arXiv subjects

Prabal Adhikari

Publications and source records attributed to Prabal Adhikari.

At least 37 records · Page 2Linked to original sources

arXiv2020

Pion and kaon condensation at zero temperature in three-flavor $χ$PT at nonzero isospin and strange chemical potentials at next-to-leading order

We consider three-flavor chiral perturbation theory ($χ$PT) at zero temperature and nonzero isospin ($μ_{I}$) and strange ($μ_{S}$) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the $π^{\pm}$-condensed phase, the $K^{\pm}$-condensed phase, and the $K^0/\bar{K}^0$-condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, $|μ_I|=m_π$, $|{1\over2}μ_I+μ_S|=m_K$, and $|-{1\over2}μ_I+μ_S|=m_K$, respectively at tree level and remains unchanged at NLO. The transition between the two condensed phases is first order. The effective potential in the pion-condensed phase is independent of $μ_S$ and in the kaon-condensed phases, it only depends on the combinations $\pm{1\over2}μ_I+μ_S$ and not separately on $μ_I$ and $μ_S$. We calculate the pressure, isospin density and the equation of state in the pion-condensed phase and compare our results with recent $(2+1)$-flavor lattice QCD data. We find that the three-flavor $χ$PT results are in good agreement with lattice QCD for $μ_I<200$ MeV, however for larger values $χ$PT produces values for observables that are consistently above lattice results. For $μ_I>200$ MeV, the two-flavor results are in better agreement with lattice data. Finally, we consider the observables in the limit of very heavy $s$-quarks, where they reduce to their two-flavor counterparts with renormalized couplings. The disagreement between the predictions of two and three flavor $χ$PT can largely be explained by the differences in the experimental values of the low-energy constants.

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arXiv2020

Multicomponent superfluidity in two-color QCD at finite density at next-to-leading order

In this paper, we study two-color, two-flavor QCD using chiral perturbation theory at next-to-leading order when the diquark chemical potential ($μ_{B}$) is equal to the isospin chemical potential ($μ_{I}$). For chemical potentials larger than the physical pion mass, the system is in a multicomponent superfluid phase with both pions and diquarks. We construct the one-loop effective potential using $χ$PT in the presence of an external multicomponent superfluid source and use the effective potential to calculate the chiral condensate, the multicomponent superfluid condensate and the (multicomponent) superfluid density. We also find the critical chemical potential and the order of the phase transition from the normal phase to the multicomponent condensed phase at next-to-leading order. The phase transition remains second order (as at tree-level) and the critical chemical potential is equal to the one-loop renormalized diquark (or pion) mass.

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arXiv2020

QCD at finite isospin density: chiral perturbation theory confronts lattice data

We consider the thermodynamics of three-flavor QCD in the pion-condensed phase at nonzero isospin chemical potential ($μ_I$) and vanishing temperature using chiral perturbation theory in the isospin limit. The transition from the vacuum phase to a superfluid phase with a Bose-Einstein condensate of charged pions is shown to be second order and takes place at $μ_I=m_π$. We calculate the pressure, isospin density, and energy density to next-to-leading order in the low-energy expansion. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor chiral perturbation theory. The agreement between the lattice results and the predictions from three-flavor chiral perturbation theory is very good for $μ_I<200$ MeV. For larger values of $μ_I$, the agreement between lattice data and the two-flavor predictions is surprisingly good and better than with the three-flavor predictions. Finally, in the limit $m_{s}\gg m_{u}=m_{d}$, we show that the three-flavor observables reduce to the two-flavor observables with renormalized parameters. The disagreement between the results for two-flavor and three-flavor $χ$PT can largely be explained by the differences in the measured low-energy constants.

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arXiv2019

Two-flavor chiral perturbation theory at nonzero isospin: Pion condensation at zero temperature

In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2+1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in $χ$PT.

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arXiv2018

Pion condensation and phase diagram in the Polyakov-loop quark-meson model

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the $μ_I$--$T$ plane where $μ_I$ is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At $T=0$, the onset of pion condensation is at $μ_I={1\over2}m_π$ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of $μ_I$ and in the $O(2)$ universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of $μ_I$ these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken $O(2)$ symmetry. We compare our results with recent lattice simulations and find overall good agreement.

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arXiv2018

Magnetic Vortex Lattices in Finite Isospin Chiral Perturbation Theory

We study finite isospin chiral perturbation theory ($χ$PT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg-Landau (GL) theory (or equivalently the Abelian Higgs model) and $χ$PT arises due to the presence of additional momentum-dependent (derivative) interactions in $χ$PT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.

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arXiv2018

Magnetic Vortices in the Abelian Higgs Model with Derivative Interactions

We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs Model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of successive approximations, which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).

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arXiv2018

Pion condensation and QCD phase diagram at finite isospin density

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study 1) the possibility of inhomogeneous chiral condensates and its competition with a homogeneous pion condensate in the $μ$--$μ_I$ plane at $T=0$ and 2) the phase diagram in the $μ_I$--$T$ plane. In the $μ$--$μ_I$ plane, we find that an inhomogeneous chiral condensate only exists for pion masses lower that 37.1 MeV and does not coexist with a homogeneous pion condensate. In the $μ_I$--$T$ plane, we find that the phase transition to a Bose-condensed phase is of second order for all values of $μ_I$ and we find that there is no pion condensation for temperatures larger than approximately 187 MeV. The chiral critical line joins the critical line for pion condensation at a point, whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of $μ_I$ these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken $O(2)$ symmetry. We compare our results with recent lattice simulations and find overall good agreement

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arXiv2018

Finite Density Two Color Chiral Perturbation Theory Revisited

We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an $SU(2)$ doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global $SU(2)$ transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

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arXiv2017

Inhomogeneous chiral condensate in the quark-meson model

The two-flavor quark-meson model is used as a low-energy effective model for QCD to study inhomogeneous chiral condensates at finite %temperature $T$ baryon chemical potential $μ_B$. The parameters of the model are determined by matching the meson and quark masses, and the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. Using a chiral-density wave ansatz for the inhomogeneity, we calculate the effective potential in the mean-field approximation and the result is completely analytic. The size of the inhomogeneous phase depends sensitively on the pion mass and whether one includes the vacuum fluctuations or not. Finally, we briefly discuss the mean-field phase diagram.

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arXiv2017

Consistent regularization and renormalization in models with inhomogeneous phases

In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.

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arXiv2017

Chiral density wave versus pion condensation in the 1+1 dimensional NJL model

In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $μ$ using dimensional regularization. The phase diagram in the $μ$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $μ>μ_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential $μ_I$. The phase diagram in the $μ_I$--$μ$ plane is mapped out and shows a rich phase structure.

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arXiv2017

Vortex solutions in the Abelian Higgs Model with a neutral scalar

We construct an extension of the Abelian Higgs model, which consists of a complex scalar field by including an additional real, electromagnetically neutral scalar field. We couple this real scalar field to the complex scalar field via a quartic coupling and investigate $U(1)$ vortex solutions in this "extended Abelian Higgs Model". Since this model has two additional homogeneous ground states, the $U(1)$ vortices that can form in this model have a richer structure than in the Abelian Higgs Model. We also find the "phase diagram" of the model showing the parameter space in which the real scalar particle condenses in the vortex state while having a zero vacuum expectation value in the homogeneous ground state.

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arXiv2017

On-shell parameter fixing in the quark-meson model

The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$ and baryon chemical potential $μ_B$. The parameters in the quark-meson model can be found by expressing them in terms of the sigma mass $m_σ$, the pion mass $m_π$, the constituent quark mass $m_q$ and the pion decay constant $f_π$. In practice, this matching is done at tree level, which is inconsistent once we take loop effects of the effective potential into account. We show how to properly perform the matching in the quark-meson model by using the on-shell and the modified minimal subtraction renormalization schemes relating the physical masses and the pion decay constant to the running mass parameter and couplings. We map out the phase diagram in the $μ_B$--$T$ plane and compare our results with other approximations.

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arXiv2015

Axial anomaly effects in finite isospin $χ$PT in a magnetic field

In this paper, we consider finite isospin chiral perturbation theory including the effects of the axial anomaly (through the Wess-Zumino-Witten term) in a strong magnetic field. We firstly prove that in a strong external magnetic field ($H_{\rm ext}$) or more precisely the Schwinger limit, where photon back-reactions are suppressed, only neutral pions can condense and the condensation of charged pions is forbidden. Secondly, we find that the $π^{0}$ domain wall is an example of a phase that can exist in a strong magnetic field and suggest the existence of a new phase transition line from the normal vacuum state to the $π^{0}$ domain wall state. This phase transition exists for non-zero pion masses if the baryon chemical potential exceeds a critical value $16πf_π^{2}m_π/eH_{\rm ext}$. The phase transition line persists away from the Schwinger limit when the photons can back-react to the external magnetic field.

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arXiv2015

Finite Isospin Chiral Perturbation Theory in a Magnetic Field

The phase diagram of finite isospin, zero temperature QCD with the pions coupled to photons in a uniform external magnetic field is explored in the low field, small isospin density regime for which chiral perturbation theory is a valid description. For realistic pion masses, the system behaves as a type-II superconductor: a uniform superconducting state is formed at low-enough magnetic fields, a vortex state for intermediate magnetic fields and finally a normal state for large magnetic fields. In each these phases (including the vortex phase), the $π^{0}$ remains uncondensed just as in the zero-external field problem. The critical magnetic field where the phase transition from the uniform superconducting state to a vortex state occurs was found numerically.

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arXiv2013

Density of Saturated Nuclear Matter at Large $N_{c}$ and Heavy Quark Mass Limits

We exhibit the existence of stable, saturated nuclear matter in the large $N_{c}$ and heavy quark mass limits of QCD. In this limit, baryons (with the same spin flavor structure) interact at leading order in $N_{c}$ via a repulsive interaction due to the Pauli exclusion principle and at subleading order in $1/N_c$ via the exchange of glueballs. Assuming that the lightest glueball is a scalar, which implies that the subleading baryon interaction is attractive, we find that nuclear matter saturates since the subleading attractive interaction is longer ranged than the leading order repulsive one. We find that the saturated matter is in the form of a crystal with either a face-centered cubic or a hexagonal-close-packed symmetry with baryon densities of $\mathcal{O}((\, \tildeα_{s} m_q (\ln (N_{c}m_{q}Λ_{\textrm{QCD}}^{-1}))^{-1})^3 )$. Remarkably, the leading order expression for the density of saturated nuclear matter is independent of the lighest glueball mass and scalar-glueball-baryon coupling in the extreme large $N_{c}$ limit or heavy quark limit (or both), which we define precisely in this work.

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arXiv2013

Mean-field theory of baryonic matter for QCD in the large $N_{c}$ and heavy quark mass limits

We discuss theoretical issues pertaining to baryonic matter in the combined heavy-quark and large $N_c$ limits of QCD. Witten's classic argument that baryons and interacting systems of baryons can be described in a mean-field approximation with each of the quarks moving in an average potential due to the remaining quarks is heuristic. It is important to justify this heuristic description for the case of baryonic matter since systems of interacting baryons are intrinsically more complicated than single baryons due to the possibility of hidden color states---states in which the subsystems making up the entire baryon crystal are not color-singlet nucleons but rather colorful states coupled together to make a color-singlet state. In this work, we provide a formal justification of this heuristic prescription. In order to do this, we start by taking the heavy quark limit, thus effectively reducing the problem to a many-body quantum mechanical system. This problem can be formulated in terms of integrals over coherent states, which for this problem are simple Slater determinants. We show that for the many-body problem, the support region for these integrals becomes narrow at large $N_c$, yielding an energy which is well-approximated by a single coherent state---that is a mean-field description. Corrections to the energy are of relative order $1/N_c$. While hidden color states are present in the exact state of the heavy quark system, they only influence the interaction energy at sub-leading order in $1/N_{c}$.

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