arXiv subjects

Markus E. Lautenbacher

Publications and source records attributed to Markus E. Lautenbacher.

5 recordsLinked to original sources

arXiv1995

Weak Decays Beyond Leading Logarithms

We review the present status of QCD corrections to weak decays beyond the leading logarithmic approximation including particle-antiparticle mixing and rare and CP violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective hamiltonians for all decays for which the next-to-leading corrections are known. Subsequently, we present the phenomenological implications of these calculations. In particular we update the values of various parameters and we incorporate new information on m_t in view of the recent top quark discovery. One of the central issues in our review are the theoretical uncertainties related to renormalization scale ambiguities which are substantially reduced by including next-to-leading order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated in various cases.

hep-ph↗

arXiv1993

An Analytic Formula and an Upper Bound for epsilon'/epsilon in the Standard Model

Using the idea of the penguin box expansion we find an analytic expression for epsilon'/epsilon in the Standard Model as a function of m_t, m_s(m_c) and two non-perturbative parameters B_6 and B_8. This formula includes next-to-leading QCD/QED short distance effects calculated recently by means of the operator product expansion and renormalization group techniques. We also derive an analytic expression for the upper bound on epsilon'/epsilon as a function of |V_cb|, |V_ub/V_cb|, B_K and other relevant parameters. Numerical examples of the bound are given.

hep-ph↗

arXiv1993

The Anatomy of $\varepsilon'/\varepsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements

We use the recently calculated two--loop anomalous dimensions of current-current operators, QCD and electroweak penguin operators to construct the effective Hamiltonian for $ΔS=1$ transitions beyond the leading logarithmic approximation. We solve the renormalization group equations and give the numerical values of Wilson coeff. functions. We propose a new semi-phenomenological approach to hadronic matrix elements which incorporates the data for $CP$-conserving $K \rightarrow ππ$ amplitudes and allows to determine the matrix elements of all $(V-A)\otimes (V-A)$ operators in any renormalization scheme and do a renormalization group analysis of all hadronic matrix elements $\langle Q_i(μ) \rangle$. We compare critically our treatment of these matrix elements with those given in the literature. We find in the NDR scheme $\epe = (6.7 \pm 2.6)\times 10^{-4}$ in agreement with the experimental findings of E731. We point out however that the increase of $\langle Q_6 \rangle$ by only a factor of two gives $\epe = (20.0 \pm 6.5)\times 10^{-4}$ in agreement with the result of NA31. The dependence of $\epe$ on $Λ_{\bar{MS}}$, $m_t$ and $\langle Q_{6,8} \rangle$ is presented.

hep-ph↗

arXiv1992

Two--Loop Anomalous Dimension Matrix for $ΔS=1$ Weak Non-Leptonic Decays II: ${\cal O}(α_e α_s)$

We calculate the $10\times 10$ two--loop anomalous dimension matrix to order $\ord(α_e α_s)$ in the dimensional regularization scheme with anticommuting $γ_5$ (NDR) which is necessary for the extension of the $ΔS=1$ weak Hamiltonian involving electroweak penguins beyond the leading logarithmic approximation. We demonstrate, how a direct calculation of penguin diagrams involving $γ_5$ in closed fermion loops can be avoided thus allowing a consistent calculation of two--loop anomalous dimensions in the simplest renormalization scheme with anticommuting $γ_5$ in $D$ dimensions. We give the necessary one--loop finite terms which allow to obtain the corresponding two--loop anomalous dimension matrix in the HV scheme with non--anticommuting $γ_5$.

hep-ph↗

arXiv1992

The Two-Loop Anomalous Dimension Matrix for $ΔS=1$ Weak Non-Leptonic Decays I: ${\cal O}(α_s^2)$

We calculate the two-loop $10 \times 10$ anomalous dimension matrix ${\cal O}(α_s^{2})$ involving current-current operators, QCD penguin operators, and electroweak penguin operators especially relevant for $ΔS=1$ weak non-leptonic decays, but also important for $ΔB=1$ decays. The calculation is performed in two schemes for $γ_{5}$: the dimensional regularization scheme with anticommuting $γ_{5}$ (NDR), and in the 't Hooft-Veltman scheme. We demonstrate how a direct calculation of diagrams involving $γ_{5}$ in closed fermion loops can be avoided thus allowing a consistent calculation in the NDR scheme. The compatibility of the results obtained in the two schemes considered is verified and the properties of the resulting matrices are discussed. The two-loop corrections are found to be substantial. The two-loop anomalous dimension matrix ${\cal O}(α_eα_s)$, required for a consistent inclusion of electroweak penguin operators, is presented in a subsequent publication.

hep-ph↗