Lattice-quantum chromodynamics (QCD) simulations and theoretical arguments hint at the existence of an intermediate phase of strongly interacting matter between a confined hadron gas and a deconfined quark-gluon plasma (QGP). We qualitatively and semiquantitatively explore and differentiate the phase structures in the temperature window from the QCD pseudocritical temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub><mo>≃</mo><mn>160</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> to the pure gluonic deconfinement temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">d</mi></mrow></msub><mo>≃</mo><mn>285</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. We propose a three-regime picture using a hadron resonance gas description augmented with the exponential spectrum of strings, corresponding to highly excited mesons and glueballs, based on the analysis of a large number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">c</mi></msub></math> of colors. We estimate the entropy density from our model to confirm that the lattice-QCD data are bracketed with three regimes, i.e., a hadron gas, a QGP, and a new phase for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub><mo>≲</mo><mi>T</mi><mo>≲</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">d</mi></mrow></msub></mrow></math>. In this new phase, which we name a spaghetti of quarks with glueballs (SQGBs), thermal degrees of freedom of quarks are liberated, yet gluons remain confined in glueballs. Since the Hagedorn temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">H</mi></mrow></msub><mo>∼</mo><mn>285</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> is universal in the meson and the glueball sectors, in the infinite-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">c</mi></msub></math> limit, the phase diagram in the plane of the baryon chemical potential and the temperature is reduced to one with the confined and deconfined phases and quarkyonic matter at high density. At large but finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">c</mi></msub></math>, an SQGB window may open between these phases. We point out that the SQGB has interesting similarities with quarkyonic matter and that this matter in the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">c</mi></msub></math> limit is confined as measured by the interaction between heavy quarks, but behaves in other respects like a quasifree gas of quarks. As a result of the extrapolation to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">c</mi></msub><mo>=</mo><mn>3</mn></math>, we present a revised phase diagram with the SQGB phase bounded by thermal crossovers. Finally, we give a quantitative analysis of chiral-symmetry restoration in the SQGB phase.

United States

Japan

Yuki Fujimoto

Kenji Fukushima

Yoshimasa Hidaka

Larry McLerran

New state of matter between the hadronic phase and the quark-gluon plasma?

We discuss a novel mechanism for the proto-neutron star acceleration assisted by the chiral separation effect, which induces an axial vector current in a dense medium. We consider the process of neutrinos scattering off the background axial vector current of electrons. We show that anisotropy of either magnetic field or density in momentum space is essential for nonzero recoil, and we call this mechanism the chiral anisotropy conversion. Assuming a strong magnetic field <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo>≃</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">T</mi></mrow></math> and anisotropy by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>10</mn><mo>%</mo></math>, we find that the chiral anisotropy conversion can yield the velocity of order of typical pulsar kicks, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>kick</mi></mrow></msub><mo>≳</mo><mn>1000</mn><mtext> </mtext><mtext> </mtext><mrow><mi>km</mi><mo>/</mo><mi mathvariant="normal">s</mi></mrow></mrow></math>.

Chengpeng Yu

Pulsar kick by the chiral anisotropy conversion

We write down an effective theory of the Polyakov loop to investigate the deconfinement phase transition of imaginary-rotating gluonic matter using the strong-coupling expansion. We find the strength of the nearest-neighbor Polyakov-loop interaction modified by the sum of contributions involving the chair-type loops along the temporal direction. Our results show that the deconfinement transition temperature increases with increasing imaginary angular velocity, which agrees with the predictions from the models and the high-temperature perturbative calculations.

Yusuke Shimada

Imaginary rotating gluonic matter at strong coupling

We establish thermodynamic stability and gauge invariance in the magnetovortical matter of Dirac fermions under the coexistent rotation and strong magnetic field. The corresponding partition function reveals that the orbital contribution to bulk thermodynamics preponderates over the conventional contribution from anomaly-related spin effects. This orbital preponderance macroscopically manifests itself in the sign inversion of the induced charge and current in the magnetovortical matter, and can be tested experimentally as the flip of the angular momentum polarization of magnetovortical matter when the magnetic field strength is increased.

China

Koichi Hattori

Kazuya Mameda

Preponderant Orbital Polarization in Relativistic Magnetovortical Matter

We present analytical and numerical calculations for the photon polarization tensor at finite temperature and density in a constant magnetic field. We first discuss the tensor decomposition in the presence of the magnetic field, which breaks rotational symmetry. Then, we analytically perform all the momentum integrations and numerically take the Landau level sum. We confirm that the imaginary part of the photon polarization tensor correctly reproduces the known result from the independent calculation. We utilize the Kramers-Kronig relation to estimate the real part numerically as a function of the momenta, the chemical potential, and the finite temperature. As an application, we consider the real photon limit and estimate the photon decay rate and the Stokes parameter in the hot and dense medium. We specifically quantify the difference between the X-mode and the O-mode with the polarization orthogonal and parallel to the magnetic field. As long as the magnetic field is weak, the decay rate of the X-mode photon is larger than that of the O-mode photon, while the O-mode becomes dominant due to the Landau level suppression of the X-mode at a strong magnetic field. We also find that the eigenmodes of the propagating photon change their polarization state with increasing density.

Tomoya Uji

Photon polarization tensor at finite temperature and density in a magnetic field

In a unified perturbative treatment from the high-density side, we compute the speed of sound and the trace anomaly as functions of the chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>μ</mi></mrow></math> for the two-color diquark superfluid, the pion-condensed high-isospin matter, and the two-flavor color superconducting (2SC) quark matter. We find that the corrections induced by the gap energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math> involve nontrivial interplay between the dimensionless magnitude <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi mathvariant="normal">Δ</mi><mo>/</mo><mi>μ</mi><mo stretchy="false">|</mo></math> and the derivative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mo>∂</mo><mi mathvariant="normal">Δ</mi><mo>/</mo><mo>∂</mo><mi>μ</mi><mo stretchy="false">|</mo></math>. Even though the gap equation has a common structure for these phases of our interest, different numerical constants cause drastic changes in the speed of sound corrections. As long as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi mathvariant="normal">Δ</mi><mo>/</mo><mi>μ</mi><mo stretchy="false">|</mo></math> is dominant over the derivative, the gap effects increase the speed of sound, which is consistent with the expected behavior of exhibiting a peak at intermediate density. We then discuss the trace anomaly which is pushed down generally by the gap effects and turns out to be negative widely in the high density regime. For demonstration of nonperturbative enhancement, we take account of the instanton-induced interaction. We confirm a further increase in the speed of sound for the two-color diquark superfluid and the pion-condensed high-isospin matter, while the speed of sound for the 2SC quark matter deviates far below the conformal limit due to the derivative contribution.

Shuhei Minato

Speed of sound and trace anomaly in a unified treatment of the two-color diquark superfluid, the pion-condensed high-isospin matter, and the 2SC quark matter

We investigate detailed properties of imaginary rotating matter with gluons and quarks at high temperature. Previously, we showed that imaginary rotation induces perturbative confinement of gluons at the rotation center. We perturbatively calculate the Polyakov loop potential and find inhomogeneous confinement above a certain threshold of imaginary angular velocity. We also evaluate the quark contribution to the Polyakov loop potential and confirm that spontaneous chiral symmetry breaking occurs in the perturbatively confined phase.

Shi Chen

Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity

We propose a novel approach to probe primordial inhomogeneity in hot and dense matter which could be realized in noncentral heavy-ion collisions. Although the Hanbury Brown and Twiss (HBT) interferometry is commonly used to infer the system size, the cluster size should be detected if substructures emerge in space. We demonstrate that a signal peak in the HBT two-particle correlation stands at the relative momentum corresponding to the spatial scale of pseudo one-dimensional modulation. We assess detectability using the data prepared by an event generator (AMPT model) with clustering implemented in the particle distribution.

Katsuya Inoue

Kenta Shigaki

Yorito Yamaguchi

Hanbury-Brown–Twiss signature for clustered substructures probing primordial inhomogeneity in hot and dense QCD matter

We discuss the baryon properties under a strong magnetic field. We adopt the Skyrme model and calculate the magnetic field dependence of the mass and the pressure distribution in the soliton. We elucidate a magnetically induced contribution to the pressure sum rule and interpret it as an extra confining force. We also quantize the soliton to estimate the difference between the proton and the neutron and find a simple relation between the pressure and the mass differences.

Zebin Qiu

Magnetic enhancement of baryon confinement modeled via a deformed Skyrmion

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, $$\alpha _s(Q^2)$$ <math> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </math> , that varies with the energy scale $$Q^2$$ <math> <msup> <mi>Q</mi> <mn>2</mn> </msup> </math> characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of $$\alpha _s$$ <math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math> at low momentum transfers limits perturbative calculations to the high-energy region where $$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$ <math> <mrow> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>≫</mo> <msubsup> <mi>Λ</mi> <mrow> <mtext>QCD</mtext> </mrow> <mn>2</mn> </msubsup> <mo>≃</mo> </mrow> </math> (250 MeV) $$^2$$ <math> <msup> <mrow></mrow> <mn>2</mn> </msup> </math> . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large $$N_c$$ <math> <msub> <mi>N</mi> <mi>c</mi> </msub> </math> -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected $$q{{\bar{q}}}$$ <math> <mrow> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, $$W^\pm $$ <math> <msup> <mi>W</mi> <mo>±</mo> </msup> </math> or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!