Additive Mass Renormalization Research Articles

Varieties and properties of central-branch Wilson fermions

We focus on the four-dimensional central-branch Wilson fermion, which makes good use of six species at the central branch of the Wilson Dirac spectrum and possesses the extra $U(1)_{\overline V}$ symmetry. With introducing new insights we discuss the prohibition of additive mass renormalization for all the six species, SSB of $U(1)_{\overline V}$ in strong-coupling QCD, the absence of the sign problem, and the usefulness for many-flavor QCD simulation. We then construct several varieties of the central-branch fermions and study their properties. In particular, we investigate the two-flavor version, where the Dirac spectrum has seven branches and two species live at the central branch. Although the hypercubic symmetry is broken, the other symmetries are the same as those of the original one. We study this setup in terms of lattice perturbation theory, strong-coupling QCD, the absence of sign problem, and the parameter tuning for Lorentz symmetry restoration. By comparing the properties of the original and two-flavor version, we find that the existence of hypercubic symmetry as well as $U(1)_{\overline V}$ is essential for the absence of additive mass renormalization of all the central-branch species. As the other two-flavor version, we investigate the central-branch staggered-Wilson fermion, which is obtained from the eight-flavor central-branch Wilson fermion via spin diagonalization. We argue that it is free from any additive mass renormalization and is regarded as a minimally doubled fermion with less symmetry breaking.

Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion

Abstract We develop a $(1+1)$D lattice $U(1)$ gauge theory in order to define the two-flavor massless Schwinger model, and discuss its connection with the Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, by $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\overline{V}}$, prohibits additive mass renormalization. Moreover, we show that the Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so a Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has a mixed ’t Hooft anomaly between $U(1)_{\overline{V}}$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of the Haldane conjecture. Furthermore, it gives a new and strict understanding on the parity-broken phase (Aoki phase) of the $2$D Wilson fermion.

Full O(a) improvement in electrostatic QCD

EQCD is a 3D bosonic theory containing SU(3) and an adjoint scalar, which efficiently describes the infrared, nonperturbative sector of hot QCD and which is highly amenable to lattice study. We improve the matching between lattice and continuum EQCD by determining the final unknown coefficient in the O(a) matching, an additive scalar mass renormalization. We do this numerically by using the symmetry-breaking phase transition point of the theory as a line of constant physics. This prepares the ground for a precision study of the transverse momentum diffusion coefficient C(qperp) within this theory. As a byproduct, we provide an updated version of the EQCD phase diagram.

Meson masses in electromagnetic fields with Wilson fermions

We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured $\rho$-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field-dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field-induced mixing between $\rho$-mesons and pions. We also derive Ward-Takashi identities for QCD+QED both in the continuum formulation and for (order $a$-improved) Wilson fermions.

Lattice simulations withNf=2+1improved Wilson fermions at a fixed strange quark mass

The explicit breaking of chiral symmetry of the Wilson fermion action results in additive quark mass renormalization. Moreover, flavour singlet and non-singlet scalar currents acquire different renormalization constants with respect to continuum regularization schemes. This complicates keeping the renormalized strange quark mass fixed when varying the light quark mass in simulations with $N_f=2+1$ sea quark flavours. Here we present and validate our strategy within the CLS (Coordinated Lattice Simulations) effort to achieve this in simulations with non-perturbatively order-$a$ improved Wilson fermions. We also determine various combinations of renormalization constants and improvement coefficients.

Many avatars of the Wilson fermion: a perturbative analysis

We explore different branches of the fermion doublers with Wilson fermion in perturbation theory, in the context of additive mass renormalization and chiral anomaly, and show that by appropriately averaging over suitably chosen branches one can reduce cut-off artifacts. Comparing the central branch with all other branches, we find that the central branch, among all the avatars of the Wilson fermion, is the most suitable candidate for exploring near conformal lattice field theories.

Numerical properties of staggered quarks with a taste-dependent mass term

Abstract The numerical properties of staggered Dirac operators with a taste-dependent mass term proposed by Adams [1, 2] and by Hoelbling [3] are compared with those of ordinary staggered and Wilson Dirac operators. In the free limit and on (quenched) interacting configurations, we consider their topological properties, their spectrum, and the resulting pion mass. Although we also consider the spectral structure, topological properties, locality, and computational cost of an overlap operator with a staggered kernel, we call attention to the possibility of using the Adams and Hoelbling operators without the overlap construction. In particular, the Hoelbling operator could be used to simulate two degenerate flavors without additive mass renormalization, and thus without fine-tuning in the chiral limit.

Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons

We calculate the critical value of the hopping parameter, ${\ensuremath{\kappa}}_{c}$, in lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for fermions and the Symanzik improved gluon action with 4- and 6-link loops. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. Our results are polynomial in ${c}_{\mathrm{SW}}$ (clover parameter) and cover a wide range of values for the Symanzik coefficients ${c}_{i}$. The dependence on the number of colors $N$ and the number of fermion flavors ${N}_{f}$ is shown explicitly. In order to compare our results to nonperturbative evaluations of ${\ensuremath{\kappa}}_{c}$ coming from Monte Carlo simulations, we employ an improved perturbation theory method for improved actions.

Observations on staggered fermions at nonzero lattice spacing

We show that the use of the fourth-root trick in lattice QCD with staggered fermions corresponds to a non-local theory at non-zero lattice spacing, but argue that the non-local behavior is likely to go away in the continuum limit. We give examples of this non-local behavior in the free theory, and for the case of a fixed topologically non-trivial background gauge field. In both special cases, the non-local behavior indeed disappears in the continuum limit. Our results invalidate a recent claim that at non-zero lattice spacing an additive mass renormalization is needed because of taste-symmetry breaking.

R-symmetry in the Q-exact [formula omitted] 2d lattice Wess–Zumino model

In this article we explore the R-symmetry of the ( 2 , 2 ) 2d Wess–Zumino model. We study whether or not this symmetry is approximately realized in the Q-exact lattice version of this theory. Our study is nonperturbative: it relies on Monte Carlo simulations with dynamical fermions. Irrelevant operators in the lattice action explicitly break the R-symmetry. In spite of this, it is found to be a symmetry of the effective potential. We find nonperturbative evidence that the nonrenormalization theorem of the continuum theory is recovered in the continuum limit; e.g., there is no additive mass renormalization. In our simulations we find that Fourier acceleration of the hybrid Monte Carlo algorithm allows us to avoid difficulties with critical slowing-down.

The [formula omitted] residual mass in lattice HQET to [formula omitted] order

We compute the so called residual mass in Lattice Heavy Quark Effective Theory to α s 3 order in the n f = 2 (unquenched) case. The control of this additive mass renormalization is crucial for the determination of the heavy quark mass from lattice simulations. We discuss the impact on an unquenched determination of the b-quark mass.

One loop matching coefficients for a variant overlap action and some of its simpler relatives

I present one-loop perturbative calculations of matching coefficients between matrix elements in continuum regulated QCD and lattice QCD with overlap fermions, with emphasis a recently-proposed variant discretization of the overlap. These fermions have extended (``fat link'') gauge connections. The scale for evaluation of the running coupling constant (in the context of the Lepage-Mackenzie fixing scheme) is also given. A variety of results (for additive mass renormalization, local currents, and some non-penguin four-fermion operators) for naive, Wilson, clover, and overlap actions are shown.

Erratum: Light quark masses with overlap fermions in quenched QCD [Phys. Rev. D64, 114508 (2001)

We present the results of a computation of the sum of the strange and average up-down quark masses with overlap fermions in the quenched approximation. Since the overlap regularization preserves chiral symmetry at finite cutoff and volume, no additive quark mass renormalization is required and the results are O(a) improved. Our simulations are performed at beta=6.0 and volume V=16^3X32, which correspond to a lattice cutoff of ~2 GeV and to an extension of ~1.4 fm. The logarithmically divergent renormalization constant has been computed non-perturbatively in the RI/MOM scheme. By using the K-meson mass as experimental input, we obtain (m_s + m_l)^RI(2 GeV) = 120(7)(21) MeV, which corresponds m_s^MS (2 GeV) = 102(6)(18) MeV if continuum perturbation theory and ChiPT are used. By using the GMOR relation we also obtain <psi psi>^MS(2 GeV)/N_f = - 0.0190(11)(33) GeV^3 = - [267(5)(15) MeV]^3.

Light quark masses with overlap fermions in quenched QCD

We present the results of a computation of the sum of the strange and average up-down quark masses with overlap fermions in the quenched approximation. Since the overlap regularization preserves chiral symmetry at finite cutoff and volume, no additive quark mass renormalization is required and the results are $\mathcal{O}(a)$ improved. Our simulations are performed at $\ensuremath{\beta}=6.0$ and volume ${V=16}^{3}\ifmmode\times\else\texttimes\fi{}32,$ which correspond to a lattice cutoff of $\ensuremath{\sim}2 \mathrm{GeV}$ and to an extension of $\ensuremath{\sim}1.4 \mathrm{fm}.$ The logarithmically divergent renormalization constant has been computed nonperturbatively in the RI/MOM scheme. By using the K-meson mass as experimental input, we obtain ${(m}_{s}+\mathrm{m\ifmmode \hat{}\else \^{}\fi{}}{)}^{\mathrm{RI}}(2 \mathrm{GeV})=120(7)(21) \mathrm{MeV},$ which corresponds to ${m}_{s}^{\overline{\mathrm{MS}}}(2 \mathrm{GeV})=102(6)(18) \mathrm{MeV}$ if continuum perturbation theory and $\ensuremath{\chi}\mathrm{PT}$ are used. By using the Gell-Mann\char21{}Oakes\char21{}Renner relation we also obtain $〈\overline{\ensuremath{\psi}}\ensuremath{\psi}{〉}^{\overline{\mathrm{MS}}}(2 \mathrm{GeV}{)/N}_{f}$ $=\ensuremath{-}0.0190(11)(33)$ ${\mathrm{GeV}}^{3}=\ensuremath{-}[267(5)(15) \mathrm{MeV}{]}^{3},$ where the errors are statistical and systematic respectively.

Topologically invariant transformation for lattice fermions

A transformation is devised to convert any lattice Dirac fermion operator into a Ginsparg-Wilson Dirac fermion operator. For the standard Wilson-Dirac lattice fermion operator, the transformed new operator is local, free of O( a) lattice artifacts, has correct axial anomaly in the trivial sector, and is not plagued by the notorious problems (e.g., additive mass renormalization) which occur to the standard Wilson-Dirac lattice fermion operator.

Solutions of the ginsparg-wilson relation and improved domain wall fermions

We discuss a number of lattice fermion actions solving the Ginsparg-Wilson relation. We also consider short ranged approximate solutions. In particular, we are interested in reducing the lattice artifacts, while avoiding (or suppressing) additive mass renormalization. In this context, we also arrive at a formulation of improved domain wall fermions.

Solutions of the Ginsparg-Wilson relation and improved domain wall fermions

We discuss a number of lattice fermion actions solving the Ginsparg-Wilson relation. We also consider short ranged approximate solutions. In particular, we are interested in reducing the lattice artifacts, while avoiding (or suppressing) additive mass renormalization. In this context, we also arrive at a formulation of improved domain wall fermions.