Kaon physics from lattice QCD

I review lattice calculations and results for hadronic parameters relevant for kaon physics, in particular the vector form factor f+(0) of semileptonic kaon decays, the ratio fK/fpi of leptonic decay constants and the kaon bag parameter BK. For each lattice calculation a colour code rating is assigned, by following a procedure which is being proposed by the Flavianet Lattice Averaging Group (FLAG), and the following final averages are obtained: f+(0)=0.962(3)(4), fK/fpi = 1.196(1)(10) and \hat BK = 0.731(7)(35). In the last part of the talk, the present status of lattice studies of non-leptonic K--> pi pi decays is also briefly summarized.Comment: Plenary talk at 27th International Symposium on Lattice Field Theory (Lattice 2009), Beijing, China, 25-31 Jul 2009. v2: two references and one comment added, typos correcte

Light quark masses and CKM matrix elements from lattice QCD

I give a brief overview of recent results from lattice QCD calculations which are relevant for the phenomenology of the Standard Model. I discuss, in particular, the lattice determination of light quark masses and the calculation of those hadronic quantities, such as semileptonic form factors, decay constants and B-parameters, which are of particular interest for the analysis of the CKM mixing matrix and the origin of CP violation.Comment: 5 pages, 4 figures, uses espcrc2.sty (included). Based on invited talk given at the QCD 98 Euroconference, Montpellier, France, 2-8 July 199

Flavour physics and Lattice QCD: averages of lattice inputs for the Unitarity Triangle Analysis

We review recent results of Lattice QCD calculations relevant for flavour physics. We discuss in particular the hadronic parameters entering the amplitudes of K0-K0bar, D0-D0bar and B0-B0bar mixing, the B- and D-meson decay constants and the form factors controlling B-meson semileptonic decays. On the basis of these lattice results, which are extensively collected in the paper, we also derive our averages of the relevant hadronic parameters.Comment: Plenary talk at IFAE 2008, Bologna, Italy, 26-28 March 200

A p-adic quasi-quadratic point counting algorithm

In this article we give an algorithm for the computation of the number of rational points on the Jacobian variety of a generic ordinary hyperelliptic curve defined over a finite field of cardinality $q$ with time complexity $O(n^{2+o(1)})$ and space complexity $O(n^2)$, where $n=\log(q)$. In the latter complexity estimate the genus and the characteristic are assumed as fixed. Our algorithm forms a generalization of both, the AGM algorithm of J.-F. Mestre and the canonical lifting method of T. Satoh. We canonically lift a certain arithmetic invariant of the Jacobian of the hyperelliptic curve in terms of theta constants. The theta null values are computed with respect to a semi-canonical theta structure of level $2^\nu p$ where $\nu >0$ is an integer and p=\mathrm{char}(\F_q)>2. The results of this paper suggest a global positive answer to the question whether there exists a quasi-quadratic time algorithm for the computation of the number of rational points on a generic ordinary abelian variety defined over a finite field.Comment: 32 page

Determination of Vus: Recent Input from the Lattice

The two most precise determinations of the CKM matrix element V_us are based on the analyses of leptonic and semileptonic kaon decays. These studies also rely on the lattice QCD calculations of two hadronic parameters, namely the ratio of the kaon and pion decay constants, f_K+/f_pi+, and the kaon semileptonic vector form factor at zero momentum transfer, f_+(0). In this talk, I review the recent lattice results for these quantities, by showing that the sub-percent accuracy required by the phenomenological analyses has been reached by lattice QCD. As best estimates of the lattice calculations I quote f_K+/f_pi+ = 1.193(4) and f_+(0)=0.965(3). I also discuss some recent theoretical progress in the evaluation of the small, but phenomenologically relevant, SU(2) isospin breaking corrections.Comment: Kaon 2013 conference proceeding

Determination of V_us: recent progresses from theory

Recent experimental and theoretical results on kaon semileptonic decays have significantly improved the determination of the CKM matrix element V_us. After briefly summarizing the impact of the new experimental determinations, I will concentrate in this talk on the theoretical progresses, coming in particular from lattice QCD calculations. These results lead to the estimate |V_us|=0.2250 +- 0.0021, in good agreement with the expectation based on the determination of |V_ud| and the unitarity of the CKM matrix.Comment: Prepared for 17th Les Rencontres de Physique de la Vallee d'Aoste: Results and Perspectives in Particle Physics, La Thuile, Italy, February 27-March 5, 200

Masses and decay constants of D(s)∗D_{(s)}^* and B(s)∗B_{(s)}^* mesons in Lattice QCD with Nf=2+1+1N_f = 2 + 1 + 1 twisted-mass fermions

We present a lattice calculation of the decay constants and masses of $D_{(s)}^*$ and $B_{(s)}^*$ mesons using the gauge configurations produced by the European Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ dynamical quarks and at three values of the lattice spacing $a \sim 0.06 - 0.09$ fm. Pion masses are simulated in the range $m_{\pi} \sim 210 - 450$ MeV, while the strange and charm quark masses are close to their physical values. We computed the ratios of vector to pseudoscalar decay constants or masses for various values of the heavy-quark mass $m_h$ in the range $0.7 m_c^{phys} \lesssim m_h \lesssim 3 m_c^{phys}$. In order to reach the physical b-quark mass, we exploited the HQET prediction that, in the static limit of infinite heavy-quark mass, all the considered ratios are equal to one. We obtain: $f_{D^*}/f_{D} = 1.078(36),$ $m_{D^*}/m_{D} = 1.0769(79)$, $f_{D^*_{s}}/f_{D_{s}} = 1.087(20)$, $m_{D^*_{s}}m_{D_{s}} = 1.0751(56)$, $f_{B^*}/f_{B} = 0.958(22)$, $m_{B^*}/m_{B} = 1.0078(15)$, $f_{B^*_{s}}/f_{B_{s}} = 0.974(10)$ and $m_{B^*_{s}}/m_{B_{s}} = 1.0083(10)$. Combining them with the corresponding experimental masses from the PDG and the pseudoscalar decay constants calculated by ETMC, we get: $f_{D^*} = 223.5(8.4)~\mathrm{MeV}$, $m_{D^*} = 2013(14)~\mathrm{MeV}$, $f_{D^*_{s}} = 268.8(6.6)~\mathrm{MeV}$, $m_{D^*_{s}} = 2116(11)~\mathrm{MeV}$, $f_{B^*} = 185.9(7.2)~\mathrm{MeV}$, $m_{B^*} = 5320.5(7.6)~\mathrm{MeV}$, $f_{B^*_{s}} = 223.1(5.4)~\mathrm{MeV}$ and $m_{B^*_{s}}= 5411.36(5.3)~\mathrm{MeV}$.Comment: 7 pages, 4 figures, in proceedings of 34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton (UK). In version v2 the quality of the figures is improve

Chirally enhanced corrections to FCNC processes in the generic MSSM

Chirally enhanced supersymmetric QCD corrections to FCNC processes are investigated in the framework of the MSSM with generic sources of flavor violation. These corrections arise from flavor-changing self-energy diagrams and can be absorbed into a finite renormalization of the squark-quark-gluino vertex. In this way enhanced two-loop and even three-loop diagrams can be efficiently included into a leading-order (LO) calculation. Our corrections substantially change the values of the parameters delta^{d,LL}_{23}, delta^{d,LR}_{23}, delta^{d,RL}_{23}, and delta^{d,RR}_{23} extracted from Br[B->X_s gamma] if tan(beta) is large. We find stronger (weaker) constraints compared to the LO result for negative (positive) values of mu. The constraints on delta^{d,LR,RL}_{13} and delta^{d,LR,RL}_{23} from B_d mixing and B_s mixing change drastically if the third-generation squark masses differ from those of the first two generations. K mixing is more strongly affected by the chirally enhanced loop diagrams and even sub-percent deviations from degenerate down and strange squark masses lead to profoundly stronger constraints on delta^{d,LR,RL}_{12}.Comment: 19 pages, 10 figure

Improved Renormalization of Lattice Operators: A Critical Reappraisal

We systematically examine various proposals which aim at increasing the accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our study: the renormalization constants of the vector and axial currents and the ratio of the renormalization constants of the scalar and pseudoscalar densities. We calculate these quantities in boosted perturbation theory, with several running boosted couplings, at the "optimal" scale q*. We find that the results of boosted perturbation theory are usually (but not always) in better agreement with non-perturbative determinations of the renormalization constants than those obtained with standard perturbation theory. The finite renormalization constants of two-fermion lattice operators are also obtained non-perturbatively, using Ward Identities, both with the Wilson and the tree-level Clover improved actions, at fixed cutoff ($\beta$=6.4 and 6.0 respectively). In order to amplify finite cutoff effects, the quark masses (in lattice units) are varied in a large interval 0<am<1. We find that discretization effects are always large with the Wilson action, despite our relatively small value of the lattice spacing ($a^{-1} \simeq 3.7$ GeV). With the Clover action discretization errors are significantly reduced at small quark mass, even though our lattice spacing is larger ($a^{-1} \simeq 2$ GeV). However, these errors remain substantial in the heavy quark region. We have implemented a proposal for reducing O(am) effects, which consists in matching the lattice quantities to their continuum counterparts in the free theory. We find that this approach still leaves appreciable, mass dependent, discretization effects.Comment: 54 pages, Latex, 5 figures. Minor changes in text between eqs.(86) and (88