Relativistic corrections to exclusive χcJ+γ production from e+e−

Abstract

We calculate in the nonrelativistic QCD (NRQCD) factorization framework all leading relativistic corrections to the exclusive production of χ cJ þ γ in e þ e − annihilation. In particular, we compute for the first time contributions induced by octet operators with a chromoelectric field. The matching coefficients multiplying production long distance matrix elements (LDMEs) are determined through perturbative matching between QCD and NRQCD at the amplitude level. Technical challenges encountered in the nonrelativistic expansion of the QCD amplitudes are discussed in detail. The main source of uncertainty comes from the not so well known LDMEs. Accounting for it, we provide the following estimates for the production cross sections at ffiffi ffi s p ¼ 10.6 GeV: σðe þ e − → χ c0 þ γÞ ¼ ð1.4 AE 0.3Þ fb, σðe þ e − → χ c1 þ γÞ ¼ ð15.0 AE 3.3Þ fb, and σðe þ e − → χ c2 þ γÞ ¼ ð4.5 AE 1.4Þ fb.

Observation of e+e−→γχc1 and search for Jia1, Wang2, Shen3 et al. 2018Phys. Rev. D164150View full textAdd to dashboardCite

“…The result is consistent with the prediction by NRQCD with all leading relativistic corrections included in Ref. [8]. Due to the large uncertainties, we do not fit the ffiffi ffi s p dependence of e þ e − → γχ c0 , e þ e − → γχ c2 , or e þ e − → γη c .…”

“…The values of n, determined from Refs. [8,10], are 1.4 for χ c0 , 2.1 for χ c1 , 2.4 for χ c2 , and 1.3 for η c in the predictions of next-to-leading order (NLO) QCD, and 1.4 for η c in leading order (LO) QCD. Possible sources of background events from ϒðnSÞ → BB (n ¼ 4, 5), ϒð5SÞ → B ðÃÞ sB ðÃÞ s , and e þ e − → qqðq ¼ u; d; s; cÞ are checked with a MC sample four times larger than the data sample, and are also generated with EvtGen [21].…”

“…Quarkonium formation is governed by nonperturbative long-distance effects [1]. Nonrelativistic quantum chromodynamics (NRQCD) factorization was used to compute the cross section for several processes, including the double-charmonium production cross section [2,3], e þ e − → γχ cJ (J ¼ 0, 1, 2) [4][5][6][7][8] and e þ e − → γη c [5,6,9,10] at B factories with relativistic and higher-order corrections included.…”

Next-to-next-to-leading-order radiative corrections to e+e− → χcJ + γ at B factory

“…Although the relativistic corrections for e + e − → χ cJ + γ have recently been thoroughly investigated in ref. [19], the corresponding uncertainties appear to be substantial, because the O(v 2 ) NRQCD matrix elements are poorly constrained. For simplicity we choose to neglect this sort of contribution in our phenomenological analysis.…”

FeynOnium: using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories

“…which enters the O(α 0 s v 2 ) differential production cross-section for e + (l 1 ) + e − (l 2 ) → χ c 0 (P )+γ(k) in the NRQCD factorization formalism [112][113][114]. Here s stands for the square of the collision energy in the center of mass frame, while the summation sign implies that we must average over the polarizations of the leptons and sum over the polarizations of the photon.…”