Gravitational attraction of ultra-relativistic matter: A new testbed for modified gravity at the Large Hadron Collider

TL;DR

The paper develops a linearized scalar-tensor gravity framework to predict the gravitational field of ultrarelativistic particle beams and their effect on nearby acceleration sensors. By solving the field equations for a moving point-like source, it derives explicit expressions for the scalar and tensor perturbations, and computes the leading transverse acceleration and momentum transfer to a test mass, including how these observables differ from General Relativity via parameters $\psi_0$, $\omega_0$, and $m_{\psi_1}$. It then outlines a concrete test scenario at the LHC: calibrate the gravitational constant with slow sources, and look for velocity-dependent deviations in the momentum transfer to sensors near the beam, with a Yukawa-type scalar correction encoded in $K_1(m_{\psi_1}\rho)$. The work demonstrates that, with ultraprecise sensors and appropriate shielding, one can constrain scalar-tensor gravity in a controlled laboratory setting and extend similar methods to broader modified gravity theories, including Brans-Dicke and $f(R)$ representations.

Abstract

We derive the scalar-tensor modification of the gravitational field of an ultrarelativistic particle beam and its effect on a test particle that is used as sensor. To do so, we solve the linearized scalar-tensor gravity field equations sourced by an energy-momentum tensor of a moving point particle. The geodesic equation and the geodesic deviation equation then predict the acceleration of the test particle as well as the momentum transfer due to a passing source. Comparing the momentum transfer predicted by general relativity and scalar tensor gravity, we find that there exists a relevant parameter regime where this difference increases significantly with the velocity of the source particle. Since ultrarelativistic particles are available at accelerators like the Large Hadron Collider, ultraprecise acceleration sensors in the vicinity of the particle beam could potentially detect deviations from general relativity or constrain modified gravity models.

Figures (4)

• Figure 1: These plots show the logarithm of the absolute value of the acceleration in $x$-direction $a_T^1$ of a test particle at rest at $y=0$ as a function of $m_{\psi_1}x$ and $m_{\psi_1}\gamma(z-vt)$ in units of $a_0=\kappa^2Mc^4(\gamma^2-1/2)m_{\psi_1}^2/(4\pi\psi_0)$ for two different values of $\sigma=(2(\gamma^2-1/2)(3+2\omega_0))^{-1}$. Left: $\sigma=0$, equivalent to the GR case times a global factor $\psi_0^{-1}$. Right: $\sigma=10^2$ on the right hand side. The two plots agree for large distances, while the modification due to the scalar field dominate at small distances.
• Figure 2: This plot shows the absolute value of the momentum transfer $\delta\boldsymbol{p}_T$ of a test particle at rest as a function of $m_{\psi_1}\rho$ in units of $\kappa^2M m c^4(\gamma^2-1/2)m_{\psi_1}/(2\pi\psi_0\gamma v)$ for different values of $\sigma=(2(\gamma^2-1/2)(3+2\omega_0))^{-1}$. For $\sigma=0$ and for large distances, the $1/\rho$-scaling of GR is recovered. For $\sigma>0$ and small distances, the modification due to the scalar field dominates.
• Figure 3: Sketch of the test-setup: measurement of the momentum transfer on a test particle in the gravitational field of a relativistic particle which moves with velocity $v$ in the $z$-direction.
• Figure 4: This plot shows the relative momentum transfer difference due to a moving source defined as the difference between the values of the transverse momentum transfer to a test particle derived from scalar-tensor theory and GR normalized by the latter. The values are given for different values of the Lorentz factor $\gamma$ and the distance between test particle and beam line $\rho$. For the plot, the scalar field parameters were chosen as $1/(3+2\omega_0)=10^{-3}$ and $1/m_{\psi_1}=10^2\,$m which are below the bounds imposed by experimental and observational tests of Yukawa type modifications of gravity (compare with Fig. 8 of Murata_2015 taking into account that $\alpha=1/(3+2\omega_0)$ and $\lambda= 1/m_{\psi_1}$). Furthermore, for the distance at which the gravitational constant is fixed by auxiliary experiments, we have used $r_0=0.1\,$m, while the plots look equivalent for other values of $r_0\lesssim 1\,$m. The plot clearly shows the advantage of tests with relativistic sources if $\rho$ and $r_0$ are small in comparison to $1/m_{\psi_1}$.