Roles of $^7$Be$(n,p)^7$Li resonances in big bang nucleosynthesis with
  time-dependent quark mass and Li reduction by a heavy quark mass
  Big bang nucleosynthesis (BBN) has been used as a probe of beyond-standard
physics in the early Universe, which includes a time-dependent quark mass m_q.
We investigate effects of a quark mass variation delta m_q on the cross
sections of the 7Be(n, p)7Li reaction and primordial light element abundances
taking into account roles of 8Be resonances in the reaction during BBN. This
resonant reaction has not been investigated although behaviors of low-lying
resonances are not trivial. It is found that a resonance at the resonance
energy E_r=0.33 MeV enhances the reaction rate and lowers the 7Li abundance
significantly when the quark mass variation is negative. Based upon up-to-date
observational limits on primordial abundances of D, 4He and Li, the quark mass
variation in the BBN epoch are derived. In a model in which the resonance
energies of the reactions 3He(d, p)4He and 3H(d, n)4He are insensitive to the
quark mass, we find that the Li abundance can be consistent with observations
for delta m_q/m_q = (4--8) times 10^{-3}.
