Abstract
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. We find that the exponentiation works, but that the net effect of the exponentiated phase operator is quite small for this problem, so that one can as well use the perturbative approach.
Highlights
There have been efforts to improve the accuracy of leading order parton shower programs by moving away from the leading color (LC) approximation in the treatment of QCD color [1,2,3,4,5,6,7,8,9]
For this effort to be consistent with quantum mechanics, one needs to work with bra and ket color amplitudes and to implement the color content of virtual graphs acting on these amplitudes [1,3,4,7,8,9]
We explore the possibility of exponentiating the contributions from the imaginary part of virtual graphs, which are proportional to iπ times a nontrivial color operator
Summary
There have been efforts to improve the accuracy of leading order parton shower programs by moving away from the leading color (LC) approximation in the treatment of QCD color [1,2,3,4,5,6,7,8,9] For this effort to be consistent with quantum mechanics, one needs to work with bra and ket color amplitudes and to implement the color content of virtual graphs acting on these amplitudes [1,3,4,7,8,9]. This operator takes the shower from an initial stage at a hard momentum scale, corresponding to a shower time t0, to a later stage with a softer momentum scale, corresponding to a shower
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