Problem In QCD Research Articles

Chiral condensate in the Schwinger model with matrix product operators

Tensor network (TN) methods, in particular the matrix product states (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the nonzero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.

Complex spectrum of finite-density lattice QCD with static quarks at strong coupling

We calculate the spectrum of transfer matrix eigenvalues associated with Polyakov loops in finite-density lattice QCD with static quarks. These eigenvalues determine the spatial behavior of Polyakov loop correlations functions. Our results are valid for all values of the gauge coupling in $1+1$ dimensions, and valid in the strong-coupling region for any number of dimensions. When the quark chemical potential $\mu$ is nonzero, the spatial transfer matrix $T_s$ is non-Hermitian. The appearance of complex eigenvalues in $T_s$ is a manifestation of the sign problem in finite-density QCD. The invariance of finite-density QCD under the combined action of charge conjugation $\mathcal{C}$ and complex conjugation $\mathcal{K}$ implies that the eigenvalues of $T_s$ are either real or part of a complex pair. Calculation of the spectrum confirms the existence of complex pairs in much of the temperature-chemical potential plane. Many features of the spectrum for static quarks are determined by a particle-hole symmetry. For $\mu$ small compared to the quark mass $M$, we typically find real eigenvalues for the lowest lying states. At somewhat larger values of $\mu,$ pairs of eigenvalues may form complex-conjugate pairs, leading to damped oscillatory behavior in Polyakov loop correlation functions. However, near $\mu=M$, the low-lying spectrum becomes real again. This is a direct consequence of the approximate particle-hole symmetry at $\mu=M$ for heavy quarks. This behavior of the eigenvalues should be observable in lattice simulations and can be used as a test of lattice algorithms. Our results provide independent confirmation of results we have previously obtained in PNJL models using complex saddle points.

Axion cooling of neutron stars

Cooling simulations of neutron stars and their comparison with the data from thermally emitting x-ray sources put constraints on the properties of axions, and by extension of any light pseudoscalar dark matter particles, whose existence has been postulated to solve the strong-CP problem of QCD. We incorporate the axion emission by pair-breaking and formation processes by $S$- and $P$-wave nucleonic condensates in a benchmark code for cooling simulations as well as provide fit formulas for the rates of these processes. Axion cooling of neutron stars has been simulated for 24 models covering the mass range 1 to 1.8 solar masses, featuring nonaccreted iron and accreted light-element envelopes, and a range of nucleon-axion couplings. The models are based on an equation state predicting conservative physics of superdense nuclear matter that does not allow for the onset of fast cooling processes induced by phase transitions to non-nucleonic forms of matter or high proton concentration. The cooling tracks in the temperature vs age plane were confronted with the (time-averaged) measured surface temperature of the central compact object in the Cas A supernova remnant as well as surface temperatures of three nearby middle-aged thermally emitting pulsars.We find that the axion coupling is limited to $f_a/10^{7}\textrm{GeV} \ge (5$--$10)$, which translates into an upper bound on axion mass $m_a \le (0.06$--$0.12)~\textrm{eV}$ for Peccei-Quinn charges of the neutron $\vert C_n \vert \sim 0.04$ and proton $\vert C_p \vert \sim 0.4$ characteristic for hadronic models of axions.

Cosmological problems of the string axion alleviated by high scale SUSY of m3/2 ≃ 10–100 TeV

The string axion may provide the most attractive solution to the strong CP problem in QCD. However, the axion energy density easily exceeds the dark matter density in the present universe due to a large decay constant around 1016 GeV, unless the initial value of the axion field is finely tuned. We show that this problem is alleviated if and only if the SUSY particle mass scale is 10–100 TeV, since the decay of the saxion can produce a large enough amount of entropy after the QCD phase transition, not disturbing the BBN prediction. The saxion decay also produces a large number of the lightest SUSY particles (LSPs). As a consequence, R-parity needs to be violated to avoid the overproduction of the LSPs. The saxion field can be stabilized with relatively simple Kähler potentials, not inducing a too large axion dark radiation. Despite the large entropy production, the observed baryon number is explained by the Affleck–Dine mechanism. Furthermore, the constraint from isocurvature perturbations is relaxed, and the Hubble constant during inflation can be as large as several ×1010 GeV.

Non-global logarithms, factorization, and the soft substructure of jets

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. We also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.

CP-safe gravity mediation and muong − 2

We propose a CP-safe gravity mediation model, where the phases of the Higgs B parameter, scalar trilinear couplings and gaugino mass parameters are all aligned. Since all dangerous CP violating phases are suppressed, we are now safe to consider low-energy SUSY scenarios. As an application, we consider a gravity mediation model explaining the observed muon $g-2$ anomaly. The CP-safe property originates in two simple assumptions: SUSY breaking in the K\"ahler potential and a shift symmetry of a SUSY breaking field $Z$. As a result of the shift symmetry, the imaginary part of $Z$ behaves as a QCD axion, leading to an intriguing possibility: the strong CP problem in QCD and the SUSY CP problem are solved simultaneously.

A matrix model for QCD

Gribov's observation that global gauge fixing is impossible has led to suggestions that there may be a deep connection between gauge fixing and confinement. We find an unexpected relation between the topological nontriviality of the gauge bundle and colored states in SU (N) Yang–Mills theory, and show that such states are necessarily impure. We approximate QCD by a rectangular matrix model that captures the essential topological features of the gauge bundle, and demonstrate the impure nature of colored states explicitly. Our matrix model also allows the inclusion of the QCD θ-term, as well as to perform explicit computations of low-lying glueball masses. This mass spectrum is gapped. Since an impure state cannot evolve to a pure one by a unitary transformation, our result shows that the solution to the confinement problem in pure QCD is fundamentally quantum information-theoretic.

Structure of Lefschetz thimbles in simple fermionic systems

The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share some features with QCD. In zero-dimensional versions of the Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition. We map out a phase diagram in the complex four-fermion coupling plane using a thimble decomposition of the path integral, and demonstrate an interesting link between anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown that the approach to the chiral limit is singular because of intricate cancellation between competing thimbles, which implies the necessity to sum up multiple thimbles related by symmetry. We also consider a Chern-Simons theory with fermions in $0+1$-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term. These prototypical examples would aid future application of this framework to bona fide QCD.

The Phase Diagram of Heavy Dense QCD with Complex Langevin Simulations

The sign problem of QCD prevents standard lattice simulations to determine the phase diagram of strong interactions with a finite chemical potential directly. Complex Langevin simulations provide an alternative method to sample path integrals with complex weights. We report on our ongoing project to determine the phase diagram of QCD in the limit of heavy quarks (HDQCD) using Complex Langevin simulations.

Complex saddle points in QCD at finite temperature and density

The sign problem in QCD at finite temperature and density leads naturally to the consideration of complex saddle points of the action or effective action. The global symmetry $\mathcal{CK}$ of the finite-density action, where $\mathcal{C}$ is charge conjugation and $\mathcal{K}$ is complex conjugation, constrains the eigenvalues of the Polyakov loop operator $P$ at a saddle point in such a way that the action is real at a saddle point, and net color charge is zero. The values of ${\mathrm{Tr}}_{F}P$ and ${\mathrm{Tr}}_{F}{P}^{\ifmmode\dagger\else\textdagger\fi{}}$ at the saddle point are real but not identical, indicating the different free energy cost associated with inserting a heavy quark versus an antiquark into the system. At such complex saddle points, the mass matrix associated with Polyakov loops may have complex eigenvalues, reflecting oscillatory behavior in color-charge densities. We illustrate these properties with a simple model which includes the one-loop contribution of gluons and two flavors of massless quarks moving in a constant Polyakov loop background. Confinement-deconfinement effects are modeled phenomenologically via an added potential term depending on the Polyakov loop eigenvalues. For sufficiently large temperature $T$ and quark chemical potential $\ensuremath{\mu}$, the results obtained reduce to those of perturbation theory at the complex saddle point. These results may be experimentally relevant for the compressed baryonic matter experiment at FAIR.

Conformal symmetry of the Lange–Neubert evolution equation

The Lange–Neubert evolution equation describes the scale dependence of the wave function of a meson built of an infinitely heavy quark and light antiquark at light-like separations, which is the hydrogen atom problem of QCD. It has numerous applications to the studies of B-meson decays. We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. Generalizing this result, we show that all heavy–light evolution kernels that appear in the renormalization of higher-twist B-meson distribution amplitudes can be written in the same form.

Hadron spectroscopy and dynamics from light-front holography and conformal symmetry

To a first semiclassical approximation one can reduce the multi-parton light-front problem in QCD to an effective one-dimensional quantum field theory, which encodes the fundamental conformal symmetry of the classical QCD Lagrangian. This procedure leads to a relativistic light-front wave equation for arbitrary spin which incorporates essential spectroscopic and non-perturbative dynamical features of hadron physics. The mass scale for confinement and higher dimensional holographic mapping to AdS space are also emergent properties of this framework.

Images of the origin of mass

Recent years have brought considerable progress with studies of the bound-state problem in continuum QCD. A small part of that made with Dyson Schwinger equations is highlighted herein. Topics covered include: opportunities provided by precision experimental studies of the (far) valence region; and capitalising upon new data on hadron elastic and transition form factors.

Tera-leptons’ shadows over Sinister Universe

The role of Sinister Heavy Fermions in Glashow’s SU(3) × SU(2) × SU(2)′ × U(1) model is to offer in a unique frame relic helium-like products (an ingenious candidate to the dark matter puzzle), a solution to the See-Saw mechanism for light neutrino masses as well as to the strong CP violation problem in QCD. The Sinister model requires three additional families of leptons and quarks, but only the lightest of them, the heavy U-quark and E-electron, are stable. Apparently the final neutral heliumlike (UUUEE) state is an ideal evanescent dark-matter candidate. However, it is reached by multi-body interactions in the early Universe along a tail of more manifest secondary frozen blocks. They should be now here polluting the surrounding matter. Moreover, in opposition to effective $$U\bar U$$ pair annihilation, there is no such an early or late tera-lepton pairs suppression because: (a) electromagnetic interactions are weaker than nuclear ones and (b) the primordial helium nucleus (4He)++ is able to attract and capture (in the first three minutes) E − fixing it into a hybrid tera-helium ion trap. This leads to a pile up of (4HeE −)+ traces, a lethal compound for any Sinister Universe. This capture leaves no tera-lepton frozen in (Ep) relic, otherwise an ideal catalyzer to achieve effective late E + E − annihilations, possibly saving the model. The (4HeE −)+ Coulomb screening is also avoiding the synthesis of the desired (UUUEE) hidden dark matter gas. The (4HeE −)+ E − behave chemically like an anomalous hydrogen isotope. Also terapositronium relics (e − E +) are over-abundant, and they behave like an anomalous hydrogen atom: these gases do not fit by many orders of magnitude the known severe bounds on hydrogen anomalous isotope, making shadows hanging over a Sinister Universe. However a surprising and resolver role for Tera-Pions in UHECR astrophysics has been revealed.

Peccei-Quinn symmetry as the origin of Dirac neutrino masses

We propose a model of Dirac neutrino masses generated at one-loop level. The origin of this mass is induced from Peccei-Quinn symmetry breaking which was proposed to solve the so-called strong CP problem in QCD, therefore, the neutrino mass is connected with the QCD scale, $\Lambda_{\rm QCD}$. We also study the parameter space of this model confronting with neutrino oscillation data and leptonic rare decays. The phenomenological implications to leptonic flavor physics such as the electromagnetic moment of charged leptons and neutrinos are studied. Axion as the dark matter candidate is one of the byproduct in our scenario. Di-photon and Z-photon decay channels in the LHC Higgs search are investigated, we show that the effects of singly charged singlet scalar can be distinguished from the general two Higgs doublet model.

Average gluon and quark jet multiplicities at higher orders

We develop a new formalism for computing and including both the perturbative and nonperturbative QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new method is motivated by recent progress in timelike small-x resummation obtained in the MS¯ factorization scheme. We obtain next-to-next-to-leading-logarithmic (NNLL) resummed expressions, which represent generalizations of previous analytic results. Our expressions depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets that are compatible with regard to the jet algorithms demonstrates by its goodness how our results solve a longstanding problem of QCD. We show that the statistical and theoretical uncertainties both do not exceed 5% for scales above 10 GeV. We finally propose to use the jet multiplicity data as a new way to extract the strong-coupling constant. Including all the available theoretical input within our approach, we obtain αs(5)(Mz)=0.1199±0.0026 in the MS¯ scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of lnx terms through the NNLL level and of lnQ2 terms by the renormalization group, in excellent agreement with the present world average.

Variational approach to the calculation of [formula omitted

A long standing problem in lattice QCD has been the discrepancy between the experimental and calculated values for the axial charge of the nucleon, gA≡GA(Q2=0). Though finite volume effects have been shown to be large, it has also been suggested that excited state effects may also play a significant role in suppressing the value of gA. In this work, we apply a variational method to generate operators that couple predominantly to the ground state, thus systematically removing excited state contamination from the extraction of gA. The utility and success of this approach is manifest in the early onset of ground state saturation and the early onset of a clear plateau in the correlation function ratio proportional to gA. Through a comparison with results obtained via traditional methods, we show how excited state effects can suppress gA by as much as 8% if sources are not properly tuned or source–sink separations are insufficiently large.

The Phase Theory towards the Unification of the Forces of Nature the Heart Beat of the Universe

A new theory has been presented, for first time, called Phase Theory, which is natural evolution of physical thought and is considered one beyond super string theory. This theory solves unsolved problems of mysterious of matter, antimatter and interactions and makes a wide step towards unification of forces of nature. In this theory, vibrating string of different frequency modes which determines different types of elementary particles is replaced by a three dimensional infinitesimal pulsating (black)holes with same frequency. Different types of elementary particles are determined by different phase angles associated with same frequency. This allows force of interactions to take place among elementary particles, without need to invoke notion of force carrier particles, as (stable) force of interactions can never take place between elementary particles at different frequencies. Besides strong mathematical proofs given in this paper to prove its truthfulness, an experimental prediction has been given to confirm theory presented in form of relation between electron radius and quarks radii. The paper shows that quarks are direct consequence of this theory, and solves the flavor problem in QCD, and gives clue to answer questions of Why are there so many flavors? The paper also derives equation of big bang theory which describes singularity of moment of creation of universe.

Sign problem and phase quenching in finite-density QCD: Models, holography, and lattice

The effect of the complex phase of the fermion determinant is a key question related to the sign problem in finite-density QCD. Recently it has been shown that ignoring the complex phase -- the phase quenching -- does not change physics in a certain region of the phase diagram when a number of colors N_c is large. In this paper we study the effect of the phase quenching within the frameworks of effective models and holographic models. We show, in a unified manner, that the phase quenching gives exact results for any fermionic observables (e.g., chiral condensate) in the mean-field approximation and for gauge-invariant gluonic observables (e.g., Polyakov loop) to one-meson-loop corrections beyond mean field. We also discuss implications for the lattice simulations and confirm good quantitative agreement between our prediction and existing lattice QCD results. Therefore the phase quenching provides rather accurate answer already at N_c=3 with small 1/N_c corrections which can be taken into account by the phase reweighting.

LargeNcequivalence and baryons

In the large ${N}_{c}$ limit, gauge theories with different gauge groups and matter content sometimes turn out to be ``large ${N}_{c}$ equivalent,'' in the sense of having a set of coincident correlation functions. Large ${N}_{c}$ equivalence has mainly been explored in the glueball and meson sectors. However, a recent proposal to dodge the fermion sign problem of QCD with a quark number chemical potential using large ${N}_{c}$ equivalence motivates investigating the applicability of large ${N}_{c}$ equivalence to correlation functions involving baryon operators. Here we present evidence that large ${N}_{c}$ equivalence extends to the baryon sector, under the same type of symmetry realization assumptions as in the meson sector, by adapting the classic Witten analysis of large ${N}_{c}$ baryons.