Lorentz violation and the electron-ion collider

We investigate the prospects for detecting violations of Lorentz symmetry in unpolarized deep inelastic electron-proton scattering in the context of the future electron-ion collider. Simulated differential cross-section data are used to place expected bounds on a class of quark-sector coefficients for Lorentz violation that induce sidereal time dependence in the scattering cross section. We find that, with $100{\mathrm{fb}}^{-1}$ of integrated luminosity, the expected bounds are in the ${10}^{-5}–{10}^{-7}$ range and are roughly two orders of magnitude stronger than those that can be extracted from existing HERA data. We also discuss the possibility of extracting bounds on the remaining time-independent coefficients.

Figure 1

Inclusive $e\text{−}p$ DIS in the one-photon exchange approximation. An electron $e^{-}$ with momentum $k$ interacts and recoils with momentum $k^{\prime }$ from a proton $P$ with momentum $p$ through the exchange of a photon $\gamma$ producing a generic final hadronic state $X$.

Figure 2

Quark ($q_f$) interaction vertices from the model Lagrange density, Eq. (13). The dot at the vertices denotes a modified vertex rule in the presence of Lorentz violation.

Figure 3

Parton-model DIS with Lorentz-violating effects. A parton carrying a momentum fraction $x_f^{\prime }=x-x_f$ propagates in a Lorentz-violating medium and interacts with an electron (see Ref. [15]). These features affect the azimuthal scattering angle $\varphi$ of the final-state electron. Dots indicate modified vertices and propagator insertions.

Figure 4

Distribution of $|c_u^{TX}|$ correlated upper limits for JLEIC1. The median value for the collection of pseudoexperiments is plotted against the variables $x$, $Q^2$, $y$ for electron energies $E_e=5$, 10 GeV and proton energies $E_p=20$, 60, 80, 100 GeV.

Figure 5

Distribution of $|c_u^{TX}|$ correlated upper limits for eRHIC1. The median value for the collection of pseudoexperiments is plotted against the variables $x$, $Q^2$, $y$ for electron energies $E_e=5$, 10 GeV and proton energies $E_p=50$, 100, 250 GeV.

Figure 6

Distribution of $|c_u^{TX}|$ correlated upper limits for eRHIC1. The median value for the collection of pseudoexperiments is plotted against the variables $x$, $Q^2$, $y$ for electron energies $E_e=15$, 20 GeV and proton energies $E_p=50$, 100, 250 GeV.

Figure 7

Upper limits for $|c_u^{TX}|$ displaying ($x$, $Q^2$, $y$) correlations. Red, Green, Blue and Black dots corresponds to bounds below the ${10}^{-5}$, ${10}^{-4}$, ${10}^{-3}$ and ${10}^{-2}$ level, respectively. Upper and lower panels correspond to JLEIC1 and eRHIC1, respectively. All upper limits assume 100% bin-to-bin correlation between experimental systematic uncertainties.