Numerical evaluation of a two loop diagram in the cutoff regularization

The sunset diagram of $\lambda\phi^4$ theory is evaluated numerically in cutoff scheme and a nonzero finite term (in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This finding dramatically reduces the critical couplings for symmetry breaking in the two loop effective potential discussed in our previous work.Comment: 6 pages, revtex, to appear in Comm. Theor. Phy

Constraints on the Brans-Dicke gravity theory with the Planck data

Based on the new cosmic CMB temperature data from the Planck satellite, the 9 year polarization data from the WMAP, the BAO distance ratio data from the SDSS and 6dF surveys, we place a new constraint on the Brans-Dicke theory. We adopt a parametrization \zeta=\ln(1+1/\omega}), where the general relativity (GR) limit corresponds to $\zeta = 0$. We find no evidence of deviation from general relativity. At 95% probability, $-0.00246 < \zeta < 0.00567$, correspondingly, the region $-407.0 < \omega <175.87$ is excluded. If we restrict ourselves to the $\zeta>0$ (i.e. $\omega >0$) case, then the 95% probability interval is $\zeta 181.65$. We can also translate this result to a constraint on the variation of gravitational constant, and find the variation rate today as $\dot{G}=-1.42^{+2.48}_{-2.27} \times 10^{-13}$yr$^{-1}$ ($1\sigma$ error bar), the integrated change since the epoch of recombination is $\delta G/G = 0.0104^{+0.0186}_{-0.0067}$ ($1\sigma$ error bar). These limits on the variation of gravitational constant are comparable with the precision of solar system experiments.Comment: 7 pages, 5 figures, 2 table