arXiv subjects
Publications and source records attributed to P. Hernandez.
We report on our first experiences in simulating Neuberger valence fermions on CLS $N_f=2$ configurations with light sea quark masses and small lattice spacings. Valence quark masses are considered that allow to explore the matching to (partially quenched) chiral perturbation theory both in the $ε$- and $p$-regimes. The setup is discussed, and first results are presented for spectral observables.
We explore realizations of minimal flavour violation (MFV) for the lepton sector. We find that it can be realized within those seesaw models where a separation of the lepton number and lepton flavour violating scales can be achieved, such as type II and inverse seesaw models. We present in particular a simple implementation of the MFV hypothesis which differs in nature from those previously discussed. It allows to reconstruct the flavour structure of the model from the values of the light neutrino masses and mixing parameters, even in the presence of CP-violating phases. Experimentally reachable predictions for rare processes such as mu --> e gamma are given.
We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a~0.09,0.12 fm and two different lattice extents L~ 1.5, 2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
A new method to determine the low-energy couplings of the $ΔS=1$ weak Hamiltonian is presented. It relies on a matching of the topological poles in $1/m^2$ of three-point correlators of two pseudoscalar densities and a four-fermion operator, measured in lattice QCD, to the same observables computed in the $ε$-regime of chiral perturbation theory. We test this method in a theory with a light charm quark, i.e. with an SU(4) flavour symmetry. Quenched numerical measurements are performed in a 2 fm box, and chiral perturbation theory predictions are worked out up to next-to-leading order. The matching of the two sides allows to determine the weak low-energy couplings in the SU(4) limit. We compare the results with a previous determination, based on three-point correlators containing two left-handed currents, and discuss the merits and drawbacks of the two procedures.
We discuss a new method to determine the low-energy couplings of the $ΔS=1$ weak Hamiltonian in the $ε$-regime. It relies on a matching of the topological poles in $1/m^2$ of three-point functions of two pseudoscalar densities and a four-fermion operator computed in lattice QCD, to the same observables in the Chiral Effective Theory. We present the results of a NLO computation in chiral perturbation theory of these correlation functions together with some preliminary numerical results.
We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a large DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm quark-mass in K-->pipi amplitudes.
A recently proposed strategy to quantify the role of the charm quark mass in the $ΔI=1/2$ rule is reviewed. Results for the low-energy couplings of the $ΔS=1$ chiral effective Hamiltonian in a theory with a light charm quark (GIM limit) are obtained through a matching of three-point correlation functions computed in Chiral Perturbation Theory and in quenched lattice QCD. We observe a large $ΔI=1/2$ enhancement, which is not large enough to explain the experimental result, but suggests significant long-distance contributions to the physical $ΔI=1/2$ which are unrelated to penguin contractions or operators.
Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("epsilon-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading Delta I = 1/2 operators. We show that the epsilon-regime offers a straightforward strategy for disentangling the coefficients of the Delta I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime ML \lsim 5.0.
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
We present our preliminary results for three-point correlation functions involving the operators entering the $Δ{S}=1$ effective Hamiltonian with an active charm quark, obtained using overlap fermions in the quenched approximation. This is the first computation carried out for valence quark masses small enough so as to permit a matching to Quenched Chiral Perturbation Theory in the $ε$-regime. The commonly observed large statistical fluctuations are tamed by means of low-mode averaging techniques, combined with restrictions to individual topological sectors. We also discuss the matching of the resulting hadronic matrix elements to the effective low-energy constants for $Δ{S}=1$ transitions. This involves (a) finite-volume corrections which can be evaluated at NLO in Quenched Chiral Perturbation Theory, and (b) the short-distance renormalization of the relevant four-quark operators in discretizations based on the overlap operator. We discuss perturbative estimates for the renormalization factors and possible strategies for their non-perturbative evaluation. Our results can be used to isolate the long-distance contributions to the $ΔI=1/2$ rule, coming from physics effects around the intrinsic QCD scale.
A $β$-beam with maximum $γ=150$ (for $\helio$ ions) or $γ=250$ (for $\neon$) could be achieved at the CERN-SPS. We study the sensitivity to $θ_{13}$ and $δ$ of such a beam as function of $γ$, optimizing with the baseline constrained to CERN-Frejus (130 km), and also with simultaneous variation of the baseline. These results are compared to the {\it standard} scenario previously considered, with lower $γ=60/100$, and also with a higher $γ\sim 350$ option that requires a more powerful accelerator. Although higher $γ$ is better, loss of sensitivity to $θ_{13}$ and $δ$ is most pronounced for $γ$ below 100.
We present a strategy designed to separate several possible origins of the well-known enhancement of the Delta{I}=1/2 amplitude in non-leptonic kaon decays. In particular, we seek to disentangle the contribution of physics at the typical QCD scale (soft-gluon exchange) from the effects at the scale of the charm quark mass. This is achieved by considering QCD with an unphysically light charm quark, so that the theory possesses an approximate SU(4)_L x SU(4)_R chiral symmetry. By computing the relevant operator matrix elements and monitoring their values as the charm quark mass departs from the SU(4)-symmetric situation, the role of the charm quark can be assessed. We study the influence of the charm quark mass in Chiral Perturbation Theory. First results from lattice simulations in the SU(4)-symmetric limit are also discussed.
Suppose that the weak interaction Hamiltonian of four-flavour SU(4) chiral effective theory is known, for a small charm quark mass m_c. We study how the weak Hamiltonian changes as the charm quark mass increases, by integrating it out within chiral perturbation theory to obtain a three-flavour SU(3) chiral theory. We find that the ratio of the SU(3) low-energy constants which mediate Delta I=1/2 and Delta I=3/2 transitions, increases rather rapidly with m_c, as \sim m_c ln (1/m_c). The logarithmic effect originates from "penguin-type" charm loops, and could represent one of the reasons for the Delta I=1/2 rule.
We report on recent work on the determination of low-energy constants describing Delta{S}=1 weak transitions, in order to investigate the origins of the Delta{I}=1/2 rule. We focus on numerical techniques designed to enhance the statistical signal in three-point correlation functions computed with overlap fermions near the chiral limit.
The precision measurement and discovery potential of a neutrino factory based on a storage ring of boosted radioactive ions ($β$-beam) is re-examined. In contrast with past designs, which assume ion $γ$ factors of $\sim 100$ and baselines of L=130 km, we emphasize the advantages of boosting the ions to higher $γ$ and increasing the baseline proportionally. In particular, we consider a medium-$γ$ scenario ($γ\sim 500$, L=730 km) and a high-$γ$ scenario ($γ\sim 2000$, L = 3000 km).The increase in statistics, which grow linearly with the average beam energy, the ability to exploit the energy dependence of the signal and the sizable matter effects at this longer baseline all increase the discovery potential of such a machine very significantly.
We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating ΔI=3/2 weak operator, at next-to-leading order in finite volume SU(3)_L x SU(3)_R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g_27, which determines the ΔI = 3/2 amplitude of the weak decays K to ππas well as the kaon mixing parameter B_K in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.
We investigate a new numerical procedure to compute fermionic correlation functions at very small quark masses. Large statistical fluctuations, due to the presence of local ``bumps'' in the wave functions associated with the low-lying eigenmodes of the Dirac operator, are reduced by an exact low-mode averaging. To demonstrate the feasibility of the technique, we compute the two-point correlator of the left-handed vector current with Neuberger fermions in the quenched approximation, for lattices with a linear extent of L~1.5 fm, a lattice spacing a~0.09 fm, and quark masses down to the epsilon-regime. By matching the results with the corresponding (quenched) chiral perturbation theory expressions, an estimate of (quenched) low-energy constants can be obtained. We find agreement between the quenched values of F extrapolated from the p-regime and extracted in the epsilon-regime.
By matching 1/m^2 divergences in finite-volume two-point correlation functions of the scalar or pseudoscalar densities with those obtained in chiral perturbation theory, we derive a relation between the Dirac operator zero-mode eigenfunctions at fixed non-trivial topology and the low-energy constants of QCD. We investigate the feasibility of using this relation to extract the pion decay constant, by computing the zero-mode correlation functions on the lattice in the quenched approximation and comparing them with the corresponding expressions in quenched chiral perturbation theory.