Inclusive production of J/ψ, ψ(2S), and Υ states in pNRQCD

Off-lightcone Wilson-line operators are constructed using local operators connected by time-like or space-like Wilson lines, which ensure gauge invariance. Off-lightcone Wilson-line operators have broad applications in various contexts. For instance, space-like Wilson-line operators play a crucial role in determining quasi-distribution functions (quasi-PDFs), while time-like Wilson-line operators are essential for understanding quarkonium decay and production within the potential non-relativistic QCD (pNRQCD) framework. In this work, we establish a systematic approach for calculating the matching from the gradient-flow scheme to the $$ \overline{\textrm{MS}} $$ MS ¯ scheme in the limit of small flow time for off-lightcone Wilson-line operators. By employing the one-dimensional auxiliary-field formalism, we simplify the matching procedure, reducing it to the matching of local current operators. We provide one-loop level matching coefficients for these local current operators. For the case of hadronic matrix element related to the quark quasi-PDFs, we show at one-loop level that the finite flow time effect is very small as long as the flow radius is smaller than the physical distance z, which is usually satisfied in lattice gradient flow computations. Applications include lattice gradient flow computations of quark/gluon quasi-PDFs, gluonic correlators related to quarkonium decay and production in pNRQCD, and spin-dependent potentials in terms of chromoelectric and chromomagnetic field insertions into a Wilson loop.

Off-lightcone Wilson-line operators in gradient flow

Brambilla,

Wang

2024

Resummation and renormalization of kinematical effects in inclusive P-wave quarkonium production

Chung

2023

We investigate the renormalization properties of the shape function formalism for inclusive production of P-wave heavy quarkonia, which arises from resumming a class of corrections coming from kinematical effects associated with the motion of the heavy quark and antiquark pair relative to the quarkonium. Such kinematical effects are encoded in the nonperturbative shape functions, which are normalized to the corresponding nonrelativistic QCD long-distance matrix elements. By using the known ultraviolet divergences in the matrix elements, we derive the large-momentum asymptotic behavior of the shape functions. This strongly constrains the form of the shape functions and significantly reduces the dependence on the nonperturbative model. Based on these results we show that the shape function formalism at loop level can be useful in taming the threshold logarithms at large transverse momentum, and at small transverse momentum the kinematical corrections reduce the sizes of χc and χb cross sections which may improve agreement with measurements.

Factorization for J/ψ leptoproduction at small transverse momentum

Echevarria,

Romera,

Taels

2024

Nonrelativistic Quantum Chromodynamics (NRQCD) breaks down in the region of low transverse momentum, where the transverse momentum of the produced quarkonium state is sensitive to multiple scattering with the incoming hadron and to soft gluon radiation. In this kinematic regime, the transverse-momentum-dependent (TMD) factorization framework is required, promoting the long-distance matrix elements (LDMEs) of NRQCD to the so-called TMD shape functions (TMDShFs), which encode both the soft gluon radiation and the formation of the heavy-quark bound state. In this work, we apply an effective-field theory approach (combining NRQCD and SCET) to the photon-gluon fusion process in inclusive J/ψ leptoproduction. We derive a factorization theorem for the cross section in terms of TMDShFs, compute these quantities at next-to-leading order, establish their evolution, and study their matching onto the corresponding LDMEs in the high-transverse-momentum region. Our results are particularly relevant to the Electron-Ion Collider, where J/ψ leptoproduction can be used to probe gluon transverse-momentum-dependent parton distribution functions (gluon TMDPDFs).