## CP3-Lecture: Spontaneous CP breaking in QCD and the axion potential: an effective Lagrangian approach I

Who: Giancarlo Rossi (Universita’ di Roma “Tor Vergata”)
When: Monday, April 9, 2018 at 14:15
Where: The CP³ meeting room

In the first of this two-lecture seminar, after a pedagogical introduction of the notion of low-energy effective Lagrangian for QCD, we recall the Witten-Veneziano solution of the so-called U_A(1) problem and its implication for the strong CP problem. We then go on by writing down the low-energy effective Lagrangian of QCD, valid for small quark masses, m, and large number of colors, N, (with mN fixed), in the presence or in the absence of a CP-breaking vacuum angle. Of special interest is the value \pi of the latter, where CP can be spontaneously broken. We show that there is a first order phase transition when the vacuum angle goes through \pi, and that the CP broken and CP unbroken regions are separated by a (hyper)surface of second order phase transitions, signalled by the vanishing of the mass of the Nambu-Goldstone boson and a divergent QCD topological susceptibility.