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.

中文翻译：

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DIS中dijet和重介子对的TMD分解

我们研究了电子-质子对撞机中深非弹性散射中双射流和重介子对产生过程的横向动量相关 (TMD) 分解框架，考虑到测量中两个硬探针的横向动量不平衡布雷特框架。对于分解定理，我们采用软共线和增强重夸克有效场理论。这两个过程的分解截面对胶子非极化和线性极化 TMD 分布敏感，需要引入新的软函数。我们在一个循环中计算新的软函数，用 δ 调节器调节快速发散。此外，使用关于重夸克喷射函数的分解一致性关系和普适性论证，