Towards string theory expectations for photon couplings to axionlike particles

Axionlike particle (ALP)–photon couplings are modeled in large ensembles of string vacua and random matrix theories. In all cases, the effective coupling increases polynomially in the number of ALPs, of which hundreds or thousands are expected in the string ensembles, many of which are ultralight. The expected value of the couplings $g_{a\gamma \gamma }\simeq {10}^{-12}{\mathrm{GeV}}^{-1}-{10}^{-10}{\mathrm{GeV}}^{-1}$ provide viable targets for future x-ray telescopes and axion helioscopes, and in some cases are already in tension with existing data.

Figure 1

The normalized distributions of ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ for our smallest $N=55$ and largest $N=235$, as well as the extrapolated distribution for the preferred value of $N=2483$ in the tree ensemble. There is a clear shift of the distribution towards larger values as $N$ grows. Current (solid) and projected (dashed) exclusion lines are presented for various experiments.

Figure 2

Top: The mean of ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ in the tree ensemble as a function of $N$, with a best-fit curve. Bottom: The SD of ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ in the tree ensemble as a function of $N$, with a best-fit curve.

Figure 3

A plot of $\mathrm{mean}({\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV}))$ versus $\mathrm{mean}({\log }_{10}({\lambda }_{\max }(K^{-1})))$. The slope of the line is $\sim 0.38$.

Figure 4

A plot of $\mathrm{mean}({\log }_{10}({\lambda }_{\max }(K^{-1})))$ versus $N$, with a best-fit line to demonstrate the correlation.

Figure 5

The normalized distributions of ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ for the hypersurfaces. Shown are the calculated distributions for $N=10$ and $N=200$, as well as the extrapolated distribution for the largest hypersurfaces at $N=491$. There is a clear shift of the distribution towards larger values as $N$ grows. Current (solid) and projected (dashed) exclusion lines are presented for various experiments.

Figure 6

The mean of ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ in the inverse Wishart model for $\sigma =1,1/\sqrt{N},1/N,1/N^2,1/N^3$ as a function of $N$, with a best-fit line of the form mean($g_{a\gamma \gamma }$) $\propto N^{\mathrm{x}}$. The models with $\sigma =1/N^2$ and $\sigma =1/N$ are the best for the string data.

Figure 7

${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$, computed in the RMT models, versus $\mathrm{mean}({\log }_{10}({\lambda }_{\max }(K^{-1})))$, with varying $\sigma$. Note that for all models both ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ and $\mathrm{mean}({\log }_{10}({\lambda }_{\max }(K^{-1})))$ increase as a function of $N$.

Figure 8

The normalized predicted distribution of ${\log }_{10}(g_{a\gamma \gamma }\times \mathrm{GeV})$ for the largest known value of $N=16103$ in the skeleton ensemble, contrasted with that predicted for the largest $N=2483$ in the tree ensemble. Current (solid) and projected (dashed) exclusion lines are presented for various experiments.