The three-loop splitting functions in QCD: The helicity-dependent case

164

Often the factorization of differential cross sections results in the definition of fundamental hadronic functions/distributions which have a double-scale evolution, as provided by a pair of coupled equations. Typically, the two scales are the renormalization and rapidity scales. The two-dimensional structure of their evolution is the object of the present study. In order to be more specific, we consider the case of the transverse momentum dependent distributions (TMD). Nonetheless, most of our findings can be used with other double-scale parton distributions. On the basis of the two-dimensional structure of TMD evolution, we formulate the general statement of the ζ-prescription introduced in [1], and we define an optimal TMD distribution, which is a scaleless model-independent universal non-perturbative function. Within this formulation the non-perturbative definition of the distribution is disentangled from the evolution, which clarifies the separation of perturbative and non-perturbative effects in the phenomenology. A significant part of this work is devoted to the study of the effects of truncation of perturbation theory on the double-scale evolution. We show that within truncated perturbation theory the solution of evolution equations is ambiguous and this fact generates extra uncertainties within the resummed cross-section. The alternatives to bypass this issue are discussed. Finally, we discuss the sources and distribution of the scale variation uncertainties.

Section: Effects Of Truncation Of Perturbation Theorymentioning

confidence: 99%

Systematic analysis of double-scale evolution

Scimemi

Vladimirov

2018

164

“…[12][13][14][15][16][17][18][19][20]. In order to obtain a finite result, appropriate ultra-violet and infrared counterterms need to be included [21][22][23][24][25][26][27][28][29]. The contributions from the emission of two partons at one loop and three partons at tree-level, however, have not been computed for arbitrary kinematics so far, but they are only known as an expansion around threshold.…”

Section: Jhep08(2015)051mentioning

confidence: 99%

Soft expansion of double-real-virtual corrections to Higgs production at N3LO

Anastasiou

Duhr

Dulat

et al. 2015

102

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N 3 LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N 3 LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.

“…Γ q cusp and Γ g cusp are the quark and gluon cusp anomalous dimensions [54,55], which are known to three loops [35]. Up to this order, they are related by Γ g cusp /Γ q cusp = C A /C F .…”

Section: Inclusive Jet Functionsmentioning

confidence: 99%

Heavy quark fragmenting jet functions

Bauer

Mereghetti

2014

Heavy quark fragmenting jet functions describe the fragmentation of a parton into a jet containing a heavy quark, carrying a fraction of the jet momentum. They are twoscale objects, sensitive to the heavy quark mass, m Q , and to a jet resolution variable, τ N . We discuss how cross sections for heavy flavor production at high transverse momentum can be expressed in terms of heavy quark fragmenting jet functions, and how the properties of these functions can be used to achieve a simultaneous resummation of logarithms of the jet resolution variable, and logarithms of the quark mass. We calculate the heavy quark fragmenting jet function G Q Q at O(α s ), and the gluon and light quark fragmenting jet functions into a heavy quark, G Q g and G Q l , at O(α 2 s ). We verify that, in the limit in which the jet invariant mass is much larger than m Q , the logarithmic dependence of the fragmenting jet functions on the quark mass is reproduced by the heavy quark fragmentation functions. The fragmenting jet functions can thus be written as convolutions of the fragmentation functions with the matching coefficients J ij , which depend only on dynamics at the jet scale. We reproduce the known matching coefficients J ij at O(α s ), and we obtain the expressions of the coefficients J gQ and J lQ at O(α 2 s ). Our calculation provides all the perturbative ingredients for the simultaneous resummation of logarithms of m Q and τ N .