TY - JOUR

T1 - Spontaneous CP breaking in QCD and the axion potential

T2 - an effective Lagrangian approach

AU - Di Vecchia, Paolo

AU - Rossi, Giancarlo

AU - Veneziano, Gabriele

AU - Yankielowicz, Shimon

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - 1/N Expansion

KW - Anomalies in Field and String Theories

UR - http://www.scopus.com/inward/record.url?scp=85039415318&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2017)104

DO - 10.1007/JHEP12(2017)104

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85039415318

SN - 1126-6708

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 12

M1 - 104

ER -