of the spectral integral equation, we consider the $b\bar b$ states and their radiative transitions. We reconstruct the $b\bar b$ interaction on the basis of data for the levels of the bottomonium states with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$ as well as the data for the radiative transitions $Υ(3S) \toγχ_{bJ}(2P) $ and $Υ(2S) \toγχ_{bJ}(1P) $ with…
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In the framework of the spectral integral equation, we consider the $b\bar b$ states and their radiative transitions. We reconstruct the $b\bar b$ interaction on the basis of data for the levels of the bottomonium states with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$ as well as the data for the radiative transitions $Υ(3S) \toγχ_{bJ}(2P) $ and $Υ(2S) \toγχ_{bJ}(1P) $ with $J=0,1,2$. We calculate bottomonium levels with the radial quantum numbers $n\le 6$, their wave functions and corresponding radiative transitions. The ratios $Br[χ_{bJ}(2P)\toγΥ(2S)]/Br[χ_{bJ}(2P)\toγΥ(1S)]$ for $J=0,1,2$ are found in the agreement with data. We determine the $b\bar b$ component of the photon wave function using the data for the $e^+e^-$ annihilation, $e^+e^- \toΥ(9460)$, $Υ(10023)$, $Υ(10036)$, $Υ(10580)$, $ Υ(10865)$, $Υ(11019)$, and predict partial widths of the two-photon decays $η_{b0}\to\ggam$, $χ_{b0}\to\ggam$, $χ_{b2}\to\ggam$ for the radial excitation states below $B\bar B$ threshold ($n\le 3$).
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Submitted 9 November, 2005; v1 submitted 31 October, 2005;
originally announced October 2005.
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Radiative decays of quarkonium states, momentum operator expansion and nilpotent operators
Authors:
A. V. Anisovich,
V. V. Anisovich,
V. N. Markov,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev
Abstract:
We present the method of calculation of radiative decays of composite quark-antiquark systems with different J^{PC}: (Q\bar Q)_{in} -> gamma (Q\bar Q)_{out}. The method is relativistic invariant, it is based on the double dispersion relation integrals over the masses of composite mesons, it can be used for the high spin particles and provides us with the gauge invariant transition amplitudes. We…
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We present the method of calculation of radiative decays of composite quark-antiquark systems with different J^{PC}: (Q\bar Q)_{in} -> gamma (Q\bar Q)_{out}. The method is relativistic invariant, it is based on the double dispersion relation integrals over the masses of composite mesons, it can be used for the high spin particles and provides us with the gauge invariant transition amplitudes. We apply this method to the case when the photon is emitted by a constituent in the intermediate state (additive quark model). We perform the momentum operator expansion of the spin amplitudes for the decay processes. The problem of nilpotent spin operators is discussed.
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Submitted 30 October, 2005; v1 submitted 6 September, 2005;
originally announced September 2005.
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The Riddle of the f0(980) and a0(980): Are They the Quark-Antiquark States?
Authors:
A. V. Anisovich,
V. V. Anisovich,
L. G. Dakhno,
V. N. Markov,
M. A. Matveev,
V. A. Nikonov,
A. V. Sarantsev
Abstract:
A list of arguments favouring quark-antiquark nature of a0(980) and f0(980) is presented.
A list of arguments favouring quark-antiquark nature of a0(980) and f0(980) is presented.
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Submitted 25 August, 2005;
originally announced August 2005.
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Sector of the $2^{++}$ mesons: observation of the tensor glueball
Authors:
V. V. Anisovich,
M. A. Matveev,
J. Nyiri,
A. V. Sarantsev
Abstract:
Data of the Crystal Barrel and L3 collaborations clarified essentially the situation in the $2^{++}$ sector in the mass region up to 2400 MeV, demonstrating the linearity of $(n,M^2)$ trajectories, where $n$ is the radial quantum number of a quark-antiquark state with mass $M$. We discuss these data and show that there exists a superfluous state for the $(n,M^2)$ trajectories: a broad resonance…
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Data of the Crystal Barrel and L3 collaborations clarified essentially the situation in the $2^{++}$ sector in the mass region up to 2400 MeV, demonstrating the linearity of $(n,M^2)$ trajectories, where $n$ is the radial quantum number of a quark-antiquark state with mass $M$. We discuss these data and show that there exists a superfluous state for the $(n,M^2)$ trajectories: a broad resonance $f_2(2000)$. We pay special attention to the reactions $p\bar p\toππ,ηη,ηη'$ in the mass region 1990--2400 MeV where, together with $f_2(2000)$, four relatively narrow resonances are seen: $f_2(1920)$, $f_2(2020)$, $f_2(2240)$, $f_2(2300)$. We analyse the branching ratios of all these resonances and show that only the decay couplings of the broad state $f_2(2000)\toπ^0π^0,ηη, ηη'$ satisfy relations inherent in the glueball decay.
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Submitted 14 June, 2005;
originally announced June 2005.
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Determination of the quarkonium--gluonium content of the isoscalar tensor resonances $f_2(1920)$, $f_2(2020)$, $f_2(2240)$, $f_2(2300)$ and of the broad state $f_2(2000)$ based on decay couplings to $π^0π^0,ηη,ηη'$
Authors:
V. V. Anisovich,
M. A. Matveev,
J. Nyiri,
A. V. Sarantsev
Abstract:
In the reactions $p\bar p\toπ^0π^0,ηη,ηη'$ there are four relatively narrow resonances $f_2(1920)$, $f_2(2020)$, $f_2(2240)$, $f_2(2300)$, and a broad one $f_2(2000)$ in the mass region 1990--2400 MeV. In the framework of quark combinatorics we carry out an analysis of the decay constants for all five resonances. It is shown that the relations for the decay constants corresponding to the broad r…
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In the reactions $p\bar p\toπ^0π^0,ηη,ηη'$ there are four relatively narrow resonances $f_2(1920)$, $f_2(2020)$, $f_2(2240)$, $f_2(2300)$, and a broad one $f_2(2000)$ in the mass region 1990--2400 MeV. In the framework of quark combinatorics we carry out an analysis of the decay constants for all five resonances. It is shown that the relations for the decay constants corresponding to the broad resonance $f_2(2000)\toπ^0π^0,ηη, ηη'$ are the same as those corresponding to a glueball. An additional argument in favour of the glueball--nature of $f_2(2000)$ is the fact that $f_2(1920)$, $f_2(2020)$, $f_2(2240)$, $f_2(2300)$ fit well the $q\bar q$ trajectories in the $(n,M^2)$-plane (where $n$ is the radial quantum number), while the broad $f_2(2000)$ resonance turns out to be an unnecessary extra state for these trajectories.
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Submitted 1 January, 2005;
originally announced January 2005.
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Quark-antiquark composite systems:the Bethe--Salpeter equation in the spectral-integration technique in the case of the different quark masses
Authors:
A. V. Anisovich,
V. V. Anisovich,
V. N. Markov,
M. A. Matveev,
A. V. Sarantsev
Abstract:
The Bethe--Salpeter equations for the quark-antiquark composite systems with different quark masses, such as $q\bar s$ (with $q=u$,$d$), $q\bar Q$ and $s \bar Q$ (with $Q=c$,$b$), are written in terms of spectral integrals. For the mesons characterized by the mass $M$, spin $J$ and radial quantum number $n$, the equations are presented for the $(n,M^2)$-trajectories with fixed $J$. In the spectr…
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The Bethe--Salpeter equations for the quark-antiquark composite systems with different quark masses, such as $q\bar s$ (with $q=u$,$d$), $q\bar Q$ and $s \bar Q$ (with $Q=c$,$b$), are written in terms of spectral integrals. For the mesons characterized by the mass $M$, spin $J$ and radial quantum number $n$, the equations are presented for the $(n,M^2)$-trajectories with fixed $J$. In the spectral-integral technique one can use the energy-dependent forces and get beyond instantaneous approximation. The mixing between states with different quark spin $S$ and angular momentum $L$ are also discussed.
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Submitted 28 January, 2004;
originally announced January 2004.
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Description of composite systems in the spectral integration technique: the gauge invariance and analyticity constraints for the radiative decay amplitudes
Authors:
V. V. Anisovich,
M. A. Matveev
Abstract:
The constraints followed from gauge invariance and analyticity are considered for the amplitudes of radiative transitions of composite systems when composite systems are treated in terms of spectral integrals. We discuss gauge-invariant amplitudes for the transitions S -> gamma S and V -> gamma S with scalar S and vector V mesons being two-particle composite systems of scalar (or pseudoscalar) c…
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The constraints followed from gauge invariance and analyticity are considered for the amplitudes of radiative transitions of composite systems when composite systems are treated in terms of spectral integrals. We discuss gauge-invariant amplitudes for the transitions S -> gamma S and V -> gamma S with scalar S and vector V mesons being two-particle composite systems of scalar (or pseudoscalar) constituents, and we demonstrate the mechanism of cancellation of false kinematical singularities. Furthermore, we explain how to generalize the performed consideration for quark-antiquark systems, in particular, for the reaction phi(1020) -> gamma f0(980). Here we also consider in more detail the quark-model non-relativistic approach for this reaction.
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Submitted 14 March, 2003;
originally announced March 2003.
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Quark-antiquark composite systems: the Bethe-Salpeter equation in the spectral-integration technique
Authors:
A. V. Anisovich,
V. V. Anisovich,
V. N. Markov,
M. A. Matveev,
A. V. Sarantsev
Abstract:
The Bethe-Salpeter equations for the light-quark composite systems, q q-bar, are written in terms of spectral integrals. For the q q-bar -mesons characterized by the mass M, spin J and radial quantum number n, the equations are presented for the following (n,M^2)-trajectories: pi_J, eta_J, a_J, f_J, rho_J, omega_J, h_J and b_J.
The Bethe-Salpeter equations for the light-quark composite systems, q q-bar, are written in terms of spectral integrals. For the q q-bar -mesons characterized by the mass M, spin J and radial quantum number n, the equations are presented for the following (n,M^2)-trajectories: pi_J, eta_J, a_J, f_J, rho_J, omega_J, h_J and b_J.
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Submitted 15 September, 2003; v1 submitted 15 August, 2002;
originally announced August 2002.
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Two-photon partial widths of tensor mesons
Authors:
A. V. Anisovich,
V. V. Anisovich,
M. A. Matveev,
V. A. Nikonov
Abstract:
We calculate partial widths of the gamma-gamma decay of the tensor q\bar q states a_2(1320), f_2(1270), f_2(1525), their radial excitations a_2(1660), f_2(1640), f_2(1800) as well as ^3F_2 q\bar q states. Calculations are performed in the framework of the same approach which was used before for the study of radiative decays f_0(980) -> gamma-gamma, a_0(980) -> gamma-gamma and phi(1020) -> gamma-…
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We calculate partial widths of the gamma-gamma decay of the tensor q\bar q states a_2(1320), f_2(1270), f_2(1525), their radial excitations a_2(1660), f_2(1640), f_2(1800) as well as ^3F_2 q\bar q states. Calculations are performed in the framework of the same approach which was used before for the study of radiative decays f_0(980) -> gamma-gamma, a_0(980) -> gamma-gamma and phi(1020) -> gamma-f_0(980): the assumption made is that of q\bar q structure of f_0(980) and a_0(980) [A.V. Anisovich et al., Phys. Lett. B 456, 80 (1999); Eur. Phys. J. A 12, 103 (2001)]. The description of the decay partial widths for a_2(1320), f_2(1270), f_2(1525) and f_0(980), a_0(980) is reached with the approximately equal radial wave functions, thus giving a strong argument in favour of the fact that these scalar and tensor mesons are to be classified as members of the same P-wave q\bar q multiplet.
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Submitted 29 April, 2002;
originally announced April 2002.
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Moment-operator expansion for the two-meson, two-photon and fermion-antifermion states
Authors:
A. V. Anisovich,
V. V. Anisovich,
V. N. Markov,
M. A. Matveev,
A. V. Sarantsev
Abstract:
A complete set of formulae in terms of the moment-operator expansion is presented for the two-meson, two-photon and fermion-antifermion states that can be used in the analysis of scalar (S) and pseudoscalar (P) meson production in anti-p p and gamma-gamma collisions: anti-p p -> SS, PP, SP and gamma gamma -> SS, PP, SP.
A complete set of formulae in terms of the moment-operator expansion is presented for the two-meson, two-photon and fermion-antifermion states that can be used in the analysis of scalar (S) and pseudoscalar (P) meson production in anti-p p and gamma-gamma collisions: anti-p p -> SS, PP, SP and gamma gamma -> SS, PP, SP.
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Submitted 11 September, 2001; v1 submitted 31 May, 2001;
originally announced May 2001.