Relativistic corrections toJ/ψexclusive and inclusive double charm production atBfactories

Abstract

In order to clarify the puzzling problems in double charm production, relativistic corrections at order v 2 to the processes e + e − → J/ψ + η c and e + e − → J/ψ + cc at B factories are studied in non-relativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from J/ψ and η c decays up to errors of order v 4 . Our results show that the relativistic correction to the exclusive process e + e − → J/ψ + η c is significant, which, when combined together with the next-toleading order α s corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process e + e − → J/ψ + 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 → J/ψ + c is significant, and QCD radiative corrections can be more essential.

Exclusive double charmonium production fromΥdecay

“…This K factor is roughly consistent with what is obtained through actual higher-order NRQCD calculations [28,30]. Although we extract this constant through the Υ(4S) → J/ψ + η c process, we will assume it is universal in all other double charmonium decay channels of Υ(nS).…”

“…This process is closely related to the contiuum J/ψ + η c production in e + e − annihilation, which has recently aroused much attention since the measurements were first released by Belle collaboration [11]. Rather unexpectedly, it is shortly found that the leading-order NRQCD prediction to the production cross section falls short of the data by about one order of magnitude [21,22], which subsequently triggered intensive theoretical efforts to resolve this alarming discrepancy [23,24,25,26,27,28,29,30].…”

“…Recent calculations indicate that the J/ψ + η c electromagnetic form factor is subject to large perturbative and relativistic corrections at B factory energy [28,30]. It seems that the disturbing discrepancy between B factories measurements and NRQCD predictions have been largely resolved once these large corrections are taken into account.…”

The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions

“…Especially, the attempts in [23,24] open a way to connect the predictions of hard quarkonium exclusive productions within the collinear factorization directly to those made within the NRQCD factorization (for examples, the many theoretical calculations based on NRQCD factorizations [25][26][27][28][29][30][31][32][33][34][35][36][37][38], triggered by the recent experimental measurements of charmonium exclusive productions at B-factories [39][40][41]). In particular, in [42,43], the authors have shown that the collinear factorization indeed can reproduce the exact asymptotic behavior of NRQCD predictions at the leading logarithms (LL) and next-toleading order (NLO) of the strong coupling α s , respectively, for a certain class of the quarkonium exclusive productions, if one employs the leading twist LCDAs calculated in [24]; and the ERBL equations can be used to resum the large logarithms appearing the NRQCD factorization calculations for the exclusive quarkonium productions, while such resummation cannot be done within the NRQCD factorization.…”

PromptJ/ψproduction in association with acc¯pair within the framework of nonrelativistic QCD via photon-photon collisions at the International Linear Collider

“…As an important example, the Belle and the LHCb collaborations [13,14] have measured the J/ψ production associated with a cc pair, which however show large discrepancies from the NRQCD predictions [15][16][17][18][19][20][21][22]. For instance, the predicted angular distribution of J/ψ is different from * Electronic address: zhansun@cqu.edu.cn † Electronic address: wuxg@cqu.edu.cn ‡ Electronic address: hfzhang@ihep.ac.cn the Belle data, and the predicted J/ψ production crosssection is lower than the LHCb data by about one order of magnitude.…”