Problem In QCD Research Articles

Probing the photon emissivity of the quark-gluon plasma without an inverse problem in lattice QCD

The thermal photon emissivity of the quark-gluon plasma is determined by the in-medium spectral function of the electromagnetic current at lightlike kinematics, σ(ω). In this work, we present the first lattice QCD results on moments of σ(ω)/ω, defined by the weight function 1/(ω2+(2πTn)2), n∈Z and computed without encountering an inverse problem. We employ two dynamical flavors of O(a)-improved Wilson fermions at a temperature T≈250 MeV and perform the continuum limit. We compare our results for the first two moments to those obtained dispersively by integrating over the spectral function computed at weak coupling by Arnold, Moore and Yaffe. Published by the American Physical Society 2024

Self-learning Monte Carlo for non-Abelian gauge theory with dynamical fermions

In this paper, we develop the self-learning Monte-Carlo (SLMC) algorithm for non-Abelian gauge theory with dynamical fermions in four dimensions to resolve the autocorrelation problem in lattice QCD. We perform simulations with the dynamical staggered fermions and plaquette gauge action by both in the hybrid Monte-Carlo (HMC) and SLMC for zero and finite temperature to examine the validity of SLMC. We confirm that SLMC can reduce autocorrelation time in non-Abelian gauge theory and reproduce results from HMC. For finite temperature runs, we confirm that SLMC reproduces correct results with HMC, including higher-order moments of the Polyakov loop and the chiral condensate. Besides, our finite temperature calculations indicate that four flavor ${\mathrm{QC}}_{2}\mathrm{D}$ with $\stackrel{^}{m}=0.5$ is likely in the crossover regime in the Colombia plot.

Search for Solar Axions via Axion-Photon Coupling with the Majorana Demonstrator.

Axions were originally proposed to explain the strong-CP problem in QCD. Through axion-photon coupling, the Sun could be a major source of axions, which could be measured in solid state detection experiments with enhancements due to coherent Primakoff-Bragg scattering. The Majorana Demonstrator experiment has searched for solar axions with a set of ^{76}Ge-enriched high purity germanium detectors using a 33kg-yr exposure collected between January, 2017 and November, 2019. A temporal-energy analysis gives a new limit on the axion-photon coupling as g_{aγ}<1.45×10^{-9} GeV^{-1} (95% confidence level) for axions with mass up to 100 eV/c^{2}. This improves laboratory-based limits between about 1 eV/c^{2} and 100 eV/c^{2}.

New way to resum the lattice QCD Taylor series equation of state at finite chemical potential

Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential ${\ensuremath{\mu}}_{B}$ is a well-known method to bypass the sign problem of lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of ${\ensuremath{\mu}}_{B}$. Recently, a way to resum the contribution of the first $N$ charge density correlation functions ${D}_{1},\dots{},{D}_{N}$ to the Taylor series to all orders in ${\ensuremath{\mu}}_{B}$ was proposed in [Phys. Rev. Lett. 128, 022001 (2022)]. The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large $N$ and ${\ensuremath{\mu}}_{B}$. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order $M$, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for ${\ensuremath{\mu}}_{B}\ensuremath{\ne}0$, here we present it for the simpler case of a finite isospin chemical potential ${\ensuremath{\mu}}_{I}$ for which there is no sign problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.

Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.

Analytic study on chiral phase transition in holographic QCD

The chiral symmetry breaking (χsb) is one of the most fundamental problems in QCD. In this paper, we calculate quark condensation analytically in a holographic QCD model dual to the Einstein-Maxwell-Dilaton (EMD) system coupled to a probe scalar field. We find that the black hole phase transition in the EMD system seriously affects χsb. At small chemical potential, χsb behaves as a crossover. For large chemical potential μ > μc, χsb becomes first order with exactly the same transition temperature as the black hole phase transition by a bypass mechanism. The phase diagram we obtained is qualitatively consistent with the recent results from lattice QCD simulations and NJL models.

Confirming the existence of the strong CP problem in lattice QCD with the gradient flow

We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07~{\rm fm} < a < 0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_{n}=-0.00152(71)\ \bar\theta\ e~\text{fm}$ and $d_{p}=0.0011(10)\ \bar\theta\ e~\text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\bar\theta\right| < 1.98\times 10^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_{p} = 0.50(59)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$ and $S_{n} = -0.10(43)\times 10^{-4}\ \bar\theta\ e~\text{fm}^3$.

The SU(3) spin model with chemical potential by series expansion techniques

The SU(3) spin model with chemical potential corresponds to a simplified version of QCD with static quarks in the strong coupling regime. It has been studied previously as a testing ground for new methods aiming to overcome the sign problem of lattice QCD. In this work we show that the equation of state and the phase structure of the model can be fully determined to reasonable accuracy by a linked cluster expansion. In particular, we compute the free energy to 14-th order in the nearest neighbour coupling. The resulting predictions for the equation of state and the location of the critical end points agree with numerical determinations to mathcal{O} (1%) and mathcal{O} (10%), respectively. While the accuracy for the critical couplings is still limited at the current series depth, the approach is equally applicable at zero and non-zero imaginary or real chemical potential, as well as to effective QCD Hamiltonians obtained by strong coupling and hopping expansions.

Quintessential inflation with a trap and axionic dark matter

We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling between the inflaton and the Peccei-Quinn (PQ) field which terminates the roll of the runaway inflaton and traps the latter at an enhanced symmetry point (ESP), thereby breaking the PQ symmetry. The kinetic density of the inflaton is transferred to the newly created thermal bath of the hot big bang due to the decay of PQ particles. The model successfully accounts for the observations of inflation and dark energy without any fine-tuning, while also resolving the strong CP problem of QCD and generating axionic dark matter, without isocurvature perturbations. Trapping the inflaton at the ESP ensures that the model does not suffer from the infamous 5th force problem, which typically plagues quintessence.

Search of QCD phase transition points in the canonical approach of the NJL model

We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.

Controlling the model sign problem via the path optimization method: Monte Carlo approach to a QCD effective model with Polyakov loop

We apply the path optimization method to a QCD effective model with the Polyakov loop at finite density to circumvent the model sign problem. The Polyakov-loop extended Nambu--Jona-Lasinio model is employed as the typical QCD effective model and then the hybrid Monte-Carlo method is used to perform the path integration. To control the sign problem, the path optimization method is used with complexification of temporal gluon fields to modify the integral path in the complex space. We show that the average phase factor is well improved on the modified integral-path compared with that on the original one. This indicates that the complexification of temporal gluon fields may be enough to control the sign problem of QCD in the path optimization method.

$$N^*$$ Structure and Strong QCD

In attempting to match QCD with Nature, it is necessary to confront the many complexities of strong, nonlinear dynamics in relativistic quantum field theory, e.g. the loss of particle number conservation, the frame and scale dependence of the explanations and interpretations of observable processes, and the evolving character of the relevant degrees-of-freedom. The peculiarities of QCD ensure that it is also the only known fundamental theory with the capacity to sustain massless elementary degrees-of-freedom, gluons and quarks; and yet gluons and quarks are predicted to acquire mass dynamically so that the only massless systems in QCD are its composite Nambu-Goldstone bosons. All other everyday bound states possess nuclear-size masses, far in excess of anything that can directly be tied to the Higgs boson. These observations highlight fundamental questions within the Standard Model: what is the source of the mass for the vast bulk of visible matter in the Universe, how is its appearance connected with confinement; how is this mass distributed within hadrons and does the distribution differ from one hadron to another? This contribution sketches insights drawn using modern methods for the continuum bound-state problem in QCD, and how they have been informed by empirical information on the hadron spectrum and nucleon-to-resonance transition form factors.

A minimal scale invariant axion solution to the strong CP-problem

We present a scale-invariant extension of the Standard model allowing for the Kim-Shifman-Vainstein-Zakharov (KSVZ) axion solution of the strong CP problem in QCD. We add the minimal number of new particles and show that the Peccei-Quinn scalar might be identified with the complex dilaton field. Scale invariance, together with the Peccei-Quinn symmetry, is broken spontaneously near the Planck scale before inflation, which is driven by the Standard Model Higgs field. We present a set of general conditions which makes this scenario viable and an explicit example of an effective theory possessing spontaneous breaking of scale invariance. We show that this description works both for inflation and low-energy physics in the electroweak vacuum. This scenario can provide a self-consistent inflationary stage and, at the same time, successfully avoid the cosmological bounds on the axion. Our general predictions are the existence of colored TeV mass fermion and the QCD axion. The latter has all the properties of the KSVZ axion but does not contribute to dark matter. This axion can be searched via its mixing to a photon in an external magnetic field.

Benchmark results in the 2D lattice Thirring model with a chemical potential

We study the two dimensional lattice Thirring model in the presence of a fermion chemical po- tential. Our model is asymptotically free, contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence it is a useful toy model for QCD, especially since it too suffers from a sign problem in the auxiliary field formulation in the presence of a fermion chemical potential. In this work we formulate the model in both the world line and fermion-bag representations and show that the sign problem can be completely eliminated with open boundary conditions when the fermions are massless. Hence we are able accurately compute a variety of interesting quantities in the model, and these results could provide benchmarks for other methods that are being developed to solve the sign problem in QCD.

Diagrammatic representation of scalar QCD and sign problem at nonzero chemical potential

We consider QCD at strong coupling with scalar quarks coupled to a chemical potential. Performing the link integrals we present a diagrammatic representation of the path integral weight. It is based on mesonic and baryonic building blocks, in close analogy to fermionic QCD. Likewise, the baryon loops are subject to a manifest conservation of the baryon number. The sign problem is expected to disappear in this representation and we do confirm this for three flavors, where a scalar baryon can be built and thus a dependence on the chemical potential occurs. For higher flavor number we analyse examples for a potential sign problem in the baryon sector and conjecture that all weights are positive upon exploring the current conservation of each flavor.

Particle distribution in intense fields in a light-front Hamiltonian approach

We study the real-time evolution of an electron influenced by intense electromagnetic fields using the time-dependent basis light-front quantization (tBLFQ) framework. We focus on demonstrating the non-perturbative feature of the tBLFQ approach through a realistic application of the strong coupling QED problem, in which the electromagnetic fields are generated by an ultra-relativistic nucleus. We calculate transitions of an electron influenced by such electromagnetic fields and we show agreement with light-front perturbation theory when the atomic number of the nucleus is small. We compare tBLFQ simulations with perturbative calculations for nuclei with different atomic numbers, and obtain the significant higher-order contributions for heavy nuclei. The simulated real-time evolution of the momentum distribution of an electron evolving inside the strong electromagnetic fields exhibits significant non-perturbative corrections comparing to light-front perturbation theory calculations. The formalism used in this investigation can be extended to QCD problems in heavy ion collisions and electron ion collisions.

Sign problem in finite density lattice QCD

The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In the canonical approach, the grand partition function is written as a fugacity expansion: $Z_G(\mu,T) = \sum_n Z_C(n,T) \xi^n$, where $\xi=\exp(\mu/T)$ is the fugacity, and $Z_C(n,T)$ are given as averages over a Monte Carlo update, $\langle z_n\rangle$. We show that the complex phase of $z_n$ is proportional to $n$ at each Monte Carlo step. Although $\langle z_n\rangle$ take real positive values, the values of $z_n$ fluctuate rapidly when $n$ is large, especially in the confinement phase, which gives a limit on $n$. We discuss possible remedies for this problem.

Overcoming the sign problem in one-dimensional QCD by new integration rules with polynomial exactness

In this paper we describe a new integration method for the groups $U(N)$ and $SU(N)$, for which we verified numerically that it is polynomially exact for $N\le 3$. The method is applied to the example of 1-dimensional QCD with a chemical potential. We explore, in particular, regions of the parameter space in which the sign problem appears due the presence of the chemical potential. While Markov Chain Monte Carlo fails in this region, our new integration method still provides results for the chiral condensate on arbitrary precision, demonstrating clearly that it overcomes the sign problem. Furthermore, we demonstrate that our new method leads to orders of magnitude reduced errors also in other regions of parameter space.

On infrared problems of effective Lagrangians of massive spin 2 fields coupled to gauge fields

In this paper we analyze the interactions of massive spin-2 particles charged under both Abelian and non-Abelian group using the Porrati–Rahman Lagrangian. This theory is valid up to an intrinsic cutoff scale. Phenomenologically a theory valid up to a cutoff scale is sensible as all known higher spin particles are non-fundamental and it is shown that indeed this action can be used to estimate some relevant cross section. Such action necessarily includes Stückelberg field and therefore it is necessary to fix the corresponding gauge symmetry. We show that this theory, when the Stückelberg symmetry is gauge-fixed, possesses a non-trivial infrared problem. A gauge fixing ambiguity arises which is akin to the Gribov problem in QCD in the Abelian case as well. In some cases (such as when the space–time is the four-dimensional torus) the vacuum copies can be found analytically. A similar phenomenon also appears in the case of Proca fields. A very interesting feature of these copies is that they arise only for “large enough” gauge potentials. This opens the possibility to avoid the appearance of such gauge fixing ambiguities by using a Gribov–Zwanziger like approach.

Progress in Lattice QCD at nonzero density using the Complex Langevin equation

Recent progress in direct simulations of QCD at nonzero chemical potentials is reported upon. After a brief introduction to the sign problem in lattice QCD and a quick description of the complex Langevin equation we show recent results and discuss open questions.