Spontaneous CP breaking and the axion potential: an effective Lagrangian approach
by
Prof.Gabriele Veneziano(Collège de France and CERN)
→
Europe/Rome
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
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.