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

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

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

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

Lattice QCD, Flavor Physics and the Unitarity Triangle Analysis

Lattice QCD has always played a relevant role in the studies of flavor physics and, in particular, in the Unitarity Triangle (UT) analysis. Before the starting of the B factories, this analysis relied on the results of lattice QCD simulations to relate the experimental determinations of semileptonic B decays, K-Kbar and B_{d,s}-B_{d,s}bar mixing to the CKM parameters. In the last years much more information has been obtained from the direct determination of the UT angles from non-leptonic B decays. In this talk, after a presentation of recent averages of lattice QCD results, we compare the outcome of the "classical" UT analysis (UTlattice) with the analysis based on the angles determinations (UTangles). We discuss the role of the different determinations of Vub, and show that current data do not favour the value measured in inclusive decays. Finally we show that the recent measurement of Delta ms, combined with Delta md and epsilonK, allows a quite accurate extraction of the values of the hadronic parameters, BK, fBs*sqrt(B_Bs) and xi. These values, obtained "experimentally" by assuming the validity of the Standard Model, are compared with the theoretical predictions from lattice QCD.Comment: Contribution to the proceedings of HQL06, Munich, October 16th-20th 2006. 11 page

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

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

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

Higher dimensional 3-adic CM construction

We find equations for the higher dimensional analogue of the modular curve X_0(3) using Mumford's algebraic formalism of algebraic theta functions. As a consequence, we derive a method for the construction of genus 2 hyperelliptic curves over small degree number fields whose Jacobian has complex multiplication and good ordinary reduction at the prime 3. We prove the existence of a quasi-quadratic time algorithm for computing a canonical lift in characteristic 3 based on these equations, with a detailed description of our method in genus 1 and 2.Comment: 23 pages; major revie