Dynamical quark mass generation

Taking inspiration from lattice QCD results, we argue that a non-perturbative mass term for fermions can be generated as a consequence of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn triggered by the explicitly breaking of chiral symmetry induced by the critical Wilson term in the action. In a pure lattice QCD-like theory this mass term cannot be separated from the unavoidably associated linearly divergent contribution. However, if QCD with a Wilson term is enlarged to a theory where also a scalar field is present, coupled to a doublet of SU(2) fermions via a Yukawa interaction, then in the phase where the scalar field takes a non-vanishing (large) expectation value, a dynamically generated and ``naturally'' light fermion mass (numerically unrelated to the expectation value of the scalar field) is seen to emerge, at a critical value of the Yukawa coupling where the symmetry of the model is maximally enhanced.Comment: 7 pages, 3 figures. Talk presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany. Submitted to "Proceedings of Science", to appear as PoS(LATTICE 2013)35

O(a^2) cutoff effects in Wilson fermion simulations

We show that the size of the O(a^2) flavour violating cutoff artifacts that have been found to affect the value of the neutral pion mass in simulations with maximally twisted Wilson fermions is controlled by a continuum QCD quantity that is fairly large and is determined by the dynamical mechanism of spontaneous chiral symmetry breaking. One can argue that the neutral pion mass is the only physical quantity blurred by such cutoff effects. O(a^2) corrections of this kind are also present in standard Wilson fermion simulations, but they can either affect the determination of the pion mass or be shifted from the latter to other observables, depending on the way the critical mass is evaluated.Comment: Contribution presented by Giancarlo Rossi on the behalf of the ETM Collaboration at Lattice 2007, the XXV International Symposium on Lattice Field Theory, held on July 30 - August 4, in Regensburg, German

Some remarks on O(a) improved twisted mass QCD

Twisted mass QCD (tmQCD) has been introduced as a solution to the problem of unphysical fermion zero modes in lattice QCD with quarks of the Wilson type. We here argue that O(a) improvement of the tmQCD action and simple quark bilinear operators can be more economical than in the standard framework. In particular, an improved and renormalized estimator of the pion decay constant in two-flavour QCD is available, given only the Sheikholeslami-Wohlert coefficient c_sw and an estimate of the critical mass m_c.Comment: Lattice2001(improvement), 3 page

Towards models with a unified dynamical mechanism for elementary particle masses

Numerical evidence for a new dynamical mechanism of elementary particle mass generation has been found by lattice simulation in a simple, yet highly non-trivial SU(3) gauge model where a SU(2) doublet of strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilson-like term. We point out that if, as a next step towards the construction of a realistic beyond-the-Standard-Model model, weak interactions are introduced, then also weak bosons get a mass by the very same non-perturbative mechanism. In this scenario fermion mass hierarchy can be naturally understood owing to the peculiar gauge coupling dependence of the non-perturbatively generated masses. Hence, if the phenomenological value of the mass of the top quark or the weak bosons has to be reproduced, the RGI scale of the theory must be much larger than $\Lambda_{QCD}$. This feature hints at the existence of new strong interactions and particles at a scale $\Lambda_T$ of a few TeV. In such a speculative framework the electroweak scale can be derived from the basic scale $\Lambda_T$ and the Higgs boson should arise as a bound state in the $WW+ZZ$ channel.Comment: 6 pages, 2 figure

Experiences with the Polynomial Hybrid Monte Carlo Algorithm

We discuss a simulation algorithm for dynamical fermions, which combines the multiboson technique with the Hybrid Monte Carlo algorithm. The algorithm turns out to give a substantial gain over standard methods in practical simulations and to be suitable for dealing with fermion zero modes in a clean and controllable way.Comment: Latex file, 1 figure, 5 pages, talk given by R.F. at the International Symposium on Lattice Field Theory, 22-26 July 1997, Edinburgh, Scotlan

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1,2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacing a. Based on the generalised transfer matrix, we define the tmQCD Schrodinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.Comment: 31 pages latex, no figure

A lattice approach to QCD in the chiral regime

Non-perturbative lattice studies of QCD in the chiral thermodynamic regime, where chiral symmetry is spontaneously broken, require to deal with almost quark zero modes in a theoretically clean and computationally efficient way. We discuss the basic features and some realistic tests of a formulation, known as lattice tmQCD, that fulfills these requirements. Based on a talk given by R. Frezzotti at the conference HEP2001 (Budapest, July 2001)Comment: Contribution to the Proceedings of the conference HEP2001 (Budapest, July 2001), to appear on JHEP-Proceedings: 11 pages, 4 figures, 1 tabl

Comparative Benchmarks of full QCD Algorithms

We report performance benchmarks for several algorithms that we have used to simulate the Schr"odinger functional with two flavors of dynamical quarks. They include hybrid and polynomial hybrid Monte Carlo with preconditioning. An appendix describes a method to deal with autocorrelations for nonlinear functions of primary observables as they are met here due to reweighting.Comment: 24 pages, 3 figures, some added discussion, version submitted to Comput. Phys. Commu

The PHMC algorithm for simulations of dynamical fermions: I -- description and properties

We give a detailed description of the so-called Polynomial Hybrid Monte Carlo (PHMC) algorithm. The effects of the correction factor, which is introduced to render the algorithm exact, are discussed, stressing their relevance for the statistical fluctuations and (almost) zero mode contributions to physical observables. We also investigate rounding-error effects and propose several ways to reduce memory requirements.Comment: Latex2e file, 4 figures, 49 page