The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example)

/pdf/volume-dependence-of-the-energy-spectrum-in-massive-quantum-21f8la269v.pdf

Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s.

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-014-2890-7.pdf

Review of lattice results concerning low-energy particle physics

Due to polarization effects, the massM of a stable particle in a quantum field theory enclosed in a large (space-like) box of sizeL and periodic boundary conditions in general differs from its infinite volume valuem. AsL increases, the finite size mass shift Δm =M−m goes to zero exponentially with a rate, which depends on the particle considered and on the spectrum of light particles in the theory. This behaviour follows from an apparently universal asymptotic formula, already presented earlier, which relates Δm to certain forward elastic scattering amplitudes. A detailed proof of this basic relation is given here to all orders of perturbation theory in arbitrary massive quantum field theories.

/pdf/volume-dependence-of-the-energy-spectrum-in-massive-quantum-2y5ny2zkkd.pdf

Volume dependence of the energy spectrum in massive quantum field theories. I. Stable particle states

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

/pdf/review-of-lattice-results-concerning-low-energy-particle-4ppyuq45zk.pdf

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG).

http://cds.cern.ch/record/177509/files/cer-000088927.pdf

Glueball masses and string tension in lattice QCD

The string and its tension in Su(3) lattice gauge theory: Towards definitive results

https://ir.lib.hiroshima-u.ac.jp/files/public/2/20315/20141016134935687340/NuclearPhysicsB_577_263.pdf

Renormalization group flow of SU(3) lattice gauge theory : Numerical studies in a two coupling space

The 0++ glueball mass in SU(3) lattice gauge theory: Towards definitive results

The Role of Center Vortices in QCD

Using a canonical formalism, we determine the equation of state and the phase diagram of eight-flavour QCD, as a function of temperature and isospin density. Two mechanisms are at work: Bose condensation of pions at high density, and deconfinement at high temperature. We study their interplay and find that on our small and coarse lattice the first order deconfinement transition appears to end at a critical point at finite density. We investigate the strength of the overlap and of the sign problems and discuss implications for the baryonic density case.

Ph. de Forcrand

Papers

The string and its tension in Su(3) lattice gauge theory: Towards definitive results

Renormalization group flow of SU(3) lattice gauge theory : Numerical studies in a two coupling space

The 0++ glueball mass in SU(3) lattice gauge theory: Towards definitive results

The Role of Center Vortices in QCD

On the phase diagram of QCD at finite isospin density