Quark-jet model for transverse momentum dependent fragmentation functions

Abstract

In order to describe the hadronization of polarized quarks, we discuss an extension of the quark-jet model to transverse momentum dependent fragmentation functions. The description is based on a product ansatz, where each factor in the product represents one of the transverse momentum dependent splitting functions, which can be calculated by using effective quark theories. The resulting integral equations and sum rules are discussed in detail for the case of inclusive pion production.In particular, we demonstrate that the 3-dimensional momentum sum rules are satisfied naturally in this transverse momentum dependent quark-jet model. Our results are well suited for numerical calculations in effective quark theories, and can be implemented in Monte-Carlo simulations of polarized quark hadronization processes. PACS numbers: 13.60.Hb, 13.60.Le, 12.39.Ki 3 Like Γ µ and σ µ , the quantity s µ is not a Lorentz 4-vector, but Einstein's summation convention still applies[50].

Dihadron fragmentation functions in the quark-jet model: Transversely polarized quarks

“…We have explicitly checked that the SIDIS DiFFs computed using the individually extracted moments via Eqs. (27) and (28) agree with the calculations using Eqs. (29) and (30).…”

“…We model the hadronization of a transversely polarized quark within the most recent extension of the quark-jet framework [27,28], in the same manner as for the longitudinally polarized quark in Ref. [29].…”

“…(21) and (22), obtained using Eqs. (27) and (28). This prescription also outlines how these quantities appear in the cross section of the integrated SIDIS cross section, first demonstrated in Ref.…”

“…A self-consistent treatment of the quark polarization within the quark-jet picture was recently developed in Ref. [27] and used to calculate the Collins fragmentation functions (FF) of a polarized light quark into pions [28].…”

Accessing quark helicity in $e^+e^-$ and SIDIS via dihadron correlations.

“…The penalty here is the additional factor C (y)/A (y). We recently used the extended quark-jet model [8] to calculate all three polarized DiFFs [4,9]. Several of the lowest Fourier cosine moments of G ⊥ 1 were calculated in Ref.…”