We show that it is possible to improve the chiral behaviour and the approach to the continuum limit of correlation functions in lattice QCD with Wilson fermions by taking arithmetic averages of correlators computed in theories regularized with Wilson terms of opposite sign. Improved hadronic masses and matrix elements can be obtained by similarly averaging the corresponding physical quantities separately computed within the two regularizations. To deal with the problems related to the spectrum of the Wilson-Dirac operator, which are particularly worrisome when Wilson and mass terms are such as to give contributions of opposite sign to the real part of the eigenvalues, we propose to use twisted-mass lattice QCD for the actual computation of the quantities taking part to the averages. The choice ±π/2 for the twisting angle is particularly interesting, as O(a) improved estimates of physical quantities can be obtained even without averaging data from lattice formulations with opposite Wilson terms. In all cases little or no extra computing power is necessary, compared to simulations with standard Wilson fermions or twisted-mass lattice QCD.

In this paper we discuss how the peculiar properties of twisted mass lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of the Wilson and mass terms in the action, it is possible to completely bypass the problem of wrong chirality and parity mixings in the computation of the CP-conserving matrix elements of the ∆S = 1, 2 effective weak hamiltonian, and at the same time have a positive determinant for pairs of non-degenerate quarks, as well as absence of O(a) discretization effects in on-shell quantities with no need of improving lattice action and operators. JHEP10(2004)070 C. Absence of the mixing of Q ± V A+AV with operators of dimension six 37 C.1 The operator Q ± [0] V A+AV 37 C.2 The operator Q ± [1] V A+AV 38

We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 ÷ 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI -MOM method. The results for the quark masses converted to the MS scheme are: m ud (2 GeV) = 3.70(17) MeV, m s (2 GeV) = 99.6(4.3) MeV and m c (m c ) = 1.348(46) GeV. We obtain also the quark mass ratios m s /m ud = 26.66(32) and m c /m s = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m u /m d = 0.470(56), leading to m u = 2.36(24) MeV and m d = 5.03(26) MeV.

We present a method to evaluate on the lattice the leading isospin breaking effects due to both the small mass difference between the up and down quarks and the QED interaction. Our proposal is applicable in principle to any QCD+QED gauge invariant hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameters (m d − mu)/ΛQCD andαem, wherem f is the renormalized quark mass andαem the renormalized fine structure constant. In this paper we discuss in detail the general strategy of the method and the conventional, although arbitrary, separation of QCD from QED isospin breaking corrections. We obtain results for the pion mass splitting, M (2)(3) and for the flavour symmetry breaking parameters R and Q. We also update our previous results for the QCD isospin breaking corrections to the K 2 decay rate and for the QCD contribution to the neutron-proton mass splitting.arXiv:1303.4896v1 [hep-lat]

The maximally twisted lattice QCD action of an SU f (2) doublet of mass degenerate Wilson quarks gives rise to a real positive fermion determinant and it is invariant under the product of standard parity times the change of sign of the coefficient of the Wilson term. The existence of this spurionic symmetry implies that O(a) improvement is either automatic or achieved through simple linear combinations of quantities taken with opposite external three-momenta. We show that in the case of maximal twist all these nice results can be extended to the more interesting case of a mass non-degenerate quark pair.

We present a non-perturbative computation of the running of the coupling α s in QCD with two flavours of dynamical fermions in the Schrödinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Λ-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Λr 0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 fm. It translates into Λ (2) MS = 245(16)(16) MeV [assuming r 0 = 0.5 fm]. The last step still has to be improved to reduce the uncertainty.

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 2 π ) h , 2k ≥ h ≥ 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 à 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 2 π ) k−1 , k ≥ 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 2 Λ 3 QCD .

We present a lattice QCD computation of the b-quark mass, the B and B_s decay constants, the B-mixing bag parameters for the full four-fermion operator basis as well as determinations for \xi and f_{Bq}\sqrt{B_i^{(q)}} extrapolated to the continuum limit and to the physical pion mass. We used N_f = 2 twisted mass Wilson fermions at four values of the lattice spacing with pion masses ranging from 280 to 500 MeV. Extrapolation in the heavy quark mass from the charm to the bottom quark region has been carried out on ratios of physical quantities computed at nearby quark masses, exploiting the fact that they have an exactly known infinite mass limit. Our results are m_b(m_b, \overline{\rm{MS}})=4.29(12) GeV, f_{Bs}=228(8) MeV, f_{B}=189(8) MeV and f_{Bs}/f_B=1.206(24). Moreover with our results for the bag-parameters we find \xi=1.225(31), B_1^{(s)}/B_1^{(d)}=1.01(2), f_{Bd}\sqrt{\hat{B}_{1}^{(d)}} = 216(10) MeV and f_{Bs}\sqrt{\hat{B}_{1}^{(s)}} = 262(10) MeV. We also computed the bag parameters for the complete basis of the four-fermion operators which are required in beyond the SM theories. By using these results for the bag parameters we are able to provide a refined Unitarity Triangle analysis in the presence of New Physics, improving the bounds coming from B_{(s)}-\bar B_{(s)} mixing