arXiv:1002.4705v1 [hep-ph] 25 Feb 2010 Masses of vector bosons in two-color dense QCD based on the hidden local symmetry Masayasu Harada, Chiho Nonaka, and Tetsuro Yamaoka Department of Physics, Nagoya University, Nagoya, 464-8602, Japan We construct a low energy effective Lagrangian for the two-color QCD including the “vector” bosons (mesons with J P = 1 − and diquark baryons with J P = 1 $^{+}$) in addition to the pseudo Nambu-Goldstone bosons with a degenerate mass M$_{π}$ (mesons with J P = 0 − and baryons with J P = 0 $^{+}$) based on the chiral symmetry breaking pattern of SU (2 N$_{f}$ ) → Sp (2 N$_{f}$ ) in the framework of the hidden local symmetry. We investigate the dependence of the “vector” boson masses on the baryon number density µ$_{B}$ . We show that the µ$_{B}$ -dependence signals the phase transition of U (1)$_{B}$ breaking. We find that it gives information about mixing among “vector” bosons: e.g. the mass difference between ρ and ω mesons is proportional to the mixing strength between the diquark baryon with J P = 1 + and the anti-baryon. We discuss the comparison with lattice data for two-color QCD at finite density. (Dated: June 7, 2018) PACS numbers: 11.30.Rd, 12.39.Fe, 05.70.Fh Quantum chromodynamics (QCD) shows various phases under extreme conditions. At very high temperature and/or density, the phase structure can be studied with perturbative approaches. However, it is difficult to study it especially near the critical temperature and/or density directly from QCD, because of the strong coupling. Lattice QCD simulation is one of powerful theoretical tools, but it is not applicable in the finite density region due to the sign problem [1]. The problem in simulations of real-life QCD at finite baryon density produces interest in the two-color QCD with quarks in the fundamental representation [2, 3], the QCD with quarks in the adjoint representation [3, 4], and so on, that are free from the sign problem. In particular, two-color QCD has some interesting features in the following respect: Color-singlet baryons appear together with ordinary mesons as Nambu-Goldstone 1. INTRODUCTION