We consider the presence of odd powers of the speed of light c in the covariant nonrelativistic expansion of General Relativity (GR). The term of order c in the relativistic metric is a vector potential that contributes at leading order in this expansion and describes strong gravitational effects outside the (post-)Newtonian regime. The nonrelativistic theory of the leading order potentials contains the full non-linear dynamics of the stationary sector of GR.

As part of its HL-LHC upgrade program, the CMS Collaboration is developing a High Granularity Calorimeter (CE) to replace the existing endcap calorimeters. The CE is a sampling calorimeter with unprecedented transverse and longitudinal readout for both electromagnetic (CE-E) and hadronic (CE-H) compartments. The calorimeter will be built with ∼30,000 hexagonal silicon modules. Prototype modules have been constructed with 6-inch hexagonal silicon sensors with cell areas of 1.1 cm 2 , and the SKIROC2-CMS readout ASIC. Beam tests of different sampling configurations were conducted with the prototype modules at DESY and CERN in 2017 and 2018. This paper describes the construction and commissioning of the CE calorimeter prototype, the silicon modules used in the construction, their basic performance, and the methods used for their calibration.

Concomitant with this increase will be an increase in the number of interactions in each bunch crossing and a significant increase in the total ionising dose and fluence. One part of this upgrade is the replacement of the current endcap calorimeters with a high granularity sampling calorimeter equipped with silicon sensors, designed to manage the high collision rates [2]. As part of the development of this calorimeter, a series of beam tests have been conducted with different sampling configurations using prototype segmented silicon detectors. In the most recent of these tests, conducted in late 2018 at the CERN SPS, the performance of a prototype calorimeter equipped with ≈12, 000 channels of silicon sensors was studied with beams of high-energy electrons, pions and muons. This paper describes the custom-built scalable data acquisition system that was built with readily available FPGA mezzanines and low-cost Raspberry PI computers.

Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a fully covariant formulation in the language of Newton-Cartan geometry but we revisit it here in a 3+1 formulation. The appropriate 3+1 formulation of General Relativity is one first described by Kol and Smolkin (KS), rather than the better known Arnowitt-Deser-Misner (ADM) formalism. As we review, the KS formulation is dual to the ADM formulation in that the role of tangent and co-tangent spaces get interchanged. In this 3+1 formulation the 1/c expansion can be performed in a more systematic and efficient fashion, something we use to extend the computation of the effective Lagrangian beyond what was previously achieved and to make a number of new all order observations.

No abstract