Implications of broken SU(4) ⊗ SU(4) and scale symmetry for the masses of charmed particles

Making use of chiral SU(4) ⊗ SU(4) and scale-symmetry breaking together with ɛ saturation we obtain limits for the charmed-pseudoscalar-meson masses. These limits only allow charmed (C=+/-1) pseudoscalar states with masses below 2.5 GeV. The existence of such states with masses above 1.5 GeV would imply strong restrictions on the theory: δ has at least dimension l_δ=1, u has at least dimension l_u=2 and the ɛ mass is higher than the upper limit noted in the Particle Data Group table. If the masses of these states are above 2 GeV, it furthermore follows than l_u=3 and l_δ=2. Assuming the Gaillard-Lee-Rosner relation between the masses of the vector mesons and the quarks, identification of the ψ(3.1) with the φ_c implies l_u=3, l_δ=2, m_ɛ~0.92 GeV, Γ_ɛ~0.42 GeV, and m_D=2.2 GeV. We have assumed integer dimensions. We have furthermore assumed that the effective m_ɛ is not much above 0.9 GeV.