Symmetry Of QCD Research Articles

Large Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c$$\\end{document} QCD phase diagram at μB=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _B=0$$\\end{document}

Lattice studies suggest that at zero baryon chemical potential and increasing temperature there are three characteristic regimes in QCD that are connected by smooth analytical crossovers: a hadron gas regime at T<Tch∼155\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T < T_{ch}\\sim 155$$\\end{document} MeV, an intermediate regime, called stringy fluid, at Tch<T<∼3Tch\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{ch}< T < \\sim 3 T_{ch}$$\\end{document}, and a quark-gluon plasma regime at higher temperatures. These regimes have been interpreted to reflect different approximate symmetries and effective degrees of freedom. In the hadron gas the effective degrees of freedom are hadrons and the approximate chiral symmetry of QCD is spontaneously broken. The intermediate regime has been interpreted as lacking spontaneous chiral symmetry breaking along with the emergence of new approximate symmetry, chiral spin symmetry, that is not a symmetry of the Dirac Lagrangian, but is a symmetry of the confining part of the QCD Lagrangian. While the high temperature regime is the usual quark-gluon plasma which is often considered to reflect “deconfinement” in some way. This paper explores the behavior of these regimes of QCD as the number of colors in the theory, Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c$$\\end{document}, gets large. In the large Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c$$\\end{document} limit the theory is center-symmetric and notions of confinement and deconfinement are unambiguous. The energy density is O(Nc0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}(N_c^0)$$\\end{document} in the meson gas, O(Nc1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {O}}}(N_c^1)$$\\end{document} in the intermediate regime and O(Nc2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {O}}}(N_c^2)$$\\end{document} in the quark-gluon plasma regime. In the large Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c$$\\end{document} limit these regimes may become distinct phases separated by first order phase transitions. The intermediate phase has the peculiar feature that glueballs should exist and have properties that are unchanged from what is seen in the vacuum (up to 1/Nc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/N_c $$\\end{document} corrections), while the ordinary dilute gas of mesons with broken chiral symmetry disappears and approximate chiral spin symmetry should emerge.

Weyl Group Symmetry as Intrinsic Color Symmetry in QCD

Weyl Group Symmetry as Intrinsic Color Symmetry in QCD

Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD

The spatial z correlators of meson operators in Nf=2+1+1 lattice QCD with optimal domain-wall quarks at the physical point are studied for seven temperatures in the range of 190–1540 MeV. The meson operators include a complete set of Dirac bilinears (scalar, pseudoscalar, vector, axial vector, tensor vector, and axial-tensor vector), and each for six flavor combinations (u¯d, u¯s, s¯s, u¯c, s¯c, and c¯c). In a recent paper [], I focused on the meson correlators of u and d quarks, and discussed their implications for the effective restoration of SU(2)L×SU(2)R and U(1)A chiral symmetries, as well as the emergence of approximate SU(2)CS chiral spin symmetry. In this work, we extend our study to meson correlators of six flavor contents, and first observe the hierarchical restoration of chiral symmetries in QCD, from SU(2)L×SU(2)R×U(1)A to SU(3)L×SU(3)R×U(1)A, and to SU(4)L×SU(4)R×U(1)A, as the temperature is increased from 190 to 1540 MeV. Moreover, we compare the temperature windows for the emergence of the approximate SU(2)CS symmetry in light and heavy vector mesons, and find that the temperature windows are dominated by the (u¯c,s¯c,c¯c) sectors. Published by the American Physical Society 2024

How many vector charmoniumlike states lie in the mass range 4.2–4.35 GeV?

In recent years many vector charmonium(like) states were reported by different electron-positron collider experiments above 4.2 GeV. However, so far, there not only exists sizable tension in the parameters of those states, but there is also no consensus on the number of the vector states in this energy range. To some extend, this might be caused by the fact that the experimental data were typically analyzed in single channel analyses employing overlapping Breit-Wigner functions, in particular ignoring the effect of opening thresholds. In this study, we focus on the mass range between 4.2 GeV and 4.35 GeV, conducting a comprehensive analysis of eight different final states in e+e− annihilation. Our findings demonstrate that, within this mass range, a single vector charmoniumlike state, exhibiting properties consistent with a D1D¯ molecular structure and characterized by a pole location spoleY(4230)=(4227±4−i2(50−2+8)) MeV, can effectively describe all the collected data. This is made possible by allowing for an interference with the well-established vector charmonium ψ(4160) along with the inclusion of the D1D¯ threshold effect. Moreover, in contrast to experimental analyses, our study reveals that the highly asymmetric total cross sections for e+e−→J/ψππ and e+e−→J/ψKK¯ around 4230 MeV stem from the same physics, rooted in the approximate SU(3) flavor symmetry of QCD. Published by the American Physical Society 2024

New Aspect of Chiral SU(2) and U(1) Axial Breaking in QCD

The violation of the U(1) axial symmetry in QCD is stricter than the chiral SU(2) breaking simply because of the presence of the quantum axial anomaly. If the QCD gauge coupling is sent to zero (the asymptotic free limit, where the U(1) axial anomaly does not exist), the strength of the U(1) axial breaking coincides with that of the chiral SU(2) breaking, which we, in short, call an axial–chiral coincidence. This coincidence is trivial since QCD then becomes a non-interacting theory. Actually, there exists another limit in the QCD parameter space, where an axial–chiral coincidence occurs even with nonzero QCD gauge coupling, which can be dubbed a nontrivial coincidence: it is the case with the massive light quarks (ml≠0) and the massless strange quark (ms=0) due to the flavor-singlet nature of the topological susceptibility. This coincidence is robust and tied to the anomalous chiral Ward–Takahashi identity, which is operative even at hot QCD. This implies that the chiral SU(2) symmetry is restored simultaneously with the U(1) axial symmetry at high temperatures. This simultaneous restoration is independent of ml(≠0) and, hence, is irrespective of the order of the chiral phase transition. In this paper, we discuss how the real-life QCD can be evolved from the nontrivial chiral–axial coincidence limit by working on a Nambu–Jona–Lasinio model with the U(1) axial anomaly contribution properly incorporated. It is shown that, at high temperatures, the large differences between the restorations of the chiral SU(2) symmetry and the U(1) axial symmetry for two light quarks and a sufficiently large current mass for the strange quark are induced by a significant interference of the topological susceptibility. Thus, the deviation from the nontrivial coincidence, which is monitored by the strange quark mass controlling the topological susceptibility, provides a new way of understanding the chiral SU(2) and U(1) axial breaking in QCD.

Dark sector effective field theory

We introduce the effective field theory of two different light dark particles interacting with the standard model (SM) light states in a single vertex, termed dark sector effective field theory (DSEFT). We focus on the new light particles with spin up to 1 and being real in essence, namely, new real scalars ϕ and S, Majorana fermions χ and ψ, and real vectors Xμ and Vμ. In the framework of low energy effective field theory with QED and QCD symmetry, the DSEFT can be classified into six categories, including the scalar-scalar-SM (ϕS-SM), fermion-fermion-SM (χψ-SM), vector-vector-SM (XV-SM), scalar-fermion-SM (ϕχ-SM), scalar-vector-SM (ϕX-SM), and fermion-vector-SM (χX-SM) cases. For each case, we construct the effective operator basis up to canonical dimension 7, which will cover most interesting phenomenology at low energy. As a phenomenological example, we investigate the longstanding neutron lifetime anomaly through the neutron dark decay modes n → χϕ or χX from the effective interactions in the fermion-scalar-SM or fermion-vector-SM case. When treating the light fermion as a dark matter candidate, we also explore the constraints from DM-neutron annihilation signal at Super-Kamiokande. We find the neutron dark decay in each scenario can accommodate the anomaly, at the same time, without contradicting with the Super-Kamiokande limit.

On the dynamical origin of the η′ potential and the axion mass

We investigate the dynamics responsible for generating the potential of the η′, the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the θ angle, and that this same potential largely determines the properties of the η′ once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N − F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F < N – 1, and in the dual gauge group for F > N + 1. For the special cases of F = N – 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1)R symmetry. We find that the η′ mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the η′ potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.

Symmetry of Dirac two-oscillator system, gauge-invariance, and Landau problem

Role of gauge symmetry in the proton spin problem has intricate and unresolved aspects. One of the interesting approaches to gain physical insights is to explore the Landau problem in this context. A detailed study using the group theoretic method to understand the Landau problem establishes the significance of the gauge transformation intimately related with the space translation symmetry. An important implication of this result is that the E(2)-like Wigner’s little group for massless particles could throw more light on the question of gauge symmetry in QED and QCD. A generalized Landau-Zeeman Hamiltonian is proposed in which Dirac two-oscillator system and the symmetry of the group SO(3,2) become important. It is argued that nontrivial topology of pure gauge field holds promise to resolve the unsettled questions.

Aspects of chiral symmetry in QCD at T=128 MeV

We investigate several aspects of chiral symmetry in QCD at a temperature of $T=128\text{ }\text{ }\mathrm{MeV}$. The study is based on a $24\ifmmode\times\else\texttimes\fi{}9{6}^{3}$ lattice-QCD ensemble with $\mathrm{O}(a)$-improved Wilson quarks and physical up, down and strange quark masses. The pion quasiparticle turns out to be significantly lighter than the zero-temperature pion mass, even though the corresponding static correlation length is shorter. We perform a quantitative comparison of our findings to predictions of chiral perturbation theory. Among several order parameters for chiral symmetry restoration, we compute the difference of the vector- and axial-vector time-dependent correlators and find it to be reduced by a factor $\ensuremath{\sim}2/3$ as compared to its vacuum counterpart.

Minimal entanglement and emergent symmetries in low-energy QCD

We study low-energy scattering of spin-$\frac{1}{2}$ baryons from the perspective of quantum information science, focusing on the correlation between entanglement minimization and the appearance of accidental symmetries. The baryon transforms as an octet under the $\mathrm{SU}(3)$ flavor symmetry and its interactions below the pion threshold are described by contact operators in an effective field theory (EFT) of QCD. Despite there being 64 channels in the 2-to-2 scattering, only six independent operators in the EFT are predicted by $\mathrm{SU}(3)$. We show that successive entanglement minimization in $\mathrm{SU}(3)$-symmetric channels are correlated with increasingly large emergent symmetries in the EFT. In particular, we identify scattering channels whose entanglement suppression are indicative of emergent $\mathrm{SU}(6), \mathrm{SO}(8), \mathrm{SU}(8)$, and $\mathrm{SU}(16)$ symmetries. We also observe the appearance of non-relativistic conformal invariance in channels with unnaturally large scattering lengths. Improved precision from lattice simulations could help determine the degree of entanglement suppression, and consequently the amount of accidental symmetry, in low-energy QCD.

Indirect detection of low-mass dark matter through the π0 and η windows

We consider the search for gamma-rays produced by the annihilation or decay of low-mass dark matter which couples to quarks. In this scenario, most of the photons are produced from the decays of $\pi^0$ or $\eta$ mesons. These decays produce distinctly different photon signatures due to the difference in meson mass. We assess the ability of the future MeV-range observatories to constrain the hadronic final states produced by dark matter annihilation or decay from the shape of the resulting photon spectrum. We then comment on how this information can be used to determine properties of the dark matter coupling to the quark current, based on the approximate symmetries of low-energy QCD.

Light Front Holographic QCD and Chiral Symmetry Breaking

Supersymmetric Light Front Holographic QCD is a holographic theory which exhibits typical features of a spontaneously broken chiral symmetry: The existence of a massless boson and different masses for vector and axial vector mesons. The reasons for the occurrence of these signatures both in LFHQCD and in standard methods is sketched and the differences are highlighted.

Noninvertible Global Symmetries in the Standard Model.

We identify infinitely many noninvertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the U(1)_{A} axial symmetry because of the Adler-Bell-Jackiw anomaly, for every rational angle 2πp/N, we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic U(1) gauge field. These conserved symmetry operators do not obey a group multiplication law, but a noninvertible fusion algebra. They act invertibly on all local operators as axial rotations, but noninvertibly on the 't Hooft lines. We further generalize our construction to QCD, and show that the coupling π^{0}F∧F in the effective pion Lagrangian is necessary to match these noninvertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.

NNLO anomalous dimension matrix for twist-two flavor-singlet operators

Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger 4−2ϵ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin N≤8.

A chiral-spin symmetry in QCD in Minkowski spacetime

In this paper, we look how to construct in Minkowski space-time a new type of \textit{chiralspin} group transformation of the spinor fields, similar to the one discovered by recent works of \textit{Glozman et al.} in the context of high temperature QCD and truncated studies in lattice calculations. Afterwards, we prove the invariance of free massless fermionic action under such group transformations, as well the invariance of the Hamiltonian of free massless fermions. At the end, the possible presence of a symmetry driven by such new \textit{chiralspin} group at high temperature QCD, also at non zero chemical potential, is discussed.

Nonperturbative running of the quark mass for Nf=3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the quark mass, for ${N}_{f}=3$ QCD with Wilson fermions in a mixed action setup, with standard Schr\"odinger functional (SF) boundary conditions for sea quarks and chirally rotated Schr\"odinger functional ($\ensuremath{\chi}\mathrm{SF}$) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor ${z}_{\mathrm{f}}({g}_{0}^{2})$ of the $\ensuremath{\chi}\mathrm{SF}$ valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios ${Z}_{S}/{Z}_{P}$ and ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ of the renormalization parameters and step scaling functions of the scalar and pseudoscalar densities. Where comparison is possible, our ${Z}_{S}/{Z}_{P}$ results are found to agree with previous determinations, based on a mass ratio method [G. M. de Divitiis et al. (ALPHA Collaboration), Eur. Phys. J. C 79, 797 (2019)] and Ward identities [ J. Heitger et al. (ALPHA Collaboration), Eur. Phys. J. C 80, 765 (2020); J. Heitger et al., Eur. Phys. J. C 81, 606 (2021)], with Schr\"odinger functional boundary conditions. The behavior of ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ confirms the theoretical expectations of $\ensuremath{\chi}\mathrm{SF}$ QCD, related to the restoration of the theory's symmetries in the continuum limit. From the step-scaling function of the pseudoscalar density we obtain the quark mass RG-running function from hadronic to perturbative energy scales. This is fully compatible with the earlier result obtained in a similar setup for Wilson quarks with Schr\"odinger functional boundary conditions [I. Campos et al., Eur. Phys. J. C 78, 387 (2018)], and provides a strong universality test for the two lattice setups.

Remarks on the QCD-electroweak phase transition in a supercooled universe

In extensions of the Standard Model with no dimensionful parameters the electroweak phase transition can be delayed to temperatures of order 100 MeV. Then the chiral phase transition of QCD can proceed with 6 massless quarks. The top-quark condensate destabilizes the Higgs potential through the Yukawa interaction, triggering the electroweak transition. Based on the symmetries of massless QCD, it has been argued that the chiral phase transition is first order. We point out that the top-Higgs Yukawa interaction is nonperturbatively large at the QCD scale, and that its effect on the chiral phase transition may not be negligible, violating some of the symmetries of massless QCD. The remaining symmetries indicate that top quarks condense in a second-order phase transition, but top condensation might also be triggered by a first-order symmetry-breaking transition in the light-quark sector.

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.

Mass radius of the proton

The mass radius is a fundamental property of the proton that so far has not been determined from experiment. Here we show that the mass radius of the proton can be rigorously defined through the formfactor of the trace of the energy-momentum tensor (EMT) of QCD in the weak gravitational field approximation, as appropriate for this problem. We then demonstrate that the scale anomaly of QCD enables the extraction of the formfactor of the trace of the EMT from the data on threshold photoproduction of $J/\psi$ and $\Upsilon$ quarkonia, and use the recent GlueX Collaboration data to extract the r.m.s. mass radius of the proton ${\rm R_m = 0.55 \pm 0.03 \ fm}$. The extracted mass radius is significantly smaller than the charge radius of the proton ${\rm R_C = 0.8409 \pm 0.0004 \ fm}$. We attribute this difference to the interplay of asymptotic freedom and spontaneous breaking of chiral symmetry in QCD, and outline future measurements needed to determine the mass radius more precisely.

Chiral magnetic properties of QCD phase-diagram

The QCD phase-diagram is studied, at finite magnetic field. Our calculations are based on the QCD effective model, the SU(3) Polyakov linear-sigma model (PLSM), in which the chiral symmetry is integrated in the hadron phase and in the parton phase, the up-, down- and strange-quark degrees of freedom are incorporated besides the inclusion of Polyakov loop potentials in the pure gauge limit, which are motivated by various underlying QCD symmetries. The Landau quantization and the magnetic catalysis are implemented. The response of the QCD matter to an external magnetic field such as magnetization, magnetic susceptibility and permeability has been estimated. We conclude that the parton phase has higher values of magnetization, magnetic susceptibility, and permeability relative to the hadron phase. Depending on the contributions to the Landau levels, we conclude that the chiral magnetic field enhances the chiral quark condensates and hence the chiral QCD phase-diagram, i.e. the hadron-parton phase-transition likely takes place, at lower critical temperatures and chemical potentials.