Maximal Twist Research Articles

Exploring twisted mass lattice QCD with the Clover term

It has been shown that in the twisted mass formulation of Lattice QCD at maximal twist large cutoff effects are generated when the quark mass becomes of O(a Lambda_QCD^2). In general, these effects can be suppressed in two ways: either by choosing the critical quark mass in an "optimal way", or by adding the Clover term to the twisted action. We investigate the second option by performing a quenched lattice QCD simulation with twisted Clover fermions and pion masses as low as 280 MeV. We show that the Clover term is indeed efficient in reducing the large cutoff effects. In particular, the so-called bending phenomenon observed in the determination of the pion decay constant is cured in this way. In addition, by using maximally twisted Clover fermions, we provide a non-perturbative determination of the vector current renormalization constant Z_V as well as of the non-perturbatively renormalized light quark masses. Finally, we calculate the connected contribution to the charged-neutral pseudoscalar meson mass splitting, finding that the introduction of the Clover term in the twisted action is also beneficial, in the quenched approximation, in reducing cutoff effects related to the isospin symmetry breaking at finite lattice spacing.

Strange quarks in quenched twisted mass lattice QCD

Two twisted doublets, one containing the up and down quarks and the other containing the strange quark with an $SU(2)$-flavor partner, are used for studies in the meson sector. The relevant chiral perturbation theory is presented, and quenched QCD simulations (where the partner of the strange quark is not active) are performed. Pseudoscalar meson masses and decay constants are computed; the vector and scalar mesons are also discussed. A comparison is made to the case of an untwisted strange quark, and some effects due to quenching, discretization, and the definition of maximal twist are explored.

Lattice QCD at maximal twist

In this review we discuss the general features of maximally twisted lattice QCD. In particular, we illustrate how automatic O(a) improvement can be achieved and how it is possible to set up a lattice regularization scheme where the problem of wrong chirality mixing (be it finite or infinite) affecting the computation of the matrix elements of the CP-conserving effective weak Hamiltonian is neatly avoided, while having at the same time a positive determinant even for non-degenerate quark pairs. The question of reducing the large cutoff effects that appear when the quark mass tends to zero as a consequence of parity and iso-spin breaking in the action is also addressed. It is shown that such dangerous lattice artifacts are strongly suppressed if the clover term is added to the action or, alternatively, the critical mass is chosen so as to enforce the restoration of parity.

TWISTED MASS LATTICE QCD AND HADRON PHENOMENOLOGY

Lattice QCD simulations with a twisted mass term (tmLQCD) offer solutions to problems associated with simulations using Wilson fermions and a standard mass term. A summary of recent results from quenched simulations using tmLQCD at maximal twist for the pion form factor and hadron spectrum is presented.

Observations on discretization errors in twisted-mass lattice QCD

I make a number of observations concerning discretization errors in twisted-mass lattice QCD that can be deduced by applying chiral perturbation theory including lattice artifacts. (1) The line along which the PCAC quark mass vanishes in the twisted mass-twisted mass plane makes an angle to the untwisted mass axis which is a direct measure of O(a) terms in the chiral Lagrangian, and is found numerically to be large; (2) Numerical results for pionic quantities in the mass plane show the qualitative properties predicted by chiral perturbation theory, in particular an asymmetry in slopes between positive and negative untwisted quark masses; (3) By extending the description of the ``Aoki regime'' (where m_q is of size a^2 Lambda_QCD^3) to next-to-leading order in chiral perturbation theory I show how the phase transition lines and lines of maximal twist (using different definitions) extend into this region, and give predictions for the functional form of pionic quantities; (4) I argue that the recent claim that lattice artifacts at maximal twist have apparent infrared singularities in the chiral limit results from expanding about the incorrect vacuum state. Shifting to the correct vacuum (as can be done using chiral perturbation theory) the apparent singularities are summed into non-singular, and furthermore predicted, forms. I further argue that there is no breakdown in the Symanzik expansion in powers of lattice spacing, and no barrier to simulating at maximal twist in the Aoki regime.

Quenched scaling of Wilson twisted mass fermions

We investigate the scaling behaviour of quenched Wilson twisted mass fermions at maximal twist applying two definitions of the critical mass. The first definition uses the vanishing of the pseudoscalar meson mass m_PS while the second employs the vanishing of the PCAC quark mass m_PCAC. We confirm in both cases the expected O(a) improvement. In addition, we show that the PCAC quark mass definition leads to substantially reduced O(a^2) cut-off effects even when the pseudoscalar meson mass m_PS is as small as 270 MeV. At a fixed value of m_PS we perform continuum limits for the vector meson mass m_V and for the pseudoscalar decay constant f_PS and discuss the renormalisation constant Z_V of the vector current.

Light quarks with twisted mass fermions

We investigate Wilson twisted mass fermions in the quenched approximation using different definitions of the critical bare quark mass mc to realize maximal twist and, correspondingly, automatic O(a) improvement for physical observables. A particular definition of mc is given by extrapolating the value of mc obtained from the PCAC relation at non-vanishing bare twisted quark mass μ to μ=0. Employing this improved definition of the critical mass the Wilson twisted mass formulation provides the possibility to perform reliable simulations down to very small quark masses with correspondingly small pion masses of mπ≃250 MeV, while keeping the cutoff effects of O(a2) under control.

Spectrum of quenched twisted mass lattice QCD at maximal twist

Hadron masses are computed from quenched twisted mass lattice QCD for a degenerate doublet of up and down quarks with the twist angle set to pi/2, since this maximally twisted theory is expected to be free of linear discretization errors. Two separate definitions of the twist angle are used, and the hadron masses for these two cases are compared. The flavor breaking, that can arise due to twisting, is discussed in the context of mass splittings within the Delta(1232) multiplet.

Twisted mass chiral perturbation theory at next-to-leading order

We study the properties of pions in twisted mass lattice QCD (with two degenerate flavors) using chiral perturbation theory (ChPT). We work to next-to-leading order (NLO) in a power counting scheme in which m_q ~ a \Lambda_QCD^2, with m_q the physical quark mass and a the lattice spacing. We argue that automatic O(a) improvement of physical quantities at maximal twist, which has been demonstrated in general if m_q >> a \Lambda_QCD^2, holds even if m_q ~ a \Lambda_QCD^2, as long as one uses an appropriate non-perturbative definition of the twist angle. We demonstrate this with explicit calculations, for arbitrary twist angle, of all pionic quantities that involve no more than a single pion in the initial and final states: masses, decay constants, form factors and condensates, as well as the differences between alternate definitions of twist angle. We also calculate the axial and pseudoscalar form factors of the pion, quantities which violate flavor and parity, and which vanish in the continuum limit. These are of interest because they are not automatically O(a) improved at maximal twist. They allow a determination of the unknown low energy constants introduced by discretization errors, and provide tests of the accuracy of ChPT at NLO. We extend our results into the regime where m_q ~ a^2 \Lambda_QCD^3, and argue in favor of a recent proposal that automatic O(a) improvement at maximal twist remains valid in this regime.

Twisted mass QCD,O(a)improvement, and Wilson chiral perturbation theory

We point out a caveat in the proof for automatic $\mathrm{O}(a)$ improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic $\mathrm{O}(a)$ improvement can fail unless the quark mass satisfies ${m}_{q}\ensuremath{\gg}{a}^{2}{\ensuremath{\Lambda}}_{\mathrm{Q}\mathrm{C}\mathrm{D}}^{3}$. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic $\mathrm{O}(a)$ improvement. In order to illustrate explicitly automatic $\mathrm{O}(a)$ improvement we compute the pion mass in the corresponding chiral effective theory. We consider different definitions for maximal twist and show explicitly the absence or presence of the leading $\mathrm{O}(a)$ effect, depending on the size of the quark mass.

Chirally improving Wilson fermions II. Four-quark operators

In this paper we discuss how the peculiar properties of twisted 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 $\Delta S=1,2$ effective weak Hamiltonian and at the same time have a positive determinant for non-degenerate quarks as well as full O($a$) improvement in on-shell quantities with no need of improving the lattice action and the operators.

Twisted-mass lattice QCD with mass non-degenerate quarks

The maximally twisted lattice QCD action of an SUf(2) doublet of mass degenerate Wilson quarks gives raise 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.

Fine structure of the ommatidia and the occurrence of rhabdomeric twist in the dorsal eye of male Bibio marci (Diptera, Nematocera, Bibionidae).

The ommatidia in the dorsal eye of male Bibio marci (March flies) are comprised of eight retinula cells (R 1--8). In the distal region, the open rhabdomeres of retinula cells 1--6 are arranged in a symmetrically circular pattern with their microvilli directed radially. Immediately beneath the crystalline cone, cell 7 forms a rhabdomere that is about 1 micrometer long and lies in the center of the circle formed by the rhabdomeres of cells 1--6. For the remaining length of an ommatidium it is replaced by the rhabdomere of retinula cell 8. The cell body of this retinula cell almost encloses its own rhabdomere by forming a deep invagination. Consequently, no ommatidial cavity is present. In the left eye rhabdomeres R 3, 5 and 6 first twist clockwise along their longitudinal axes, while rhabdomeres R 1, 2, 4 and 8 twist counterclockwise. Opposite twisting is observed in the right eye. The twist rate varies along the length of the rhabdomeres. In a middle region of 60 micrometers, within which the direction of twist does not change, the maximal twist rates are approximately 2 degrees--5 degrees/micrometers in R 1--6 and even higher in R 8. In a proximal region, the direction of twist is reversed, but the initial orientation of the microvilli not reestablished. Both the cross-sectional shape of the rhabdomeres and their geometric arrangement in the retinula change along with the twisting. It is substantiated that the rhabdomeric twist is not due to artifactual deformation.