O(αs3)O(α^3_s) calculations for the inclusive determination of ∣Vcb∣|V_{cb}|

For the determination of the Cabbibo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from inclusive data precise knowledge of the semileptonic $b→c$ decay rate is necessary. Since this observable has a bad convergence behavior when the heavy quark masses are expressed in the on-shell or $\overline{MS}$ scheme the latest determinations have been obtained in the so called kinetic mass scheme. The relation between the different schemes needs to be known to high precision as well. In this proceedings we present our recent calculations which push the precision of both ingredients to $O(α^3_s$). The results can be used to improve the inclusive determination of $|V_{cb}|$

Massive form factors at O(αs3)\mathcal{O}(\alpha_s^3)

We report on our recent calculation of massive quark form factors using a semi-numerical approach based on series expansions of the master integrals around singular and regular kinematic points and numerical matching. The methods allows to cover the whole kinematic range of negative and positive values of the virtuality $s$ with at least seven significant digits accuracy.Comment: 9 pages, 3 figures, contribution to the proceedings of Loops and Legs in Quantum Field Theory (LL2022), Ettal, German

O(αs3)\mathcal{O}(\alpha_s^3) calculations for the inclusive determination of ∣Vcb∣|V_{cb}|

For the determination of the Cabbibo-Kobayashi-Maskawa matrix element |Vcb| from inclusive data precise knowledge of the semileptonic b→c decay rate is necessary. Since this observable has a bad convergence behavior when the heavy quark masses are expressed in the on-shell or MS¯¯¯¯¯¯¯ scheme the latest determinations have been obtained in the so called kinetic mass scheme. The relation between the different schemes needs to be known to high precision as well. In this proceedings we present our recent calculations which push the precision of both ingredients to O(α3s). The results can be used to improve the inclusive determination of |Vcb|

Double hard scattering without double counting

Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.Comment: 80 pages, 20 figures. v2: clarifications in section 4, extended section 8, small changes elsewher

Towards gg→HHgg\to HH at next-to-next-to-leading order: light-fermionic three-loop corrections

We consider light-fermion three-loop corrections to $gg\to HH$ using forward scattering kinematics in the limit of a vanishing Higgs boson mass, which covers a large part of the physical phase space. We compute the form factors and discuss the technical challenges. The approach outlined in this letter can be used to obtain the full virtual corrections to $gg\to HH$ at next-to-next-to-leading order.Comment: 12 page

Kinetic Heavy Quark Mass to Three Loops

We compute three-loop corrections to the relation between the heavy quark masses defined in the pole and kinetic schemes. Using known relations between the pole and $\overline{\mathrm{MS}}$ quark masses, we can establish precise relations between the kinetic and $\overline{\mathrm{MS}}$ charm and bottom masses. As compared to two loops, the precision is improved by a factor of 2 to 3. Our results constitute important ingredients for the precise determination of the Cabibbo-Kobayashi–Maskawa matrix element |V$_{cb}$| at Belle II

Relation between the MS‾\overline{\mathrm{MS}} and the kinetic mass of heavy quarks

We compute the relation between the pole mass and the kinetic mass of a heavy quark to three loops. Using the known relation between the pole and the $\overline{\mathrm{MS}}$ mass we obtain precise conversion relations between the $\overline{\mathrm{MS}}$ and kinetic masses. The kinetic mass is defined via the moments of the spectral function for the scattering involving a heavy quark close to threshold. This requires the computation of the imaginary part of a forward-scattering amplitude up to three-loop order. We discuss in detail the expansion procedure and the reduction to master integrals. For the latter analytic results are provided. We apply our result both to charm and bottom quark masses. In the latter case we compute and include finite charm quark mass effects. Furthermore, we determine the large-${\beta}_{0}$ result for the conversion formula at four-loop order. For the bottom quark we estimate the uncertainty in the conversion between the $\overline{\mathrm{MS}}$ and kinetic masses to about 15 MeV which is an improvement by a factor of 2--3 as compared to the two-loop formula. The improved precision is crucial for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$ at Belle II