T-odd transverse momentum dependent gluon fragmentation functions in a spectator model

Xiupeng Xie; Zhun Lu

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T-odd transverse momentum dependent gluon fragmentation functions in a spectator model

Xiupeng Xie, Zhun Lu

High Energy Physics - Phenomenology · Submitted 19 May 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We obtain analytical expressions for the four T-odd TMD fragmentation functions of the gluon.

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We present a model calculation of the T-odd transverse momentum dependent (TMD) gluon fragmentation functions for a spin-1/2 hadron. Our model is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle, which is considered to be on-shell. We consider the effect of the gluon exchange to calculate all necessary one-loop diagrams for the gluon-gluon correlation functions. Two out of four one-loop diagrams give sizeable contributions to the fragmentation functions. We obtain analytical expressions for the four T-odd TMD fragmentation functions of the gluon. We also provide numerical results on the z-dependence and $k_T$-dependence of the fragmentation functions.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a model calculation of the T-odd transverse momentum dependent (TMD) gluon fragmentation functions for a spin-1/2 hadron.	contribution 1.00	0.95	0.21	asserted 0.99
s1	Our model is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle, which is considered to be on-shell.	method 0.99	0.54	0.05	asserted 0.92
s2	We consider the effect of the gluon exchange to calculate all necessary one-loop diagrams for the gluon-gluon correlation functions.	method 1.00	0.92	0.04	asserted 0.96
s3	Two out of four one-loop diagrams give sizeable contributions to the fragmentation functions.	result 1.00	0.94	0.15	asserted 1.00
s4	We obtain analytical expressions for the four T-odd TMD fragmentation functions of the gluon.	result 0.86	0.97	0.34	asserted 1.00
s5	We also provide numerical results on the z-dependence and $k_T$-dependence of the fragmentation functions.	result 0.91	0.95	0.14	asserted 1.00

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Original abstract

We present a model calculation of the T-odd transverse momentum dependent (TMD) gluon fragmentation functions for a spin-1/2 hadron. Our model is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle, which is considered to be on-shell. We consider the effect of the gluon exchange to calculate all necessary one-loop diagrams for the gluon-gluon correlation functions. Two out of four one-loop diagrams give sizeable contributions to the fragmentation functions. We obtain analytical expressions for the four T-odd TMD fragmentation functions of the gluon. We also provide numerical results on the z-dependence and $k_T$-dependence of the fragmentation functions.

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1 arXiv paper cite this in 2 sentences

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These applications include quark TMDs of the pions [ref] , transverse momentum dependent (TMD) fragmentation functions (FFs) of pions and kaons [ref] , and, more recently, both T-even and T-odd gluon TMDs and TMD FFs [ref] .

T-odd transverse momentum dependent gluon distributions for tensor polarized deuteron in a spectator model · Introduction · 0.80

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Uses the method or tool of 4 papers

We can decompose the gluon fragmentation correlator and define eight leading-twist TMD FFs of the gluon through the following projection [ref] [equation] and the four T-odd gluon TMD FFs can be projected into [equation] Here, we have used the symmetric transverse tensor $δ_T^i j =-g_T^i j$ with $g_T^i j = g^i j-n_+^i n_-^j-n_+^j n_-^i$, the anti-symmetric transverse tensor $ϵ_T^i j$ with $ϵ_T^1 2=1$, and a symmetrization operator $Ŝ$ for a generic tensor $O^ij$ which is defined as: [equation]

Transverse momentum dependence in gluon distribution and fragmentation functions · Analytic calculation of the T-odd FFs of a spin-1/2 hadron · 0.85
Following Refs. [ref] , we apply the dipolar form factor [equation] where $κ_1,2$ are free parameters, and $Λ_X=k_T^max$ is cut-off parameter in order to regularize the divergence.

Transverse-momentum-dependent gluon distribution functions in a spectator model · Analytic calculation of the T-odd FFs of a spin-1/2 hadron · 0.97
Following Refs. [ref] , we apply the dipolar form factor [equation] where $κ_1,2$ are free parameters, and $Λ_X=k_T^max$ is cut-off parameter in order to regularize the divergence.

T-even transverse momentum dependent gluon fragmentation functions in a spectator model · Analytic calculation of the T-odd FFs of a spin-1/2 hadron · 0.97

Uses data or values from 1 paper

The original values of the parameters (AKK08) from Ref. [ref] are presented in Table [ref].

T-even transverse momentum dependent gluon fragmentation functions in a spectator model · Numerical Results · 0.99

Cites as background 4 papers

The kind of coupling $g_1,2(k^2)$ has several different choices in the literature [ref] .

Transverse-momentum distributions in a diquark spectator model · Analytic calculation of the T-odd FFs of a spin-1/2 hadron · 0.89
The twist-3 fragmentation functions $H̃(z,k_T^2)$, $H(z,k_T^2)$, $G̃^⊥(z,k_T^2)$ and $G^⊥(z,k_T^2)$ [ref] have also been calculated within the spectator model.

Twist-3 fragmentation functions in a spectator model with gluon rescattering · Introduction · 0.89
The twist-3 fragmentation functions $H̃(z,k_T^2)$, $H(z,k_T^2)$, $G̃^⊥(z,k_T^2)$ and $G^⊥(z,k_T^2)$ [ref] have also been calculated within the spectator model.

Twist-3 T-odd fragmentation functions $G^\perp$ and $\tilde{G}^\perp$ in a spectator model · Introduction · 0.89

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