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Title: Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Abstract

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bb 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 c-bar) states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J{sub PC} = 0{sup -+}, 1{sup --}, 0{sup ++}, 1{sup ++}, 2{sup ++}, 1{sup +-} and radiative transitions {psi}(2S) {sup {yields}} {gamma}{chi}{sub c0}(1P), {gamma}{chi}{sub c1}(1P), {gamma}{chi}{sub c2}(1P), {gamma}{chi}{sub c}(1S) and {chi}{sub c0}(1P), {chi}{sub c1}(1P), {chi}{sub c2}(1P) {sup {yields}} {gamma}J/{psi}. The c-c levels and their wave functions are calculated for the radial excitations with n {<=} 6. Also, we determine the c-c component of the photon wave function using the e{sup +}e{sup -}-annihilation data: e{sup +}e{sup -} {sup {yields}} J/{psi}(3097), {psi}(3686), {psi}(3770), {psi}(4040), {psi}(4160), {psi}(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states {eta}{sub c0}(1S), {chi}{sub c0}(1P), {chi}{sub c2}(1P) {sup {yields}} {gamma}{gamma} and n = 2 states {eta}{sub c0}(2S) {sup {yields}} {gamma}{gamma}, {chi}{sub c0}(2P) {sup {yields}} {gamma}{gamma}. We discuss the status of themore » recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either {chi}{sub c1}(2P) or {eta}{sub c2}(1D), while Y(3941) is {chi}{sub c2}(2P)« less

Authors:
; ; ; ;  [1]
  1. Russian Academy of Sciences, Petersburg Nuclear Physics Institute (Russian Federation)
Publication Date:
OSTI Identifier:
21075933
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 70; Journal Issue: 2; Other Information: DOI: 10.1134/S1063778807020184; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANNIHILATION; BOTTOMONIUM; COMPUTER CALCULATIONS; ELECTRON-POSITRON INTERACTIONS; ELECTRONS; EXCITATION; INTEGRAL EQUATIONS; J PSI-3097 MESONS; PARTICLE DECAY; PHOTONS; POSITRONS; PSI-3770 MESONS; PSI-4040 MESONS; PSI-4160 MESONS; PSI-4415 MESONS; QUARK-ANTIQUARK INTERACTIONS; RADIATIVE DECAY; S STATES; SPECTRAL FUNCTIONS; WAVE FUNCTIONS

Citation Formats

Anisovich, V. V., Dakhno, L. G., Matveev, M. A., Nikonov, V. A., and Sarantsev, A. V.. Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia. United States: N. p., 2007. Web. doi:10.1134/S1063778807020184.
Anisovich, V. V., Dakhno, L. G., Matveev, M. A., Nikonov, V. A., & Sarantsev, A. V.. Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia. United States. doi:10.1134/S1063778807020184.
Anisovich, V. V., Dakhno, L. G., Matveev, M. A., Nikonov, V. A., and Sarantsev, A. V.. Thu . "Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia". United States. doi:10.1134/S1063778807020184.
@article{osti_21075933,
title = {Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia},
author = {Anisovich, V. V. and Dakhno, L. G. and Matveev, M. A. and Nikonov, V. A. and Sarantsev, A. V.},
abstractNote = {Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bb 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 c-bar) states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J{sub PC} = 0{sup -+}, 1{sup --}, 0{sup ++}, 1{sup ++}, 2{sup ++}, 1{sup +-} and radiative transitions {psi}(2S) {sup {yields}} {gamma}{chi}{sub c0}(1P), {gamma}{chi}{sub c1}(1P), {gamma}{chi}{sub c2}(1P), {gamma}{chi}{sub c}(1S) and {chi}{sub c0}(1P), {chi}{sub c1}(1P), {chi}{sub c2}(1P) {sup {yields}} {gamma}J/{psi}. The c-c levels and their wave functions are calculated for the radial excitations with n {<=} 6. Also, we determine the c-c component of the photon wave function using the e{sup +}e{sup -}-annihilation data: e{sup +}e{sup -} {sup {yields}} J/{psi}(3097), {psi}(3686), {psi}(3770), {psi}(4040), {psi}(4160), {psi}(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states {eta}{sub c0}(1S), {chi}{sub c0}(1P), {chi}{sub c2}(1P) {sup {yields}} {gamma}{gamma} and n = 2 states {eta}{sub c0}(2S) {sup {yields}} {gamma}{gamma}, {chi}{sub c0}(2P) {sup {yields}} {gamma}{gamma}. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either {chi}{sub c1}(2P) or {eta}{sub c2}(1D), while Y(3941) is {chi}{sub c2}(2P)},
doi = {10.1134/S1063778807020184},
journal = {Physics of Atomic Nuclei},
number = 2,
volume = 70,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • We continue the investigation of mesons in terms of the spectral integral equation initiated before for the bb-bar and cc-bar systems; we consider the light-quark (u, d, s) mesons with masses M {<=} 3 GeV. The calculations have been performed for the mesons lying on linear trajectories in the (n, M{sup 2}) planes, where n is the radial quantum number. Our consideration relates to the qq-bar states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as {pi}(0{sup -+}), {rho}(1{sup --}), {omega}(1{sup --}), {phi}(1{sup --}), a{sub 0}(0{sup ++}), a{sub 1}(1{sup ++}),more » a{sub 2}(2{sup ++}), b{sub 1}(1{sup +-}), f{sub 2}(2{sup ++}), {pi}{sub 2}(2{sup -+}), {rho}{sub 3}(3{sup --}), {omega}{sub 3}(3{sup --}), {phi}{sub 3}(3{sup --}), {pi}{sub 4}(4{sup -+}) at n {<=} 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 {pi}, a{sub 0}(980), a{sub 2}(1320), f{sub 2}(1285), f{sub 2}(1525) and radiative transitions {rho}, {omega} {sup {yields}} {gamma}{pi}, which 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.« less
  • In the framework of the spectral integral equation, we consider the bb-bar states and their radiative transitions. We reconstruct the bb-bar interaction on the basis of data for the levels of the bottomonium states with J{sup PC} = 0{sup -+}, 1{sup --}, 0{sup ++}, 1{sup ++}, 2{sup ++} as well as the data for the radiative transitions {gamma} (3S) {sup {yields}} {sub {gamma}}{sub {chi}}{sub bJ}(2P) and {gamma}(2S) {sup {yields}} {sub {gamma}}{sub {chi}}{sub bJ}(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n {<=} 6, their wave functions, and corresponding radiative transitions. The ratiosmore » Br[{sub {chi}}{sub bJ}(2P) {sup {yields}} {sub {gamma}}{gamma}(2S)]/Br[{sub {chi}}{sub bJ}(2P) {sup {yields}} {sub {gamma}}{gamma}(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the bb-bar component of the photon wave function using the data for the e{sup +}e{sup -} annihilation, e{sup +}e{sup -} {sup {yields}} {gamma}(9460), {gamma}(10 023), {gamma}(10 036), {gamma}(10 580), {gamma}(10 865), {gamma}(11 019), and predict partial widths of the two-photon decays {eta}b0 {sup {yields}} {gamma}{gamma}, {chi}b0 {sup {yields}} {gamma}{gamma}, {chi}b2 {sup {yields}} {gamma}{gamma} for the radial excitation states below the BB-bar threshold (n {<=} 3)« less
  • The Bethe-Salpeter equations for quark-antiquark composite systems with different quark masses, such as qs-bar (with q = u,d ), qQ-bar, and sQ-bar (with Q = c,b), are written in terms of spectral integrals. For mesons characterized by the mass M, spin J, and radial quantum number n, the equations are written for the (n, M{sup 2}) trajectories with fixed J. The mixing between states with different quark spin S and angular momentum L is also discussed.
  • A multipole expansion of the color gauge field is shown to yield selection rules and rate estimates for hadronic transitions between nonrelativistic quark-antiquark bound states. The non-Abelian character of the field is of critical importance in determining the selection rules for the leading (''allowed'') transition.
  • Cross sections and asymmetries for massive quark-antiquark production in electron-positron collisions at the {ital Z}{sub 0} resonance are calculated, for the case of longitudinally polarized electrons. The polarizaton of {ital Z}{sub 0}, {ital P}{sub {ital Z}0}, for the initial electron polarization {ital P}{sub {minus}} is composed of {ital P}{sub {minus}} and the ``natural`` polarization {ital P}{sub {ital Z}}{sup 0}(0)=2{ital av}/({ital v}{sup 2}+{ital a}{sup 2}), and the composition rule for polarization is given. The cross section differential in the quark emission polar angle {theta} is obtained in terms of form factors which are given as functions of the quark mass {italmore » m}{sub {ital f}} in exact form. Convenient expansions to order {ital m}{sub {ital f}}{sup 2} are found and compared to previously published results. For the asymmetries the {ital Z}{sub 0} polarization plays an important role. It is shown that for the forward-backward quark asymmetry {ital A}{sub FB}({ital P}{sub {minus}}) and the forward-backward left-right asymmetry {ital A}{sub FB,}{ital LR}({ital P}{sub {minus}}) the quark dependence is the same including radiative corrections, with the relations {ital A}{sub FB}({ital P}{sub {minus}}):{ital A}{sub FB}(0):{ital A}{sub FB,}{ital LR}({ital P}{sub {minus}}) ={ital P}{sub {ital Z}}{sup 0}({ital P}{sub {minus}}):{ital P}{sub {ital Z}}{sup 0}(0):{ital P}{sub {minus}}.« less