Exponentiating virtual imaginary contributions in a parton shower

Understand

The operator in a parton shower algorithm that represents the imaginary part of virtual Feynman graphs has a non-trivial color structure and is large because it is proportional to a factor of $4\pi$.

• In order to improve the treatment of color in a parton shower, it may help to exponentiate this phase operator.
• We show that it is possible to do so by exponentiating matrices that are no larger than $14\times14$.
• Using the example of the probability to have a gap in the rapidity interval between two high transverse momentum jets, we test this exponentiation algorithm by comparing to the result of treating the phase operator perturbatively.