$SU(2)$ Gauge Theory with Two Fundamental Flavours: Scalar and Pseudoscalar Spectrum

Abstract

We investigate the scalar and pseudoscalar spectrum of the $SU(2)$ gauge theory with $N_f=2$ flavours of fermions in the fundamental representation using non perturbative lattice simulations. We provide first benchmark estimates of the mass of the lightest $0(0^{+})$ ($\sigma$), $0(0^{-})$ (${\eta }^{\prime }$) and $1(0^{+})$ ($a_0$) states, including estimates of the relevant disconnected contributions. We find $m_{a_0}/F_{\mathrm{PS}}=16.7(4.9)$, $m_{\sigma }/F_{\mathrm{PS}}=19.2(10.8)$ and $m_{{\eta }^{\prime }}/F_{\mathrm{PS}}=12.8(4.7)$. These values for the masses of light scalar states provide crucial information for composite extensions of the Standard Model from the unified Fundamental Composi te Higgs-Technicolor theory \cite{Cacciapaglia:2014uja} to models of composite dark matter.

Comments: 18 pages, 9 figures