Wilson Twisted Mass Fermions Research Articles

Finite temperature QCD phase transition and its scaling window from Wilson twisted mass fermions

We study the properties of finite temperature QCD using lattice simulations with Nf = 2 + 1 + 1 Wilson twisted mass fermions for pion masses from physical up to heavy quark regime. In particular, we investigate the scaling properties of the chiral phase transition close to the chiral limit. We found compatibility with O(4) universality class for pion masses up to physical and in the temperature range [120 : 300] MeV. We also discuss other alternatives, including mean field behaviour or Z2 scaling. We provide an estimation of the critical temperature in the chiral limit, T0 = 134−4+6 MeV, which is stable against various scaling scenarios.

QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions

We study the scaling properties of the finite temperature QCD phase transition, for light quark masses ranging from the heavy quark regime to their physical values. The lattice results are obtained in the fixed scale approach from simulations of Nf=2+1+1 flavours of Wilson fermions at maximal twist. We identify an order parameter free from the linear contributions in mass due to additive renormalization and regular terms in the Equation of State, which proves useful for the assessment of the hypothesized universal behaviour. We find compatibility with the 3D O(4) universality class for the physical pion mass and temperatures 120 MeV ≲T≲300 MeV. We discuss violation of scaling at larger masses and a possible cross-over to mean field behaviour. The chiral extrapolation T0=134−4+6 MeV of the pseudocritical temperature is robust against predictions of different universality classes and consistent with its estimate from the O(4) Equation of State for the physical pion mass.

Lattice continuum-limit study of nucleon parton quasidistribution functions

The parton quasidistribution functions approach provides a path to computing parton distribution functions (PDFs) using lattice QCD. This approach requires matrix elements of a power-divergent operator in a nucleon at high momentum and one generically expects discretization effects starting at first order in the lattice spacing $a$. Therefore, it is important to demonstrate that the continuum limit can be reliably taken and to understand the size and shape of lattice artifacts. In this work, we report a calculation of isovector unpolarized and helicity PDFs using lattice ensembles with ${N}_{f}=2+1+1$ Wilson twisted mass fermions, a pion mass of approximately 370 MeV, and three different lattice spacings. Our results show a significant dependence on $a$, and the continuum extrapolation produces a better agreement with phenomenology. The latter is particularly true for the antiquark distribution at small momentum fraction $x$, where the extrapolation changes its sign.

Finite temperature QCD with $$N_f=2+1+1$$ Wilson twisted mass fermions at physical pion, strange and charm masses

We discuss recent progress in studying Quantum Chromodynamics at finite temperature using $N_f=2+1+1$ Wilson twisted mass fermions. Particular interest is in QCD symmetries and their breaking and restoration. First, we discuss the behaviour of the $\eta'$ meson at finite temperature, which is tightly connected to the axial and chiral symmetries. The results suggest a small decrease of the $\eta'$ mass in the pseudo-critical region coming close to the non-anomalous contribution and subsequent growth at large temperatures. Second, we present the first results of lattice simulations of Quantum Chromodynamics with $N_f=2+1+1$ twisted mass Wilson fermions at physical pion, strange and charm masses. We estimate the chiral pseudo-critical temperatures for different observables. Our preliminary results are consistent with a second order transition in the chiral limit, however other scenarios are not excluded.

Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field

Parton quasidistribution functions provide a path toward an abinitio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the modified minimal subtraction (MS[over ¯]) scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters, we show the effect of renormalization on nucleon matrix elements with a pion mass of approximately 370MeV and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Flavor-singlet meson decay constants from Nf=2+1+1 twisted mass lattice QCD

We present an improved analysis of our lattice data for the $\eta$--$\eta'$ system, including a correction of the relevant correlation functions for residual topological finite size effects and employing consistent chiral and continuum fits. From this analysis we update our physical results for the masses $M_\eta=557(11)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $M_{\eta'}=911(64)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $\phi=38.8(2.2)_\mathrm{stat}(2.4)_{\chi\mathrm{PT}}^\circ$ in excellent agreement with other results from phenomenology. Similarly, we include an analysis for the decay constant parameters, leading to $f_l=125(5)_\mathrm{stat}(6)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $f_s=178(4)_\mathrm{stat}(1)_{\chi\mathrm{PT}}\,\mathrm{MeV}$. The second error reflects the uncertainty related to the chiral extrapolation. The data used for this study has been generated on gauge ensembles provided by the European Twisted Mass Collaboration with $N_f=2+1+1$ dynamical flavors of Wilson twisted mass fermions. These ensembles cover a range of pion masses from $220\,\mathrm{MeV}$ to $500\,\mathrm{MeV}$ and three values of the lattice spacing. Combining our data with a prediction from chiral perturbation theory, we give an estimate for the physical $\eta,\eta' \rightarrow \gamma\gamma$ decay widths and the singly-virtual $\eta,\eta'\rightarrow\gamma\gamma^*$ transition form factors in the limit of large momentum transfer.

The η′ meson at the physical point with Nf = 2 Wilson twisted mass fermions

We present results for the η′ meson and the topological susceptibility in Nf = 2 flavour lattice QCD. The results are obtained using Wilson twisted mass fermions at maximal twist with pion masses ranging from 340 MeV down to the physical point. A comparison to literature values is performed giving a handle on discretisation effects.

First physics results at the physical pion mass from Nf=2 Wilson twisted mass fermions at maximal twist

We present physics results from simulations of QCD using ${N}_{f}=2$ dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations are enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, $a\ensuremath{\approx}0.09\text{ }\text{ }\mathrm{fm}$. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the $\mathrm{\ensuremath{\Delta}}$ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.

Position space method for the nucleon magnetic moment in lattice QCD

The extraction of the magnetic form factor of the nucleon at zero momentum transfer is usually performed by adopting a parametrization for its momentum dependence and fitting the results obtained at finite momenta. We present a position space method that allows us to remove the momentum prefactor in the form factor decomposition and hence compute the magnetic form factor directly at zero momentum without the need to assume a functional form for its momentum dependence. The method is explored on one ensemble using $N_f=2+1+1$ Wilson twisted mass fermions with a light quark mass corresponding to $M_\pi\approx373\mathrm{GeV}$ and a lattice spacing of $a\approx0.082\mathrm{fm}$. We obtain results for the isovector magnetic moment and for the proton and neutron magnetic moments. The value we find for the isovector magnetic moment is larger as compared to fitting the form factor at the discrete values of the lattice momentum transfers using a dipole Ansatz, bringing it closer to the experimental value.

Non-perturbative test of the Witten-Veneziano formula from lattice QCD

We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with $N_f=2+1+1$ dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU$(2)$ chiral limits we compare both sides and find good agreement within uncertainties.

Extraction of the isovector magnetic form factor of the nucleon at zero momentum

The extraction of the magnetic form factor of the nucleon at zero momentum transfer is usually performed by adopting a parametrization for its momentum dependence and fitting the results obtained at finite momenta. We present position space methods that rely on taking the derivative of relevant correlators to extract directly the magnetic form factor at zero momentum without the need to assume a functional form for its momentum dependence. These methods are explored on one ensemble using Nf = 2+1+1 Wilson twisted mass fermions.

Equation of state of quark-gluon matter from lattice QCD with two flavors of twisted mass Wilson fermions

We report on lattice QCD results for the thermodynamic equation of state of quark-gluon matter obtained with ${N}_{f}=2$ degenerate quark flavors. For the fermion field discretization we are using the Wilson twisted mass prescription. Simulations have been carried out at three values of the bare quark masses corresponding to pion masses of $\ensuremath{\sim}360$, $\ensuremath{\sim}430$ and $\ensuremath{\sim}640\text{ }\text{ }\mathrm{MeV}$. We highlight the importance of a good control of the lattice cutoff dependence of the trace anomaly which we have studied at several values of the inverse temperature ${T}^{\ensuremath{-}1}=a{N}_{\ensuremath{\tau}}$ with a timelike lattice extent up to ${N}_{\ensuremath{\tau}}=12$. We contrast our results with those of other groups obtained for ${N}_{f}=0$ and ${N}_{f}=2+1$. At low temperature we also confront them with hadron resonance gas model predictions for the trace anomaly.

Towards the equation of state of quark-gluon matter from lattice QCD with Wilson twisted mass fermions

This contribution gives an overview of a long-term study of quark-gluon matter under extreme conditions employing Euclidean lattice discretized Quantum Chromodynamics (QCD) with Wilson twisted mass fermions and improved gauge actions. The analysis relies on methods and results of the European Twisted Mass Collaboration at zero temperature. We will start for two mass-degenerate light flavour degrees of freedom with a thorough investigation of the three-dimensional phase diagram of the bare coupling and the two mass-related parameters. Then for the same case we are going to describe the search for the pseudo-critical behaviour at various quark mass values. We shall discuss the behaviour of the (pseudo-)critical temperature Tc as a function of the (charged) pion mass mπ and the difficulty to extract the chiral limit in order to establish or reject the conjectured O(4)-universality. For the two-flavour case we shall further present very recent results for the thermodynamic Equation of State at non-zero temperature. Finally we will provide a view on an ongoing first exploration of QCD thermodynamics under the inclusion of virtual strange and charm quarks at their realistic mass values.

Short distance singularities and automatic O(a) improvement: the cases of the chiral condensate and the topological susceptibility

Short-distance singularities in lattice correlators can modify their Symanzik expansion by leading to additional O($a$) lattice artifacts. At the example of the chiral condensate and the topological susceptibility, we show how to account for these lattice artifacts for Wilson twisted mass fermions and show that the property of automatic O($a$) improvement is preserved at maximal twist.

B-physics from Nf = 2 tmQCD: the Standard Model and beyond

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.

Chiral Ward identities, automatic [formula omitted] improvement and the gradient flow

Non-singlet chiral Ward identities for fermionic operators at positive flow-time are derived using standard techniques based on local chiral variations of the action and of local operators. The gradient flow formalism is applied to twisted mass fermions and it is shown that automatic O(a) improvement for Wilson twisted mass fermions at maximal twist is a property valid also at positive flow-time. A definition of the chiral condensate that is multiplicatively renormalizable and automatically O(a) improved is then derived.

Lattice investigation of the scalar mesons a 0(980) and κ using four-quark operators

We carry out an exploratory study of the isospin one a0(980) and the isospin one-half kappa scalar mesons using Nf=2+1+1 Wilson twisted mass fermions at one lattice spacing. The valence strange quark is included as an Osterwalder-Seiler fermion with mass tuned so that the kaon mass matches the corresponding mass in the unitary Nf=2+1+1 theory. We investigate the internal structure of these mesons by using a basis of four-quark interpolating fields. We construct diquark-diquark and molecular-typecinterpolating fields and analyse the resulting correlation matrices keeping only connected contributions. For both channels, the low-lying spectrum is found to be consistent with two-particle scattering states. Therefore, our analysis shows no evidence for an additional state that can be interpreted as either a tetraquark or a tightly-bound molecular state.

Quark mass and chiral condensate from the Wilson twisted mass lattice quark propagator

In this work, we report about the determination of nonperturbative OPE parameters from fits of continuum perturbation theory to the Landau gauge quark propagator. The propagators are computed numerically using lattice QCD with Nf=2 dynamical Wilson twisted mass fermions. We use four different values of the lattice spacing ranging from about 0.1 fm to about 0.05 fm as well as several quark masses per lattice spacing. This allows us to obtain continuum results for the chiral condensate and the average up/down quark mass. The main results are the average up/down quark mass m_q = 3.0(4)(2) MeV at the physical point and a value of the chiral condensate of -(299(26)(29) MeV)^3 in the chiral limit, both in the MSbar scheme at 2 GeV. We have also studied nonperturbative contaminations of our results at small values of the momenta, which are often interpreted as the contribution of the gluon condensate A^2. We do see contributions from such terms, which are, however, not stable over the order in perturbation theory.

A quenched study of the Schrödinger functional with chirally rotated boundary conditions: Applications

In a previous paper (González López, et al., 2013) [1], we have discussed the non-perturbative tuning of the chirally rotated Schrödinger functional (χSF). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in González López et al. (2013) [1] we perform scaling and universality tests analyzing the residual O(a) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the χSF we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist.

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

We present a lattice QCD determination of the b quark mass and of the B and B s decay constants, performed with N f = 2 twisted mass Wilson fermions, by simulating at four values of the lattice spacing. In order to study the b quark on the lattice, two methods are adopted in the present work, respectively based on suitable ratios with exactly known static limit and on the interpolation between relativistic data, evaluated in the charm mass region, and the static point, obtained by simulating the HQET on the lattice. The two methods provide results in good agreement. For the b quark mass in the $ \overline {\text{MS}} $ scheme and for the decay constants we obtain $ {\overline m_b}\left( {{{\overline m }_b}} \right) $ = 4.29(14) GeV, f B = 195(12) MeV, f Bs = 232(10) MeV and f Bs /f B = 1.19(5). As a byproduct of the analysis we also obtain the results for the f D and f Ds decay constants: f D = 212(8) MeV, f Ds = 248(6) MeV and f Ds /f D = 1.17(5).