Implications of the CP asymmetry in semileptonic B decay

Recent experimental searches for $A_{SL}$, the CP asymmetry in semileptonic B decay, have reached an accuracy of order one percent. Consequently, they give meaningful constraints on new physics. We find that cancellations between the Standard Model (SM) and new physics contributions to $B^0 - \bar B^0$ mixing cannot be as strong as was allowed prior to these measurements. The predictions for this asymmetry within the SM and within models of minimal flavor violation (MFV) are below the reach of present and near future measurements. Including order $m_c^2/m_b^2$ and $\Lambda_{QCD}/m_b$ corrections we obtain the SM prediction: $-1.3 \times 10^{-3} < A_{SL} < -0.5 \times 10^{-3}$. Future measurements can exclude not only the SM, but MFV as well, if the sign of the asymmetry is opposite to the SM or if it is same-sign but much enhanced. We also comment on the CP asymmetry in semileptonic $B_s$ decay, and update the range of the angle $\beta_s$ in the SM: $0.026 < \sin2\beta_s < 0.048$.Comment: 16 pages, a sign typo in eq.(11) fixed, to appear in Phys. Rev.

Rare K and B Decays in the Littlest Higgs Model without T-Parity

We analyze rare K and B decays in the Littlest Higgs (LH) model without T-parity. We find that the final result for the Z^0-penguin contribution contains a divergence that is generated by the one-loop radiative corrections to the currents corresponding to the dynamically broken generators. Including an estimate of these logarithmically enhanced terms, we calculate the branching ratios for the decays K^+ -> pi^+ nu bar nu, K_L -> pi^0 nu bar nu, B_{s,d} -> mu^+ mu^- and B -> X_{s,d} nu bar nu. We find that for the high energy scale f=O(2-3) TeV, as required by the electroweak precision studies, the enhancement of all branching ratios amounts to at most 15% over the SM values. On the technical side we identify a number of errors in the existing Feynman rules in the LH model without T-parity that could have some impact on other analyses present in the literature. Calculating penguin and box diagrams in the unitary gauge, we find divergences in both contributions that are cancelled in the sum except for the divergence mentioned above.Comment: 39 pages, 8 figures, typos corrected, comment on (2.17) and (2.18) added, references added, results unchange

Waiting for Clear Signals of New Physics in B and K Decays

We classify the extensions of the Standard Model (SM) according to the structure of local operators in the weak effective Hamiltonian and the presence or absence of new flavour and CP-violating interactions beyond those represented by the CKM matrix. In particular we review characteristic properties of models with minimal flavour violation (MFV), models with significant contributions from Higgs penguins and models with enhanced Z^0 penguins carrying a large new CP-violating phase. Within the latter models, the anomalous behaviour of certain B\to\pi K observables implies large departures from the SM predictions for rare and CP-violating K and B decays. Most spectacular is the enhancement of Br(K_L->pi^0 nu nubar) by one order of magnitude and a strong violation of the MFV relation (\sin2\beta)_{\pi\nu\bar\nu}=(\sin2\beta)_{\psi K_S}. On the other hand our prediction for (\sin2\beta)_{\phi K_S}\approx 0.9 differs from the Belle result by the sign but is consistent with the BaBar value. We give a personal shopping list for the coming years.Comment: Main latex-file, 4 figures, 22 page

Exploring the flavour structure of the MSSM with rare K decays

We present an extensive analysis of rare K decays, in particular of the two neutrino modes K+->pi+ nu nu-bar and KL->pi0 nu nu-bar, in the Minimal Supersymmetric extension of the Standard Model. We analyse the expectations for the branching ratios of these modes, both within the restrictive framework of the minimal flavour violation hypothesis and within a more general framework with new sources of flavour-symmetry breaking. In both scenarios, the information that can be extracted from precise measurements of the two neutrino modes turn out to be very useful in restricting the parameter space of the model, even after taking into account the possible information on the mass spectrum derived from high-energy colliders, and the constraints from B-physics experiments. In the presence of new sources of flavour-symmetry breaking, additional significant constraints on the model can be derived also from the two KL->pi0 l+l- modes.Comment: 22 pages, 10 figures (high quality figures available on request

Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order

We calculate the complete NNLO QCD corrections to the charm contribution of the rare decay K+ -> pi+ nu nu-bar. We encounter several new features, which were absent in lower orders. We discuss them in detail and present the results for the 2-loop matching conditions of the Wilson coefficients, the 3-loop anomalous dimensions, and the 2-loop matrix elements of the relevant operators that enter the NNLO renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the NNLO QCD corrections leads to a significant reduction of the theoretical uncertainty from 9.8% down to 2.4% in the relevant parameter Pc, implying the leftover scale uncertainties in BR(K+ -> pi+ nu nu-bar) and in the determination of |V_td|, sin(2 beta), and gamma from the K -> pi nu nu system to be 1.3%, 1.0%, 0.006, and 1.2 degrees, respectively. For the charm quark MSbar mass mc=(1.30+-0.05) GeV and |V_us|= 0.2248 the NLO value Pc=0.37+-0.06 is modified to Pc=0.38+-0.04 at the NNLO level with the latter error fully dominated by the uncertainty in mc. We present tables for Pc as a function of mc and alphas(MZ) and a very accurate analytic formula that summarizes these two dependences as well as the dominant theoretical uncertainties. Adding the recently calculated long-distance contributions we find BR(K+ -> pi+ nu nu-bar)=(8.0+-1.1)*10^-11 with the present uncertainties in mc and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. We also emphasize that improved calculations of the long-distance contributions to K+ -> pi+ nu nu-bar and of the isospin breaking corrections in the evaluation of the weak current matrix elements from K+ -> pi0 e+ nu would be valuable in order to increase the potential of the two golden K -> pi nu nu decays in the search for new physics.Comment: 74 pages, 28 figures. Erratum added: We correct the treatment of anomalous triangle diagrams. The associated numerical correction is below a permille; v3: Typographical mistakes in (108), (111) and (112) corrected. Thanks to Xu Feng for pointing them out. Numerical results unchange

Bounds on the Unitarity Triangle, sin⁡2β\sin 2\beta and K→πννˉK\to\pi\nu\bar\nu Decays in Models with Minimal Flavour Violation

We present a general discussion of the unitarity triangle from $\epsilon_K$, $\Delta M_{d,s}$ and $K \to \pi\nu\overline{\nu}$ in models with minimal flavour violation (MFV), allowing for arbitrary signs of the generalized Inami--Lim functions $F_{tt}$ and $X$ relevant for $(\epsilon_K,\Delta M_{d,s})$ and $K \to \pi\nu\overline{\nu}$, respectively. In the models in which $F_{tt}$ has a sign opposite to the one in the Standard Model, i.e. $F_{tt}<0$, the data for $(\epsilon_K, \Delta M_{d,s})$ imply an absolute lower bound on the $B_d\to\psi K_{S}$ CP asymmetry $a_{\psi K_S}$ of 0.69, which is substantially stronger than 0.42 arising in the case of $F_{tt}>0$. An important finding of this paper is the observation that for given $Br(K^+\to\pi^+\nu\overline{\nu})$ and $a_{\psi K_S}$ only two values for $Br(K_{L}\to\pi^0\nu\overline{\nu})$, corresponding to the two signs of $X$, are possible in the full class of MFV models, independently of any new parameters arising in these models. This provides a powerful test for this class of models. Moreover, we derive absolute lower and upper bounds on $Br(K_{L}\to\pi^0\nu\overline{\nu})$ as functions of $Br(K^+\to\pi^+\nu\overline{\nu})$. Using the present experimental upper bounds on $Br(K^+\to\pi^+\nu\overline{\nu})$ and $|V_{ub}/V_{cb}|$, we obtain the absolute upper bound $Br(K_{L}\to\pi^0\nu\overline{\nu})< 7.1 \cdot 10^{-10}$ (90% C.L.).Comment: 25 pages, LaTeX, 4 figures. Few comments and one figure in view of new B-factory results added, conclusions unchange

Constraints on Masses of Charged PGBs in Technicolor Model from Decay b→sγ b \to s \gamma

In this paper we calculate the contributions to the branching ratio of $B\to X_s \gamma$ from the charged Pseudo-Goldstone bosons appeared in one generation Technicolor model. The current $CLEO$ experimental results can eliminate large part of the parameter space in the $m(P^\pm) - m(P_8^\pm)$ plane, and specifically, one can put a strong lower bound on the masses of color octet charged PGBs $P_8^\pm$: $m(P^{\pm}_8) > 400\;GeV$ at $90\%C.L$ for free $m(P^{\pm})$.Comment: 9 pages, 3 figures(uuencoded), Minor changes(Type error), to appear in Phys. Rev.

Implications of the Top Quark Mass Measurement for the CKM Parameters, xsx_s and CP Asymmetries

Motivated by the recent determination of the top quark mass by the CDF collaboration, \mt =174 \pm 10 ^{+13}_{-12} GeV, we review and update the constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model. In performing our fits, we use inputs from the measurements of the following quantities: (i) \abseps, the CP-violating parameter in $K$ decays, (ii) \delmd, the mass difference due to the \bdbdbar\ mixing, (iii) the matrix elements \absvcb and \absvub, and (iv) $B$-hadron lifetimes. We find that the allowed region of the unitarity triangle is very large, mostly due to theoretical uncertainties. (This emphasizes the importance of measurements of CP-violating rate asymmetries in the $B$ system.) Nevertheless, the present data do somewhat restrict the allowed values of the coupling constant product $f_{B_d}\sqrt{\hat{B}_{B_d}}$ and the renormalization-scale invariant bag constant $\hat{B}_K$. With the updated CKM matrix we present the currently-allowed range of the ratio $\vert V_{td}/V_{ts} \vert$, as well as the standard model predictions for the \bsbsbar\ mixing parameter \xs and the quantities $\sin 2\alpha$, $\sin 2\beta$ and $\sin^2\gamma$, which characterize the CP-asymmetries in $B$-decays. The ALEPH collaboration has recently reported a significant improvement on the lower limit on the \bs-\bsb mass difference, $\Delta M_s/\Delta M_d > 11.3$ (95\% C.L.). This has interesting consequences for the CKM parameters which are also worked out. NOTE: this is a revised and updated version of our previous paper.Comment: LaTeX, 27 pages, 16 uuencoded figures (enclosed), CERN-TH.7398/94, UdeM-GPP-TH-94-0

Connections between epsilon'/epsilon and Rare Kaon Decays in Supersymmetry

We analyze the rare kaon decays $K_L \to \pi^0 \nu \bar \nu$, $K^+ \to \pi^+ \nu \bar \nu$, $K_L \to \pi^0 e^+ e^-$ and $K_L \to \mu^+ \mu^-$ in conjunction with the CP violating ratio $\epsilon'/\epsilon$ in a general class of supersymmetric models in which $Z$- and magnetic-penguin contributions can be substantially larger than in the Standard Model. We point out that radiative effects relate the double left-right mass insertion to the single left-left one, and that the phenomenological constraints on the latter reflect into a stringent bound on the supersymmetric contribution to the $Z$ penguin. Using this bound, and those coming from recent data on $\epsilon'/\epsilon$ we find {\rm BR}(K_L \to \pi^0 \nu \bar \nu)\lsim 1.2\cdot 10^{-10}, {\rm BR}(K^+ \to \pi^+ \nu \bar \nu)\lsim 1.7\cdot 10^{-10}, {\rm BR}(K_L \to \pi^0 e^+ e^-)_{\rm dir}\lsim 2.0\cdot 10^{-11}, assuming the usual determination of the CKM parameters and neglecting the possibility of cancellations among different supersymmetric effects in $\epsilon'/\epsilon$. Larger values are possible, in principle, but rather unlikely. We stress the importance of a measurement of these three branching ratios, together with improved data and improved theory of $\epsilon'/\epsilon$, in order to shed light on the realization of various supersymmetric scenarios. We reemphasize that the most natural enhancement of $\epsilon'/\epsilon$, within supersymmetric models, comes from chromomagnetic penguins and show that in this case sizable enhancements of $BR(K_L \to \pi^0 e^+ e^-)_{\rm dir}$ can also be expected.Comment: 40 pages, 5 figure

Particle-Antiparticle Mixing, epsilon_K, Delta Gamma_q, A_SL^q, A_CP(B_d -> psi K_S), A_CP(B_s -> psi phi) and B -> X_{s,d} gamma in the Littlest Higgs Model with T-Parity

We calculate a number of observables related to particle-antiparticle mixing in the Littlest Higgs model with T-parity (LHT). The resulting effective Hamiltonian for Delta F=2 transitions agrees with the one of Hubisz et al., but our phenomenological analysis goes far beyond the one of these authors. In particular, we point out that the presence of mirror fermions with new flavour and CP-violating interactions allows to remove the possible Standard Model (SM) discrepancy between the CP asymmetry S_{psi K_S} and large values of |V_ub| and to obtain for the mass difference Delta M_s < (Delta M_s)_SM as suggested by the recent result by the CDF collaboration. We also identify a scenario in which simultaneously significant enhancements of the CP asymmetries S_{phi psi} and A_SL^q relative to the SM are possible, while satisfying all existing constraints, in particular from the B -> X_s gamma decay and A_CP(B -> X_s gamma) that are presented in the LHT model here for the first time. In another scenario the second, non-SM, value for the angle gamma=-(109+-6) from tree level decays, although unlikely, can be made consistent with all existing data with the help of mirror fermions. We present a number of correlations between the observables in question and study the implications of our results for the mass spectrum and the weak mixing matrix of mirror fermions. In the most interesting scenarios, the latter one turns out to have a hierarchical structure that differs significantly from the CKM one.Comment: 51 pages, 20 figures, 1 table. Extended discussion of the phases in the new mixing matrix V_Hd, some references added or updated, conclusions unchanged. Final version published in JHE