Friday, February 21, 2020, 2:00 pm — Building 510, CFNS Room 2-38
We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function's anomalous dimension (that of twist-two local operators) in the forward scattering regime, using kT-factorization and BFKL theory, to the case of fragmentation function by exploiting the mapping between the dynamics of eikonal lines on transverse-plane to the celestial-sphere. Critically, to correctly resum the anomalous dimension of the fragmentation function under this mapping, one must pay careful attention to the role of regularization, despite the manifest collinear or infra- red finiteness of the BFKL equation. The anomalous dependence on energy in the celestial case, arising due to the mismatch of dimensionality between positions and angles, drives the differences between the space-like and time-like anomalous dimension of parton densities, even in a conformal theory. The second approach adapts an angular-ordered evolution equation, but working in 4 − 2epsilon dimensions at all angles. The two approaches are united by demanding that the anomalous dimension in 4 − 2epsilon dimensions for the PDF determines the kernel for the angular-ordered evolution to all orders.
Hosted by: Nikhil Karthik
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