QCD Vacuum Research Articles

Dipole polarizabilities of light pseudoscalar mesons within the domain model of the QCD vacuum

Dipole polarizabilities of light pseudoscalar mesons are calculated in the framework of the mean field approach to QCD vacuum and bosonization based on the statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields, the domain model of QCD vacuum. In this approach, a nonlocal effective action of meson fields is derived that describes all possible strong, weak, and electromagnetic interactions of meson fields including their excited states. The considered mean field implements confinement and chiral symmetry, which manifests itself both in the properties of quark and gluon fields as well as upon bosonization, in the mass spectrum, decays constants and form factors of nonlocal colorless hadrons, and leads to the qualitatively distinctive features of the effective meson action. Particularly relevant to the subject of the present paper are the nonlocality of meson-quark-antiquark vertices and the absence of poles at real momenta in the propagators of scalar meson fields composed of light quark-antiquark pairs. In view of this, studying the role of manifest nonlocality of mesons and contribution of intermediate scalar meson fields in formation of the polarizabilities is of special interest. It turns out that, for charged pions and kaons, this contribution is substantial but not the largest one. Nonlocal nature of mesons provides an additional contribution so that calculated polarizabilities are in reasonable agreement with COMPASS experimental data and chiral perturbation theory.

Hadronic structure on the light front. VII. Pions and kaons and their partonic distributions

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. The spontaneous breaking of chiral symmetry on the light front, is shown to parallel that in the rest frame, where the non-local instanton induced $^\prime$t Hooft interaction plays a central role. By rewriting this interaction solely in terms of the good component of the fermionic field, a scalar chiral condensate emerges in the mean-field approximation, which is identical to the one obtained in the rest frame. The pions and kaons emerge as deeply bound Goldstone modes in the chiral limit, with the scalar-isoscalar sigma meson mode as a threshold state with zero binding. We explicitly derive the light front distribution amplitudes (DAs) and partonic functions (PDFs) for these mesons. The DAs and PDFs are in good agreement with those extracted from the QCD instanton vacuum in the rest frame, using the large momentum effective theory (LaMET). The QCD evolved DAs and PDFs compare well with available measurements, as well as recent lattice results.

The superluminous vacuum

The Standard Cosmological and Particle Models of physics have set both in their formalism an absolute limit, the speed of light c or else called the speed of causality and claim that this is also a physical limit in nature in our visible Universe. This however, we claim is also unproven up to today and nature has always imposed exceptions and violations in accepted theories many times in the past and proved that these were merely human formalism and experiments artifacts and used technology restrictions and that physical limits and rules are constantly broken and bend in nature. We hereby will try to theoretically demonstrate, why and how the very existence and empirical evidence in our Universe of vacuum space, either in its theorized ideal absolute form thus free space or partially vacuum characterized as QED or QCD vacuum and its zero-point energy and fluctuations, maybe actually the biggest proof in nature for superluminous energy being possible without violating causality. That the apparent effect of “nothingness” of vacuum space maybe the evidence for superluminocity and was right in front of us all this time hidden. We herein try to answer a fundamental physics question why vacuum space appears to us, basically, as nothing assuming that ‘nothing’ does not exists in nature and why a hypothetical superluminous vibration, Planck sized particle generates apparent nothingness in our spacetime. The novelty of the research herein infers that free space is the dark energy and which is superluminous energy.

Photons production in heavy-ion collisions as a signal of deconfinement phase

The photon production due to conversion of two gluons into a photon, $$gg\rightarrow \gamma $$ , in the presence of the background gauge fields is studied within the specific mean-field approach to QCD vacuum. In this approach, mean field in the confinement phase is represented by the statistical ensemble of almost everywhere homogeneous abelian (anti-)self-dual gluon configurations, while the deconfined phase can be characterized by the purely chromomagnetic fields. The probability of gluon conversion of two gluons into a photon vanishes in the confinement phase due to the randomness of the background field configurations. The anisotropic strong electromagnetic field, generated in the collision of relativistic heavy ions, serves as a catalyst for deconfinement with the appearance of an anisotropic purely chromomagnetic mean field. Respectively, deconfined phase is characterized by nonzero probability of the conversion of two gluons into a photon with strongly anisotropic angular distribution.

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge

Tools necessary for quantum simulations of $1+1$ dimensional quantum chromodynamics are developed. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site with the gauge fields included via nonlocal interactions. Classical computations and $D$-wave's quantum annealer advantage are used to determine the hadronic spectrum, enabling a decomposition of the masses and a study of quark entanglement. Color ``edge'' states confined within a screening length of the end of the lattice are found. IBM's seven-qubit quantum computers, ibmq_jakarta and ibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor QCD with one spatial site. More generally, the Hamiltonian and quantum circuits for time evolution of $1+1$ dimensional $SU({N}_{c})$ gauge theory with ${N}_{f}$ flavors of quarks are developed, and the resource requirements for large-scale quantum simulations are estimated.

Search for the chiral magnetic effect in Au+Au collisions at [formula omitted] GeV with the STAR forward event plane detectors

A decisive experimental test of the Chiral Magnetic Effect (CME) is considered one of the major scientific goals at the Relativistic Heavy-Ion Collider (RHIC) towards understanding the nontrivial topological fluctuations of the Quantum Chromodynamics vacuum. In heavy-ion collisions, the CME is expected to result in a charge separation phenomenon across the reaction plane, whose strength could be strongly energy dependent. The previous CME searches have been focused on top RHIC energy collisions. In this Letter, we present a low energy search for the CME in Au+Au collisions at sNN=27 GeV. We measure elliptic flow scaled charge-dependent correlators relative to the event planes that are defined at both mid-rapidity |η|<1.0 and at forward rapidity 2.1<|η|<5.1. We compare the results based on the directed flow plane (Ψ1) at forward rapidity and the elliptic flow plane (Ψ2) at both central and forward rapidity. The CME scenario is expected to result in a larger correlation relative to Ψ1 than to Ψ2, while a flow driven background scenario would lead to a consistent result for both event planes. In 10-50% centrality, results using three different event planes are found to be consistent within experimental uncertainties, suggesting a flow driven background scenario dominating the measurement. We obtain an upper limit on the deviation from a flow driven background scenario at the 95% confidence level. This work opens up a possible road map towards future CME search with the high statistics data from the RHIC Beam Energy Scan Phase-II.

Hadronic structure on the light front. III. The Hamiltonian, heavy quarkonia, spin, and orbit mixing

This is the third paper on hadronic light-front wave functions. We derive a light-front Hamiltonian from first principles, using the key features of the QCD vacuum at low resolution. In the first approximation, it gives transverse oscillator and longitudinal harmonic modes, and yields the correct Regge trajectories. For heavy quarkonia, we compare its spectrum to that obtained from the usual Schr\"odinger equation in the rest frame. We use the same approach for light quarks, and investigate the role of confinement and chiral symmetry breaking in the quark-antiquark sector. We then study spin-spin and spin-orbit mixing, resulting in e.g. quadrupole moments of vector mesons. For the light mesons, we show how to extend the famed 't Hooft interaction to the light front, which solves the U(1) problem and helps produce a light pion. We use the ensuing light front wave functions to derive the pertinent parton distribution functions, parton amplitudes, and low energy constants.

Hadronic structure on the light front. I. Instanton effects and quark-antiquark effective potentials

This is the first of a sequence of papers that addresses the nonperturbative origin of the central and spin-dependent forces between quarks. Its main thrust is a focus on meson spectroscopy in the center-of-mass frame. We suggest a novel ``dense instanton ensemble'' model for the QCD vacuum, to explain the interquark forces in mesons, from quarkonia to heavy-light and light-light ones. The sequels will show how to export these interactions to the light front, and derive the corresponding Hamiltonians, mesonic, and baryonic light front wave functions. The ultimate aim of the series is to bridge the gap between hadronic spectroscopy and partonic observables.

Hadronic structure on the light front. V. Diquarks, nucleons, and multiquark Fock components

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. In this paper we focus on the importance of diquark correlations, which we describe by a quasi-local four-fermion effective 't Hooft interaction induced by instantons. The same interaction is also shown to generate extra quark-antiquark pair of the "sea". Its higher order iteration can be included via "pion-mediation": both taken together yield a quantitative description of the observed flavor asymmetry of antiquarks sea. Finally we discuss the final step needed to bridge the gap between hadronic spectroscopy and parton observables, by forward DGLAP evolution towards the chiral upper scale of $\sim 1\, {\rm GeV}^2$.

Phenomenology of strong interactions: towards an effective theory for low energy QCD

In this paper, we develop models applicable to phenomenological particle physics by using the string analogy of particles. These theories can be used to investigate the phenomenology of confinement, deconfinement, chiral condensate, QGP phase transitions, and even the evolution of the early universe. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, QCD vacuum, and color superconductivity can also be investigated in these model frameworks. We use one of the models to describe the phenomenon of color confinement among glueballs at the end of the paper. The models are built based on the Dirac–Born–Infeld (DBI) action modified for open strings with their endpoints on a Dp-brane or brane–anti-brane at a tachyonic vacuum.

Confronting anomalous kaon correlations measured in Pb-Pb collisions at sNN=2.76 TeV

This paper uses simple models to interpret recent measurements of anomalously strong correlations between neutral and charged kaon production performed at the LHC for high-energy heavy-ion collisions. Thermal models, including charge conservation effects, are found to be insufficient to explain the data for the most central collisions. More exotic conjectures involving coherent emission can reproduce the observations if 30% of the kaons are emitted from coherent sources in the most central collisions. Such coherence might be related to the melting and re-freezing of the QCD vacuum.

Electromagnetic field effects and anomalous chiral phenomena in heavy-ion collisions at intermediate and high energy

&lt;sec&gt;Heavy-ion collisions can produce high-temperature and high-density quantum chromodynamics (QCD) matter under extremely strong electromagnetic fields, which triggers off many important anomalous chiral phenomena, such as the chiral magnetic effect and chiral magnetic wave. The anomalous chiral phenomena can help to find the evidence of &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$\cal{CP}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; symmetry breaking in the strong interaction, deepen the understanding of the QCD vacuum fluctuations, and disclose the mystery of asymmetry of antimatter-matter in the universe. &lt;/sec&gt;&lt;sec&gt;In this paper, firstly, the magnetic fields are investigated for small and large colliding systems at relativistic heavy ion collider (RHIC) and large hadron collider (LHC). These studies indicate that collision energy and initial nucleon structure have significant effects on magnetic fields. And, the lifetimes of magnetic field in different media are very different in heavy-ion collisions. Then, in order to study the chiral magnetic effect, some experimental observables are studied by using a multi-phase transport model without or with different strengths of the chiral magnetic effect. For small systems, if QGP exists, the chiral magnetic effect could be observed in the peripheral collisions. For isobaric collisions, the correlators with respect to the spectator plane can imply a much cleaner signal of chiral magnetic effect than that with respect to the participant plane. Our results support that the strength of chiral magnetic effect may be absent or small in isobaric collisions. Next, some new strategies are applied to study the chiral magnetic wave. Moreover, a novel mechanism for the electric quadrupole moment can also explain the charge-dependent elliptic flow of pions generated by the chiral magnetic wave. In addition, some interesting phenomena also occur, owing to the magnetic field in heavy-ion collisions at intermediate energy. The directed flow and elliptic flow of photons have no effect on magnetic field at &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$p_{\rm T}&lt;25$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; GeV. However, because of the magnetic field, the directed flow of photons decreases and the elliptic flow of photons increases at &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$p_{\rm T}&gt;25$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; GeV. Besides, the magnetic field has a significant effect on giant dipole resonance, i.e. the magnetic field increases the angular momentum and enhances some observables of the giant dipole resonance spectrum. In conclusion, magnetic field plays a key role in heavy-ion collisions at both high energy and intermediate energy. It provides an unprecedented opportunity for studying the microscopic laws of nuclear physics. However, there are still many unsolved problems that need further studying in the future.&lt;/sec&gt;

Is the right-handed current contribution to B¯→Xulν decays corrected by the nontrivial vacuum in QCD?

We study violation of quark-hadron duality for $\overline{B}\ensuremath{\rightarrow}{X}_{u}l\ensuremath{\nu}$ and $D\ensuremath{\rightarrow}{X}_{d}l\ensuremath{\nu}$ decays in the presence of the right-handed current operator. For this case, we show that duality violation has some aspects different from the standard model due to the existence of an instanton. In particular, the fermionic zero mode of an intermediate light quark can give a nonvanishing contribution owing to its chirality structure. A duality-violating component that arises from a single instanton is then analytically extracted as a finite-distance singularity, leading to an oscillatory correction to the observable in Minkowski space. Finally, we show that the size of duality violation for the lepton energy distribution in $\overline{B}$ decays can be comparable to the chirally suppressed perturbative contribution, although the absolute size depends on the detail of the QCD vacuum.

The strong CP problem solved by itself due to long-distance vacuum effects

The vacuum of quantum chromodynamics has an incredibly rich structure at the nonperturbative level, which is intimately connected with the topology of gauge fields, and put to a test by the strong CP problem. We investigate the long-distance properties of the theory in the presence of the topological θ term. This is done on the lattice, using the gradient flow to isolate the long-distance modes in the functional integral measure and tracing it over successive length scales. The key point is that the vacuum splits into disconnected topological sectors with markedly different physical characteristics, which gives rise to a nontrivial behavior depending on θ. We find that the color fields produced by quarks and gluons are screened, and confinement is lost, for bare vacuum angles |θ|>0, thus providing a natural solution of the strong CP problem. The renormalized vacuum angle θ is found to flow to zero in the infrared limit, leading to a self-consistent solution within QCD.

Determination of the Collins-Soper kernel from cross-sections ratios

The Collins-Soper kernel is a powerful tool for studying the properties of the QCD vacuum and an essential component of the transverse momentum dependent (TMD) factorization theorem. In this paper, we present a novel method for determining the Collins-Soper kernel directly from the comparison of differential cross sections measured at different energies. The method relies solely on the structure of the TMD factorization theorem and thus also provides a direct test of the theorem validity. With minor modifications, the procedure can be applied to the real measured data for Drell-Yan and SIDIS processes. As a demonstration, we analyze the pseudodata generated by the CASCADE event generator and determine the Collins-Soper kernel suggested by the parton branching model.

Topological susceptibility in finite temperature QCD with physical (u/d,s,c) domain-wall quarks

We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3 \times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T > T_c \sim 150 $ MeV. The topological charge of each gauge configuration is measured by the clover charge in the Wilson flow at the same flow time in physical units, and the topological susceptibility $ \chi_t(a,T) $ is determined for each ensemble with lattice spacing $a$ and temperature $T$. Using the topological susceptibility $\chi_t(a,T) $ of 15 gauge ensembles with three lattice spacings and different temperatures in the range $T \sim 155-516 $ MeV, we extract the topological susceptibility $\chi_t(T)$ in the continuum limit. To compare our results with others, we survey the continuum extrapolated $\chi_t(T)$ in lattice QCD with $N_f=2+1(+1)$ dynamical quarks at/near the physical point, and discuss their discrepancies. Moreover, a detailed discussion on the reweighting method for domain-wall fermion is presented.

Dual QCD thermodynamics at finite temperature and chemical potential

A Dual QCD formulation for [Formula: see text] color gauge has been developed in terms of dual gauge potentials, building on our previously published study for the [Formula: see text] case with zero bario-chemical potential [H. C. Chandola, G. Punetha and H. Dehnen, Nucl. Phys. A 945, 226 (2016).] and taking into account the local as well as topological structure of the color gauge group into its dynamics. For the purpose of examining the nonperturbative characteristics of QCD, the dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been examined. The thermal behavior of the nonperturbative QCD vacuum has been investigated for exploring the dynamics of quark-hadron phase transition at finite chemical potential. Related thermodynamic quantities and equation of state (EoS) to characterize quark matter have also been discussed within the framework of dual QCD-based hadronic bag which guarantees the critical parameters and the associated critical points for quark-hadron phase transition. These thermodynamic quantities are expected to play important roles in understanding the order of quark-hadron phase transition and are likely to predict the features of a first-order quark-hadron phase transition for finite chemical potential. Moreover, we have investigated the bulk properties of quark matter by constructing the free energy change and the associated surface tension for quark-hadron phase transition. For consistency and compatibility check, we have also compared our results with state-of-the-art three-loop Hard Thermal Loop perturbative results and available lattice QCD results and in the process found reasonable agreements.

Phases of rotating baryonic matter: non-Abelian chiral soliton lattices, antiferro-isospin chains, and ferri/ferromagnetic magnetization

A chiral soliton lattice (CSL), proposed as the ground state of rotating baryonic matter at a finite density, is shown to be unstable in a large parameter region for two flavors owing to pion condensations, leading to two types of non-Abelian (NA) CSL phases (dimer and deconfining phases). We determine the phase diagram where the dimer phase meets the other phases and QCD vacuum at three tricritical points. The critical angular velocity of NA-CSLs is lower than that of η-CSL. Each NA soliton carries an isospin, and an antiferro-isospin chain is formed leading to gapless isospinons. The anomalous coupling to the magnetic field makes the NA-CSL (η-CSL) ferrimagnetic (ferromagnetic).

On the conformal spin dependence of the perturbative QCD vacuum singularity

We study the four-gluon scattering amplitude in the high energy limit of QCD written in terms of its conformal expansion. We highlight the need to include both even and odd conformal spin contributions in order to map it to an iterative representation in rapidity and transverse momentum space which we have evaluated numerically. By Fourier expanding in a set of three azimuthal angles, we find a new form for the amplitude in terms of 4F3 hypergeometric functions. An alternative formulation is possible when connecting this Fourier expansion with Bessel kernels studied in analytic number theory.

New interpretation of the chiral phase transition: Violation of the trilemma in QCD

We find that the chiral phase transition (chiral crossover) in QCD at physical point is triggered by big imbalance among three fundamental quantities essential for the QCD vacuum structure: susceptibility functions for the chiral symmetry, axial symmetry, and the topological charge. The balance, dobbed the QCD trilemma, is unavoidably violated when one of the magnitudes among them is highly dominated, or suppressed. Based on a three-flavor Nambu-Jona-Lasinio model, we explicitly evaluate the amount of violation of the QCD trilemma at physical point, and show that the violation takes place not only at vacuum, but even in a whole temperature regime including the chiral crossover epoch. This work confirms and extends the suggestion recently reported from lattice QCD with 2 flavors on dominance of the axial and topological susceptibilities left in the chiral susceptibility at high temperatures. It turns out that the imbalance is essentially due to the flavor symmetry violation of the lightest three flavors, and the flavor breaking specifically brings enhancement of the axial anomaly contribution in the chiral order parameter, while the the strength of the axial breaking and the transition rate of the topological charge are fairly insensitive to the flavor symmetry. The violation of QCD trilemma and its flavor dependence can be tested by lattice simulations with 2 + 1 flavors in the future, and would also give a new guiding principle to explore the flavor dependence of the chiral phase transition, such as the Columbia plot, including possible extension with external fields.