Abstract
We study a transverse momentum dependent (TMD) factorization framework for the processes of dijet and heavy-meson pair production in deep-inelastic-scattering in an electron-proton collider, considering the measurement of the transverse momentum imbalance of the two hard probes in the Breit frame. For the factorization theorem we employ soft-collinear and boosted-heavy-quark effective field theories. The factorized cross-section for both processes is sensitive to gluon unpolarized and linearly polarized TMD distributions and requires the introduction of a new soft function. We calculate the new soft function here at one-loop, regulating rapidity divergences with the δ-regulator. In addition, using a factorization consistency relation and a universality argument regarding the heavy-quark jet function, we obtain the anomalous dimension of the new soft function at two and three loops.
Highlights
Factorization of the cross-section holds and incoming gluons constitute the dominant effect
We study a transverse momentum dependent (TMD) factorization framework for the processes of dijet and heavy-meson pair production in deep-inelastic-scattering in an electron-proton collider, considering the measurement of the transverse momentum imbalance of the two hard probes in the Breit frame
The absence of a color neutral scalar at low energies has driven the attention to quarkonium production both in semi-inclusive deep inelastic scattering (SIDIS) at Electron Ion Collider (EIC) and LHC [3, 8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]
Summary
We discuss the factorization of the cross-section for the dijet case in DIS within the soft-collinear effective theory (SCET). We do not give a detailed derivation of the factorization theorem, but we rather summarize the final result. We present the NLO calculation for the new three-direction soft function and perform a consistency check of our results using the invariance of the cross-section under renormalization group evolution. The notation and kinematics that we develop here are useful for the heavy-meson pair production presented in the subsequent section
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