Abstract
One can use more than one scale variable to specify the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. Considering $e^+e^-$ annihilation, we use two variables, with shower evolution following a special path in this two dimensional space. In addition, we treat in a special way the part of the splitting function that has a soft emission singularity but no collinear singularity. This leads to certain advantages compared to the usual shower formulation with only one scale variable.
Highlights
In a parton shower event generator, one can view the parton state as evolving according to an operator based renormalization group equation
VIII, we find that the choices made in the previous sections give us a substantially improved treatment of SU(3) color within the context of a first order parton shower
The evolution Uð1; 0Þ, using Dðso1Þftðμ⃗ Þ, comes first, followed by evolution Uð∞; 1Þ, using Dðs1cÞðμ⃗ Þ with an ordering prescription such as angular ordering, Λ ordering, or kT ordering. This two scale formulation of a parton shower is reminiscent of soft-collinear effective theory (SCET)
Summary
In a parton shower event generator, one can view the parton state as evolving according to an operator based renormalization group equation. It may be possible to divide the shower splitting functions into separate terms such that one of the terms is not sensitive to one of the scales in the sense that no singularity is encountered when this scale approaches zero When this happens, we can modify the definition of the unresolved region for this term in a way that makes this term exactly independent of this scale. We explore the additional freedom obtained by using two scales instead of one This general concept works for proton-proton, eÆ-proton, and eþe− collisions. There are two appendices, A with details about kinematics and splitting functions and B with some results about the summation of large logarithms
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