B¯→Xsγin two universal extra dimensions

Abstract

We calculate the leading order corrections to the $\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ decay in the standard model with two large flat universal extra dimensions. We find that the contributions involving the exchange of Kaluza-Klein modes of the physical scalar field ${a}_{(kl)}^{\ifmmode\pm\else\textpm\fi{}}$ depend logarithmically on the ultraviolet cutoff scale $\ensuremath{\Lambda}$. We emphasize that all flavor-changing neutral current transitions suffer from this problem. Although the ultraviolet sensitivity weakens the lower bound on the inverse compactification radius $1/R$ that follows from $\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$, the constraint remains stronger than any other available direct measurement. After performing a careful study of the potential impact of cutoff and higher-order effects, we find $1/R>650\text{ }\text{ }\mathrm{GeV}$ at 95% confidence level if errors are combined in quadrature. Our limit is at variance with the parameter region $1/R\ensuremath{\lesssim}600\text{ }\text{ }\mathrm{GeV}$ preferred by dark matter constraints.