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Title: Relativistic corrections to J/{psi} exclusive and inclusive double charm production at B factories

Abstract

In order to clarify the puzzling problems in double-charm production, relativistic corrections at order v{sup 2} to the processes e{sup +}e{sup -}{yields}J/{psi}+{eta}{sub c} and e{sup +}e{sup -}{yields}J/{psi}+cc at B factories are studied in nonrelativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from J/{psi} and {eta}{sub c} decays up to errors of order v{sup 4}. Our results show that the relativistic correction to the exclusive process e{sup +}e{sup -}{yields}J/{psi}+{eta}{sub c} is significant, which, when combined together with the next-to-leading-order {alpha}{sub s} corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process e{sup +}e{sup -}{yields}J/{psi}+cc the relativistic correction is tiny and negligible. The physical reason for the above difference between exclusive and inclusive processes largely lies in the fact that in the exclusive process the relative momentum between quarks in charmonium substantially reduces the virtuality of the gluon that converts into a charm quark pair, but this is not the case for the inclusive process, in which the charm quark fragmentation c{yields}J/{psi}+c is significant, and QCD radiative corrections can be more essential.

Authors:
;  [1];  [1];  [2]
  1. Department of Physics, Peking University, Beijing 100871 (China)
  2. (World Laboratory), Beijing 100080 (China)
Publication Date:
OSTI Identifier:
21020271
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.75.074011; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CROSS SECTIONS; ELECTRON-POSITRON INTERACTIONS; ELECTRONS; ERRORS; ETA C-2980 MESONS; GLUONS; J PSI-3097 MESONS; MATRIX ELEMENTS; PARTICLE DECAY; POSITRONS; PSI-3770 MESONS; QUANTUM CHROMODYNAMICS; QUARKS; RADIATIVE CORRECTIONS; RELATIVISTIC RANGE

Citation Formats

He Zhiguo, Fan Ying, Chao Kuangta, and China Center of Advanced Science and Technology. Relativistic corrections to J/{psi} exclusive and inclusive double charm production at B factories. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.074011.
He Zhiguo, Fan Ying, Chao Kuangta, & China Center of Advanced Science and Technology. Relativistic corrections to J/{psi} exclusive and inclusive double charm production at B factories. United States. doi:10.1103/PHYSREVD.75.074011.
He Zhiguo, Fan Ying, Chao Kuangta, and China Center of Advanced Science and Technology. Sun . "Relativistic corrections to J/{psi} exclusive and inclusive double charm production at B factories". United States. doi:10.1103/PHYSREVD.75.074011.
@article{osti_21020271,
title = {Relativistic corrections to J/{psi} exclusive and inclusive double charm production at B factories},
author = {He Zhiguo and Fan Ying and Chao Kuangta and China Center of Advanced Science and Technology},
abstractNote = {In order to clarify the puzzling problems in double-charm production, relativistic corrections at order v{sup 2} to the processes e{sup +}e{sup -}{yields}J/{psi}+{eta}{sub c} and e{sup +}e{sup -}{yields}J/{psi}+cc at B factories are studied in nonrelativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from J/{psi} and {eta}{sub c} decays up to errors of order v{sup 4}. Our results show that the relativistic correction to the exclusive process e{sup +}e{sup -}{yields}J/{psi}+{eta}{sub c} is significant, which, when combined together with the next-to-leading-order {alpha}{sub s} corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process e{sup +}e{sup -}{yields}J/{psi}+cc the relativistic correction is tiny and negligible. The physical reason for the above difference between exclusive and inclusive processes largely lies in the fact that in the exclusive process the relative momentum between quarks in charmonium substantially reduces the virtuality of the gluon that converts into a charm quark pair, but this is not the case for the inclusive process, in which the charm quark fragmentation c{yields}J/{psi}+c is significant, and QCD radiative corrections can be more essential.},
doi = {10.1103/PHYSREVD.75.074011},
journal = {Physical Review. D, Particles Fields},
number = 7,
volume = 75,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • The inclusive J/{psi} production in e{sup +}e{sup -}{yields}J/{psi}cc at B factories is one of the most challenging open problems in heavy quarkonium physics. The observed cross section of this double-charm production process is larger than existing leading order (LO) QCD predictions by a factor of 5. In the nonrelativistic QCD (NRQCD) factorization formalism, we calculate the next-to-leading order (NLO) QCD virtual and real corrections to this process, and find that these corrections can substantially enhance the cross section with a K factor of about 1.8. We further take into account the feeddown contributions from higher charmonium states [mainly the {psi}(2S)more » as well as {chi}{sub cJ}] and the two-photon contributions, and find that the discrepancy between theory and experiment can be largely removed.« less
  • We study the first-order relativistic correction to the associated production of J/{psi} with light hadrons at B factory experiments at {radical}(s)=10.58 GeV, in the context of nonrelativistic QCD (NRQCD) factorization. We employ a strategy for NRQCD expansion that slightly deviates from the orthodox doctrine, in that the matching coefficients are not truly of a ''short-distance'' nature, but explicitly depend upon physical kinematic variables rather than partonic ones. Our matching method, with validity guaranteed by the Gremm-Kapustin relation, is particularly suited for the inclusive quarkonium production and decay processes with involved kinematics, exemplified by the process e{sup +}e{sup -}{yields}J/{psi}+gg considered inmore » this work. Despite some intrinsic ambiguity affiliated with the order-v{sup 2} NRQCD matrix element, if we choose its value as what has been extracted from a recent Cornell-potential-model-based analysis, including the relative order-v{sup 2} effect is found to increase the lowest-order prediction for the integrated J/{psi} cross section by about 30%, and exert a modest impact on J/{psi} energy, angular and polarization distributions except near the very upper end of the J/{psi} energy. The order-v{sup 2} contribution to the energy spectrum becomes logarithmically divergent at the maximum of J/{psi} energy. A consistent analysis may require that these large end-point logarithms be resummed to all orders in {alpha}{sub s}.« less
  • In nonrelativistic quantum chromodynamics (NRQCD), we study the next-to-leading order (NLO) QCD radiative correction to the color-octet J/{psi} inclusive production at B factories. Compared with the leading-order (LO) result, the NLO QCD corrections are found to enhance the short-distance coefficients in the color-octet J/{psi} production e{sup +}e{sup -{yields}}cc({sup 1}S{sub 0}{sup (8)} or {sup 3}P{sub J}{sup (8)})g (with J=0, 1, 2) by a factor of about 1.9. Moreover, the peak at the end point in the J/{psi} energy distribution predicted at LO can be smeared by the NLO corrections, but the major color-octet contribution still comes from the large energy regionmore » of J/{psi}. By fitting the latest data of {sigma}(e{sup +}e{sup -{yields}}J/{psi}+X{sub non-cc}) observed by Belle, we find that the values of color-octet matrix elements are much smaller than expected earlier by using the naive velocity scaling rules or extracted from fitting experimental data with LO calculations. As the most stringent constraint by setting the color-singlet contribution to be zero in e{sup +}e{sup -{yields}}J/{psi}+X{sub non-cc}, we get an upper limit of the color-octet matrix element, <0|O{sup J/{psi}[1S{sub 0}{sup (8)}]}|0>+4.0<0|O{sup J/{psi}[3P{sub 0}{sup (8)}]}|0>/m{sub c}{sup 2}<(2.0{+-}0.6)x10{sup -2} GeV{sup 3} at NLO in {alpha}{sub s}.« less
  • In heavy quarkonium production, the measured ratio R{sub cc}={sigma}[J/{psi}+cc+X]/{sigma}[J/{psi}+X] at B factories is much larger than existing theoretical predictions. To clarify this discrepancy, in nonrelativistic QCD we find the next-to-leading-order (NLO) QCD correction to e{sup +}e{sup -}{yields}J/{psi}+gg can enhance the cross section by about 20%. Together with the calculated NLO result for e{sup +}e{sup -}{yields}J/{psi}+cc, we show that the NLO corrections can significantly improve the fit to the ratio R{sub cc}. The effects of leading logarithm resummation near the end point on the J/{psi} momentum distribution and total cross section are also considered. Comparison of the calculated cross section formore » e{sup +}e{sup -}{yields}J/{psi}+gg with the observed cross section for e{sup +}e{sup -}{yields}J/{psi}+non-(cc) is expected to provide unique information on the issue of color-octet contributions.« less
  • We calculate the next-to-leading-order (NLO) QCD corrections to e{sup +}e{sup -}{yields}J/{psi}gg via color singlet J/{psi}({sup 3}S{sub 1}) at the B factories. The result shows that the cross section is enhanced to 0.373 pb by a K factor (NLO/LO) of about 1.21. By considering its dependence on the charm quark mass and renormalization scale, the NLO cross section can range from 0.294 to 0.409 pb. Further including the {psi}{sup '} feed-down, {sigma}[e{sup +}e{sup -}{yields}J/{psi}X(non-cc)] is enhanced by another factor of about 1.29 and reach 0.482 pb. In addition, the momentum distributions of J/{psi} production and polarization are presented. Recent measurements frommore » Belle agree well with our prediction for the cross section and momentum distribution. It is expected that this process can serve as a very good channel to clarify the J/{psi} polarization puzzle by performing further experimental measurements.« less