On the spectral density of the Wilson operator

We summarize our recent determination [1] of the spectral density of the Wilson operator in the p-regime of Wilson chiral perturbation theory. We discuss the range of validity of our formula and a possible extension to our computation in order to better understand the behaviour of the spectral density in a finite volume close to the threshold.Comment: 7 pages, 2 figures, Proceedings for the XXIX International Symposium on Lattice Field Theor

Corrections to the Banks-Casher relation with Wilson quarks

The Banks-Casher relation links the spectral density of the Dirac operator with the existence of a chiral condensate and spontaneous breaking of chiral symmetry. This relation receives corrections from a finite value of the quark mass, a finite space-time volume and, if evaluated on a discrete lattice, from the finite value of the lattice spacing a. We present a status report of a determination of these corrections for Wilson quarks.Comment: 6 pages, 4 figures, Chiral Dynamics 2012 proceedin

The epsilon regime with twisted mass Wilson fermions

We investigate the leading lattice spacing effects in mesonic two-point correlators computed with twisted mass Wilson fermions in the epsilon-regime. By generalizing the procedure already introduced for the untwisted Wilson chiral effective theory, we extend the continuum chiral epsilon expansion to twisted mass WChPT. We define different regimes, depending on the relative power counting for the quark masses and the lattice spacing. We explicitly compute, for arbitrary twist angle, the leading O(a^2) corrections appearing at NLO in the so-called GSM^* regime. As in untwisted WChPT, we find that in this situation the impact of explicit chiral symmetry breaking due to lattice artefacts is strongly suppressed. Of particular interest is the case of maximal twist, which corresponds to the setup usually adopted in lattice simulations with twisted mass Wilson fermions. The formulae we obtain can be matched to lattice data to extract physical low energy couplings, and to estimate systematic uncertainties coming from discretization errors.Comment: 26 pages, 3 figure

Beyond-the-Standard-Model matrix elements with the gradient flow

At the Forschungszentrum Juelich (FZJ) we have started a long-term program that aims to determine beyond-the-Standard-Model (BSM) matrix elements using the gradient flow, and to understand the impact of BSM physics in nucleon and nuclear observables. Using the gradient flow, we propose to calculate the QCD component of key beyond the Standard Model (BSM) matrix elements related to quark and strong theta CP violation and the strange content within the nucleon. The former set of matrix elements impacts our understanding of Electric Dipole Moments (EDMs) of nucleons and nuclei (a key signature of BSM physics), while the latter contributes to elastic recoil of Dark Matter particles off nucleons and nuclei. If successful, these results will lay the foundation for extraction of BSM observables from future low-energy, high-intensity and high-accuracy experimental measurements.Comment: 7 pages, 2 figures, presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014). Correct version of proceedings. Different wording of few paragraphs and different notation on few formulas. Added 1 referenc

HMC algorithm with multiple time scale integration and mass preconditioning

We describe a new HMC algorithm variant we have recently introduced and extend the published results by preliminary results of a simulation with a pseudo scalar mass value of about 300 MeV. This new run confirms our expectation that simulations with such pseudo scalar mass values become feasible and affordable with our HMC variant. In addition we discuss simulations from hot and cold starts at a pseudo scalar mass value of about 300 MeV, which we performed in order to test for possible meta-stabilities.Comment: 6 pages, Talk presented at Lattice 2005 (machines and algorithms

Renormalization constants of local operators within the Schr\"odinger functional scheme

We define, within the Schr\"odinger functional (SF) scheme, the matrix elements of the twist-2 operators corresponding to the first two moments of non-singlet parton density, and the first moment of singlet parton densities. We perform a lattice one-loop calculation that fixes the relation between the SF scheme and other common schemes and shows the main source of lattice artefacts. Few remarks on the improvement case are added.Comment: Presented at LATTICE99, 3 page

Scaling test of quenched Wilson twisted mass QCD at maximal twist

We present the results of an extended scaling test of quenched Wilson twisted mass QCD. We fix the twist angle by using two definitions of the critical mass, the first obtained by requiring the vanishing of the pseudoscalar meson mass m_PS for standard Wilson fermions and the second by requiring restoration of parity at non-zero value of the twisted mass mu and subsequently extrapolating to mu=0. Depending on the choice of the critical mass we simulate at values of beta in [5.7,6.45], for a range of pseudoscalar meson masses 250 MeV < m_PS < 1 GeV and we perform the continuum limit for the pseudoscalar meson decay constant f_PS and various hadron masses (vector meson m_V, baryon octet m_oct and baryon decuplet m_dec) at fixed value of r_0 m_PS. For both definitions of the critical mass, lattice artifacts are consistent with O(a) improvement. However, with the second definition, large O(a^2) discretization errors present at small quark mass with the first definition are strongly suppressed. The results in the continuum limit are in very good agreement with those from the Alpha and CP-PACS Collaborations.Comment: 6 pages, Talk presented at Lattice 2005, Dublin, 25-30 July 200

Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the relative power counting $m\sim a \Lambda_{\rm QCD}^2$: in this situation discretisation effects can be treated as perturbation of the continuum behaviour. While this framework fails to describe lattice spectral density close to the threshold, it allows nevertheless to investigate important properties of the spectrum of the Wilson Dirac operator. We discuss the range of validity of our results and the possible implications in understanding the phase diagram of Wilson fermions.Comment: 27 pages, 4 figures; few typos corrected, added footnote, published versio

Expansion coefficient of the pseudo-scalar density using the gradient flow in lattice QCD

We use the Yang-Mills gradient flow to calculate the pseudo-scalar expansion coefficient $c_P^*(t_f)$. This quantity is a key ingredient to obtaining the chiral condensate and strange quark content of the nucleon using the Lattice QCD formulation, which can ultimately determine the spin independent (SI) elastic cross section of dark matter models involving WIMP-nucleon interactions. The goal, using the gradient flow, is to renormalize the chiral condensate and the strange content of the nucleon without a power divergent subtraction. Using Chiral symmetry and the small flow time expansion of the gradient flow, the scalar density at zero flow time can be related to the pseudo-scalar density at non zero flow time. By computing the flow time dependance of the pseudo-scalar density over multiple lattices box sizes, lattice spacings and pion masses, we can obtain the scalar density of the nucleon. Our lattice ensembles are $N_{f}=2+1$, PCAC-CS gauge field configurations, varying over $m_{\pi}\approx \{410,570,700\}$~MeV at $a=0.0907$~fm, with additional ensembles that vary $a\approx \{0.1095,0.0936,0.0684\}$~fm at $m_{\pi} \approx 700$~MeV