arXiv subjects
Publications and source records attributed to Stefan Herrlich.
We briefly sketch the calculation of the effective low-energy $|ΔS|=2$-hamiltonian in the next-to-leading order of renormalization group improved perturbation theory. The result for the coefficient $η_3^\star$ is discussed. Further we present a 1996 update of our phenomenological analysis of the unitarity triangle where we include the information available on $B^0-\bar{B^0}$-mixing.
I present the calculation of the QCD short distance coefficient $η_3$ of the $|ΔS|=2$-hamiltonian in the next-to-leading order (NLO) of renormalization group improved perturbation theory. It involves the two-loop mixing of bilocal structures composed of two $|ΔS|=1$ operators into $|ΔS|=2$ operators. The next-to-leading order corrections enhance $η_3$ by 27\% to $η_3=0.47\errorpm{0.03}{0.04}$ thereby affecting the phenomenology of the CP-parameter $ε_K$ sizeably. $η_3$ depends on the physical input parameters $m_t$, $m_c$ and $Λ_{MSbar}$ only weakly. The quoted error stems from factorization scale dependences, which have reduced compared to the old leading log result. We further discuss some field theoretical aspects of the calculation such as the renormalization group equation for Green's functions with two operator insertions and the renormalization scheme dependence caused by the presence of evanescent operators. This article is based on work done in collaboration with U.~Nierste.
We present the complete next-to-leading order short-distance QCD corrections to the effective \dstwo -hamiltonian in the Standard Model. The calculation of the coefficient $η_3$ is described in great detail. It involves the two-loop mixing of bilocal structures composed of two \dsone\ operators into \dstwo\ operators. The next-to-leading order corrections enhance $η_3$ by 27\% to $η_3=0.47 \errorpm{+0.03}{-0.04}$ thereby affecting the phenomenology of $ε_K$ sizeably. $η_3$ depends on the physical input parameters $m_t$, $m_c$ and $\laMSb$ only weakly. The quoted error stems from renormalization scale dependences, which have reduced compared to the old leading log result. The known calculation of $η_1$ and $η_2$ is repeated in order to compare the structure of the three QCD coefficients. We further discuss some field theoretical aspects of the calculation such as the renormalization group equation for Green's functions with two operator insertions and the renormalization scheme dependence caused by the presence of evanescent operators.
The anomalous dimension matrix of dimensionally regularized four-quark operators is known to be affected by evanescent operators, which vanish in $D=4$ dimensions. Their definition, however, is not unique, as one can always redefine them by adding a term proportional to $(D-4)$ times a physical operator. In the present paper we compare different definitions used in the literature and find that they correspond to different renormalization schemes in the physical operator basis. The scheme transformation formulae for the Wilson coefficients and the anomalous dimension matrix are derived in the next-to-leading order. We further investigate the proper treatment of evanescent operators in processes appearing at second order in the effective four-fermion interaction such as particle-antiparticle mixing, rare hadron decays or inclusive decays.
We have calculated the short distance QCD coefficient η_3 of the effective |ΔS|=2-hamiltonian in the next-to-leading order. Since now all coefficients η_1, η_2 and η_3 are known beyond the leading log approximation, one can achieve a much higher precision in the theoretical analysis of ε_K. The measured value for ε_K$ yields a lower bound on each of |V_{cb}|, |V_{ub}/V_{cb}|, the top quark mass $m_t$ and the non- perturbative parameter B_K as a function of the remaining three quantities. We discuss the implications on the CKM phase δ, |V_{td}| and the key quantity for all CP-violating processes, Im λ_t = Im [V^*_{ts} V_{td}]. These quantities and the improved Wolfenstein parameters \barρand \barηare tabulated and the shape of the unitarity triangle is discussed. We compare the range for |V_{td}| with the one obtained from the analysis of B^0--\bar{B^0} mixing. For 0.037 \leq |V_{cb}| \leq 0.043, 0.06 \leq |V_{ub}/V_{cb}| \leq 0.10 and 0.65 \leq B_K \leq 0.85 we find from a combined analysis of ε_K and the B^0--\bar{B^0} mixing paramater x_d: 49^{\circ} \leq δ\leq 146^{\circ}, 7.4 \cdot 10^{-3} \leq |V_{td}| \leq 12.4 \cdot 10^{-3}, 0.85 \cdot 10^{-4} \leq \imag λ_t \leq 1.60 \cdot 10^{-4}, -0.36 \leq \barρ\leq 0.28 and 0.21 \leq \barη\leq 0.44. We predict the mass difference of the $B_s^0$ system to lie in the range 6.5 ps^{-1} \leq Δm_{B_s} \leq 28 ps^{-1}. Finally we have a 1995 look at the K_L--K_S mass difference.