Perspectives of measuring the gravitational attraction of ultra-relativistic particle beams: A new testbed for gravitational theory at the Large Hadron Collider

The Newtonian law of non-relativistic gravity has been tested in many laboratory experiments with very high precision. In contrast, the gravitational field of ultra-relativistic matter, dominated by kinetic energy and stresses, has not been measured directly. In this talk, I will present our results about the gravitational field of moving source masses in general relativity and scalar-tensor theory [1]. The latter serves as an example showing that ultra-relativistic source velocities can significantly enhance the difference in the gravitational effect on test particles predicted by theories of modified gravity and general relativity. This makes new regimes of gravitational theory accessible for tests in principle. I will then report on the perspectives to detect the gravitational attraction due to proton bunches at the Large Hadron Collider (LHC) [2-4], in particular, with quantum optomechanical sensors, and shortly discuss the possibility of employing coherent averaging techniques with many detectors around the LHC's proton beam to facilitate the measurement [5].

[1] C Pfeifer, DR, D Braun, Physical Review D 111 (8), 084073, https://doi.org/10.1103/PhysRevD.111.084073 <https://doi.org/10.1103/ PhysRevD.111.084073

[2] F Spengler, DR, D Braun, New Journal of Physics 24 (5), 053021, https://dx.doi.org/10.1088/1367-2630/ac5372 https://dx.doi.org/10.1088/1367-2630/ac5372

[3] R. Cai, C. Maccani, P. Hermes, S. Redaelli, D. Braun, DR, Proceedings of the 16th International Particle Accelerator Conference, JACoW Publishing

[4] Daniel Braun, Rongrong Cai, Pascal Hermes, Marta Maria Marchese, Stefan Nimmrichter, Christian Pfeifer, DR, Stefano Redaelli, Hendrik Ulbricht, arXiv:2504.10942

[5] Marta Maria Marchese, Daniel Braun, Stefan Nimmrichter, DR, arxiv.org/abs/2602.08981