arXiv subjects

Patrick Kneschke

Publications and source records attributed to Patrick Kneschke.

9 recordsLinked to original sources

arXiv2021

The muon magnetic moment in the 2HDM: complete two-loop result

We study the ${\text{2HDM}}$ contribution to the muon anomalous magnetic moment $a_μ$ and present the complete two-loop result, particularly for the bosonic contribution. We focus on the Aligned ${\text{2HDM}}$, which has general Yukawa couplings and contains the type I, II, X, Y models as special cases. The result is expressed with physical parameters: three Higgs boson masses, Yukawa couplings, two mixing angles, and one quartic potential parameter. We show that the result can be split into several parts, each of which has a simple parameter dependence, and we document their general behavior. Taking into account constraints on parameters, we find that the full ${\text{2HDM}}$ contribution to $a_μ$ can accommodate the current experimental value, and the complete two-loop bosonic contribution can amount to $(2\cdots 4)\times 10^{-10}$, more than the future experimental uncertainty.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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

hep-ph↗

arXiv2018

Bose-Einstein condensation and pion stars

Pion stars consisting of Bose-Einstein condensed charged pions have recently been proposed as a new class of compact stars. We use the two-particle irreducible effective action to leading order in the $1/N$-expansion to describe charged and neutrals pions as well as the sigma particle. Tuning the parameters in the Lagrangian correctly, the onset of Bose-Einstein condesation of charged pions is exactly at $μ_I=m_π$, where $μ_I$ is the isospin chemical potential. We calculate the pressure, energy density, and equation of state, which are used as input to the Tolman-Oppenheimer-Volkov equations. Solving these equations, we obtain the mass radius-relation for pion stars. Global electric charge neutrality is ensured by adding the contribution to the pressure and energy density from a gas of free relativistic leptons. We compare our results with those of recent lattice simulations and find good agreement. The masses of the pion stars are up to approximately 200 solar masses while the corresponding radii are of the order of $10^5$ km.

hep-ph↗

arXiv2018

Chiral density wave versus pion condensation at finite density

The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$, baryon chemical potential $μ_B$, and isospin chemical potential $μ_I$. The parameters of the model are determined by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. In this paper, we study the possibility of different phases at zero temperature. In particular, we investigate the competition between an inhomogeneous chiral condensate and a pion condensate. For the inhomogeneity, we use a chiral-density wave ansatz. For a sigma mass of $600$ MeV, we find that an inhomogeneous chiral condensate exist only for pion masses below approximately 37 MeV. We also show that due to our parameter fixing, the onset of pion condensation takes place exactly at $μ_I={1\over2}m_π$ in accordance with exact results.

hep-ph↗

arXiv2017

Inhomogeneous phases at finite density in an external magnetic field

The two-flavor quark-meson model is used as a low-energy effective model for QCD to study inhomogeneous chiral condensates at finite quark chemical potential $μ$ in a constant magnetic background $B$. We determine the parameters of the model 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. We calculate the free energy in the mean-field approximation for a chiral density wave using dimensional regularization. The system has a surprisingly rich phase structure.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗