Lattice Field Theory and Computational Particle Physics
This research program in Lattice Field Theory and Computational Particle Physics started in 2001 as a collaboration among researchers from Ferrara, Milano, Parma, Genova and the National Laboratories in Frascati. We plan to continue the collaboration in 2007. Our goal was, and still is, to develop the best possible theoretical tools and computational methods to be applied to non-perturbative QCD, to statistical mechanics and to other interesting problems, like turbulent dynamics. The programs are usually run on the most competitive computing facilities, like the available APE1000 units in Milano, an APE/next unit dedicated to the collaboration, operational since end 2005, and a number of PC clusters designed and assembled by the collaboration (Milano, Parma, Ferrara). The new APE/next machine provides a substantial boost in computing power and will significantly cut computing time. Most members of the collaboration have been or are still now actively contributing to the development of the APE project.
Last year work was focused on new lattice formulations of QCD (Milano, Parma), Stochastic perturbation theory (Parma), Supersymmetry on the lattice (Parma), QCD at nonzero temperature and density (Milano, Genova, Frascati), thermal field theory out of equilibrium (Milano, Parma), Spin models (Milano), Turbulence (Ferrara).
Here are some of the results achieved in the course of the last twelve months:
1) The first MC simulation of four quarks (two degenerate and two split, like u,d,s,c) has been performed in the formalism of twisted mass Wilson fermions, a relevant step towards fully realistic theory (a).
2) The calculation of Renormalization constants via numerical stochastic perturbation theory for quark bilinears to three loops (b).
3) The calculation of the leading coefficient in the weak coupling expansion of hot QCD pressure (c).
4) The study of the large volume limit of topological susceptibility (d).
5) The study of disorder lines in the quantum "annni" model (e).
6) The study of topological susceptibility across the finite density transition for two-colour QCD (f)
7) The introduction of a new efficient algorithm for Ising and CP(n) models (g,h).
8) A combinatorial algorithm for counting fermionic/bosonic "words" (i)
9) The high temperature expansions for the two- and four-point functions of the Euclidean $\phi^4$ model in 3 dimensions has been extendend to the to the 25th order (l)
10) A detailed numerical study of the long time dynamics of the classical phi^4 model in 3+1 dimension, providing quantitative evidence for thermalization at intermediate wavelengths through a smooth ultraviolet cascade (m)
Research program for 2007
In lattice QCD (LQCD), we aim further testing the simulation algorithms for the unquenched theory with four dynamical flavours (up, down; strange and charm, the latter two non-degenerate in mass) and possibly improving those for the two-flavour theory. In collaboration with other groups, we plan to apply these methods (using both PC's and apeNEXT or apemille) to the evaluation of meson masses and decay constants and possibly the bag parameter of the Kaon. Within the framework of unquenched NSPT computation of quark bilinears is under way. Further applications of the NSPT method may concern: evaluation of renormalization constants and improvement coefficients for a variety of LQCD actions; perturbation theory around non-trivial topological background.
We intend to continue numerical and analytical studies of the out-of-equilibrium dynamics of field theoretical models of fundamental physics. This is relevant per se, as a basic conceptual issue, as well as in view of applications to early cosmology (e.g. reheating and thermalization at the end of the inflationary era) and to present days experiments such as heavy ion collisions.
We plan to extend our work on the automated derivation and the analysis of high temperature expansions (equivalently strong coupling expansions) relevant for the study of critical properties of spin systems (or equivalently scalar field theories on a lattice).
We shall extend the ideas about the exact formulation of supersymmetry on the lattice to theories with a gauge symmetry, in particular N=1 Super Yang-Mills theory and 2-dimensional N=2 SYM theory.
We shall perform numerical simulations of the Wess-Zumino model with exact supersimmetry on the lattice. in order to check non perturbatively the WT identities. We will also try to extend our calculations to higher orders, in particular to g^3.
Lattice simulations of QCD with chemical potential (in collaboration with I.O.Stamatescu): while lattice simulations of QCD at small \mu and high temperature gradually improve, there are no studies yet at large $\mu$ and small temperatures. We will study this high density region (which are relevant for astrophysics) that can be obtained from QCD by small order hopping parameter expansion at large \mu. We will study various observables on the chemical potential and on the temperature for one and 3-flavors. Particularly interesting is the behavior of the di-quark correlators in 3-flavors QCD which becomes increasingly flat at large \mu, leading to a strongly increasing susceptibility. This may be signal for the development of a condensate with color-flavor locking. Simulations on larger lattices would be essential to check this conjecture.
We shall explore more thouroughly the highly non perturbative region above the critical point , and finite baryon density (Strongly interactive\Quark Gluon Plasma), by means of analytic continuation from imaginary mu on the MI11 apemille. (PR, GE, LNF)
We are mapping the phase diagram of QCD with a twisted mass term in the hopping, twist, coupling space. This algorithm has been implemented and tested on apeNEXT and might well become the algorithm of choice for QCD thermodynamics.(with DESY)
We will continue our study of two color QCD, with emphasys of micorscopic and topological properties. (with Humboldt-Universitata, Berlin)
We plan to higly optimise the PHMC for dynamical simulations of Nf=2+1+1 Wilson twisted mass quarks and to collect more weak matrix element data for the evaluation of non-perturbative QCD effects on the effective electroweak Hamiltonian (e.g: bar(K) - K mixing for indirect CP-violation). We intend to perform a high statistics study of the Polyakov loop in lattice gauge models. We plan to numerically study the color string effects on the interquark potential. [Numeric Stocastic Perturbation Theory (Miccio ---> Di Renzo)]
We plan to perform MonteCarlo studies of the 2d Potts model in the limiting case of q=4 states and continue the computation of high-order strong coupling expansions in lattice (non-gauge) field models. We intend to continue the study, both analytical and numerical (Montecarlo and molecular dynamics), of the selfgravitating gas, to better understand the dilute/collapses phase transition.
We intend to continue numerical and analytical studies of the out-of-equilibrium dynamics of field theoretical models of fundamental physics. In particular we plan to include quantum effects in the numerical study of thermalization and to extend to gauge theories the improved Hartree-Fock approximation.
Further details can be found in each site presentations.
a) Numerical simulation of QCD with u, d, s and c quarks in the twisted-mass Wilson formulation, T.Chiarappa, F.Farchioni, K.Jansen, I.Montvay, E.E.Scholz, L.Scorzato, T.Sudmann, C.Urbach, hep-lat/060611
b) Wilson fermions quark bilinears to three loops, F. Di Renzo, A. Mantovi, V. Miccio, C. Torrero, L. Scorzato, hep-lat//0509158
c) The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure, F. Di Renzo, M. Laine, V. Miccio, Y. Schroder, C. Torrero, hep-lat//0605042
d) B. Alles, M. D'Elia, A. Di Giacomo, ``Analyticity in theta on the lattice and the large volume limit of the topological susceptibility''
Phys Rev D 71:034503 (2005).
e) Density matrix renormalization group study of the disorder line
in the quantum annni model. M. Beccaria, M. Campostrini, A. Feo
cond-mat/0511658 Phys.Rev.B 73, 052402 (2006)
f) Behaviour of the topological susceptibility in two colour QCD across the finite density transition, B. Alles (INFN Pisa), M. D'Elia (Univ. Genoa), M. P. Lombardo (INFN Frascati)
g) Efficient Cluster Algorithm for CP(N-1) Models, B.B Beard (Christian Brothers U.), M. Pepe (INFN-Milan & Bern U.), S. Riederer, U.-J. Wiese (Bern U.)
h) A new efficient Cluster Algorithm for the Ising Model, Matthias Nyfeler, Michele Pepe, Uwe-Jens Wiese (University of Bern), hep-lat/0510040
i) Supersymmetry and Combinatorics, E. Onofri, G. Veneziano, J. Wosiek
l) P. Butera, M. Comi, "The $\phi^4(3)$ lattice field theory viewed from the high-temperature side'', Phys.Rev.B72, 014442 (2005).
m) C. Destri, H. J. de Vega, "Ultraviolet cascade in the thermalization of the classical $\phi^4$ theory in $3+1 $ dimensions", Phys. Rev. D 73, 025014 (2006).