Search

The CKM unitarity precision test of the Standard Model requires a systematic treatment of electromagnetic and strong corrections for semi-leptonic decays. Electromagnetic corrections require the renormalization of a semileptonic four-fermion operator. In this work we calculate the $\mathcal{O}(αα_s)$ perturbative scheme conversion between the $\bar{\rm MS}$ scheme and several momentum-space subtraction schemes, which can also be implemented on the lattice. We consider schemes defined by MOM and SMOM kinematics and emphasize the importance of the choice of projector for each scheme. The conventional projector, that has been used in the literature for MOM kinematics, generates QCD corrections to the conversion factor that do not vanish for $α=0$ and which generate an artificial dependence on the lattice matching scale that would only disappear after summing all orders of perturbation theory. This can be traced to the violation of a Ward identity that holds in tha $α=0$ limit. We show how to remedy this by judicious choices of projector, and prove that the Wilson coefficients in those schemes are free from pure QCD contributions. The resulting Wilson coefficients (and operator matrix elements) have greatly reduced scale dependence. Our choice of the $\bar{\rm MS}$ scheme over the traditional $W$-mass scheme is motivated by the fact that, besides being more tractable at higher orders, unlike the latter it allows for a transparent separation of scales. We exploit this to obtain renormalization-group-improved leading-log and next-to-leading-log strong corrections to the electromagnetic contributions and study the (QED-induced) dependence on the lattice matching scale., 1+22 pages

This Report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The main goal of the working group was to present the state-of-the-art of Higgs physics at the LHC, integrating all new results that have appeared in the last few years. The first part compiles the most up-to-date predictions of Higgs boson production cross sections and decay branching ratios, parton distribution functions, and off-shell Higgs boson production and interference effects. The second part discusses the recent progress in Higgs effective field theory predictions, followed by the third part on pseudo-observables, simplified template cross section and fiducial cross section measurements, which give the baseline framework for Higgs boson property measurements. The fourth part deals with the beyond the Standard Model predictions of various benchmark scenarios of Minimal Supersymmetric Standard Model, extended scalar sector, Next-to-Minimal Supersymmetric Standard Model and exotic Higgs boson decays. This report follows three previous working-group reports: Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002), Handbook of LHC Higgs Cross Sections: 2. Differential Distributions (CERN-2012-002), and Handbook of LHC Higgs Cross Sections: 3. Higgs properties (CERN-2013-004). The current report serves as the baseline reference for Higgs physics in LHC Run 2 and beyond., Comment: 869 pages, 295 figures, 248 tables and 1645 citations. Working Group web page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG

Rare decays were essential in the discovery of the CKM mechanism of flavour and CP violation and are highly sensitive probes of physics beyond the Standard Model. In this summary the current status and future prospects of experimental measurements and the Standard Model theory predictions of various rare B, D and K decay observables are discussed. The specific new physics sensitivities of each mode are also briefly reviewed.

Combining our results for various O(alpha_s^2) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find BR(B -> X_s gamma) = (3.15 +_ 0.23) x 10^-4 for E_gamma > 1.6 GeV in the B-meson rest frame. The four types of uncertainties: non-perturbative (5%), parametric (3%), higher-order (3%) and m_c-interpolation ambiguity (3%) have been added in quadrature to obtain the total error., Comment: 4 pages, 4 figures. Version accepted by the PRL. Words disallowed by the journal removed from the title. References updated and a note added

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., 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 unchanged

We calculate the charm-quark contribution to the decay K_L -> mu^+ mu^- in next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P_c from +/-22% down to +/-7%, corresponding to scale uncertainties of +/-3% and +/-6% in the short-distance part of the branching ratio and the determination of the Wolfenstein parameter rhobar from K_L -> mu^+ mu^-. The error in P_c = 0.115 +/- 0.018 is now in equal shares due to the combined scale uncertainties and the current uncertainty in the charm-quark mass. We find BR (K_L -> mu^+ mu^-)_SD = (0.79 +/- 0.12) x 10^-9, with the present uncertainty in the Cabibbo-Kobayashi-Maskawa matrix element V_td being the dominant individual source in the quoted error., 5 pages, 2 figures; Note added concerning the erroneous treatment of anomalous triangle diagrams. The associated numerical effect is negligible. arXiv admin note: substantial text overlap with arXiv:hep-ph/0508165

Combining our results for various O(alpha_s^2) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find BR(B -> X_s gamma) = (3.15 +_ 0.23) x 10^-4 for E_gamma > 1.6 GeV in the B-meson rest frame. The four types of uncertainties: non-perturbative (5%), parametric (3%), higher-order (3%) and m_c-interpolation ambiguity (3%) have been added in quadrature to obtain the total error., 4 pages, 4 figures. Version accepted by the PRL. Words disallowed by the journal removed from the title. References updated and a note added

We calculate the charm quark contribution to the rare decay K+ -> pi+ nu anti-nu in the next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter Pc from +/- 10.1% down to +/- 2.4%, corresponding to scale uncertainties of +/- 1.3%, +/- 1.0%, +/- 0.006 and +/- 1.2 degrees in BR(K+ -> pi+ nu anti-nu) and in |V_td|, sin(2 beta) and gamma extracted from the K -> pi nu anti-nu system. The error in Pc = 0.37 +/- 0.04 is now fully dominated by the current uncertainty of +/- 3.8% in the charm quark mass mc. We find BR(K+ -> pi+ nu anti-nu) = (8.0 +/- 1.1) * 10^-11, where the quoted error stems almost entirely from the present uncertainties in mc and the Cabibbo-Kobayashi-Maskawa elements., Comment: 4 pages, 2 figures; Note added concerning the erroneous treatment of anomalous triangle diagrams. The associated numerical effect is negligible

We analyze the CP violating ratio epsilon'/epsilon and rare K and B decays in the MSSM with minimal flavour and CP violation, including NLO QCD corrections and imposing constraints on the supersymmetric parameters coming from epsilon, B_{d,s}^0-\bar B_{d,s}^0 mixings, B to X_s gamma, Delta rho in the electroweak precision studies and from the lower bound on the neutral Higgs mass. We provide a compendium of phenomenologically relevant formulae in the MSSM. Denoting by T(Q) the MSSM prediction for a given quantity normalized to the Standard Model result we find the ranges: 0.53 < T(epsilon'/epsilon) < 1.07, 0.65 < T(K^+ to pi^+ nu nubar) < 1.02, 0.41 < T(K_L to pi^0 nu nubar) < 1.03, 0.48 < T(K_L to pi^0 e^+ e^-) < 1.10, 0.73 < T(B to X_s nu nubar) < 1.34 and 0.68 < T(B_s to mu^+ mu^-) < 1.53. We point out that these ranges will be considerably reduced when the lower bounds on the neutral Higgs mass and tan beta improve. Some contour plots illustrate the dependences of the quantities above on the relevant supersymmetric parameters. As a byproduct of this work we update our previous analysis of epsilon'/epsilon in the SM and find in NDR epsilon'/epsilon = (9.2^{+6.8}_{-4.0}), a value 15 % higher than in our 1999 analysis., 44 pages, 7 figures

We analyze the CP violating ratio \epe=epsilon'/epsilon in the Standard Model in view of the new KTeV results. We review the present status of the most important non-perturbative parameters B_6, B_8, B_K and of the strange quark mass m_s. We also briefly discuss the issues of final state interactions and renormalization scheme dependence. Updating the values of the CKM parameters, of m_t and Lambda (MSbar) and using Gaussian errors for the experimental input and flat distributions for the theoretical parameters we find \epe substantially below the NA31 and KTeV data: \epe= (7.7^{+6.0}_{-3.5}) 10^{-4} and \epe= (5.2^{+4.6}_{-2.7}) 10^{-4} in the NDR and HV renormalization schemes respectively. A simple scanning of all input parameters gives on the other hand 1.05 10^{-4} < \epe < 28.8 10^{-4} and 0.26 10^{-4} < \epe < 22.0 10^{-4} respectively. Analyzing the dependence on various parameters we find that only for extreme values of B_6, B_8 and m_s and suitable values of CKM parameters and Lambda(MSbar), the ratio \epe can be made consistent with data. We analyze the impact of these data on the lower bounds for Im(V_{td}V_{ts}^*), Br(K_L to pi^0 nu barnu), Br(K_L to pi^0e^+e^-)_{dir} and on tan(beta) in the Two Higgs Doublet Model II., main latex-file, 4 figures and related latex files, 47 pages

Higher order corrections are a fundamental ingredient for the analysis of physical ob- servables. They are essential to improve the precision of theory predictions within the Standard Model which then lead to an increased sensitivity of these observables to physics beyond the Standard Model. In this thesis we compute higher order QCD corrections to the effective Lagrangian for weak decays. We combine previous results for the Next-to-Next-to-Leading order in the five-flavour theory with new matching calculations. This allows us to determine the effective Lagrangian in the four- and in the three-flavour theory for current-current and QCD penguin operators. We discuss explicitly the relevant steps required for a proper matching calculation, in particular the cancellation of the ultra-violet and infra-red divergences. We also introduce a new formalism that leads to scale and scheme independent intermediate results. Moreover the scheme change for the electroweak penguin operators at the Next-to-Leading or- der is calculated, and the one-loop and two-loop anomalous dimensions for a general number of flavours in the modern basis is presented for the first time in this thesis. In addition we present an updated QCD×QED running. Here a detailed discussion is provided to explain the problem with the singularities when the eigenvalues of the anomalous dimension matrix differ by a factor $2\beta_{00}^s$. Finally we apply the result to the theory prediction of the CP-conserving hadronic kaon decays, and the $\varepsilon^\prime/\varepsilon$ observable, reducing the perturbative uncertainty by a factor 0.12 at NNLO level.