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

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

A trivariate interpolation algorithm using a cube-partition searching procedure

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

Piecewise linearisation of the first order loss function for families of arbitrarily distributed random variables

We discuss the problem of computing optimal linearisation parameters for the first order loss function of a family of arbitrarily distributed random variable. We demonstrate that, in contrast to the problem in which parameters must be determined for the loss function of a single random variable, this problem is nonlinear and features several local optima and plateaus. We introduce a simple and yet effective heuristic for determining these parameters and we demonstrate its effectiveness via a numerical analysis carried out on a well known stochastic lot sizing problem

Dispersionless propagation of electron wavepackets in single-walled carbon nanotubes

We investigate the propagation of electron wavepackets in single-walled carbon nanotubes via a Lindblad-based density-matrix approach that enables us to account for both dissipation and decoherence effects induced by various phonon modes. We show that, while in semiconducting nanotubes the wavepacket experiences the typical dispersion of conventional materials, in metallic nanotubes its shape remains essentially unaltered, even in the presence of the electron-phonon coupling, up to micron distances at room temperature.Comment: 4 pages, 2 figures, accepted by Appl. Phys. Let

Diagonal automorphisms of the 22-adic ring C∗C^*-algebra

The $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$ naturally contains a copy of the Cuntz algebra $\mathcal{O}_2$ and, a fortiori, also of its diagonal subalgebra $\mathcal{D}_2$ with Cantor spectrum. This paper is aimed at studying the group ${\rm Aut}_{\mathcal{D}_2}(\mathcal{Q}_2)$ of the automorphisms of $\mathcal{Q}_2$ fixing $\mathcal{D}_2$ pointwise. It turns out that any such automorphism leaves $\mathcal{O}_2$ globally invariant. Furthermore, the subgroup ${\rm Aut}_{\mathcal{D}_2}(\mathcal{Q}_2)$ is shown to be maximal abelian in ${\rm Aut}(\mathcal{Q}_2)$. Saying exactly what the group is amounts to understanding when an automorphism of $\mathcal{O}_2$ that fixes $\mathcal{D}_2$ pointwise extends to $\mathcal{Q}_2$. A complete answer is given for all localized automorphisms: these will extend if and only if they are the composition of a localized inner automorphism with a gauge automorphism.Comment: Improved exposition and corrected some typos and inaccuracie

A look at the inner structure of the 2-adic ring C*-algebra and its automorphism groups

We undertake a systematic study of the so-called 2-adic ring C\u87-algebra Q2. This is the universal C\u87-algebra generated by a unitary U and an isometry S2 such that S2U = U2S2 and S2S\u87 2+US2S\u87 2U\u87 = 1. Notably, it contains a copy of the Cuntz algebra O2 = C\u87(S1;S2) through the injective homomorphism mapping S1 to US2. Among the main results, the relative commutant C\u87(S2)\u9c 9 Q2 is shown to be trivial. This in turn leads to a rigidity property enjoyed by the inclusion O2 ` Q2, namely the endomorphisms of Q2 that restrict to the identity on O2 are actually the identity on the whole Q2. Moreover, there is no conditional expectation from Q2 onto O2. As for the inner structure of Q2, the diagonal subalgebra D2 and C\u87(U) are both proved to be maximal abelian in Q2. The maximality of the latter allows a thorough investigation of several classes of endomorphisms and automorphisms of Q2. In particular, the semigroup of the endomorphisms xing U turns out to be a maximal abelian subgroup of Aut(Q2) topologically isomorphic with C(T;T). Finally, it is shown by an explicit construction that Out(Q2) is uncountable and non- abelian