The QCD axion at finite density
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Springer
Received: May 27, 2020 Accepted: June 30, 2020 Published: July 29, 2020
Reuven Balkin, Javi Serra, Konstantin Springmann and Andreas Weiler Physik-Department, Technische Universit¨ at M¨ unchen, James-Franck-Strasse 1, 85748 Garching, Germany
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We show how the properties of the QCD axion change in systems at finite baryonic density, such as neutron stars. At nuclear saturation densities, where corrections can be reliably computed, we find a mild reduction of the axion mass and up to an order of magnitude enhancement in the model-independent axion coupling to neutrons. At moderately higher densities, if realized, meson (kaon) condensation can trigger axion condensation. We also study the axion potential at asymptotically large densities, where the color-superconducting phase of QCD potentially leads to axion condensation, and the mass of the axion is generically several orders of magnitude smaller than in vacuum due to the suppressed instantons. Several phenomenological consequences of the axion being sourced by neutron stars are discussed, such as its contribution to their total mass, the presence of an axionic brane, or axion-photon conversion in the magnetosphere. Keywords: Beyond Standard Model, Chiral Lagrangians, CP violation, Thermal Field Theory ArXiv ePrint: 2003.04903
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)221
JHEP07(2020)221
The QCD axion at finite density
Contents 1 Introduction
2
2 Axion potential in vacuum
4
3 Chemical potential in quantum field theory
6
U(1) toy model
7
3.2
Meson condensation
8
4 Nuclear phase
12
4.1
Quark condensates
13
4.2
Kaon condensation
16
4.3
Axion couplings
22
5 CFL phase
27
5.1
Kinetic terms
29
5.2
Mass terms
29
5.3
Non-perturbative terms
30
5.4
Axion potential
31
6 Axion sourcing observables
33
6.1
Free (vacuum) energy
34
6.2
Axion brane
35
6.3
Axion-EM conversion
35
6.4
Long-range force
36
7 Conclusions and outlook
37
A Axion mass calculation with instantons
38
B Baryon-ChPT with non-trivial vacuum alignment
40
B.1 Adding chemical potential
41
B.2 Non-linear field basis
42
C Axion mass in Kaon-condensed phase
–1–
44
JHEP07(2020)221
3.1
1
Introduction
The QCD axion is one of the best motivated particles for physics beyond the Standard Model (SM). The Nambu-Goldstone boson [1, 2] of a spontaneously broken U(1)PQ PecceiQuinn symmetry anomalous under QCD [3], the axion makes the effective QCD θ angle unphysical and it allows QCD dynamics [4] to solve its strong-CP problem, thus explaining the absence of CP violation in the interactions of hadrons, in particular the electric dipole moment of the neutron [5, 6]. In addition, the axion constitutes a viable and attractive candidate for dark matter [7–9].
In this paper we contribute to the global effort in the search for the QCD axion by presenting a first comprehensive study of how its pr
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