Abstract
We consider idealized parton shower event generators that treat parton spin and color exactly, leaving aside the choice of practical approximations for spin and color. We investigate how the structure of such a parton shower generator is related to the structure of QCD. We argue that a parton shower with splitting functions proportional to $\alpha_s$ can be viewed not just as a model, but as the lowest order approximation to a shower that is defined at any perturbative order. To support this argument, we present a formulation for a parton shower at order $\alpha_s ^k$ for any $k$. Since some of the input functions needed are specified by their properties but not calculated, this formulation does not provide a useful recipe for an order $\alpha_s ^k$ parton shower algorithm. However, in this formulation we see how the operators that generate the shower are related to operators that specify the infrared singularities of QCD.
Highlights
Parton shower event generators for hadron collisions, such as HERWIG [1], PYTHIA [2], and SHERPA [3], perform calculations of cross sections according to an approximation to the standard model or its possible extensions
We consider an idealized version of a parton shower generator in which one accounts exactly for spin and color
The formulas for the shower automatically includes factors that sum threshold logarithms [35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80]. These factors are not included in current parton shower generators at even leading order, except for DEDUCTOR [32,33]
Summary
Parton shower event generators for hadron collisions, such as HERWIG [1], PYTHIA [2], and SHERPA [3], perform calculations of cross sections according to an approximation to the standard model or its possible extensions. The formulas for the shower automatically includes factors that sum threshold logarithms [35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80] These factors are not included in current parton shower generators at even leading order, except for DEDUCTOR [32,33]. The parton evolution kernels play a role in our formalism, it is not a central role
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