Transverse-Momentum-Dependent Distributions with Jets

Abstract

We investigate the use of jets to measure transverse momentum dependent distributions (TMDs). The example we use to present our framework is the dijet momentum decorrelation at lepton colliders. Translating this momentum decorrelation into an angle θ 1, we analyze the factorization of the cross section for the cases θ R, θ ∼ R and θ R, where R is the jet radius. Critically, for the Winner-Take-All axis, the jet TMD has the same double-scale renormalization group evolution as TMD fragmentation functions for all radii R. TMD fragmentation functions in factorization theorems may then simply be replaced by the jet TMDs we calculate, and all ingredients to perform the resummation to next-to-next-to-leading logarithmic accuracy are available. Our approach also applies to semi-inclusive deep inelastic scattering (SIDIS), where a jet instead of a hadron is measured in the final state, and we find a clean method to probe the intrinsic transverse momentum of quarks and gluons in the proton that is less sensitive to final-state nonperturbative effects.

Probing transverse-momentum distributions with groomed jets

“…Because of the factorization theorem, the TMDs have several universal features like rapidity and renormalization scale evolution, which should be also tested including their (universal) non-perturbative part. Recently some of us have considered the possibility to define a jet-TMD, replacing a final state hadron with a jet [6][7][8] in SIDIS and e + e − processes. The check of this possibility has revealed that standard jet definitions are compatible with a factorization theorem only in the case of small enough radii, which is a not obvious experimental condition in the planned electron-hadron collider like EIC or LHeC.…”

“…Instead large jet-radii need a specific definition of jet, which allows soft radiation to be independent of radius. In [7,8] this was achieved using the winner-take-all (WTA) axis [9], and the perturbative calculations were done with a precision similar to the case of fragmenting hadrons.…”

“…The operator definition of the soft function (see refs. [1,2,25]) is given by 7) where N R = N c for S n/n in the fundamental and N 2 c − 1 for the adjoint representation of SU (N c ). This function has been calculated at NNLO in [26].…”

Transverse parton distribution and fragmentation functions at NNLO: the quark case

“…However, in certain regions of phase space, the transverse momenta of the partons become relevant, and one needs the transverse momentum dependent PDFs (TMDPDFs) and FFs (TMDFFs) in the corresponding factorization formulas. This is case for the small transverse momentum (Q T ) region in the Drell-Yan process [3][4][5][6][7][8][9][10][11], and also for similar regions in, e.g., semi-inclusive deep-inelastic scattering (SIDIS) [12][13][14][15][16], electron-positron annihilation to hadrons and jets [17][18][19][20][21][22], Higgs boson production [23][24][25][26][27][28][29][30], top quark pair production [31][32][33][34], as well as Energy-Energy Correlator (EEC) in the back-to-back limit at both lepton and hadron colliders [35,36]. To improve the theoretical predictions for these observables, it is desirable to have precise knowledges about these basic objects.…”

Transverse parton distribution and fragmentation functions at NNLO: the gluon case

“…Analytical calculations, phenomenological applications, and experimental determinations of the TMD distributions play important role in understanding the structure of hadrons [1,2]. TMDPDFs and TMDFFs have important applications in collider processes, such as Drell-Yan [3][4][5][6][7][8][9][10][11] and Higgs production [12][13][14][15][16][17][18][19], top quark pair production [20][21][22][23], hadronic J/ψ production, semi-inclusive deep-inelastic scattering [24][25][26][27][28], hadron or jet production in electron-positron annihilation [29][30][31][32][33][34], and energy correlators in both e + e − and hadron colliders [29,35,36]. The TMDPDFs and TMDFFs are intrinsically non-perturbative objects.…”