arXiv subjects

Krishna Rajagopal

Publications and source records attributed to Krishna Rajagopal.

At least 109 records · Page 6Linked to original sources

arXiv2006

An AdS/CFT Calculation of Screening in a Hot Wind

One of the challenges in relating experimental measurements of the suppression in the number of J/ψmesons produced in heavy ion collisions to lattice QCD calculations is that whereas the lattice calculations treat J/ψmesons at rest, in a heavy ion collision a c\bar c pair can have a significant velocity with respect to the hot fluid produced in the collision. The putative J/ψfinds itself in a hot wind. We present the first rigorous non-perturbative calculation of the consequences of a wind velocity v on the screening length L_s for a heavy quark-antiquark pair in hot N=4 supersymmetric QCD. We find L_s(v,T) = f(v)[1-v^2]^{1/4}/πT with f(v) only mildly dependent on v and the wind direction. This L_s(v,T)\sim L_s(0,T)/\sqrtγ velocity scaling, if realized in QCD, provides a significant additional source of J/Ψsuppression at transverse momenta which are high but within experimental reach.

hep-ph↗

arXiv2006

Stress-free BCS pairing in color superconductors is impossible

Cold, asymptotically dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all quarks pair in a particularly symmetric fashion. At smaller densities, taking into account a nonzero strange quark mass and electric and color neutrality, the CFL phase requires pairing of quarks with mismatched Fermi momenta. We present a classification of all other possible, less symmetric, pairing patterns and prove that none of them can avoid this mismatch. This result suggests unconventional, e.g., spatially inhomogeneous, superconducting phases for moderate densities.

nucl-th↗

arXiv2006

Calculating the Jet Quenching Parameter from AdS/CFT

Models of medium-induced radiative parton energy loss account for the strong suppression of high-pT hadron spectra in $\sqrt{s_{NN}}=200$ GeV Au-Au collisions at RHIC in terms of a single "jet quenching parameter'' $\hat q$. The available suite of jet quenching measurements make $\hat q$ one of the experimentally best constrained properties of the hot fluid produced in RHIC collisions. We observe that $\hat q$ can be given a model-independent, nonperturbative, quantum field theoretic definition in terms of the short-distance behavior of a particular light-like Wilson loop. We then use the AdS/CFT correspondence to obtain a strong-coupling calculation of $\hat q$ in hot N=4 supersymmetric QCD, finding $\hat{q}_{SYM} = 26.69 \sqrt{α_{SYM} N_c} T^3$ in the limit in which both $N_c$ and $4πα_{SYM} N_c$ are large. We thus learn that at strong coupling $\hat q$ is not proportional to the entropy density $s$, or to some "number density of scatterers'' since, unlike the number of degrees of freedom, $\hat q$ does not grow like $N_c^2$.

hep-ph↗

arXiv2006

Color Superconductivity in Dense, but not Asymptotically Dense, Quark Matter

At ultra-high density, matter is expected to form a degenerate Fermi gas of quarks in which there is a condensate of Cooper pairs of quarks near the Fermi surface: color superconductivity. In this chapter we review some of the underlying physics, and discuss outstanding questions about the phase structure of ultra-dense quark matter. We then focus on describing recent results on the crystalline color superconducting phase that may be the preferred form of cold, dense but not asymptotically dense, three-flavor quark matter. The gap parameter and free energy for this phase have recently been evaluated within a Ginzburg-Landau approximation for many candidate crystal structures. We describe the two that are most favorable. The robustness of these phases results in their being favored over wide ranges of density. However, it also implies that the Ginzburg-Landau approximation is not quantitatively reliable. We describe qualitative insights into what makes a crystal structure favorable which can be used to winnow the possibilities. We close with a look ahead at the calculations that remain to be done in order to make quantitative contact with observations of compact stars.

hep-ph↗

arXiv2006

The Crystallography of Strange Quark Matter

Cold three-flavor quark matter at large (but not asymptotically large) densities may exist as a crystalline color superconductor. We explore this possibility by calculating the gap parameter Delta and free energy Omega(Delta) for possible crystal structures within a Ginzburg-Landau approximation, evaluating Omega(Delta) to order Delta^6. We develop a qualitative understanding of what makes a crystal structure stable, and find two structures with particularly large values of Delta and the condensation energy, within a factor of two of those for the CFL phase known to characterize QCD at asymptotically large densities. The robustness of these phases results in their being favored over wide ranges of density and though it also implies that the Ginzburg-Landau approximation is not quantitatively reliable, previous work suggests that it can be trusted for qualitative comparisons between crystal structures. We close with a look ahead at the calculations that remain to be done in order to make contact with observed pulsar glitches and neutron star cooling.

hep-ph↗

arXiv2006

The Crystallography of Three-Flavor Quark Matter

We analyze and compare candidate crystal structures for the crystalline color superconducting phase that may arise in cold, dense but not asymptotically dense, three-flavor quark matter. We determine the gap parameter Delta and free energy Omega(Delta) for many possible crystal structures within a Ginzburg-Landau approximation, evaluating Omega(Delta) to order Delta^6. In contrast to the two-flavor case, we find a positive Delta^6 term and hence an Omega(Delta) that is bounded from below for all the structures that we analyze. This means that we are able to evaluate Delta and Omega as a function of the splitting between Fermi surfaces for all the structures we consider. We find two structures with particularly robust values of Delta and the condensation energy, within a factor of two of those for the CFL phase which is known to characterize QCD at asymptotically large densities. The robustness of these phases results in their being favored over wide ranges of density. However, it also implies that the Ginzburg-Landau approximation is not quantitatively reliable. We develop qualitative insights into what makes a crystal structure favorable, and use these to winnow the possibilities. The two structures that we find to be most favorable are both built from condensates with face-centered cubic symmetry: in one case, the and condensates are separately face centered cubic; in the other case and combined make up a face centered cube.

hep-ph↗

arXiv2006

Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity

It is an open challenge to analyze the crystalline color superconducting phases that may arise in cold dense, but not asymptotically dense, three-flavor quark matter. At present the only approximation within which it seems possible to compare the free energies of the myriad possible crystal structures is the Ginzburg-Landau approximation. Here, we test this approximation on a particularly simple "crystal" structure in which there are only two condensates $ \sim Δ\exp(i {\bf q_2}\cdot {\bf r})$ and $ \sim Δ\exp(i {\bf q_3}\cdot {\bf r})$ whose position-space dependence is that of two plane waves with wave vectors ${\bf q_2}$ and ${\bf q_3}$ at arbitrary angles. For this case, we are able to solve the mean-field gap equation without making a Ginzburg-Landau approximation. We find that the Ginzburg-Landau approximation works in the $Δ\to 0$ limit as expected, find that it correctly predicts that $Δ$ decreases with increasing angle between ${\bf q_2}$ and ${\bf q_3}$ meaning that the phase with ${\bf q_2}\parallel {\bf q_3}$ has the lowest free energy, and find that the Ginzburg-Landau approximation is conservative in the sense that it underestimates $Δ$ at all values of the angle between ${\bf q_2}$ and ${\bf q_3}$.

hep-ph↗

arXiv2006

The Stability of Strange Star Crusts and Strangelets

We construct strangelets, taking into account electrostatic effects, including Debye screening, and arbitrary surface tension sigma of the interface between vacuum and quark matter. We find that there is a critical surface tension sigma_crit below which large strangelets are unstable to fragmentation and below which quark star surfaces will fragment into a crystalline crust made of charged strangelets immersed in an electron gas. We derive a model-independent relationship between sigma_crit and two parameters that characterize any quark matter equation of state. For reasonable model equations of state, we find sigma_crit typically of order a few MeV/fm^2. If sigma <= sigma_crit, the size-distribution of strangelets in cosmic rays could feature a peak corresponding to the stable strangelets that we construct.

hep-ph↗

arXiv2006

Stressed pairing in conventional color superconductors is unavoidable

At sufficiently high densities, cold dense three-flavor quark matter is in the color-flavor locked (CFL) phase, in which all nine quarks pair in a particularly symmetric fashion. Once the heaviness of the strange quark (mass $m_s$) and the requirements of electric and color neutrality are taken into account, the CFL pattern of color superconductivity requires the pairing of quarks that would, in the absence of pairing, have Fermi momenta that differ by of order $m_s^2/μ$, with $μ$ the quark number chemical potential. This means that at sufficiently small $μ$, the ``stress'' on the pairing is large enough that the system can lower its energy by breaking pairs, resulting in some unconventional color superconductor which includes gapless excitations, spatial inhomogeneity, counter-propagating currents, or all three. In this paper we ask whether there is some less symmetric but still conventional pattern of pairing that can evade the stress. In other words, is there a pattern of pairing in which, once electric and color neutrality are imposed by suitable chemical potentials, pairing only occurs among those quarks whose Fermi momenta would be equal in the absence of pairing? We use graph-theoretical methods to classify 511 patterns of conventional color superconducting pairing, and show that none of them meet this requirement. All feel a stress, and all can be expected to become unstable to gapless modes at a density comparable to that at which the CFL phase becomes unstable.

hep-ph↗

arXiv2005

A Hot Water Bottle for Aging Neutron Stars

The gapless color-flavor locked (gCFL) phase is the second-densest phase of matter in the QCD phase diagram, making it a plausible constituent of the core of neutron stars. We show that even a relatively small region of gCFL matter in a star will dominate both the heat capacity C_V and the heat loss by neutrino emission L_ν. The gCFL phase is characterized by an unusual quasiparticle dispersion relation that makes both its specific heat c_V and its neutrino emissivity epsilon_νparametrically larger than in any other phase of nuclear or quark matter. During the epoch in which the cooling of the star is dominated by direct Urca neutrino emission, the presence of a gCFL region does not strongly alter the cooling history because the enhancements of C_V and L_νcancel against each other. At late times, however, the cooling is dominated by photon emission from the surface, so L_νis irrelevant, and the anomalously large heat capacity of the gCFL region keeps the star warm. The temperature drops with time as T\sim t^{-1.4} rather than the canonical T\sim t^{-5}. This provides a unique and potentially observable signature of gCFL quark matter.

astro-ph↗

arXiv2005

From Entropy and Jet Quenching to Deconfinement?

The challenge of demonstrating that the matter produced in heavy ion collisions is a deconfined quark-gluon plasma, as predicted by lattice QCD calculations, is the challenge of measuring the number of thermodynamic degrees of freedom ν~ ε/T^4 at the time t0 at which the matter comes into approximate local thermal equilibrium and begins to behave like a hydrodynamic fluid. Data from experiments done at the Relativistic Heavy Ion Collider have been used to estimate t0 and to put a lower bound on the energy density ε(t0). However, measuring νhas seemed out of reach, because no current data serve even as qualitative proxies for the temperature T(t0). We point out that νmay equally appropriately be defined via ν~s^4/epsilon^3, where s is the entropy density, which can be estimated from the measured final state entropy. This estimate is based on the testable assumption of an isentropic expansion. The observation of jet quenching has the potential to provide an upper bound on the energy density at early times. Our goal is to motivate such an analysis by pointing out that it would set a lower bound on ν.

hep-ph↗

arXiv2004

Heating (Gapless) Color-Flavor Locked Quark Matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass Ms. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number and Delta is the gap in the CFL phase. We find this distinction blurred at nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu, we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do not make any small-Ms approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of Ms that there are no strange quarks present.

hep-ph↗

arXiv2004

Evaluating the Gapless Color-Flavor Locked Phase

In neutral cold quark matter that is sufficiently dense that the strange quark mass M_s is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We recently argued that the next phase down in density (as a function of decreasing quark chemical potential mu or increasing strange quark mass M_s) is the new ``gapless CFL'' (``gCFL'') phase in which only seven quasiparticles have a gap, while there are gapless quasiparticles described by two dispersion relations at three momenta. There is a continuous quantum phase transition from CFL to gCFL quark matter at M_s^2/mu approximately equal to 2*Delta, with Delta the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination "Q-tilde" of electric and color charges, but it is a Q-tilde-conductor with gapless Q-tilde-charged quasiparticles and a nonzero electron density. In this paper, we evaluate the gapless CFL phase, in several senses. We present the details underlying our earlier work which showed how this phase arises. We display all nine quasiparticle dispersion relations in full detail. Using a general pairing ansatz that only neglects effects that are known to be small, we perform a comparison of the free energies of the gCFL, CFL, 2SC, gapless 2SC, and 2SCus phases. We conclude that as density drops, making the CFL phase less favored, the gCFL phase is the next spatially uniform quark matter phase to occur. A mixed phase made of colored components would have lower free energy if color were a global symmetry, but in QCD such a mixed phase is penalized severely.

hep-ph↗

arXiv2004

Gapless CFL and its competition with mixed phases

We recently argued that as the density of quark matter decreases, there is a continuous transition from the color-flavor-locked (CFL) phase to a gapless "gCFL" phase. The reason is the growing importance of the strange quark mass, and the constraint of electric/color neutrality. In this paper we discuss mixed phases that achieve neutrality by charge seperation, and might offer an alternative to the gCFL phase. We find that none of the obvious mixtures is favored relative to gCFL.

hep-ph↗

arXiv2004

Gapless Color-Flavor-Locked Quark Matter

In neutral cold quark matter that is sufficiently dense that the strange quark mass M_s is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We argue that as a function of decreasing quark chemical potential mu or increasing M_s, there is a quantum phase transition from the CFL phase to a new ``gapless CFL phase'' in which only seven quasiparticles have a gap. The transition occurs where M_s^2/mu is approximately equal to 2*Delta, with Delta the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination Qtilde of electric and color charges, but it is a Qtilde-conductor with a nonzero electron density. These electrons and the gapless quark quasiparticles make the low energy effective theory of the gapless CFL phase and, consequently, its astrophysical properties are qualitatively different from those of the CFL phase, even though its U(1) symmetries are the same. Both gapless quasiparticles have quadratic dispersion relations at the quantum critical point. For values of M_s^2/mu above the quantum critical point, one branch has conventional linear dispersion relations while the other branch remains quadratic, up to tiny corrections.

hep-ph↗

arXiv2002

The crystallography of color superconductivity

We describe the crystalline phase of color superconducting quark matter. This phase may occur in quark matter at densities relevant for compact star physics, with possible implications for glitch phenomena in pulsars. We use a Ginzburg-Landau approach to determine that the crystal has a face-centered-cubic (FCC) structure. Moreover, our results indicate that the phase is robust, with gaps, critical temperature, and free energy comparable to those of the color-flavor-locked (CFL) phase. Our calculations also predict ``crystalline superfluidity'' in ultracold gases of fermionic atoms.

hep-ph↗

arXiv2002

Absence of two-flavor color-superconductivity in compact stars

The simplest pattern of color superconductivity involves BCS pairing between up and down quarks. We argue that this ``2SC'' phase will not arise within a compact star. A macroscopic volume of quark matter must be electrically neutral and must be a color singlet. Satisfying these requirements imposes a significant free energy cost on the 2SC phase, but not on color-flavor locked (CFL) quark matter, in which up, down and strange quarks all pair. As a function of increasing density, therefore, one may see a single phase transition from hadronic matter directly to CFL quark matter. Alternatively, there may be an intervening phase in which the different flavors self-pair, or pair with each other in a non-BCS pattern, such as in a crystalline color superconductor.

hep-ph↗

arXiv2002

The Crystallography of Color Superconductivity

We develop the Ginzburg-Landau approach to comparing different possible crystal structures for the crystalline color superconducting phase of QCD, the QCD incarnation of the Larkin-Ovchinnikov-Fulde-Ferrell phase. In this phase, quarks of different flavor with differing Fermi momenta form Cooper pairs with nonzero total momentum, yielding a condensate that varies in space like a sum of plane waves. We work at zero temperature, as is relevant for compact star physics. The Ginzburg-Landau approach predicts a strong first-order phase transition (as a function of the chemical potential difference between quarks) and for this reason is not under quantitative control. Nevertheless, by organizing the comparison between different possible arrangements of plane waves (i.e. different crystal structures) it provides considerable qualitative insight into what makes a crystal structure favorable. Together, the qualitative insights and the quantitative, but not controlled, calculations make a compelling case that the favored pairing pattern yields a condensate which is a sum of eight plane waves forming a face-centered cubic structure. They also predict that the phase is quite robust, with gaps comparable in magnitude to the BCS gap that would form if the Fermi momenta were degenerate. These predictions may be tested in ultracold gases made of fermionic atoms. In a QCD context, our results lay the foundation for a calculation of vortex pinning in a crystalline color superconductor, and thus for the analysis of pulsar glitches that may originate within the core of a compact star.

hep-ph↗