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Kay Schönwald

Publications and source records attributed to Kay Schönwald.

46 records · Page 3Linked to original sources
arXiv2022

On the relation between the $\overline{\mathrm{MS}}$ 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 $\overline{\rm MS}$ mass we obtain precise conversion relations between the $\overline{\rm MS}$ 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-$β_0$ result for the conversion formula at four-loop order. For the bottom quark we estimate the uncertainty in the conversion between the $\overline{\rm MS}$ and kinetic masses to about 15 MeV which is an improvement by a factor two to three 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.

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arXiv2021

$\mathcal{O}(α_s^3)$ corrections to semileptonic $b \to c$ decays in the heavy daughter approximation

We present our recent calculation of the third order corrections to the semileptonic $b \to c$ and the muon decays. The calculation has been performed in an expansion around the limit $m_c \sim m_b$, but shows decent convergence even for $m_c=0$ from which the contribution to the muon decay can be extracted. For the semileptonic $b \to c$ decay we find large perturbative corrections in the on-shell scheme which can be significantly reduced by changing to the kinetic scheme for the bottom quark mass. These results are important input for the inclusive determination of $|V_{cb}|$ and the Fermi coupling constant $G_F$.

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arXiv2021

Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays

We compute corrections of order $α_s^3$ to the decay $b \to c \ell \barν$ taking into account massive charm quarks. In the on-shell scheme large three-loop corrections are found. However, in the kinetic scheme the three-loop corrections are below 1\% and thus perturbation theory is well under control. We furthermore provide results for the order $α_s^3$ corrections to $b \to u \ell \barν$ and the third-order QED corrections to the muon decay which will be important input for reducing the uncertainty of the Fermi coupling constant $G_F$.

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arXiv2021

A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\rm MS}$-pole quark mass relation

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 $\overline{\rm MS}$ 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.

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arXiv2020

The 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 $\overline{\rm MS}$ quark masses we can establish precise relations between the kinetic and $\overline{\rm MS}$ charm and bottom masses. As compared to two loops, the precision is improved by a factor two to three. Our results constitute important ingredients for the precise determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ at Belle~II.

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arXiv2020

Exact results for $Z_m^{\rm OS}$ and $Z_2^{\rm OS}$ with two mass scales and up to three loops

We consider the on-shell mass and wave function renormalization constants $Z_m^{\rm OS}$ and $Z_2^{\rm OS}$ up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $\sqrt{1-τ^2}$ and $\sqrt{1-τ^2}/τ$ which extends the findings from Ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order ${\cal O}(ε^2)$ and ${\cal O}(ε)$ at two- and three-loop order which are crucial ingrediants for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

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arXiv2017

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.

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arXiv2016

Leptoquark Flavor Patterns & B Decay Anomalies

Flavor symmetries that explain masses and mixings of the standard model fermions dictate flavor patterns for the couplings of scalar and vector leptoquarks to the standard model fermions. A generic feature is that couplings to $SU(2)$-doublet leptons are suppressed at least by one spurion of the discrete non-abelian symmetry breaking, responsible for neutrino mixing, while couplings to charged lepton singlets can be order one. We obtain testable patterns including those that predominantly couple to a single lepton flavor, or two, or in a skewed way. They induce lepton non-universality, which we contrast to current anomalies in $B$-decays. We find maximal effects in $R_{D}$ and $R_{D^*}$ at the level of $\sim$10 percent and few percent, respectively, while leptoquark effects in $R_{K^{(*)}}$ can reach order few$\times 10$ percent. Predictions for charm and kaon decays and $μ-e$ conversion are worked out.

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