arXiv subjects

Robert D. Pisarski

Publications and source records attributed to Robert D. Pisarski.

At least 55 records · Page 3Linked to original sources

arXiv2020

Free energy of a Holonomous Plasma

At a nonzero temperature T, a constant field $\overline{A}_0 \sim T/g$ generates nontrivial eigenvalues of the thermal Wilson line. We discuss contributions to the free energy of such a holonomous plasma when the coupling constant, $g$, is weak. We review the computation to $\sim g^2$ by several alternate methods, and show that gauge invariant sources, which are nonlinear in the gauge potential $A_0$, generate novel contributions to the gluon self energy at $\sim g^2$. These ensure the gluon self energy remains transverse to $\sim g^2$, and are essential in computing contributions to the free energy at $\sim g^3$ for small holonomy, $\overline{A}_0 \sim T$. We show that the contribution $\sim g^3$ from off-diagonal gluons is discontinuous as the holonomy vanishes. The contribution from diagonal gluons is continuous as the holonomy vanishes, but sharply constrains the possible sources which generate nonzero holonomy, and must involve an infinite number of Polyakov loops.

hep-ph↗

arXiv2019

The Myriad Uses of Instantons

In quantum chromodynamics (QCD), the role which topologically non-trivial configurations play in splitting the singlet pseudo-Goldstone meson, the $η^\prime$, from the octet is familiar. In addition, such configurations contribute to other processes which violate the axial $U(1)_A$ symmetry. While the nature of topological fluctuations in the confined phase is still unsettled, at temperatures well above that for the chiral phase transition, they can be described by a dilute gas of instantons. We show that instantons of arbitrary topological charge $Q$ generate anomalous interactions between $2 N_f |Q|$ quarks, which for $Q = 1$ make the $η^\prime$ heavy. For two flavors we compute an anomalous quartic meson coupling and discuss its implications for the phenomenology of the chiral phase transition. A dilute instanton gas suggests that for cold, dense quarks, instantons do not evaporate until very high densities, when the baryon chemical potential is $\gtrsim 2$ GeV.

hep-ph↗

arXiv2019

Emergent QCD Kondo effect in two-flavor color superconducting phase

We show that effective coupling strengths between ungapped and gapped quarks in the two-flavor color superconducting (2SC) phase are renormalized by logarithmic quantum corrections. We obtain a set of coupled renormalization-group (RG) equations for two distinct effective coupling strengths arising from gluon exchanges carrying different color charges. The diagram of RG flow suggests that both of the coupling strengths evolve into a strong-coupling regime as we decrease the energy scale toward the Fermi surface. This is a characteristic behavior observed in the Kondo effect, which has been known to occur in the presence of impurity scatterings via non-Abelian interactions. We propose a novel Kondo effect emerging without doped impurities, but with the gapped quasiexcitations and the residual SU(2) color subgroup intrinsic in the 2SC phase, which we call the 2SC Kondo effect.

hep-ph↗

arXiv2018

Thermal effective potential for the Polyakov loop to higher loop order

This is a progress report on the calculation of the effective potential for the Polyakov loop in $SU(N)$ pure gauge theory beyond two-loop order. We introduce a new approach using the Poisson resummation formula to compute sum-integrals with the holonomy. We show partial results for the free energy at order $g^3$ and $g^4$.

hep-th↗

arXiv2018

Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics

We consider the phase diagram of hadronic matter as a function of temperature, T , and baryon chemical potential, mu. Currently the dominant paradigm is a line of first order transitions which ends at a critical endpoint. In this work we suggest that spatially inhomogenous phases are a generic feature of the hadronic phase diagram at nonzero mu and low T . Familiar examples are pion and kaon condensates. At higher densities, we argue that these condensates connect onto chiral spirals in a quarkyonic regime. Both of these phases exhibit the spontaneous breaking of a global U(1) symmetry and quasi-long range order, analogous to smectic liquid crystals. We argue that there is a continuous line of first order transitions which separate spatially inhomogenous from homogenous phases, where the latter can be either a hadronic phase or a quark-gluon plasma. While mean field theory predicts that there is a Lifshitz point along this line of first order transitions, in three spatial dimensions strong infrared fluctuations wash out any Lifshitz point. Using known results from inhomogenous polymers, we suggest that instead there is a Lifshitz regime. Non-perturbative effects are large in this regime, where the momentum dependent terms for the propagators of pions and associated modes are dominated not by terms quadratic in momenta, but quartic. Fluctuations in a Lifshitz regime may be directly relevant to the collisions of heavy ions at (relatively) low energies, sqrt(s)/A : 1 to 20 GeV.

hep-ph↗

arXiv2018

How the axial anomaly controls flavor mixing among mesons

It is well known that because of the axial anomaly in QCD, mesons with $J^P = 0^-$ are close to $SU(3)_{\mathrm{V}}$ eigenstates: the $eta^\prime(958)$ meson is largely a singlet, and the $η$ meson an octet. In contrast, states with $J^P = 1^-$ are flavor diagonal: \textit{e.g.}, the $ϕ(1020)$ is almost pure $\bar{s} s$. Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of $G_{\mathrm{fl}} = SU(3)_{\mathrm{L}} \times SU(3)_{\mathrm{R}}$. We construct effective Lagrangians from terms invariant under $G_{\mathrm{fl}}$, and introduce the concept of \textit{hetero-} and \textit{homo}chiral multiplets. Because of the axial anomaly, only terms invariant under the $Z(3)_{\mathrm{A}}$ subgroup of the axial $U(1)_{\mathrm{A}}$ enter. For heterochiral multiplets, which begin with that including the $η$ and $η^\prime(958)$, there are $Z(3)_{\mathrm{A}}$ invariant terms with low mass dimension which cause states to mix according to $SU(3)_{\mathrm{V}}$ flavor. For homochiral multiplets, which begin with that including the $ϕ(1020)$, there are no $Z(3)_{\mathrm{A}}$ invariant terms with low mass dimension, and so states are diagonal in flavor. In this way we predict the flavor mixing for the heterochiral multiplet with spin one, as well as for hetero- and homochiral multiplets with spin two and spin three.

hep-ph↗

arXiv2017

Possible higher order phase transition in large-$N$ gauge theory at finite temperature

We analyze the phase structure of $SU(\infty)$ gauge theory at finite temperature using matrix models. Our basic assumption is that the effective potential is dominated by double-trace terms for the Polyakov loops. As a function of the temperature, a background field for the Polyakov loop, and a quartic coupling, it exhibits a universal structure: in the large portion of the parameter space, there is a continuous phase transition analogous to the third-order phase transition of Gross, Witten and Wadia, but the order of phase transition can be higher than third. We show that different confining potentials give rise to drastically different behavior of the eigenvalue density and the free energy. Therefore lattice simulations at large $N$ could probe the order of phase transition and test our results.

hep-th↗

arXiv2017

Finite-temperature phase transitions of third and higher order in gauge theories at large $N$

We study phase transitions in $SU(\infty)$ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. We speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infinite $N$.

hep-th↗

arXiv2017

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

In the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at $T\simeq M_{W,Z}$. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles valid in a wide range of temperature, to all orders in interactions of the standard model, and to leading order mixing angle $θ\ll 1$. Production rates and effective mixing angles depend sensitively on helicity. Positive helicity states interact more weakly with the medium and their effective mixing angle is not modified significantly whereas the mixing angle for negative helicity is strongly suppressed by the medium. If $M_s \lesssim 8.35\,\mathrm{MeV}$, there are fewer states with negative helicity produced than those with positive helicity. There is an MSW resonance in the absence of lepton asymmetry, but is screened by the damping rate, without production enhancement. Negative helicity states freeze-out at $T^-_f\simeq 5\,\mathrm{GeV}$ and positive helicity states freeze-out at $T^+_f \simeq 8\,\mathrm{GeV}$, both distributions are far from thermal. Negative helicity states feature a broader momentum distribution than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime and cosmological constraints to be the sole dark matter component in the universe but might solve the $^{7}Li$ problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. We argue that heavy sterile neutrinos with lifetime $\leq 1/H_0$ reach local thermodynamic equilibrium.

hep-ph↗

arXiv2016

Volume dependence of baryon number cumulants and their ratios

We explore the influence of finite volume effects on baryon number fluctuations in a non-perturbative chiral model. In order to account for soft modes, we use the functional renormalization group in a finite volume, using a smooth regulator function in momentum space. We compare the results for a smooth regulator with those for a sharp (or Litim) regulator, and show that in a finite volume, the latter produces spurious artifacts. In a finite volume there are only apparent critical points, about which we compute the ratio of the fourth to the second order cumulant of quark number fluctuations. When the volume is sufficiently small the system has two apparent critical points; as the system size decreases, the location of the apparent critical point can move to higher temperature and lower chemical potential.

hep-ph↗

arXiv2016

Chiral matrix model of the semi-Quark Gluon Plasma in QCD

A chiral matrix model applicable to QCD with 2+1 flavors is developed. This requires adding a SU(3)_L x SU(3)_R x Z(3)_A nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. In addition to the usual symmetry breaking term, linear in the current quark mass m_qk, at a nonzero temperature T it is necessary to add a new term, ~ m_qk T^2. The parameters of the gluon part of the matrix model are identical to that for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, eta, and eta'. The temperature for the chiral crossover at T_chi = 155 MeV is determined by adjusting the Yukawa coupling y. We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent beta - 1. We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the chi_2n. Especially sensitive tests are provided by chi_4 - chi_2 and by chi_6, which changes in sign about T_chi. The behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T_chi, that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice.

hep-ph↗

arXiv2016

How tetraquarks can generate a second chiral phase transition

We consider how tetraquarks can affect the chiral phase transition in theories like QCD, with light quarks coupled to three colors. For two flavors the tetraquark field is an isosinglet, and its effect is minimal. For three flavors, however, the tetraquark field transforms in the same representation of the chiral symmetry group as the usual chiral order parameter, and so for very light quarks there may be two chiral phase transitions, which are both of first order. In QCD, results from the lattice indicate that any transition from the tetraquark condensate is a smooth crossover. In the plane of temperature and quark chemical potential, though, a crossover line for the tetraquark condensate is naturally related to the transition line for color superconductivity. For four flavors we suggest that a triquark field, antisymmetric in both flavor and color, combine to form hexaquarks.

hep-ph↗

arXiv2015

Dilepton and photon production in the presence of a nontrivial Polyakov loop

We calculate the production of dileptons and photons in the presence of a nontrivial Polyakov loop in QCD. This is applicable to the semi-Quark Gluon Plasma (QGP), at temperatures above but near the critical temperature for deconfinement. The Polyakov loop is small in the semi-QGP, and near unity in the perturbative QGP. Working to leading order in the coupling constant of QCD, we find that there is a mild enhancement, ~ 20%, for dilepton production in the semi-QGP over that in the perturbative QGP. In contrast, we find that photon production is strongly suppressed in the semi-QGP, by about an order of magnitude, relative to the perturbative QGP. In the perturbative QGP photon production contains contributions from 2->2 scattering and collinear emission with the Landau- Pomeranchuk-Migdal (LPM) effect. In the semi-QGP we show that the two contributions are modified differently. The rate for 2->2 scattering is suppressed by a factor which depends upon the Polyakov loop. In contrast, in an SU(N) gauge theory the collinear rate is suppressed by 1/N, so that the LPM effect vanishes at infinite N. To leading order in the semi-QGP at large N, we compute the rate from 2->2 scattering to the leading logarithmic order and the collinear rate to leading order.

hep-ph↗

arXiv2015

Correlation functions of Polyakov loops at tree level

We compute the correlation functions of Polyakov loops in $SU(N_c)$ gauge theories by explicitly summing all diagrams at tree level in two special cases, for $N_c = 2$ and $N_c = \infty$. When $N_c =2$ we find the expected we find Coulomb-like behavior at short distances, $\sim 1/x$ as the distance $x \rightarrow 0$. In the planar limit at $N_c = \infty$ we find a weaker singularity, $\sim 1/\sqrt{x}$ as $x \rightarrow 0$. In each case, at short distances the behavior of the correlation functions between two Polyakov loops, and the corresponding Wilson loop, are the same. We suggest that such non-Coulombic behavior is an artifact of the planar limit.

hep-ph↗

arXiv2014

Universality of plasmon excitations in Dirac semimetals

The recent experimental discovery of ${\rm Cd_3 As_2}$ and ${\rm Na_3 Bi}$ Dirac semimetals enables the study of the properties of chiral quasi-particles in three spatial dimensions. As demonstrated by photoemission, Dirac semimetals are characterized by a linear dispersion relation for fermion quasi-particles, and thus represent three dimensional analogs of graphene. While the distinctive behavior of chiral fermions (e.g. Klein tunneling) is already evident in two dimensional graphene, the physics of chirality in three dimensions opens a number of new possibilities. In this paper we investigate the properties of the collective plasmon excitations in Dirac semimetals by using the methods of relativistic field theory. We find a strong and narrow plasmon excitation whose frequency is in the terahertz (THz) range which may be important for practical applications. The properties of the plasmon appear universal for all Dirac semimetals, due to the large degeneracy of the quasi-particles and the small Fermi velocity, $v_F \ll c$. This universality is closely analogous to the phenomenon of "dimensional transmutation", that is responsible for the emergence of dimensionful scales in relativistic field theories such as Quantum Chromodynamics, the modern theory of nuclear physics.

cond-mat.mes-hall↗

arXiv2014

Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions

We use an effective matrix model to study deconfinement in a pure SU(Nc) gauge theory, without quarks, in d=2+1 dimensions. Expanding about a constant background A0 field we construct an effective potential for the eigenvalues of the thermal Wilson line for general Nc and in the large-Nc limit. The numerical results are presented using one, two, and four free parameters, which are determined by fitting directly to the lattice data for the pressure. The matrix model shows a good agreement with numerical lattice simulations for the pressure and the interaction measure, starting from the perturbative limit up to the critical temperature. For the pressure, the details of A0- dependent nonperturbative terms are relevant only in a narrow transition region below ~1.2 Td. This is also the range where the Polyakov loop deviates notably from one. In accordance with the lattice results we find that, up to a trivial factor Nc^2-1, there is only a mild dependence on the number of colors.

hep-ph↗

arXiv2013

Collisional energy loss above the critical temperature in QCD

We compute the collisional energy loss for a heavy quark above the critical temperature in Quantum ChromoDynamics (QCD). We work in the semi Quark-Gluon Plasma, which assumes that this region is dominated by the non-trivial holonomy of the thermal Wilson line. Relative to the result to leading order in perturbation theory, at a fixed value of the coupling constant we generically we find that collisional energy loss is suppressed by powers of the Polyakov loop, l < 1. For small values of the loop, this suppression is linear for the scattering off of light quarks, and quadratic for the scattering off of gluons, or for Compton scattering.

hep-ph↗

arXiv2013

Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions

We use matrix models to characterize deconfinement at a nonzero temperature T for an SU(2) gauge theory in three spacetime dimensions. At one loop order, the potential for a constant vector potential A0 is ~T^3 times a trilogarithm function of A0/T. In addition, we add various nonperturbative terms to model deconfinement. The parameters of the model are adjusted by fitting the lattice results for the pressure. The nonperturbative terms are dominated by a constant term ~T^2Td, where Td is the temperature for deconfinement. Besides this constant, we add terms which are nontrivial functions of A0/T, both ~T^2Td and ~TTd^2. There is only a mild sensitivity to the details of these nonconstant terms. Overall we find a good agreement with the lattice results. For the pressure, the conformal anomaly, and the Polyakov loop the nonconstant terms are relevant only in a narrow region below ~1.2Td. We also compute the 't Hooft loop, and find that the details of the nonconstant terms enter in a much wider region, up to ~4Td.

hep-ph↗