Sudakov form factor

The Sudakov form factors described the probability of partons radiating from partons before and after the hard process at the parton shower. The factors indicate the probability with which a parton does not emit an additional parton in the development of the virtuality of the particle from to . One therefore speaks of non-radiation probabilities. ${\displaystyle \Delta _{F}(Q^{2},q^{2})}$ ${\displaystyle F}$ ${\displaystyle q^{2}}$ ${\displaystyle Q^{2}}$

Derivation

The basis for the derivation is the following differential equation, which describes the radiation frequency in the Parto evolution after increasing : ${\displaystyle q^{2}}$

${\displaystyle {\frac {\mathrm {d} N}{\mathrm {d} (q^{2})}}=-{\frac {N}{q^{2}}}{\frac {\alpha s}{2\pi }}\int _{Q_{0}^{2}/q^{2}}^{1-Q_{0}^{2}/q^{2}}\mathrm {d} zP_{FG}(z)}$

This involves using the Parton before radiation and designates the Parton after radiation. The parton emitted is already determined by this information. The are the unregularisierten Kollinearsplitting functions (See also DGLAP equations # splitting functions .) ${\displaystyle F}$ ${\displaystyle G}$ ${\displaystyle P_{FG}}$

From this one obtains for the Sudakov form factors by solving the above equation and normalizing: ${\displaystyle N}$

${\displaystyle \Delta _{F}(Q^{2},q^{2})=\exp \left(-\int _{q^{2}}^{Q^{2}}{\frac {\mathrm {d} k^{2}}{k^{2}}}{\frac {\alpha s}{2\pi }}\int _{Q_{0}^{2}/q^{2}}^{1-Q_{0}^{2}/q^{2}}\mathrm {d} zP_{FG}(z)\right)}$

where all possible values ​​are added implicitly in the exponent ${\displaystyle G}$

Individual evidence

1. ^ Andy Buckley et al .: General-purpose event generators for LHC physics . In: Physics Reports . tape 504 , no. 5 , July 1, 2011, p. 145-233 , doi : 10.1016 / j.physrep.2011.03.005 , arxiv : 1101.2599 [abs] .
2. ^ Stefan Gieseke: Uncertainties of Sudakov form factors . In: Journal of High Energy Physics . tape 2005 , no. 01 , February 2005, p. 058-058 , doi : 10.1088 / 1126-6708 / 2005/01/058 , arxiv : hep-ph / 0412342 .