Constraining the time variation of the coupling constants from cosmic
  microwave background: effect of \Lambda_{QCD}
  We investigate constraints on the time variation of the fine structure
constant between the recombination epoch and the present epoch,
\Delta\alpha/\alpha \equiv (\alpha_{rec} - \alpha_{now})/\alpha_{now}, from
cosmic microwave background (CMB) taking into account simultaneous variation of
other physical constants, namely the electron mass m_{e} and the proton mass
m_{p}. In other words, we consider the variation of Yukawa coupling and the QCD
scale \Lambda_{QCD} in addition to the electromagnetic coupling. We clarify
which parameters can be determined from CMB temperature anisotropy in terms of
singular value decomposition. Assuming a relation among variations of coupling
constants governed by a single scalar field (the dilaton), the 95% confidence
level (C.L.) constraint on \Delta\alpha/\alpha is found to be -8.28 \times
10^{-3} < \Delta\alpha/\alpha < 1.81 \times 10^{-3}, which is tighter than the
one obtained by considering only the change of \alpha and m_{e}. We also obtain
the constraint on the time variation of the proton-to-electron mass ratio \mu
\equiv m_{p}/m_{e} to be -0.52 < \Delta\mu/\mu < 0.17 (95% C.L.) under the same
assumption. Finally, we also implement a forecast for constraints from the
PLANCK survey.
