ηcProduction at the LHC Challenges Nonrelativistic QCD Factorization

Abstract

We analyze the first measurement of ηc production, performed by the LHCb Collaboration, in the nonrelativistic-QCD (NRQCD) factorization framework at next-to-leading order (NLO) in the strong-coupling constant αs and the relative velocity v of the bound quarks including the feeddown from hc mesons. Converting the long-distance matrix elements (LDMEs) extracted by various groups from J/ψ yield and polarization data to the ηc case using heavy-quark spin symmetry, we find that the resulting NLO NRQCD predictions greatly overshoot the LHCb data, while the color-singlet model provides an excellent description.PACS numbers: 12.38. Bx, 12.39.St, 13.85.Ni, 14.40.Pq Despite concerted experimental and theoretical efforts ever since the discovery of the J/ψ meson in the November revolution of 1974 (The Nobel Prize in Physics 1976), the genuine mechanism underlying the production and decay of heavy quarkonia, which are QCD bound states of a heavy quark Q = c, b and its antiparticle Q, has remained mysterious. The effective quantum field theory of nonrelativistic QCD (NRQCD) [1] endowed with an appropriate factorization theorem [2] arguably constitutes the most probable candidate theory at the present time. This implies a separation of process-dependent shortdistance coefficients (SDCs), to be calculated perturbatively as expansions in the strong-coupling constant α s , from supposedly universal long-distance matrix elements (LDMEs), to be extracted from experiment. The relative importance of the latter is subject to velocity scaling rules [3], which predict each of the LDMEs to scale with a definite power of the heavy-quark velocity v. In this way, the theoretical predictions are organized as double expansions in α s and v. A crucial feature of this formalism is that the QQ pair can at short distances be produced in any Fock state n = 2S+1 L [a] J with definite spin S, orbital angular momentum L, total angular momentum J, and color multiplicity a = 1, 8. In this way, it complements the color-singlet (CS) model (CSM), which only includes the very 2S+1 L [1] J state of the physical quarkonium, and thus cures a severe conceptual shortcoming of the latter, namely the existence of uncanceled infrared (IR) singularities beyond L = 0. However, the CSM does provide IR-finite NLO predictions for S-wave charmonia, such as the η c and J/ψ mesons considered here.Despite its theoretical rigor, NRQCD factorization has reached the crossroads in the J/ψ case. While a global fit [4] to the J/ψ yields measured in hadroproduction, photoproduction, γγ scattering, and e + e − annihilation successfully pins down the leading color-octet (CO) LDMEs,, in compliance with the velocity scaling rules, the resulting predictions for J/ψ polarization in hadroproduction are in striking disagreement with measurements at the Fermilab Tevatron and the CERN LHC [5]. Vice versa, fits to data on J/ψ yield and polarization in hadroproduction work reasonably well [6][7][8], but hopelessly fail in comparisons to the world's data from other than hadronic collis...

Challenges in Heavy Flavor and Quarkonium Production inp + pCollisions at the LHC

“…In addition, the LDMEs fit to collider data do not agree with the integrated cross sections, dσ/dy| y=0 [33]. Recent measurements of the η c at forward rapidity in LHCb [34] strongly disagree with the p T distributions calculated assuming heavy quark spin symmetry [35]. These recent results will be briefly discussed here.…”

“…[35] to compare the results of all four fits to the η c p T distributions measured by LHCb at forward rapidity at √ s = 7 and 8 TeV. The NRQCD calculations all lie above the η c data at high p T .…”

“…The NRQCD calculations all lie above the η c data at high p T . Indeed, the best description of these data is achieved with the color singlet model [35]. A different approach was taken in Ref.…”

Update on Heavy Flavor Production in Cold Matter

“…In addition, the LDMEs fit to collider data do not agree with the integrated cross sections, dσ/dy| y=0 [27]. Recent measurements of the η c at forward rapidity in LHCb [28] strongly disagree with the p T distributions calculated assuming heavy quark spin symmetry [29].…”

Sivers effect in inelastic J/ψ photoproduction in ep↑ collision in color octet model

“…Moreover, gluon and heavy quark fragmentation also contribute for quarkonium production significantly at P T > 4 GeV [54], which are excluded by imposing P T cut. The feed-down contribution from an excited state ψð2SÞ and the decay of χ c states contribution to J=ψ are 15% [41] and 1% [53,55] respectively, are not considered in this work. Therefore, we impose the following kinematical cut 0.3 < z ≤ 0.9 to account for inelastic photoproduction [55,56] events only.…”