Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory

The determination of $\vert V_{us}\vert$ from kaon semileptonic decays requires the value of the form factor $f_+(q^2=0)$, which can be calculated precisely on the lattice. We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_+(q^2)$ with three light flavors. We consider both the case of a mixed action, where the valence and sea sectors have different staggered actions, and the standard case where these actions are the same. The momentum transfer $q^2$ of the form factor is allowed to have an arbitrary value. We give results for the generic situation where the $u$, $d$, and $s$ quark masses are all different, $N_f=1+1+1$, and for the isospin limit, $N_f=2+1$. The expression we obtain for $f_+(q^2)$ is independent of the mass of the (valence) spectator quark. In the limit of vanishing lattice spacing, our results reduce to the one-loop continuum partially quenched expression for $f_+(q^2)$, which has not previously been reported in the literature for the $N_f=1+1+1$ case. Our expressions have already been used in staggered lattice analyses of $f_+(0)$, and should prove useful in future calculations as well.Comment: 33 pages, 5 figures; v2: some referencing change

Recent results from the NA48 experiment at CERN: CP violation and CKM parameter Vus

Several recent results from the NA48 experiment are presented: a measurement $|\eta_{+-}|$, search for CP violating phenomena in $K^\pm\to3\pi$ decays, and a measurement of $|V_{us}|$.Comment: A talk given at the 2007 Europhysics Conference on High Energy Physics. 3 page

Determination of the Chiral Couplings L_10 and C_87 from Semileptonic Tau Decays

Using recent precise hadronic tau-decay data on the V-A spectral function, and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10^r(M_rho) and C_87^r(M_rho). These two low-energy constants appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L_10^r(M_rho) = -(5.22\pm 0.06)10^{-3}. Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06\pm 0.39)10^{-3} and C_87^r(M_rho) = (4.89\pm 0.19)10^{-3}GeV^{-2}. In the SU(2) chiral effective theory, the corresponding low-energy coupling takes the value \overline l_5 = 13.30 \pm 0.11 at order p^4, and \overline l_5 = 12.24 \pm 0.21 at order p^6.Comment: 17 pages, 3 figures, v2: Added reference, published versio

B_K from improved staggered quarks

We compare calculations of B_K with improved staggered quarks (HYP, Asqtad) and demonstrate the improved scaling behaviour that this gives rise to over previous calculations with unimproved staggered quarks. This enables us to perform the calculation of B_K on the MILC dynamical configurations (n_f=2+1), for which we give preliminary results.Comment: 3 pages, 3 figures. Talk presented at Lattice 2004(weak), Fermilab, June 21-26, 200

Stochastic locality and master-field simulations of very large lattices

In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.Comment: Talk given at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain; LaTeX source with 6 figure

Four-point functions and kaon decays in a minimal AdS/QCD model

We study the predictions of holographic QCD for various observable four-point quark flavour current-current correlators. The dual 5-dimensional bulk theory we consider is a $SU(3)_L \times SU(3)_R$ Yang Mills theory in a slice of $AdS_5$ spacetime with boundaries. Particular UV and IR boundary conditions encode the spontaneous breaking of the dual 4D global chiral symmetry down to the $SU(3)_V$ subgroup. We explain in detail how to calculate the 4D four-point quark flavour current-current correlators using the 5D holographic theory, including interactions. We use these results to investigate predictions of holographic QCD for the $\Delta I = 1/2$ rule for kaon decays and the $B_K$ parameter. The results agree well in comparison with experimental data, with an accuracy of 25% or better. The holographic theory automatically includes the contributions of the meson resonances to the four-point correlators. The correlators agree well in the low-momentum and high-momentum limit, in comparison with chiral perturbation theory and perturbative QCD results, respectively.Comment: Published version, title changed to conform with Journal format, references and clarifying remarks added, 40 pages, 5 figure

K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2

We present the analytical results for the K -> 3 pi final state interactions at next-to-leading order (NLO) in CHPT. We also study the recent Cabibbo's proposal to measure the pi-pi scattering lenghts combination a_0-a_2 from the cusp effect in the pi^0-pi^0 energy spectrum at threshold for K^+ -> pi^0 pi^0 pi^+ and K_L -> pi^0 pi^0 pi^0$, and give the relevant formulas to describe it at NLO. For that, we use the NLO CHPT expression to fit the real part of K -> 3 pi to data while the pi-pi scattering lenghts are treated non-perturbatively. Using them, we make a quantitative estimate of the theoretical uncertaintity of the a_0-a_2 determination at NLO in our approach and obtain that it is not smaller than 5 % if added quadratically and 7 % if linearly for K^+ -> pi^0 pi^0 pi^+. One gets similar theoretical uncertainties if the neutral K_L -> pi^0 pi^0 pi^0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lenghts. All the numbers we present are in the isospin limit apart of two-pion phase space factors which are physical. We compare our results for the cusp effect with Cabibbo and Isidori's results and discuss the differences and agreements. We also comment on the apperance of the singularity at the K -> 3 pi pseudo-threshold s=(m_K-m_pi)^2 in the discontinuity that defines the cusp.Comment: 31 pages, 8 figures. v2=v3 Added the full contributions to the cusp from the real part of the discontinuity. v4 Improved text. Matches published versio