Speaker
Prof.
Sinya Aoki
(Kyoto University)
Description
We investigate some aspects of 2-flavor QCD with $m_u¥not= m_d$ at low-energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at $m_u=0$ for the fixed $m_d¥not=0$, the neutral pion mass becomes zero at two critical values of $m_u$, between which the neutral pion field
condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the ChPT diverges at these two critical points. We briefly discuss a possibility that $m_u=0$ can be defined by the vanishing the "topological susceptibility. We finally analyze the case of
$m_u=m_d=m$ with $¥theta=¥pi$, which is equivalent to $m_u= - m_d=-m$ with $¥theta = 0$ by the chiral rotation. In this case, the $¥eta$ condensation occurs at small $m$, violating the CP symmetry spontaneously. Deep in the $¥eta$ condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at
small $m$ that $m_¥pi^2 = O(m^2)$, which, however, is shown to be consistent with the chiral Ward-Takahashi identities.
Primary author
Prof.
Sinya Aoki
(Kyoto University)
Co-author
Dr
Michael Creutz
(Brookhaven National Laboratory)
