M. Rogal's research while affiliated with Karlsruhe Institute of Technology and other places

... In particular, the matrix elements for the one-loop 2 → 3 process are known [11][12][13][14]. Furthermore, progress was also made in the determination of infra-red (IR) subtraction terms which are needed to regularize IR divergences in collinear and soft regions of the phase space during the integration [15][16][17][18][19]. Finally, the one-loop squared matrix elements were calculated in [20][21][22]. Analytic results for the interference between two-loop 2 → 2 diagrams and tree-level amplitudes are available only in part. ...

... The purely virtual contributions entail the square of one-loop scattering amplitudes and the two-loop scattering amplitudes. The squared one-loop amplitudes are known [49][50][51]. The complete computation of the two-loop amplitudes has been carried out numerically [52,53]. ...

... The purely virtual contributions entail the square of one-loop scattering amplitudes and the two-loop scattering amplitudes. The squared one-loop amplitudes are known [49][50][51]. The complete computation of the two-loop amplitudes has been carried out numerically [52,53]. ...

... In the DIS regime, these structure functions can be expressed in the framework of perturbative QCD as the factorised convolution of parton distribution functions (PDFs) [26][27][28] and hardscattering partonic cross sections. Their state-of-the-art calculation is based on PDFs and hard-scattering coefficient functions evaluated at next-to-next-to-leading order (NNLO) in the strong coupling α s expansion, with partial and exact [29][30][31] results also available one perturbative order higher (N 3 LO) and used in [32] to extract the proton PDFs. Furthermore, heavy quark (charm, bottom, and top) mass effects can be accounted for by means of general-mass variable-flavour-number (GM-VFN) schemes [33][34][35][36]. ...

... [12][13][14]: the cross section for inclusive DIS for quark external states, projected onto the structure functions F a , is related by the optical theorem to the imaginary parts of the corresponding amplitudes for photon-quark forward scattering. Via a dispersion relation the coefficients of [(2 p · q)/Q 2 ] N = 1/x N lead to the even-integer (see also ref. [31]) Mellin-N moments with β 0 = 11 − 2/3 n f etc in QCD [32,33], the left-hand-side of eq. (2.5) can be written as The quantity Z ns which renormalizes the non-singlet quark distributions is given by ...

... Clearly, these new precision measurements are to be accompanied by accurate theoretical calculations of the corresponding observables. As is already the standard for LHC computations, next-to-next-to-leading-order (NNLO) calculations are becoming a benchmark for polarized processes, with results already available for inclusive processes, such as Drell-Yan [12] and DIS processes [13,14], the helicity splitting functions [15][16][17], and the recent addition of exclusive processes like jet production in DIS [18,19], W-boson production in proton-proton collisions [20], and semi-inclusive DIS (in approximate form) [21,22]. This matching of the state of the art precision in polarized cross sections to the one of its corresponding unpolarized counterpart, for example, to perform a detailed study of spin asymmetries and eventually reach NNLO accuracy in the extraction of helicity PDFs. ...

... CP-odd scalar and h, H F is CP-even scalar so, once the couplings with left and right fields are written in terms of Dirac fields, the Hermitian part of the coupling in Eq. (2.12) gives rise to an i ¼ ffiffiffiffiffiffi −1 p coupling for h, H F , and a γ 5 coupling for A F . So the result of the top-quark loop integral is different for h, H F , and A F[98,99]. ...

... The fixed order cross section is further improved by performing threshold resummation at the next-to-next-to-leading logarithmic (NNLL) accuracy [18][19][20][21] and to the third logarithmic accuracy (N3LL) [22,23] as well as resummation of π 2 terms [24] arising from the timelike Sudakov form factor. The finite top mass effect is also known at NLO [25,26], partially at NNLO with top mass expansion [27][28][29][30], and recently to exact NNLO [31] where an increment of 0.6% is observed compared to the HEFTapproximation. The electroweak corrections are also known to NLO [32,33] which amount to a positive correction of about 5% compared to NNLO QCD. ...

... [1][2][3][4]. First computations at three loop level go back to large-mass expansions in the top quark mass [5,6]. More recent results exploit the partial knowledge of the threshold behavior of the form factors [7] and apply the techniques of Padé approximations [8], which JHEP03(2021)127 in principle is sufficient for phenomenology. ...

... As indicated in (1), the four terms depend on the scale, although this dependence is obviously cancelled in the sum. The QCD evolution kernels of the quark and gluon helicities were obtained at leading order (LO) in [2,3], at nextto-leading order (NLO) in [4][5][6][7], and more recently at next-to-next-to-leading order (NNLO) in [8][9][10]. On the other hand, the QCD evolution kernels for the quark and gluon OAM distributions are known only at LO [11][12][13]. ...