arXiv subjects
Publications and source records attributed to Andrzej J. Buras.
We review several aspects of the recent theoretical progress in K and B decays including the impact of the top quark discovery on rare and CP violating decays. In particular we summarize the present status of next-to-leading QCD calculations in this field stressing their importance in the determination of the parameters in the Cabibbo-Kobayashi-Maskawa matrix.
We discuss several aspects of rare decays and CP violation in the standard model including the impact of the recent top quark discovery. In particular we review the present status of next-to-leading QCD calculations in this field stressing their importance in the determination of the parameters in the Cabibbo-Kobayashi-Maskawa matrix. We emphasize that the definitive tests of the standard model picture of rare decays and CP violation will come through a {\it simultaneous} study of CP asymmetries in $B_{d,s}^0$ decays, the rare decays $K^+ \to π^+ν\barν$ and $K_L \to π^0ν\barν$, and $(B^0_d-\bar B^0_d)/(B^0_s-\bar B^0_s)$.
We point out that the measurement of just the two branching fractions \linebreak $B(K^+\toπ^+ν\barν)$ and $B(K_L\toπ^0ν\barν)$ can in a theoretically clean manner determine $\sin 2β$ almost independently of $m_t$ and $V_{cb}$. This allows to obtain an interesting relation between the CP asymmetry $A_{CP}(ψK_S)$ in B physics and the branching ratios for these two rare K decays. The recently calculated next-to-leading order QCD corrections improve the accuracy of this analysis. We find typically $Δ\sin 2β=\pm 0.11$ provided $B(\kpn)$ and $B(\klpn)$ are measured within $\pm 10\%$ accuracy. With decreasing uncertainty in $Λ_{\overline{MS}}$ and $m_c$ this error could be reduced to $Δ\sin 2β< \pm 0.10$. The determination of $\sin 2α$ and $\sin 2γ$ on the other hand is rather poor. However respectable determinations of the Wolfenstein parameter $η$ and of $\mid V_{td}\mid$ can be obtained.
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.
We point out that the lower bound on $m_t$ from the CP violation parameter $ε_K$ has increased considerably. Using Wolfenstein parametrization of the CKM matrix we derive an analytic expression for this bound as a function of $\mid V_{cb}\mid, \mid V_{ub}/V_{cb}\mid$ and the non-perturbative parameter $B_K$. For $B_K\leq 0.80,\mid V_{cb} \mid\leq 0.040$ and $\mid V_{ub}/V_{cb}\mid\leq 0.10$ we find $m_t > 130 GeV$. However, for $B_K \leq 0.70, \mid V_{cb}\mid \leq 0.038 $ and $\mid V_{ub}/V_{cb}\mid \leq 0.08$ the bound is raised to $m_t > 205~GeV$. The lower bound on $m_t$ from $B^o-\bar B^o$ mixing is also reconsidered.
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.
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 $γ_5$.
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.