arXiv subjects

A. Vaquero

Publications and source records attributed to A. Vaquero.

23 records · Page 2Linked to original sources

arXiv2010

The Aoki phase revisited

In order to elucidate the vacuum structure of the Aoki phase, we carried out a numerical investigation of QCD with two flavours of Wilson fermions, within the p.d.f. framework and in the absence of external sources. The simulations performed at V = 44 suggest a rich vacuum structure, where the observable $i\barψγ_5ψ$ is allowed to take non-zero values of the same order of magnitude than the order parameter of the Aoki phase $i\barψγ_5τ_3ψ$. However, the simulation at higher volumes V = 6^4 suffers from large statistical errors.

hep-lat↗

arXiv2010

Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions

The Vafa-Witten arguments on the realization of parity and flavour symmetries in the QCD vacuum do not apply to two lattice regularizations of QCD which are able to reproduce the chiral anomaly: Wilson fermions and Ginsparg-Wilson fermions. We show here how using the last regularization one can get, from first principles, that the more standard order parameters for these symmetries take a vanishing vacuum expectation value for any number of flavours, if quarks have a non-vanishing mass.

hep-lat↗

arXiv2009

Understanding the Aoki phase

The vacuum structure of QCD with two degenerated flavours of Wilson fermions is discussed by means of the p.d.f. (probability distribution function) formalism. Under certain assumptions, either new phases related to Aoki's appear, characterized by a non-vanishing expectation value of the condensate $i\barψ_uγ_5ψ_u + i\barψ_dγ_5ψ_d$, enriching the standard picture of the QCD vacuum structure with Wilson fermions; or the eigenvalues of the Dirac-Wilson operator must comply with a non-trivial, infinite set of sum rules, enforcing the currently accepted structure of the Aoki vacuum. The same scenario is analyzed using the Ginsparg-Wilson regularization. In this case, the absence of any parity and/or flavour breaking phase is proved for a non-zero value of the fermion mass.

hep-lat↗

arXiv2009

QCD with two flavors of Wilson fermions: The QCD vacuum, the Aoki vacuum and other vacua

We discuss the vacuum structure of QCD with two flavors of Wilson fermions. We derive two possible scenarios: (i) If the spectral density $ρ_U(λ,κ)$ of the overlap hamiltonian in a fixed background gauge field is not symmetric in $λ$, Hermiticity is violated and Hermiticity violation effects could influence numerical determinations of the $η$ meson mass if we are not near enough to the continuum limit, where Hermiticity should be recovered; (ii) otherwise we argue that, under certain assumptions, new phases appear beside the Aoki phase, which can be characterized by a nonvanishing vacuum expectation value of $i\barψ_uγ_5ψ_u+i\barψ_dγ_5ψ_d$, and with vacuum states that cannot be connected with the Aoki vacua by parity-flavor symmetry transformations. Quenched numerical simulations suggest that the second scenario is more likely realized.

hep-lat↗

arXiv2008

Parity realization in Vector-like theories from Fermion Bilinears

We reconsider in this paper the old aim of trying to understand if the observed realization of discrete symmetries as Parity or CP in the QCD vacuum can be satisfied from first principles. We show how under the appropriate assumptions implicitely done by Vafa and Witten in their old paper on parity realization in vector-like theories, all parity and CP odd operators constructed from fermion bilinears of the form $\barψ\tilde Oψ$ should take a vanishing vacuum expectation value in a vector-like theory with N degenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the impossibility to break spontaneously the flavour symmetry in a vector-like theory plays a fundamental role.

hep-th↗