scholarly journals The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential

2010 ◽  
Vol 2010 (6) ◽  
Author(s):  
Christoph Lehner ◽  
Shoji Hashimoto ◽  
Tilo Wettig
Keyword(s):  
Chemical Potential ◽  
Leading Order ◽  
Epsilon Expansion

scholarly journals Two-flavor chiral perturbation theory at nonzero isospin: pion condensation at zero temperature

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Patrick Kneschke
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Condensed Phase ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Tree Level ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensation

Abstract 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 $$\chi $$χPT.

scholarly journals Quark and pion condensates at finite isospin density in chiral perturbation theory

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensate ◽  
Independent Analysis ◽  
Model Independent

AbstractIn this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential $$\mu _I$$ μ I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

scholarly journals ON PHASE DIAGRAM OF GROSS-NEVEU MODEL AT FINITE TEMPERATURE, DENSITY AND CONSTANT CURVATURE

1995 ◽  
Vol 10 (24) ◽  
pp. 1777-1785 ◽  
Author(s):  
SHINYA KANEMURA ◽  
HARU-TADA SATO
Keyword(s):  
Constant Curvature ◽  
Finite Temperature ◽  
Critical Line ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Critical Surface ◽  
Leading Order ◽  
Third Order ◽  
Curvature Approximation ◽  
Gross Neveu Model

We discuss a phase structure of chiral symmetry breaking in the Gross-Neveu model at finite temperature, density and constant curvature. The effective potential is evaluated in the leading order of the 1/N-expansion and in a weak curvature approximation. The third-order critical line is found on the critical surface in the parameter space of temperature, chemical potential and constant curvature.

scholarly journals Improving the cold quark-matter pressure via soft interactions at N3LO

2022 ◽  
Vol 258 ◽  
pp. 05004
Author(s):  
Tyler Gorda
Keyword(s):  
Equation Of State ◽  
Quark Matter ◽  
Chemical Potential ◽  
High Momentum ◽  
Leading Order ◽  
Coupling Constant ◽  
Baryon Chemical Potential ◽  
Long Wavelength ◽  
Lengthy Calculation ◽  
Soft Interactions

The propagation of long-wavelength gluons through a dense QCD medium at high baryon chemical potential μB is qualitatively modified by the effects of screening, arising from scatterings off the high-momentum quarks in the medium. This same screening phenomenon also impacts gluons occurring in loop corrections to the pressure of cold quark matter, leading to contributions from the parametric scale αs1/2μB, starting at next-to-next-to-leading order (N2LO) in the strong coupling constant αs. At next-to-next-to-next-to-leading order (N3LO), interactions between these long-wavelength gluonic modes contribute to the pressure. These interaction corrections have recently been computed in Ref [1, 2], and the inclusion of these interactions slightly improves the convergence of the equation of state of cold quark matter. In these proceedings, we present these results and provide details summarizing how this lengthy calculation was performed.

scholarly journals PHASE STRUCTURE OF A FOUR- AND EIGHT-FERMION INTERACTION MODEL AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL IN ARBITRARY DIMENSIONS

2010 ◽  
Vol 25 (25) ◽  
pp. 4757-4774 ◽  
Author(s):  
MASAKO HAYASHI ◽  
TOMOHIRO INAGAKI ◽  
WATARU SAKAMOTO
Keyword(s):  
Finite Temperature ◽  
Phase Structure ◽  
Chemical Potential ◽  
Interaction Model ◽  
Leading Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Arbitrary Space ◽  
Arbitrary Dimensions ◽  
First Order Phase

The phase structure of a four- and eight-fermion interaction model is investigated at finite temperature and chemical potential in arbitrary space–time dimensions, 2 ≤ D < 4. The effective potential and the gap equation are calculated in the leading order of the 1/N expansion. If the first order phase transition takes place, the phase boundary dividing the symmetric and the broken phase is modified by the eight-fermion interaction.

scholarly journals Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kevin Goldstein ◽  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Black Hole ◽  
Chemical Potential ◽  
Specific Region ◽  
Partition Functions ◽  
Potential Space ◽  
Leading Order ◽  
Yang Mills ◽  
Superconformal Index ◽  
Chemical Potentials ◽  
Entropy Functions

Abstract We compute the superconformal index of the $$ \mathcal{N} $$ N = 4 SU(N) Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS5 black hole and its “twin saddle” respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.

Center-symmetric effective theory for two-color quark matter

Open Physics ◽  
2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Order Parameter ◽  
Large Scale ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Polyakov Loop ◽  
Effective Theory ◽  
Leading Order ◽  
Baryon Chemical Potential ◽  
Yang Mills ◽  
Model Independent

AbstractWe revisit the center-symmetric dimensionally reduced effective theory for two-color Yang-Mills theory at high temperature. This effective theory includes an order parameter for deconfinement and thus allows to broaden the range of validity of the conventional three-dimensional effective theory (EQCD) towards the confining phase transition. We extend the previous results by including the effects of massive quarks with nonzero baryon chemical potential. The parameter space of the theory is constrained by leading-order matching to the Polyakov loop effective potential of two-color QCD. Once all the parameters are fixed, the effective theory can provide model-independent predictions for the physics above the deconfinement transition, thus bridging the gap between large-scale numerical simulations and semi-analytical calculations within phenomenological models.

scholarly journals Asymmetric dark matter from semi-annihilation

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Avirup Ghosh ◽  
Deep Ghosh ◽  
Satyanarayan Mukhopadhyay
Keyword(s):  
Dark Matter ◽  
Cp Violation ◽  
Chemical Potential ◽  
Unstable State ◽  
Annihilation Process ◽  
Leading Order ◽  
Complex Scalar ◽  
Pair Annihilation ◽  
S Matrix ◽  
Asymmetric Dark Matter

Abstract We show that a general semi-annihilation scenario, in which a pair of dark matter (DM) particles annihilate to an anti-DM, and an unstable state that can mix with or decay to standard model states, can lead to particle anti-particle asymmetry in the DM sector. The present DM abundance, including the CP-violation in the DM sector and the resulting present asymmetry are determined entirely by a single semi-annihilation process at next-to-leading order. For large CP-violation in this process, we find that a nearly complete asymmetry can be obtained in the DM sector, with the observed DM density being dominated by the (anti-)DM particle. The presence of additional pair-annihilation processes can modify the ratio of DM and anti-DM number densities further, if the pair-annihilation is active subsequent to the decoupling of the semi-annihilation. For such a scenario, the required CP-violation for generating the same present asymmetry is generically much smaller, as compared to the scenario with only semi-annihilation present. We show that a minimal model with a complex scalar DM with cubic self-interactions can give rise to both semi- and pair-annihilations, with the required CP-violation generated at one-loop level. We also find that the upper bound on the DM mass from S-matrix unitarity in the purely asymmetric semi-annihilation scenario, with maximal CP-violation, is around 15 GeV, which is much stronger than in the WIMP and previously considered asymmetric DM cases, due to the required large non-zero chemical potential for such asymmetric DM.

scholarly journals Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Martin A. Mojahed
Keyword(s):  
Phase Diagram ◽  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Low Energy ◽  
Leading Order ◽  
Loop Order ◽  
Chiral Perturbation ◽  
Model Calculations ◽  
Symmetric Phase

AbstractWe consider two-flavor chiral perturbation theory ($$\chi $$ χ PT) at finite isospin chemical potential $$\mu _I$$ μ I and finite temperature T. We calculate the effective potential and the quark and pion condensates as functions of T and $$\mu _I$$ μ I to next-to-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the $$\mu _I$$ μ I –T plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $$\chi $$ χ PT, which is in agreement with model calculations and lattice simulations. Finally, we calculate the pressure to two-loop order in the symmetric phase for nonzero $$\mu _I$$ μ I and find that $$\chi $$ χ PT seems to be converging very well.

Sign in / Sign up

Export Citation Format

Share Document