Recent searches for solar axions and large extra dimensions

We analyze the data from two recent experiments designed to search for solar axions within the context of multidimensional theories of the Kaluza-Klein type. In these experiments, axions were supposed to be emitted from the solar core, in $M1$ transitions between the first excited state and the ground state of ${}^{57}\mathrm{Fe}$ and ${}^{7}\mathrm{Li}.$ Because of the high multiplicity of axionic Kaluza-Klein states which couple with the strength of ordinary QCD axions, we obtain much more stringent experimental limits on the four-dimensional Peccei-Quinn breaking scale ${f}_{\mathrm{PQ}},$ compared with the solar QCD axion limit. Specifically, for the ${}^{57}\mathrm{Fe}$ experiment, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1\ifmmode\times\else\texttimes\fi{}{10}^{6} \mathrm{GeV}$ in theories with two extra dimensions and a higher-dimensional gravitational scale ${M}_{H}$ of order 100 TeV, and ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1\ifmmode\times\else\texttimes\fi{}{10}^{6} \mathrm{GeV}$ in theories with three extra dimensions and ${M}_{H}$ of order 1 TeV (to be compared with the QCD axion limit, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}8\ifmmode\times\else\texttimes\fi{}{10}^{3} \mathrm{GeV}).$ For the ${}^{7}\mathrm{Li}$ experiment, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{5} \mathrm{GeV}$ and $3.4\ifmmode\times\else\texttimes\fi{}{10}^{5} \mathrm{GeV},$ respectively (to be compared with the QCD axion limit, ${f}_{\mathrm{PQ}}\ensuremath{\gtrsim}1.9\ifmmode\times\else\texttimes\fi{}{10}^{2} \mathrm{GeV}).$ It is an interesting feature of our results that, in most cases, the obtained limit on ${f}_{\mathrm{PQ}}$ cannot be coupled with the mass of the axion, which is essentially set by the (common) radius of the extra dimensions.