Light meson physics from maximally twisted mass lattice QCD

Abstract

We present a comprehensive investigation of light meson physics using maximally twisted mass fermions for N f = 2 mass-degenerate quark flavours. By employing four values of the lattice spacing, spatial lattice extents ranging from 2.0 fm to 2.5 fm and pseudo scalar masses in the range 280 m PS 650 MeV we control the major systematic effects of our calculation. This enables us to confront our N f = 2 data with SU(2) chiral perturbation theory and extract low energy constants of the effective chiral Lagrangian and derived quantities, such as the light quark mass.

Determination of low-energy constants of Wilson chiral perturbation theory

“…In numerical simulations, maximal twist is achieved by tuning the value of the hopping parameter κ = 1/(2m 0,l + 8) to its critical value κ crit by tuning the PCAC quark mass m PCAC to zero. The expected O(a 2 ) scaling of physical observables when performing the continuum limit extrapolation has been confirmed in the quenched approximation [58][59][60][61] and with N f = 2 [62][63][64][65] and N f = 2 + 1 + 1 [7,66,67] dynamical quarks.…”

“…In this section, we again determine the LECs W 6,8 , but this time using N f = 2 flavours of Wilson twisted mass fermions and the tree-level Symanzik improved gauge action [3,65,72]. We already anticipate that a smaller set of ensembles and of measurements of the relevant pion masses are available in this case, in comparison to the N f = 2 + 1 + 1 case discussed previously.…”

“…(3.2). This effect, which is expected to vanish in physical quantities at a rate of O(a 2 ) when approaching the continuum limit, has been observed to be numerically small in most of the observables which have been analysed [7,[62][63][64][65][66] An exception to this observed small isospin breaking effects is found in the case of the neutral pseudoscalar mass. Indeed, isospin breaking induces a mass-splitting between charged and neutral pion masses.…”

“…Indeed, isospin breaking induces a mass-splitting between charged and neutral pion masses. Dedicated numerical studies indicate that while in the charged pion mass only very mild cutoff effects are present, the neutral pion mass is instead affected by significant O(a 2 ) effects [7,62,65,67,68]. An analysis based on the Symanzik expansion indicates that isospin breaking affects only a limited set of observables in a sizeable way, namely the neutral pion mass and kinematically related quantities [69,70].…”

Lattice QCD determination of m b , f B and f Bs with twisted mass Wilson fermions

“…The calculation is based on the N f = 2 gauge field configurations generated by the European Twisted Mass (ETM) Collaboration with the tree-level improved Symanzik gauge action [9] and the twisted mass quark action [10] at maximal twist, discussed in detail in [11][12][13][14][15][16][17]. We simulated N f = 2 mass-degenerate dynamical quarks, whose mass is eventually extrapolated to the physical isospin averaged mass of the up and down quarks, m u/d .…”