Proton collisions at the LHC can be very complicated. Sometimes they produce hundreds of tiny particles, like pions; on rare occasions, they form very heavy particles, such as the Higgs boson. And then there are the rather unspectacular collisions – when protons bounce off each other and change the direction of their momentum. These are elastic scattering interactions. While the kinematics of these processes can be quite simple, studying them can reveal the complex dynamics that govern proton interactions.
Physicists use the “Mandelstam” variable (you) (related to the scattering angle), to describe these elastic scattering events. At an LHC collision energy of 13 TeV, for scattering at angles below 5 µrad (|you| 2), the events are dominated by the interactions between the electric charges of the protons (the “Coulomb interaction”). For scattering angles greater than 15 µrad (|you| > 0.01 GeV2), nuclear interactions dominate. For scattering angles between 5 and 15 µrad (|t| between 0.001 and 0.01 GeV2), Coulomb and nuclear interactions contribute with a similar magnitude. Since the effects of these interactions cannot be distinguished for a single event, quantum mechanical interferences occur. The amplitude and the sign of this interference depend on the complex phase between the Coulomb and nuclear scattering amplitudes.
In a new result presented at ICHEP 2022, ATLAS physicists set out to measure proton scattering at microradian angles and study this quantum interference. Their analysis required a dedicated experimental setup: first, the LHC magnets had to be tuned to a special “high β* optics” setting, which gives the proton beams a very small angular dispersion. Second, special detectors were needed far from the central interaction point but very close to the proton beam. The ATLAS experiment has a detector system – called ALFA – built exactly for this task. The ALFA detectors are installed about 240 meters on either side of the ATLAS cavern inside “Roman pots”, and can take measurements a few millimeters from the center of the beam.
In a new result presented at ICHEP 2022, ATLAS physicists set out to measure proton scattering at microradian angles.
With this setup in place, ATLAS researchers measured the trajectories of protons after they passed through the fields of several LHC magnets. The scattering angle is reconstructed from the trajectory measurement. Due to the principles of conservation of energy and momentum, many constraints are present in the event. For example, if one proton diffused up, the other had to diffuse down. It also allowed physicists to determine several other variables in the analysis, from alignment to rejection of background processes. Many other ingredients of the analysis were achieved in a data-driven manner, including determining the properties of high β* optics and the efficiency of event reconstruction.
The new ATLAS analysis examines the you Elastic scattering spectrum in proton-proton collisions at 13 TeV. The measurement was made for |you| between 0.00025 and 0.46 GeV2. Figure 1 shows the results in the range of smallest scattering angles (|you| 2), where the contributions of the different mechanisms are easily visible.
Elastic scattering measurements can be related to other processes occurring on proton-proton hadronic interactions. This relationship allowed the researchers to calculate several other basic parameters, such as the total proton-proton cross section (σearly) and the ratio of the real and imaginary parts of the elastic scattering amplitude (ρ). The ρ ratio determines the complex phase between the Coulomb and the nuclear amplitudes, directly affecting the interference contribution.
Figure 2 presents the ATLAS σearly and the measurement of ρ as well as other measurements of these quantities and predictions as a function of the energy of the center of mass. The new total cross section measurement, which is the most accurate at high energies, confirms the trend of σearly increases with the energy of the center of mass. The measurement of ρ, which disagrees with pre-LHC theoretical expectations, suggests that either the increase in σearly with center-of-mass energy will eventually slow down, or that the hadronic interactions of protons and antiprotons remain different at high center-of-mass energies.
ATLAS physicists are now turning to LHC Run 3, where a special last run is planned at the highest energies to complete the ALFA program.