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

Paolo Di Vecchia, Giancarlo Rossi*, Gabriele Veneziano, Shimon Yankielowicz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number104
JournalJournal of High Energy Physics
Issue number12
StatePublished - 1 Dec 2017


FundersFunder number
ISF Center of Excellence
Israel-Germany Foundation
US-Israel Binational Science Foundation
Bloom's Syndrome Foundation
German-Israeli Foundation for Scientific Research and Development
Israeli Centers for Research Excellence1937/12


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    • Anomalies in Field and String Theories


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