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Register a new userQuark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
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We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of non-standard Feynman integrals with rapidity divergence. We introduce a set of generalized Integration-By-Parts equations, which allows an algorithmic evaluation of such integrals using the machinery of modern Feynman integral calculation.
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Jets constructed via clustering algorithms (e.g., anti-$k_T$, soft-drop) have been proposed for many precision measurements, such as the strong coupling $alpha_s$ and the nucleon intrinsic dynamics. However, the theoretical accuracy is affected by missing QCD corrections at higher orders for the jet functions in the associated factorization theorems. Their calculation is complicated by the jet clustering procedure. In this work, we propose a method to evaluate jet functions at higher orders in QCD. The calculation involves the phase space sector decomposition with suitable soft subtractions. As a concrete example, we present the quark-jet function using the anti-$k_T$ algorithm with E-scheme recombination at next-to-next-to-leading order.
We present the results of our QCD analysis for non-singlet unpolarized quark distributions and structure function $F_2(x,Q^2)$ up to N$^3$LO. In this regards 4-loop anomalous dimension can be obtain from the Pade approximations. The analysis is based on the Jacobi polynomials expansion of the structure function. New parameterizations are derived for the non-singlet quark distributions for the kinematic wide range of $x$ and $Q^2$. Our calculations for non-singlet unpolarized quark distribution functions up to N$^3$LO are in good agreement with available theoretical models. The higher twist contributions of $F_2^{p,d}(x,Q^2)$ are extracted in the large $x$ region in N$^3$LO analysis. The values of $Lambda_{QCD}$ and $alpha_s(M_z^2)$ are determined.
We determine an approximate expression for the O(alpha_s^3) contribution chi_2 to the kernel of the BFKL equation, which includes all collinear and anticollinear singular contributions. This is derived using recent results on the relation between the GLAP and BFKL kernels (including running-coupling effects to all orders) and on small-x factorization schemes. We present the result in various schemes, relevant both for applications to the BFKL equation and to small-x evolution of parton distributions.
We present the first calculation of the next-to-next-to-leading order threshold soft function for top quark pair production at hadron colliders, with full velocity dependence of the massive top quarks. Our results are fully analytic, and can be entirely written in terms of generalized polylogarithms. The scale-dependence of our result coincides with the well-known two-loop anomalous dimension matrix including the three-parton correlations, which at the two-loop order only appear when more than one massive partons are involved in the scattering process. In the boosted limit, our result exhibits the expected factorization property of mass logarithms, which leads to a consistent extraction of the soft fragmentation function. The next-to-next-to-leading order soft function obtained in this paper is an important ingredient for threshold resummation at the next-to-next-to-next-to-leading logarithmic accuracy.
We present a first analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order accuracy in QCD based on single-inclusive pion production in electron-positron annihilation. Special emphasis is put on the technical details necessary to perform the QCD scale evolution and cross section calculation in Mellin moment space. We demonstrate how the description of the data and the theoretical uncertainties are improved when next-to-next-to-leading order QCD corrections are included.
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