Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production

Abstract

We briefly review the framework of fragmenting jet functions (FJFs) introduced in soft collinear effective theory (SCET) to describe the fragmentation of an identified hadron within a jet. We illustrate how FJFs can be integrated with the leading power (LP) factorization in non-relativistic quantum chromodynamics (NRQCD) in studies of quarkonium production within jets. We present recent theoretical, experimental, and computational developments. We also present the framework of transverse momentum dependent (TMD) FJFs which describe the fragmentation of a hadron within a jet and the transverse momentum of the identified hadron is measured with respect to the jet axis. We show how the measurement of the transverse momentum spectrum can help discriminate between the leading production mechanisms of J/ψ.

An effective field theory approach to quarkonium at small transverse momentum

“…The scaling of the relevant degrees of freedom, in light-cone coordinates (p + , p − , p ⊥ ), can be written in terms of λ as collinear: p µ c ∼ Q(λ 2 , 1, λ) n soft: p µ s ∼ Q(λ, λ, λ) n . (2.13) Q is the typical hard scale and n µ = (1, 0, 0, 1) is the four-vector along which we expand in light-cone coordinates, 14) where p − = n • p, p + =n • p, andn µ = (1, 0, 0, −1) such that n 2 =n 2 = 0 and n •n = 2. We separate the label and residual components of momenta as follows:…”

“…Processes for which such factorization theorems exist are Drell-Yan and Higgs production [6,7], semiinclusive DIS (SIDIS) [8,9], and electron-positron annihilation to di-hadrons [10,11] (see JHEP04(2020)122 also refs. [12][13][14][15][16][17][18][19][20] for processes involving jets). In these theorems the differential cross section is written in terms of various perturbative and non-perturbative functions up to power corrections.…”

Quarkonium TMD fragmentation functions in NRQCD

“…q T M , the quarkonium TMD fragmentation within jets was studied in refs. [9,71]. The framework discussed here can be extended and applied to such studies in the small transverse momentum limit, q T M .…”

Jet energy drop

“…[15][16][17][18][19][20][21][22][23][24], and for related recent theoretical calculations of groomed jet substructure observables see refs. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”