S-parameter and pseudo-Nambu-Goldstone boson mass from lattice QCD

Understand

We present a lattice calculation of $L_{10}$, one of the low energy constants in Chiral Perturbation Theory, and the charged-neutral pion squared mass splitting, using dynamical overlap fermion.

• Exact chiral symmetry of the overlap fermion allows us to reliably extract these quantities from the difference of the vacuum polarization functions for vector and axial-vector currents.
• In the context of the technicolor models, these two quantities are read as the $S$-parameter and the pseudo-Nambu-Goldstone boson mass respectively, and play an important role in discriminating the models from others.
• This calculation can serve as a feasibility study of the lattice techniques for more general technicolor gauge theories.