arXiv subjects

Krishna Rajagopal

Publications and source records attributed to Krishna Rajagopal.

At least 127 records · Page 7Linked to original sources

arXiv2002

Mass-Induced Crystalline Color Superconductivity

We demonstrate that crystalline color superconductivity may arise as a result of pairing between massless quarks and quarks with nonzero mass m_s. Previous analyses of this phase of cold dense quark matter have all utilized a chemical potential difference δμto favor crystalline color superconductivity over ordinary BCS pairing. In any context in which crystalline color superconductivity occurs in nature, however, it will be m_s-induced. The effect of m_s is qualitatively different from that of δμin one crucial respect: m_s depresses the value of the BCS gap Δ_0 whereas δμleaves Δ_0 unchanged. This effect in the BCS phase must be taken into account before m_s-induced and δμ-induced crystalline color superconductivity can sensibly be compared.

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arXiv2001

Crystalline Color Superconductivity

We give an introduction crystalline color superconductivity, arguing that it is likely to occur wherever quark matter in which color-flavor locking does not occur is found. We survey the properties of this form of quark matter, and argue that its presence in a compact star may result in pulsar glitches, and thus in observable consequences. However, elucidation of this proposal requires an understanding of the crystal structure, which is not yet in hand.

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arXiv2001

Illuminating Dense Quark Matter

We imagine shining light on a lump of cold dense quark matter, in the CFL phase and therefore a transparent insulator. We calculate the angles of reflection and refraction, and the intensity of the reflected and refracted light. Although the only potentially observable context for this phenomenon (reflection of light from and refraction of light through an illuminated quark star) is unlikely to be realized, our calculation casts new light on the old idea that confinement makes the QCD vacuum behave as if filled with a condensate of color-magnetic monopoles.

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arXiv2001

Langevin Evolution of Disoriented Chiral Condensate

As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this evolution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region of disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a theory which is ultraviolet cutoff independent and that reproduces quantitatively the expected equilibrium behavior of the quantum field theory of pions and sigma fields over a wide range of temperatures. Finally, we estimate the viscosity $η(T)$, which controls the dynamical timescale in the Langevin equation, by requiring that the timescale for DCC decay agrees with previous calculations. The resulting $η(T)$ is larger than that found perturbatively. We also determine the temperature below which the classical field Langevin equation ceases to be a good model for the quantum field dynamics.

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arXiv2001

The Minimal CFL-Nuclear Interface

At nuclear matter density, electrically neutral strongly interacting matter in weak equilibrium is made of neutrons, protons and electrons. At sufficiently high density, such matter is made of up, down and strange quarks in the color-flavor locked phase, with no electrons. As a function of increasing density (or, perhaps, increasing depth in a compact star) other phases may intervene between these two phases which are guaranteed to be present. The simplest possibility, however, is a single first order phase transition between CFL and nuclear matter. Such a transition, in space, could take place either through a mixed phase region or at a single sharp interface with electron-free CFL and electron-rich nuclear matter in stable contact. Here we construct a model for such an interface. It is characterized by a region of separated charge, similar to an inversion layer at a metal-insulator boundary. On the CFL side, the charged boundary layer is dominated by a condensate of negative kaons. We then consider the energetics of the mixed phase alternative. We find that the mixed phase will occur only if the nuclear-CFL surface tension is significantly smaller than dimensional analysis would indicate.

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arXiv2001

Opening the Crystalline Color Superconductivity Window

Cold dense quark matter is in a crystalline color superconducting phase wherever pairing occurs between species of quarks with chemical potentials whose difference δμlies within an appropriate window. If the interaction between quarks is modeled as point-like, this window is rather narrow. We show that when the interaction between quarks is modeled as single-gluon exchange, the window widens by about a factor of ten at accessible densities and by much larger factors at higher density. This striking enhancement reflects the increasingly (1+1)-dimensional nature of the physics at weaker and weaker coupling. Our results indicate that crystalline color superconductivity is a generic feature of the phase diagram of cold dense quark matter, occurring wherever one finds quark matter which is not in the color-flavor locked phase. If it occurs within the cores of compact stars, a crystalline color superconducting region may provide a new locus for glitch phenomena.

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arXiv2001

A Diagrammatic Approach to Crystalline Color Superconductivity

We present a derivation of the gap equation for the crystalline color superconducting phase of QCD which begins from a one-loop Schwinger-Dyson equation written using a Nambu-Gorkov propagator modified to describe the spatially varying condensate. Some aspects of previous variational calculations become more straightforward when rephrased beginning from a diagrammatic starting point. This derivation also provides a natural base from which to generalize the analysis to include quark masses, nontrivial crystal structures, gluon propagation at asymptotic densities, and nonzero temperature. In this paper, we analyze the effects of nonzero temperature on the crystalline color superconducting phase.

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arXiv2001

Crystalline Color Superconductivity

In any context in which color superconductivity arises in nature, it is likely to involve pairing between species of quarks with differing chemical potentials. For suitable values of the differences between chemical potentials, Cooper pairs with nonzero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. Unlike the original LOFF state, these crystalline quark matter condensates include both spin zero and spin one Cooper pairs. We explore the range of parameters for which crystalline color superconductivity arises in the QCD phase diagram. If in some shell within the quark matter core of a neutron star (or within a strange quark star) the quark number densities are such that crystalline color superconductivity arises, rotational vortices may be pinned in this shell, making it a locus for glitch phenomena.

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arXiv2000

The Condensed Matter Physics of QCD

Important progress in understanding the behavior of hadronic matter at high density has been achieved recently, by adapting the techniques of condensed matter theory. At asymptotic densities, the combination of asymptotic freedom and BCS theory make a rigorous analysis possible. New phases of matter with remarkable properties are predicted. They provide a theoretical laboratory within which chiral symmetry breaking and confinement can be studied at weak coupling. They may also play a role in the description of neutron star interiors. We discuss the phase diagram of QCD as a function of temperature and density, and close with a look at possible astrophysical signatures.

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arXiv2000

Color Superconductivity in Compact Stars

After a brief review of the phenomena expected in cold dense quark matter, color superconductivity and color-flavor locking, we sketch some implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars. We give a more detailed summary of our recent work on crystalline color superconductivity and the consequent realization that (some) pulsar glitches may originate in quark matter.

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arXiv2000

The Phases of QCD in Heavy Ion Collisions and Compact Stars

I review arguments for the existence of a critical point in the QCD phase diagram as a function of temperature and baryon chemical potential. I describe how heavy ion collision experiments at the SPS and RHIC can discover the tell-tale signatures of such a critical point, thus mapping this region of the QCD phase diagram. I then review the phenomena expected in cold dense quark matter: color superconductivity and color-flavor locking. I close with a snapshot of ongoing explorations of the implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars.

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arXiv2000

On the Applicability of Weak-Coupling Results in High Density QCD

Quark matter at asymptotically high baryon chemical potential is in a color superconducting state characterized by a gap Delta. We demonstrate that although present weak-coupling calculations of Delta are formally correct for mu -> Infinity, the contributions which have to this point been neglected are large enough that present results can only be trusted for mu >> mu_c ~ 10^8 MeV. We make this argument by using the gauge dependence of the present calculation as a diagnostic tool. It is known that the present calculation yields a gauge invariant result for mu -> Infinity; we show, however, that the gauge dependence of this result only begins to decrease for mu > mu_c, and conclude that the result can certainly not be trusted for mu < mu_c. In an appendix, we set up the calculation of the influence of the Meissner effect on the magnitude of the gap. This contribution to Delta is, however, much smaller than the neglected contributions whose absence we detect via the resulting gauge dependence.

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arXiv2000

Traversing the QCD Phase Transition: Quenching Out of Equilibrium vs. Slowing Out of Equilibrium vs. Bubbling Out of Equilibrium

I review arguments for the existence of a critical point E in the QCD phase diagram as a function of temperature T and baryon chemical potential μ. I describe how heavy ion collision experiments at the SPS and RHIC can discover the tell-tale signatures of such a critical point, thus mapping this region of the QCD phase diagram. I contrast the different ways in which the matter produced in a heavy ion collision can be driven out of equilibrium: quenching out of equilibrium (possible, but not guaranteed, if the transition region is traversed at μ<< μ_E) vs. slowing out of equilibrium (guaranteed for μ\sim μ_E) vs. bubbling out of equilibrium (possible, but not guaranteed, for μ>> μ_E). Quenching or bubbling create and amplify distinct, detectable, non-gaussian fluctuations. In contrast, slowing out of equilibrium reduces the magnitude of the specific, detectable, gaussian fluctuations which signal the presence of the critical point.

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arXiv2000

Collision-Induced Decay of Metastable Baby Skyrmions

Many extensions of the standard model predict heavy metastable particles which may be modeled as solitons (skyrmions of the Higgs field), relating their particle number to a winding number. Previous work has shown that the electroweak interactions admit processes in which these solitons decay, violating standard model baryon number. We motivate the hypothesis that baryon-number-violating decay is a generic outcome of collisions between these heavy particles. We do so by exploring a 2+1 dimensional theory which also possesses metastable skyrmions. We use relaxation techniques to determine the size, shape and energy of static solitons in their ground state. These solitons could decay by quantum mechanical tunneling. Classically, they are metastable: only a finite excitation energy is required to induce their decay. We attempt to induce soliton decay in a classical simulation by colliding pairs of solitons. We analyze the collision of solitons with varying inherent stabilities and varying incident velocities and orientations. Our results suggest that winding-number violating decay is a generic outcome of collisions. All that is required is sufficient (not necessarily very large) incident velocity; no fine-tuning of initial conditions is required.

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arXiv2000

Slowing Out of Equilibrium Near the QCD Critical Point

The QCD phase diagram may feature a critical end point at a temperature T and baryon chemical potential $μ$ which is accessible in heavy ion collisions. The universal long wavelength fluctuations which develop near this Ising critical point result in experimental signatures which can be used to find the critical point. The magnitude of the observed effects depends on how large the correlation length $ξ$ becomes. Because the matter created in a heavy ion collision cools through the critical region of the phase diagram in a finite time, critical slowing down limits the growth of $ξ$, preventing it from staying in equilibrium. This is the fundamental nonequilibrium effect which must be calculated in order to make quantitative predictions for experiment. We use universal nonequilibrium dynamics and phenomenologically motivated values for the necessary nonuniversal quantities to estimate how much the growth of $ξ$ is slowed.

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arXiv1999

Mapping the QCD Phase Diagram

I review recent theoretical developments which show how a key qualitative feature of the QCD phase diagram, namely a critical point which in a sense defines the landscape which heavy ion collision experiments are seeking to map, can be discovered. The map of the phase diagram which I sketch is based on reasonable inference from universality, lattice gauge theory and models; the discovery of the critical point would provide an experimental foundation for the central qualitative feature of the landscape. I also review recent progress in our understanding of cold, dense quark matter, as may occur in the cores of neutron stars. In this regime, quarks form Cooper pairs. The formation of such superconducting phases requires only weak attractive interactions, as provided by one-gluon exchange at asymptotically high density; these phases may nevertheless break chiral symmetry (by locking flavor symmetries to color symmetry) and may have excitations which are indistinguishable from those in a confined phase. Mapping this part of the phase diagram will require a better understanding of how the presence of color superconductivity and color-flavor locking affects neutron star phenomenology.

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arXiv1999

How to Find the QCD Critical Point

The event-by-event fluctuations in heavy ion collisions carry information about the thermodynamic properties of the hadronic system at the time of freeze-out. By studying these fluctuations as a function of varying control parameters, such as the collision energy, it is possible to learn much about the phase diagram of QCD. As a timely example, we stress the methods by which present experiments at the CERN SPS can locate the second order critical point at which a line of first order phase transitions ends. Those event-by-event signatures which are characteristic of freeze-out in the vicinity of the critical point will exhibit nonmonotonic dependence on control parameters. We focus on observables constructed from the multiplicity and transverse momenta of charged pions. We find good agreement between NA49 data and thermodynamic predictions for the noncritical fluctuations of such observables. We then analyze the effects due to the critical fluctuations of the sigma field. We estimate the size of these nonmonotonic effects which appear near the critical point, including restrictions imposed by finite size and finite time.

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arXiv1998

The QCD Tricritical Point: Beyond Monotony in Heavy Ion Physics

I first sketch recent developments concerning the phase diagram of strongly interacting matter as a function of temperature and baryon density, obtained using a model for two-flavor QCD in which the interaction between quarks is modelled on that induced by instantons. The phase diagram has a chiral symmetry breaking vacuum, a color superconductor phase at high density, and a mixed phase in between which can describe nuclear matter if the high density regions in the mixed phase form droplets. This is amusingly similar to the phase diagram of the copper oxide superconductors, although their critical temperatures are smaller by a factor of about 10^{-9} and their mixed phase seems to form stripes, rather than droplets. This and other approaches to QCD with two massless quarks suggests the existence of a tricritical point on the boundary of the phase with spontaneously broken chiral symmetry. In QCD with massive quarks there is then a critical point at the end of a first order transition line. We discuss possible experimental signatures of this point, which provide information about its location and properties. We propose a combination of event-by-event observables, including suppressed fluctuations in T and mu and, simultaneously, enhanced fluctuations in the multiplicity of soft pions. As a control parameter (like the collision energy) is varied, the fluctuations of appropriate event-by-event observables should therefore have minima or maxima. Experimental detection of these non-monotonic signatures would confirm that the matter was initially above the chiral phase transition, increasing our confidence in the interpretation of monotonic changes in other observables, and would teach us much about the QCD phase diagram.

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