Degenerate Flavors Research Articles

Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals

Dirac semimetal is a phase of matter whose elementary excitation is described by the relativistic Dirac equation. In the limit of zero mass, its parity-time symmetry enforces the Dirac fermion in the momentum space, which is composed of two Weyl fermions with opposite chirality, to be non-chiral. Inspired by the flavor symmetry in particle physics, we theoretically propose a massless Dirac-like equation yet linking two Weyl fields with the identical chirality by assuming isospin symmetry, independent of the space-time rotation exchanging the two fields. Dramatically, such symmetry is hidden in certain solid-state spin-1/2 systems with negligible spin-orbit coupling, where the spin degree of freedom is decoupled with the lattice. Therefore, the existence of the corresponding quasiparticle, dubbed as flavor Weyl fermion, cannot be explained by the conventional (magnetic) space group framework. The 4-fold degenerate flavor Weyl fermion manifests linear dispersion and a Chern number of 2, leading to a robust network of topologically protected Fermi arcs throughout the Brillouin zone. For material realization, we show that the transition-metal chalcogenide CoNb3S6 with experimentally confirmed collinear antiferromagnetic order is ideal for flavor Weyl semimetal under the approximation of vanishing spin-orbit coupling. Our work reveals a counterpart of the flavor symmetry in magnetic electronic systems, leading to further possibilities of emergent phenomena in quantum materials.

Goldstone boson scattering with a light composite scalar

The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studies) on Goldstone boson scattering, employing a dilaton effective field theory (EFT) at the tree level. The EFT gives a good description of the scattering data, insofar as the magnitude of deviations between EFT and lattice data are no larger than the expected size of next-to-leading order corrections in the EFT.

Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

Dissecting the Delta I=1/2 rule at large N_c

We study the scaling of kaon decay amplitudes with the number of colours, N_c, in a theory with four degenerate flavours, N_f=4. In this scenario, two current-current operators, Q^pm , mediate Delta S=1 transitions, such as the two isospin amplitudes of non-leptonic kaon decays for Krightarrow (pi pi )_{I=0,2}, A_0 and A_2. In particular, we concentrate on the simpler Krightarrow pi amplitudes, A^pm , mediated by these two operators. A diagrammatic analysis of the large-N_c scaling of these observables is presented, which demonstrates the anticorrelation of the leading {{mathcal {O}}}(1/N_c) and {{mathcal {O}}}(N_f/N_c^2) corrections in both amplitudes. Using our new N_f=4 and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the Delta I=1/2 rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, g^pm , can be determined. A NLO estimate of the K rightarrow (pi pi )_{I=0,2} isospin amplitudes can then be derived, which is in good agreement with the experimental value.

Topological susceptibility in QCD with two flavors and 3-5 colors: A pilot study

I present a calculation of the topological susceptibility $\chi_T$ in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate flavors of fermions. The results lie on a common curve when expressed in terms of the combination $N_c m_{PS}^2 t_0$ where $m_{PS}$ is the pseudoscalar meson mass and $t_0$ is the flow parameter. $\chi_T$ approaches its quenched value as the pseudoscalar mass becomes large. The lattice simulations use clover fermions. They are done at a single lattice spacing, roughly matched across $N_c$, and over a restricted range of fermion masses.

Nucleon Electromagnetic Structure from Lattice QCD

We present an evaluation of nucleon to Δ electromagnetic form factors within Lattice QCD. The EMR and CMR ratios are calculated both in the quenched theory and using two degenerate flavors of dynamical Wilson fermions. We obtain values in qualitative agreement to experiment. In addition, we evaluate the isovector Sachs electromagnetic form factors of the nucleon both in the quenched and unquenched theory for momentum transfer squared in the range between 0.1 and 2 GeV2. The nucleon magnetic moment and r.m.s. radii are obtained using chiral effective theory to extrapolate to the physical pion mass.

Calculating the equation of state of dense quark-gluon plasma using the complex Langevin equation

The pressure and energy density of the quark-gluon plasma at finite baryon chemical potential are calculated using the Complex Langevin equation. The stout smearing procedure is generalized for the SL(3,$\mathcal{C}$) manifold allowing the usage of an improved action in the Complex Langevin setup. Four degenerate flavors of staggered quarks with $m_\pi=500-700$ MeV are used with a tree-level Symanzik improved gauge action on $16^3 \times 8 $ lattices. Results are compared to the Taylor expansion and good agreement is found for small chemical potentials.

Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model, with two, three degenerate flavors (Nf = 2, 3) and two light plus one heavier flavor (Nf = 2 + 1). It is shown that in quark mass plane (mu/d − ms) chiral phase transition is second order at a certain critical line, by which the whole plane is divided into first order and crossover regions. The critical exponents β and δ, describing critical behavior of chiral condensate along temperature axis and light quark mass axis, are extracted both numerically and analytically. The model gives the critical exponents of the values beta =frac{1}{2},delta =3 and beta =frac{1}{3},delta =3 for Nf = 2 and Nf = 3 respectively. For Nf = 2 + 1, in small strange quark mass (ms) region, the phase transitions for strange quark and u/d quarks are strongly coupled, and the critical exponents are beta =frac{1}{3},delta =3 ; when ms is larger than ms,t = 0.290 GeV, the dynamics of light flavors (u, d) and strange quarks decoupled and the critical exponents for ūu and overline{d}d becomes beta =frac{1}{2},delta =3 , exactly the same as Nf = 2 result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at ms,t = 0.290 GeV, at which beta =frac{1}{4},delta =5 . In some sense, the current results is still at mean field level, and we also showed the possibility to go beyond mean field approximation by including the higher power of scalar potential and the temperature dependence of dilaton field, which might be reasonable in a full back-reaction model. The current study might also provide reasonable constraints on constructing a realistic holographic QCD model, which could describe both chiral dynamics and glue-dynamics correctly.

Single flavour optimisations to Hybrid Monte Carlo

It has become increasingly important to include one or more individual flavours of dynamical fermion in lattice QCD simulations. This is due in part to the advent of QCD+QED calculations, where isospin symmetry breaking means that the up, down, and strange quarks must be treated separately. These single-flavour pseudofermions are typically implemented as rational approximations to the inverse of the fermion matrix, using the technique known as Rational Hybrid Monte Carlo (RHMC). Over the years, a wide range of methods have been developed for accelerating simulations of two degenerate flavours of pseudofermion, while there are comparatively fewer such techniques for single-flavour pseudofermions. Here, we investigate two different filtering methods that can be applied to RHMC for simulating single-flavour pseudofermions, namely polynomial filtering (PF-RHMC), and filtering via truncations of the ordered product (tRHMC). A novel integration step-size tuning technique based on the characteristic scale is also introduced. Studies are performed on two different lattice volumes, demonstrating that one can achieve significant reductions in the computational cost of single-flavour simulations with these filtering techniques.

Domain wall fermion QCD with the exact one flavor algorithm

Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$, where $\mathscr{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $\mathscr{D}^{\dagger} \mathscr{D}$ --- in particular, no square root is necessary --- enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors --- such as the strange or charm --- computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $\Delta I = 1/2$ $K \rightarrow \pi \pi$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $\mathscr{D}$, and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to re-use the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2+1 flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.

Single flavour filtering for RHMC in BQCD

Filtering algorithms for two degenerate quark flavours have advanced to the point that, in 2+1 flavour simulations, the cost of the strange quark is significant compared with the light quarks. This makes efficient filtering algorithms for single flavour actions highly desirable, in particular when considering 1+1+1 flavour simulations for QED+QCD. Here we discuss methods for filtering the RHMC algorithm that are implemented within BQCD, an open-source Fortran program for Hybrid Monte Carlo simulations.

Electromagnetic corrections to the hadronic vacuum polarization of the photon within QEDL and QEDM

We compute the leading QED corrections to the hadronic vacuum polarization (HVP) of the photon, relevant for the determination of leptonic anomalous magnetic moments, al. We work in the electroquenched approximation and use dynamical QCD configurations generated by the CLS initiative with two degenerate flavors of nonperturbatively O(a)-improved Wilson fermions. We consider QEDL and QEDM to deal with the finite-volume zero modes. We compare results for the Wilson loops with exact analytical determinations. In addition we make sure that the volumes and photon masses used in QEDM are such that the correct dispersion relation is reproduced by the energy levels extracted from the charged pions two-point functions. Finally we compare results for pion masses and the HVP between QEDL and QEDM. For the vacuum polarization, corrections with respect to the pure QCD case, at fixed pion masses, turn out to be at the percent level.

Chiral phase transition of three flavor QCD with nonzero magnetic field using standard staggered fermions

Lattice simulations for (2+1)-flavor QCD with external magnetic field demon-strated that the quark mass is one of the important parameters responsible for the (inverse) magnetic catalysis. We discuss the dependences of chiral condensates and susceptibilities, the Polyakov loop on the magnetic field and quark mass in three degenerate flavor QCD. The lattice simulations are performed using standard staggered fermions and the plaquette action with spatial sizes Nσ = 16 and 24 and a fixed temporal size Nτ = 4. The value of the quark masses are chosen such that the system undergoes a first order chiral phase transition and crossover with zero magnetic field. We find that in light mass regime, the quark chiral condensate undergoes magnetic catalysis in the whole temperature region and the phase transition tend to become stronger as the magnetic field increases. In crossover regime, deconfinement transition temperature is shifted by the magnetic field when quark mass ma is less than 0:4. The lattice cutoff effects are also discussed.

Investigation of the scalar spectrum in SU (3) with eight degenerate flavors

The Lattice Strong Dynamics collaboration is investigating the properties of a SU(3) gauge theory with [Formula: see text] light fermions on the lattice. We measure the masses of the lightest pseudoscalar, scalar and vector states using simulations with the nHYP staggered-fermion action on large volumes and at small fermion masses, reaching [Formula: see text]. The axial-vector meson and the nucleon are also studied for the same range of fermion masses. One of the interesting features of this theory is the dynamical presence of a light flavor-singlet scalar state with [Formula: see text] quantum numbers that is lighter than the vector resonance and has a mass consistent with the one of the pseudoscalar state for the whole fermion mass range explored. We comment on the existence of such state emerging from our lattice simulations and on the challenges of its analysis. Moreover we highlight the difficulties in pursuing simulations in the chiral regime of this theory using large volumes.

Theta dependence in holographic QCD

We study the effects of the CP-breaking topological θ-term in the large Nc QCD model by Witten, Sakai and Sugimoto with Nf degenerate light flavors. We first compute the ground state energy density, the topological susceptibility and the masses of the lowest lying mesons, finding agreement with expectations from the QCD chiral effective action. Then, focusing on the Nf = 2 case, we consider the baryonic sector and determine, to leading order in the small θ regime, the related holographic instantonic soliton solutions. We find that while the baryon spectrum does not receive mathcal{O}left(theta right) corrections, this is not the case for observables like the electromagnetic form factor of the nucleons. In particular, it exhibits a dipole term, which turns out to be vector-meson dominated. The resulting neutron electric dipole moment, which is exactly the opposite as that of the proton, is of the same order of magnitude of previous estimates in the literature. Finally, we compute the CP-violating pion-nucleon coupling constant {overline{g}}_{pi N;N} , finding that it is zero to leading order in the large Nc limit.

Adaptive aggregation-based domain decomposition multigrid for twisted mass fermions

The Adaptive Aggregation-based Domain Decomposition Multigrid method (arXiv:1303.1377) is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of hundred times compared to the conjugate gradient algorithm for the physical value of the pion mass. A thorough analysis of the aggregation parameters is presented, which provides a novel insight into multigrid methods for lattice QCD independently of the fermion discretization.

Axial charges of hyperons and charmed baryons usingNf=2+1+1twisted mass fermions

The axial couplings of the low lying baryons are evaluated using a total of five ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using the Iwasaki gauge action and two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values at two values of the coupling constant. The lattice spacings, determined using the nucleon mass, are $a=0.082$ fm and $a=0.065$ fm and the simulations cover a pion mass in the range of about 210 MeV to 430 MeV. We study the dependence of the axial couplings on the pion mass in the range of about 210 MeV to 430 MeV as well as the $SU(3)$ breaking effects as we decrease the light quark mass towards its physical value.

Parton Distribution Functions from Lattice QCD

We present recent results on the first moments of parton distributions using gauge configurations generated with two degenerate flavors of light twisted mass quarks with pion mass fixed approximately to its physical value. We also present a first study of the vector parton distribution function using a twisted mass ensemble at pion mass of 373 MeV.

Deconfinement transition at high isospin chemical potential and low temperature

We consider QCD with two degenerate flavors of light quarks (up and down) at asymptotically high isospin (μI) with zero baryon chemical potential (μB) and calculate for the first time a quantitative expression for the critical temperature of the deconfinement transition in this regime. At high isospin chemical potential and sufficiently low temperatures this theory becomes equivalent to a pure Yang–Mills theory and accordingly has a first order deconfinement phase transition. Although this was conjectured in a seminal paper by Son and Stephanov in the year 2001, the critical temperature of this deconfinement phase transition was not computed. This paper computes the energy scale associated with this transition as a function of the chemical potential μI by relating the parameters of the equivalent Yang–Mills theory to those of the underlying theory. We also relate the equation of state in one strongly interacting regime of QCD namely at finite isospin density to that in pure Yang–Mills, with the latter being amenable to straightforward numerical calculation. Our results for the critical temperature of deconfinement transition can be compared with future lattice calculations.

Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory

We study an SU(3) gauge theory with ${N}_{f}=8$ degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate $⟨\overline{\ensuremath{\psi}}\ensuremath{\psi}⟩$ and electroweak $S$ parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the ${N}_{f}=8$ spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do not strongly disfavor the hypothesis of mass-deformed infrared conformality. Compared to ${N}_{f}=2$ we observe a significant enhancement of $⟨\overline{\ensuremath{\psi}}\ensuremath{\psi}⟩$ relative to the symmetry breaking scale $F$, similar to the situation for ${N}_{f}=6$. The reduction of the $S$ parameter, related to parity doubling in the vector and axial-vector channels, is also comparable to our six-flavor results.