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A bstract The Standard Model prediction for μ - e scattering at Next-to-Next-to-Leading Order (NNLO) contains non-perturbative QCD contributions given by diagrams with a hadronic vacuum polarization insertion in the photon propagator. By taking advantage of the hyperspherical integration method, we show that the subset of hadronic NNLO corrections where the vacuum polarization appears inside a loop, the irreducible diagrams, can be calculated employing the hadronic vacuum polarization in the space-like region, without making use of the R ratio and time-like data. We present the analytic expressions of the kernels necessary to evaluate numerically the two types of irreducible diagrams: the two-loop vertex and box corrections. As a cross check, we evaluate these corrections numerically and we compare them with the results given by the traditional dispersive approach and with analytic two-loop vertex results in QED.

A bstract General analyses of B -physics processes beyond the Standard Model require accounting for operator mixing in the renormalization-group evolution from the matching scale down to the typical scale of B physics. For this purpose the anomalous dimensions of the full set of local dimension-six operators beyond the Standard Model are needed. We present here for the first time a complete and non-redundant set of dimension-six operators relevant for B -meson mixing and decay, together with the complete one-loop anomalous dimensions in QCD and QED. These results are an important step towards the automation of general New Physics analyses.

A bstract We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter x and the dimension d , in the whole kinematic range of x . The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the MS ¯ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

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.

We present in a full analytic form the partial widths for the lepton flavour violating decays μ ± → e ± e + e - and τ ± → ℓ ± ℓ ′ + ℓ ′ - , with ℓ , ℓ ′ = μ , e , mediated by neutrino oscillations in the one-loop diagrams. Compared to the first result by Petcov (Sov J Nucl Phys 25:340, 1977), obtained in the zero momentum limit P ≪ m ν ≪ M W , we retain full dependence on P , the momenta and masses of external particles, and we determine the branching ratios in the physical limit m ν ≪ P ≪ M W . We show that the claim presented in Pham (Eur Phys J C8:513, 1999) that the τ → ℓ ℓ ′ ℓ ′ branching ratios could be as large as 10 - 14 , as a consequence of keeping the P dependence, is flawed. We find rates of order 10 - 55 , even smaller than those obtained in the zero momentum limit, as the latter prediction contains an unphysical logarithmic enhancement.

A bstract We compute next-to-next-to-leading order corrections to the semileptonic decay rate of B mesons for arbitrary values of the final-state quark mass. For the contribution with one massive quark in the final state, we extend the literature result and obtain analytic expressions in terms of iterated integrals. For the complete contribution, which also includes contributions with three massive quarks in the final state, we present a semi-analytic method, which leads to a precise approximation formula for the decay rate. Our results agree with the expansions available for b → cℓ ν ¯ ℓ and b → uℓ ν ¯ ℓ in the literature. The main emphasize of this paper is on the technical aspects of the calculation which are useful for a wider range of applications.

The determination of Vcb relies on the Heavy-Quark Expansion and the extraction of the non-perturbative matrix elements from inclusive b → c decays. The proliferation of these matrix elements complicates their extraction at 1/mb4 and higher, thereby limiting the Vcb extraction. Reparametrization invariance links different operators in the Heavy-Quark expansion thus reducing the number of independent operators at 1/mb4 to eight for the total rate. We show that this reduction also holds for spectral moments as long as they are defined by reparametrization invariant weight-functions. This is valid in particular for the leptonic invariant mass spectrum (q2), i.e. the differential rate and its moments. Currently, Vcb is determined by fitting the energy and hadronic mass moments, which do not manifest this parameter reduction and depend on the full set of 13 matrix elements up to 1/mb4. In light of this, we propose an experimental analysis of the q2 moments to open the possibility of a model-independent Vcb extraction from semileptonic decays including the 1/mb4 terms in a fully data-driven way.

A bstract We compute next-to-next-to-leading order QCD corrections to the partonic processes b → c u ¯ d and b → c c ¯ s , which constitute the dominant decay channels in standard model predictions for B-meson lifetimes within the heavy quark expansion. We consider the contribution from the four-quark operators O 1 and O 2 in the ∆ B = 1 effective Hamiltonian. The decay rates are obtained from the imaginary parts of four-loop propagator-type diagrams. We compute the corresponding master integrals using the “expand and match” approach which provides semi-analytic results for the physical charm and bottom quark masses. We show that the dependence of the decay rate on the renormalization scale is significantly reduced after including the next-to-next-to-leading order corrections. Furthermore, we compute next-to-next-to-leading order corrections to the Cabibbo-Kobayashi-Maskawa-suppressed decay channels b → u c ¯ s and b → u u ¯ d .

A bstract The determination of V cb relies on the Heavy-Quark Expansion and the extraction of the non-perturbative matrix elements from inclusive b → c decays. The proliferation of these matrix elements complicates their extraction at 1/ m b 4 and higher, thereby limiting the V cb extraction. Reparametrization invariance links different operators in the Heavy-Quark expansion thus reducing the number of independent operators at 1/ m b 4 to eight for the total rate. We show that this reduction also holds for spectral moments as long as they are defined by reparametrization invariant weight-functions. This is valid in particular for the leptonic invariant mass spectrum ( q 2 ), i.e. the differential rate and its moments. Currently, V cb is determined by fitting the energy and hadronic mass moments, which do not manifest this parameter reduction and depend on the full set of 13 matrix elements up to 1/ m b 4 . In light of this, we propose an experimental analysis of the q 2 moments to open the possibility of a model-independent V cb extraction from semileptonic decays including the 1/ m b 4 terms in a fully data-driven way.

A correction to this paper has been published: https://doi.org/10.1007/JHEP10(2024)144