New test of Lorentz symmetry using ultrahigh-energy cosmic rays

We propose an innovative test of Lorentz symmetry by observing pairs of simultaneous parallel extensive air showers produced by the fragments of ultrahigh-energy cosmic ray nuclei which disintegrated in collisions with solar photons. We show that the search for a cross-correlation of showers in arrival time and direction becomes background free for an angular scale $\lesssim 3°$ and a time window $\mathcal{O}(10\mathrm{s})$. We also show that if the solar photo-disintegration probability of helium is $\mathcal{O}({10}^{-5.5})$ then the hunt for spatiotemporal coincident showers could be within range of existing cosmic ray facilities, such as the Pierre Auger Observatory. We demonstrate that the actual observation of a few events can be used to constrain Lorentz violating dispersion relations of the nucleon.

Figure 1

${\log }_{10}{p}_2(\alpha ,t)$ for different total number of events (from left to right $N={10}^4$, ${10}^5$, ${10}^6$), and different lifetimes of the experiment (from top to bottom $T/\mathrm{yr}=5$, 10, 20). $T=10\mathrm{yr}$ and $T=20\mathrm{yr}$ are scales compatible with Auger, while $T=5\mathrm{yr}$ is an approximation for the life span of the prospective experiment POEMMA [45].

Figure 2

Relation between the $p$-value and $z$, the number of standard deviations away from the mean, for a normal distribution.

Figure 3

Sensitivity to $\zeta$ as a function of $\varkappa$ for $n=0$ (left) and $n=1$ (right). We have taken ${ϵ}_{\mathrm{th}}^{\prime }=20\mathrm{MeV}$ and $E={10}^{9.3}\mathrm{GeV}$. The embedded box details the restricted interval of $\varkappa$ for which $\zeta >0$. The shaded band indicates the region for which $\zeta <{\zeta }_{\mathrm{null}}$.

Figure 4

Allowed (shaded) $\varkappa$ region as a function of $A$, for $n=0$. The lower and upper curves are ${\varkappa }_{\min }$ and ${\varkappa }_{\max }$, respectively.