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Register a new userReducing cutoff effects in maximally twisted lattice QCD close to the chiral limit
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When analyzed in terms of the Symanzik expansion, lattice correlators of multi-local (gauge-invariant) operators with non-trivial continuum limit exhibit in maximally twisted lattice QCD ``infrared divergent cutoff effects of the type a^{2k}/(m_pi^2)^{h}, 2kgeq hgeq 1 (k,h integers), which tend to become numerically large when the pion mass gets small. We prove that, if the action is O(a) improved a` la Symanzik or, alternatively, the critical mass counter-term is chosen in some ``optimal way, these lattice artifacts are reduced to terms that are at worst of the order a^{2}(a^2/m_pi^2)^{k-1}, kgeq 1. This implies that the continuum extrapolation of lattice results is smooth at least down to values of the quark mass, m_q, satisfying the order of magnitude inequality m_q >a^2Lambda^3_{rm QCD}.
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We present a comprehensive investigation of light meson physics using maximally twisted mass fermions for two 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 MeV to 650 MeV we control the major systematic effects of our calculation. This enables us to confront our data with chiral perturbation theory and extract low energy constants of the effective chiral Lagrangian and derived quantities, such as the light quark mass, with high precision.
Previous extrapolations of lattice QCD results for the nucleon mass to the physically relevant region of small quark masses, using chiral effective field theory, are extended and expanded in several directions. A detailed error analysis is performed. An approach with explicit delta(1232) degrees of freedom is compared to a calculation with only pion and nucleon degrees of freedom. The role of the delta(1232) for the low-energy constants of the latter theory is elucidated. The consistency with the chiral perturbation theory analysis of pion-nucleon scattering data is examined. It is demonstrated that this consistency can indeed be achieved if the delta(1232) dominance of the P-wave pion-nucleon low-energy constant c3 is accounted for. Introduction of the delta(1232) as an explicit propagating degree of freedom is not crucial in order to describe the quark-mass dependence of the nucleon mass, in contrast to the situation with spin observables of the nucleon. The dependence on finite lattice volume is shown to yield valuable additional constraints. What emerges is a consistent and stable extrapolation scheme for pion masses below 0.6 GeV.
In this contribution, a first look at simulations using maximally twisted mass Wilson fermions at the physical point is presented. A lattice action including clover and twisted mass terms is presented and the Monte Carlo histories of one run with two mass-degenerate flavours at a single lattice spacing are shown. Measurements from the light and heavy-light pseudoscalar sectors are compared to previous $N_f = 2$ results and their phenomenological values. Finally, the strategy for extending simulations to $N_f = 2 + 1 + 1$ is outlined.
Discretization effects of lattice QCD are described by Symanziks effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $sim a^n [bar g^2(a^{-1})]^{hatgamma_1} sim a^n left[frac{1}{-log(aLambda)}right]^{hatgamma_1}$. For spectral quantities, $n=d$ is given in terms of the (lowest) canonical dimension, $d+4$, of the operators in the local effective Lagrangian and $hatgamma_1$ is proportional to the leading eigenvalue of their one-loop anomalous dimension matrix $gamma^{(0)}$. We determine $gamma^{(0)}$ for Yang-Mills theory ($n=2$) and discuss consequences in general and for perturbatively improved short distance observables. With the help of results from the literature, we also discuss the $n=1$ case of Wilson fermions with perturbative O$(a)$ improvement and the discretization effects specific to the flavor currents. In all cases known so far, the discretization effects are found to disappear faster than the naive $sim a^n$ and the log-corrections are a rather weak modification -- in contrast to the two-dimensional O(3) sigma model.
Quenched QCD simulations on three volumes, $8^3 times$, $12^3 times$ and $16^3 times 32$ and three couplings, $beta=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass ($mres$) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings much larger values of $L_s$ are required to achieve a given physical value of $mres$. For $beta=6.0$ and $L_s=16$, we find $mres/m_s=0.033(3)$, while for $beta=5.7$, and $L_s=48$, $mres/m_s=0.074(5)$, where $m_s$ is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of $m_pi^2$ in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in $f_pi$ over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.
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