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On the dependence of QCD splitting functions on the choice of the evolution variable. (English) Zbl 1390.81185
Summary: We show that already at the NLO level the DGLAP evolution kernel $$P_{qq}$$ starts to depend on the choice of the evolution variable. We give an explicit example of such a variable, namely the maximum of transverse momenta of emitted partons and we identify a class of evolution variables that leave the NLO $$P_{qq}$$ kernel unchanged with respect to the known standard $$\overline{\mathrm{MS}}$$ results. The kernels are calculated using a modified Curci-Furmanski-Petronzio method which is based on a direct Feynman-graphs calculation.

##### MSC:
 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
##### Keywords:
NLO computations; QCD phenomenology
Herwig++
Full Text:
##### References:
 [1] Bengtsson, M.; Sjöstrand, T., A comparative study of coherent and noncoherent parton shower evolution, Nucl. Phys., B 289, 810, (1987) [2] Sjöstrand, T., A model for initial state parton showers, Phys. Lett., B 157, 321, (1985) [3] T. Sjöstrand and P.Z. Skands, Transverse-momentum-ordered showers and interleaved multiple interactions, Eur. Phys. J.C 39 (2005) 129 [hep-ph/0408302] [INSPIRE]. [4] Bahr, M.; etal., HERWIG++ physics and manual, Eur. Phys. J., C 58, 639, (2008) [5] Curci, G.; Furmanski, W.; Petronzio, R., Evolution of parton densities beyond leading order: the nonsinglet case, Nucl. Phys., B 175, 27, (1980) [6] Ellis, RK; Georgi, H.; Machacek, M.; Politzer, HD; Ross, GG, Factorization and the parton model in QCD, Phys. Lett., B 78, 281, (1978) [7] G. Heinrich, Improved techniques to calculate two-loop anomalous dimensions in QCD, Ph.D. thesis, Swiss Federal Institute of Technology, Zurich (1998). http://dx.doi.org/10.3929/ethz-a-001935934. [8] Jadach, S.; Kusina, A.; Skrzypek, M.; Slawinska, M., Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution, JHEP, 08, 012, (2011) · Zbl 1298.81392 [9] O. Gituliar, Higher-Order Corrections in QCD Evolution Equations and Tools for Their Calculation, arXiv:1403.6897 [INSPIRE]. [10] Gituliar, O.; Jadach, S.; Kusina, A.; Skrzypek, M., On regularizing the infrared singularities in QCD NLO splitting functions with the new principal value prescription, Phys. Lett., B 732, 218, (2014) · Zbl 1360.81297 [11] M. Skrzypek, O. Gituliar, S. Jadach and A. Kusina, The new PV prescription for IR singularities of NLO splitting functions, PoS(LL2014)059 [arXiv:1407.6261] [INSPIRE]. · Zbl 1360.81297
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