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Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach

Using the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first orde...

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Autores principales: Di Vecchia, Paolo, Rossi, Giancarlo, Veneziano, Gabriele, Yankielowicz, Shimon
Lenguaje:eng
Publicado: 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP12(2017)104
http://cds.cern.ch/record/2282514
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author Di Vecchia, Paolo
Rossi, Giancarlo
Veneziano, Gabriele
Yankielowicz, Shimon
author_facet Di Vecchia, Paolo
Rossi, Giancarlo
Veneziano, Gabriele
Yankielowicz, Shimon
author_sort Di Vecchia, Paolo
collection CERN
description Using the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first order phase transitions as one crosses θ = π, while on the (hyper)surface separating the two regions, there are second order phase transitions signalled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the CP spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised if the QCD parameters fall in the above mentioned CP broken region, in spite of the fact that the axion solves the strong-CP problem. These last results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.
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spelling cern-22825142023-10-04T06:56:50Zdoi:10.1007/JHEP12(2017)104http://cds.cern.ch/record/2282514engDi Vecchia, PaoloRossi, GiancarloVeneziano, GabrieleYankielowicz, ShimonSpontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approachgr-qcGeneral Relativity and Cosmologyhep-thParticle Physics - TheoryUsing the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first order phase transitions as one crosses θ = π, while on the (hyper)surface separating the two regions, there are second order phase transitions signalled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the CP spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised if the QCD parameters fall in the above mentioned CP broken region, in spite of the fact that the axion solves the strong-CP problem. These last results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.Using the well-known low-energy effective Lagrangian of QCD --valid for small (non-vanishing) quark masses and a large number of colors-- we study in detail the regions of parameter space where $CP$ is spontaneously broken/unbroken for a vacuum angle $\theta= \pi$. In the $CP$-broken region there are first order phase transitions as one crosses $\theta=\pi$, while on the (hyper)surface separating the two regions, there are second order phase transitions signaled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the $CP$ spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised when the QCD parameters fall in the above mentioned $CP$-broken region, in spite of the fact that the axion solves the strong-$CP$ problem. These latter results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.arXiv:1709.00731CERN-TH-2017-186NORDITA-2017-093TAUP-3023-17oai:cds.cern.ch:22825142017-09-03
spellingShingle gr-qc
General Relativity and Cosmology
hep-th
Particle Physics - Theory
Di Vecchia, Paolo
Rossi, Giancarlo
Veneziano, Gabriele
Yankielowicz, Shimon
Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
title Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
title_full Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
title_fullStr Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
title_full_unstemmed Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
title_short Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
title_sort spontaneous $cp$ breaking in qcd and the axion potential: an effective lagrangian approach
topic gr-qc
General Relativity and Cosmology
hep-th
Particle Physics - Theory
url https://dx.doi.org/10.1007/JHEP12(2017)104
http://cds.cern.ch/record/2282514
work_keys_str_mv AT divecchiapaolo spontaneouscpbreakinginqcdandtheaxionpotentialaneffectivelagrangianapproach
AT rossigiancarlo spontaneouscpbreakinginqcdandtheaxionpotentialaneffectivelagrangianapproach
AT venezianogabriele spontaneouscpbreakinginqcdandtheaxionpotentialaneffectivelagrangianapproach
AT yankielowiczshimon spontaneouscpbreakinginqcdandtheaxionpotentialaneffectivelagrangianapproach