Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays

We evaluate the complete four-loop anomalous dimension matrix that is necessary for determining the effective flavour-changing neutral current couplings qbar-q'-gamma and qbar-q'-g at the next-to-next-to-leading order in QCD. The resulting O(alpha_s^2(mu_b)) correction to the B -> X_s gamma branching ratio amounts to around -2.9% for mu_b = 5 GeV, and -4.4% for mu_b = 2.5 GeVComment: 19 page

Completing the Calculation of BLM corrections to B -> Xs gamma

Perturbative O(alpha_s^2) corrections to BR(B -> Xs gamma) in the BLM approximation receive contributions from two-, three- and four-body final states. While all the two-body results are well established by now, the other ones have remained incomplete for several years. Here, we calculate the last contribution that has been missing to date, namely the one originating from interference of the current-current and gluonic dipole operators (K_18^{(2)beta_0} and K_{28}^{(2)beta_0}). Moreover, we confirm all the previously known results for BLM corrections to the photon energy spectrum that involve the current-current operators (e.g., K_{22}^{(2)beta_0} and K_{27}^{(2)beta_0}). Finally, we also confirm the recent findings of Ferroglia and Haisch on self-interference of the gluonic dipole operator (K_{88}^{(2)beta_0}).Comment: 5 pages, 2 ps figure

Weak radiative decays of the B meson and bounds on MH± in the Two-Higgs-Doublet Model

In a recent publication (Abdesselam et al. arXiv:1608.02344 ), the Belle collaboration updated their analysis of the inclusive weak radiative B -meson decay, including the full dataset of (772±11)×106BB¯ pairs. Their result for the branching ratio is now below the Standard Model prediction (Misiak et al. Phys Rev Lett 114:221801, 2015 , Czakon et al. JHEP 1504:168, 2015 ), though it remains consistent with it. However, bounds on the charged Higgs boson mass in the Two-Higgs-Doublet Model get affected in a significant manner. In the so-called Model II, the 95% C.L. lower bound on MH± is now in the 570–800 GeV range, depending quite sensitively on the method applied for its determination. Our present note is devoted to presenting and discussing the updated bounds, as well as to clarifying several ambiguities that one might encounter in evaluating them. One of such ambiguities stems from the photon energy cutoff choice, which deserves re-consideration in view of the improved experimental accuracy

The O(alpha_em/alpha_s) correction to BR[B -> X_s gamma]

We evaluate the O(alpha_em/alpha_s) correction to the rate of B -> X_s gamma decay, i.e. we resum all the 0[ alpha_em ln M_W^2/m_b^2 x (alpha_s ln M_W^2/m_b^2)^n ] corrections for n=0,1,2,... Our calculation differs from the previously available one by that it takes into account the complete relevant set of operators. The correction is found to be negligible, i.e. it is below 1%, in accordance with the former results.Comment: 6 pages, no figure

Three-Loop Mixing of Dipole Operators

We calculate the complete three-loop O(alpha_s^3) anomalous dimension matrix for the dimension-five dipole operators that arise in the Standard Model after integrating out the top quark and the heavy electroweak bosons. Our computation completes the three-loop anomalous dimension matrix of operators that govern low-energy |Delta F| = 1 flavor-changing processes, and represents an important ingredient of the next-to-next-to-leading order QCD analysis of the Bbar -> X_s gamma decay.Comment: 4 pages, 1 figure; journal version, text below Eq. (7) correcte

QCD corrections to FCNC decays mediated by Z-penguins and W-boxes

QCD corrections are evaluated to FCNC processes like $B \to X_s \nu \bar{\nu}$, $K \to \pi \nu \bar{\nu}$, $B \to l^+ l^-$ or $K_L \to \mu^+ \mu^-$, i.e. to processes mediated by effective operators containing neutrino currents or axial leptonic currents. Such operators originate from $W$-box and $Z$-penguin diagrams in the Standard Model. QCD corrections to them are given by two-loop diagrams. We confirm results for those diagrams which are already present in the literature. However, our analytical expressions for the Wilson coefficients disagree, due to a subtlety in regulating spurious IR divergences. The numerical effect of the disagreement is rather small. The size of the perturbative QCD corrections compared to the leading terms depends on the renormalization scheme used at the leading order. It varies from 0 to around 15% for a reasonable class of schemes. The uncertainty originating from uncalculated higher-order (three-loop) QCD corrections is expected to be around 1% .Comment: 12 pages, latex, 7 ps figure

On The Dimensional Methods in Rare b Decays

Since several years there exists a question whether the dimensional reduction and the usual dimensional regularization give different results for the QCD-improved $b \rightarrow s \gamma$ and $b \rightarrow s$ $gluon$ decay rates. Here it is demonstrated explicitly that this is not the case: As long as physically meaningful quantities are considered, the results obtained with help of both techniques agree.Comment: 14 pages (including 1 page figures

Tree-level contributions to B -> Xs gamma

Weak radiative decay B -> X_s gamma is known to be a loop-generated process. However, it does receive tree-level contributions from CKM-suppressed b -> u ubar s gamma transitions. In the present paper, we evaluate such contributions together with similar ones from the QCD penguin operators. For a low value of the photon energy cutoff E_0 ~ m_b/20 that has often been used in the literature, they can enhance the inclusive branching ratio by more than 10%. For E_0 = 1.6 GeV or higher, the effect does not exceed 0.4%, which is due to phase-space suppression. Our perturbative results contain collinear logarithms that depend on the light quark masses m_q (q=u,d,s). We have allowed m_b/m_q to vary from 10 to 50, which corresponds to values of m_q that are typical for the constituent quark masses. Such a rough method of estimation may be improved in the future with the help of fragmentation functions once the considered effects begin to matter in the overall error budget for BR(B -> X_s gamma).Comment: v3: Corrected factors of 2 in the subdominant T_3 contributions. Minor changes in the numerical results (Table II

Direct CP Violation in K_L --> \pi^0 e^+e^- Beyond Leading Logarithms

We analyze the direct CP violation in the rare decay K_L --> Pi^0 e+e- with QCD effects taken into account consistently in the next-to-leading order. We calculate the two-loop mixing between the four-quark \Delta S=1 operators and the operator Q_7V = (sd)_(V-A)(ee)_V in the NDR and HV renormalization schemes. Using the known two-loop anomalous dimension matrix of the four-quark operators, we find that the coefficient C_7V(\mu) depends only very weakly on \mu, renormalization scheme and \Lambda_MSbar. The next-to-leading QCD corrections enhance the direct CP violating contribution over its leading order estimate so that it remains dominant in spite of the recent decrease of |V_ub/V_cb| and |V_cb|. We expect typically BR(K_L --> \pi^0 e^+ e^-)_dir ~ 6*10^(-12), although values as high as 10^(-11) are not yet excluded.Comment: 35 pages (with 9 PostScript figures available separately), Munich Technical University preprint TUM-T31-60/94, Max-Planck Institute preprint MPI-Ph/94-1