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Abstract We study the impact of third-order QCD corrections for several kinematic moments of the inclusive semileptonic B decays, to first order in the 1/m b expansion. We consider the first four moments of the charged-lepton energy E R spectrum, the total leptonic invariant mass q 2 and the hadronic invariant mass M X 2 $$ {M}_X^2 $$ . No experimental cuts are applied. Our analytic results are obtained via an asymptotic expansion around the limit m b ~ m c . After converting the scheme for the bottom mass to the kinetic scheme we compare the size of higher QCD corrections to the contributions from 1/ m b 2 $$ {m}_b^2 $$ and 1/ m b 3 $$ {m}_b^3 $$ power corrections and to the relative uncertainties.

Abstract We present a NNLO QCD accurate event generator for direct photon pair production at hadron colliders, based on the MiNNLO PS formalism, within the Powheg Box Res framework. Despite the presence of the photons requires the use of isolation criteria, our generator is built such that no technical cuts are needed at any stage of the event generation. Therefore, our predictions can be used to simulate kinematic distributions with arbitrary fiducial cuts. Furthermore, we describe a few modifications of the MiNNLO PS formalism in order to allow for a setting of the renormalization and factorization scales more similar to that of a fixed-order computation, thus reducing the numerical impact of higher-order terms beyond the nominal accuracy. Finally, we show several phenomenological distributions of physical interest obtained by showering the generated events with Pythia8, and we compare them with the 13 TeV data from the ATLAS Collaboration.

While significant effort has been devoted to precision calculations of the production of two Higgs bosons via gluon fusion, the treatment of their decays in this process has only recently begun to attract attention. It has been found that fixed-order QCD corrections to fiducial di-Higgs decay rates involving the $$b\\overline{b }$$ decay channel can be substantial. Considering $$HH\\to b\\overline{b }\\gamma \\gamma $$ , we show that such corrections arise predominantly from sensitivity to soft and collinear QCD radiation at fixed order, and that they are largely washed out once parton showers are included.

Abstract Through the calculation of the matrix element of the singlet axial-current operator between the vacuum and a pair of gluons in dimensional regularization with an anti-commuting γ 5 defined in a Kreimer-scheme variant, we find that additional renormalization counter-terms proportional to the Chern-Simons current operator are needed starting from O $$ \\mathcal{O} $$ ( α s 2 $$ {\\alpha}_s^2 $$ ) in QCD. This is in contrast to the well-known purely multiplicative renormalization of the singlet axial-current operator defined with a non-anticommuting γ 5. Consequently, without introducing compensation terms in the form of additional renormalization, the Adler-Bell-Jackiw anomaly equation does not hold automatically in the bare form in this kind of schemes. We determine the corresponding (gauge-dependent) coefficient to O $$ \\mathcal{O} $$ ( α s 3 $$ {\\alpha}_s^3 $$ ) in QCD, using a variant of the original Kreimer prescription which is implemented in our computation in terms of the standard cyclic trace together with a constructively-defined γ 5. Owing to the factorized form of these divergences, intimately related to the axial anomaly, we further performed a check, using concrete examples, that with γ 5 treated in this way, the axial-current operator needs no more additional renormalization in dimensional regularization but only for non-anomalous amplitudes in a perturbatively renormalizable theory. To be complete, we provide a few additional ingredients needed for a proposed extension of the algorithmic procedure formulated in the above analysis to potential applications to a renormalizable anomaly-free chiral gauge theory, i.e. the electroweak theory.

We consider the three-loop mixed strong-electroweak $$\\left(\\mathcal{O}\\left(\\alpha {\\alpha }_{s}^{2}\\right)\\right)$$ corrections to the quark form factor. We compute the master integrals which are appearing in the Feynman diagrams containing a single massive boson in the loop. We use the state-of-the-art method of differential equations to compute all 303 of them, expressing the results in terms of generalized polylogarithms. We encounter multiple square roots that cannot be simultaneously rationalized using a single transformation. Applying concurrent transformations allows us to express the results through generalized polylogarithms with a simple alphabet, but with multiple interdependent arguments.

We compute the one-loop corrections to gg → $$t\\overline{t }H$$ up to order $$\\mathcal{O}\\left({\\epsilon }^{2}\\right)$$ in the dimensional-regularization parameter. We apply the projector method to compute polarized amplitudes, which generalize massless helicity amplitudes to the massive case. We employ a semi-numerical strategy to evaluate the scattering amplitudes. We express the form factors through scalar integrals analytically, and obtain separately integration by parts reduction identities in compact form. We integrate numerically the corresponding master integrals with an enhanced implementation of the Auxiliary Mass Flow algorithm. Using a numerical fit method, we concatenate the analytic and the numeric results to obtain fast and reliable evaluation of the scattering amplitude. This approach improves numerical stability and evaluation time. Our results are implemented in the Mathematica package TTH.

We present an analytic reconstruction of one-loop amplitudes for the process $$ 0\\to \\overline{q} qt\\overline{t}H $$ 0 → q ¯ qt t ¯ H . Our calculation is a novel use of analytic reconstruction, retaining explicit covariance in the massive spin states through the massive spinor-helicity formalism. The analytic reconstruction relies on embedding the massive five-point kinematics in a fully massless eight-point phase space while still building a minimal ansatz directly in the five-point phase space. In order to obtain compact analytic expressions it is necessary to identify suitable partial fraction decompositions and extract common numerator factors, which we achieve through careful inspection of limits in which pairs of denominators vanish. We find that the resulting amplitudes are more numerically efficient than ones computed using automatic methods but that the gains are not as significant as in the massless case, at least at present. The method opens the door to applications at two-loop order, where numerical efficiency and improvements in the reconstruction methodology are more crucial, especially with regards to the number of free parameters in the ansatz.

A bstract We compute the cross section for the inclusive photoproduction of a pair of jets at next-to-leading order accuracy in the Color Glass Condensate (CGC) effective theory. The aim is to study the back-to-back limit, to investigate whether transverse momentum dependent (TMD) factorization can be recovered at this perturbative order. In particular, we focus on large Sudakov double logarithms, which are dominant terms in the TMD evolution kernel. Interestingly, the kinematical improvement of the low- x resummation scheme turns out to play a crucial role in our analysis.

Abstract We present a computation of the one-loop QCD corrections to top-quark pair production in association with a W boson, including terms up to order ε 2 in dimensional regularization. Providing a first glimpse into the complexity of the corresponding two-loop amplitude, this result is a first step towards a description of this process at next-to-next-to-leading order (NNLO) in QCD. We perform a tensor decomposition and express the corresponding form factors in terms of a basis of independent special functions with compact rational coefficients, providing a structured framework for future developments. In addition, we derive an explicit analytic representation of the form factors, valid up to order ε 0, expressed in terms of logarithms and dilogarithms. For the complete set of special functions required, we obtain a semi-numerical solution based on generalized power series expansion.

A bstract The method of canonical differential equations is an important tool in the calculation of Feynman integrals in quantum field theories. It has been realized that the canonical bases are closely related to d -dimensional d log-form integrands. In this work, we explore the generalized loop-by-loop Baikov representation, and clarify its relation and difference with Feynman integrals using the language of intersection theory. We then utilize the generalized Baikov representation to construct d -dimensional d log-form integrands, and discuss how to convert them to Feynman integrals. We describe the technical details of our method, in particular how to deal with the difficulties encountered in the construction procedure. Our method provides a constructive approach to the problem of finding canonical bases of Feynman integrals, and we demonstrate its applicability to complicated scattering amplitudes involving multiple physical scales.