Transverse momentum distributions of heavy hadrons and polarized heavy quarks

In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry $$ {A}_{TU,T}^{\cos \left({\phi}_S-{\hat{\phi}}_{S_h}\right)} $$ A TU , T cos ϕ S − ϕ ̂ S h from polarized semi-inclusive hadron-in-jet production in polarized pp collisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry, $$ {A}_{TU,L}^{\cos \left({\phi}_q-{\phi}_S\right)} $$ A TU , L cos ϕ q − ϕ S from polarized exclusive hadron-in-jet production in polarized ep collisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements.

Polarized fragmenting jet functions in inclusive and exclusive jet production

Kang,

Xing,

Zhao

et al. 2024

Heavy quark transverse momentum dependent fragmentation

Dai,

Kim,

Leibovich

2024

In this paper, we investigate the heavy quark (HQ) mass effects on the transverse momentum dependent fragmentation function (TMDFF). We first calculate the one-loop TMDFF initiated by a heavy quark. We then investigate the HQ TMDFF in the limit where the transverse momentum, q⊥ is small compared to the heavy quark mass, q⊥ ≪ m and also in the opposite limit where q⊥ ≫ m. As applications of the HQ TMDFF, we study the HQ transverse momentum dependent jet fragmentation function, where the heavy quark fragments into a jet containing a heavy hadron, and we investigate a heavy hadron’s transverse momentum dependent distribution with respect to the thrust axis in e+e− collisions.

Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order

von Kuk,

Michel,

Sun

2024

The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-z behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s .