arXiv subjects
Publications and source records attributed to Matthias Steinhauser.
We discuss recent higher order calculations to properties of $B$ mesons. This includes next-to-next-to-leading order corrections to nonleptonic and next-to-next-to-next-to-leading order corrections to semileptonic $B$ meson decays. The latter is important in connection to the determination of the CKM matrix element $V_{cb}$. We also discuss next-to-next-to-leading order corrections to the width difference in the neutral $B$ meson system.
Higgs boson pair production plays an important role in the determination of the Higgs boson self coupling. The predictions based on next-to-leading order corrections show a large dependence on the renormalization scheme of the top quark mass, which requires a next-to-next-to-leading order calculation. We discuss the current status and show first results of the three-loop virtual corrections.
We compute next-to-next-to-leading order QCD corrections to the partonic processes $b\to c \bar{u} d$ and $b\to c \bar{c} s$, 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 $ΔB =1$ 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 $b \to u \bar c s$ and $b \to u \bar u d$.
In these proceedings, we consider the factorizable contributions of the two-loop electroweak corrections to Higgs boson pair production at the Large Hadron Collider. We discuss the classification of factorizable diagrams and their renormalization. Compact analytic results for the renormalized form factors are presented in a computer-readable form.
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.
We compute three-loop corrections to the process $gg\to HH$ originating from one-particle reducible diagrams. This requires the computation of two-loop corrections to the gluon-gluon-Higgs vertex with an off-shell gluon. We describe in detail our approach to obtain semi-analytic results for the vertex form factors and present results for the two form factors contributing to Higgs boson pair production.
We provide details to several technical aspects which are important for the calculation of next-to-next-to-leading order corrections to the mixing of neutral $B$ mesons. This includes the computation of the master integrals for finite charm and bottom quark masses, traces over products of up to 22 $γ$ matrices and tensor integrals with up to rank 11.
This report summarises recent advances made in the calculation of the NNLO QCD corrections to the width difference $ΔΓ_s$ in the $B_s-\overline{B}_s$ system. The inclusion of the effects due to current-current operators leads to an updated prediction of $ΔΓ_s = (0.076\pm 0.017)\,\text{ps}^{-1}$, which narrows the gap between theory and experiment.
We compute three-loop vertex corrections to $b\to sγ$ induced by current-current operators. The results are presented as expansions in $m_c/m_b$ with numerical coefficients which allow to cover all relevant values for the heavy quark masses in different renormalization schemes. Moreover we provide for the first time analytic results for the next-to-leading order contribution. Our results present an important building block to the next-to-next-to-leading order interference contributions of the current-current operators $Q_1$ and $Q_2$ with the electric dipole operator $Q_7$.
We compute two-loop electroweak corrections to Higgs boson pair and Higgs plus jet production, taking into account all sectors of the Standard Model. All diagrams with virtual top quarks are computed in an expansion for large top quark mass up to order $1/m_t^8$ or more. We present analytic results for the form factors and discuss the convergence properties. For the process $gg\to gH$ we also consider QCD corrections in the large-$m_t$ limit.
We discuss recent (semi) analytic results for $2\to 2$ processes with massive internal and external particles in various regions of phase space. In the physical applications we restrict ourselves to $gg\to HH$.
We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.
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 $b\to c\ell \barν_\ell$ and $b\to u\ell \barν_\ell$ 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.
We consider two-loop corrections to $2\to 2$ scattering processes with massive particles in the final state and massive particles in the loop. We discuss the combination of analytic expansions in the high-energy limit and for small Mandelstam variable~$t$. For the example of double Higgs boson production we show that the whole phase space can be covered and time-consuming numerical integrations can be avoided.
We compute three-loop corrections to the singlet form factors for massive quarks using a semi-analytic method which provides precise results over the whole kinematic range. Particular emphasis is put on the anomaly contribution originating from an external axial-vector current. We also discuss in detail the contribution for a pseudoscalar current and verify the chiral Ward identity to three-loop order. Explicit results are presented for the low- and high-energy regions and the expansions around threshold.
We analytically compute two-loop Yukawa corrections to Higgs boson pair production in the high-energy limit. Such corrections are generated by an exchange of a Higgs boson between the virtual top quark lines. We propose two approaches to obtain expansions of the massive two-loop box integrals and show that precise results are obtained for transverse momenta of the Higgs bosons above about 150 GeV. We discuss in detail the computation of all 140 master integrals and present analytic results.
We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy $s$ which allows to cover the whole kinematic range for negative and positive values of $s$. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.
We extend the theoretical prediction for the width difference $ΔΓ_q$ in the mixing of neutral $B$ mesons in the Standard Model to next-to-next-to-leading order in $α_s$. To this aim we calculate three-loop diagrams with two $|ΔB|=1$ current-current operators analytically. In the matching between $|ΔB|=1$ and $|ΔB|=2$ effective theories we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix $Z_{ij}$ for the $|ΔB|=2$ operators and the $\mathcal{O}(α_s^2)$ corrections to the finite renormalization that ensures the $1/m_b$ suppression of the operator $R_0$ at two-loop order. Our theoretical prediction reads $ΔΓ_s/ΔM_s = {(4.33\pm 0.93)\cdot 10^{-3}}$ if expressed in terms of the bottom mass in the $\overline{\rm MS}$ scheme and $ΔΓ_s/ΔM_s = {(4.20\pm 0.95)\cdot 10^{-3}}$ for the use of the potential-subtracted mass. While the controversy on $|V_{cb}|$ affects both $ΔΓ_s$ and $ΔM_s$, the ratio $ΔΓ_s/ΔM_s$ is not affected by the uncertainty in $|V_{cb}|$ .