Proton collisions at the LHC can be very complicated. Sometimes, they produce hundreds of tiny particles, like pions; on rare occasions, they make very heavy particles, like the Higgs boson. And then there are the rather unspectacular collisions – when the protons basically bounce off each other and change their directions and momenta. These are elastic scattering interactions. While the kinematics of these processes may be quite simple, their study can reveal the complex dynamics that govern proton interactions.

Physicists use the “Mandelstam” variable (t) (related to the scattering angle), to describe these elastic-scattering events. At 13 TeV LHC collision energy, for scattering at angles smaller than 5 µrad (|t| < 0.001 GeV²), events are dominated by interactions between the electric charges of the protons (the “Coulomb interaction”). For scattering angles above 15 µrad (|t| > 0.01 GeV²), nuclear interactions dominate. For scattering angles between 5 and 15 µrad (|t| between 0.001 and 0.01 GeV²), both Coulomb and nuclear interactions contribute with similar magnitude. Since the effects of these interactions cannot be distinguished for a single event, quantum-mechanical interference occurs. The magnitude and sign of this interference depends 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, LHC magnets had to be tuned to a special “high-β* optics'' setting, which gives the proton beams a very small angular spread. Second, special detectors were needed far away from the central interaction point but very close to the proton beam. The ATLAS experiment has a system of detectors – called ALFA – built for exactly this task. ALFA detectors are installed ~240 metres on either side of the ATLAS cavern inside “Roman pots”, and can take measurements just a few millimetres from the beam centre.

With this setup in place, ATLAS researchers measured the trajectories of protons after they had traversed fields of several LHC magnets. The scattering angle is reconstructed from the trajectory measurement. Because of the principles of energy and momentum conservation, many constraints are present in the event. For example, if one proton scattered upwards, the other one had to scatter downwards. This also allowed physicists to determine several other variables in the analysis, from alignment to the rejection of background processes. Many other ingredients of the analysis were obtained in a data-driven way, including the determination of the properties of the high-β* optics and the event reconstruction efficiency.

ATLAS’ new analysis examines the t spectrum of elastic scattering in 13 TeV proton-proton collisions. The measurement was performed for |t| between 0.00025 and 0.46 GeV². Figure 1 shows the results in the range of the smallest scattering angles (|t| < 0.02 GeV²), where the contributions from different mechanisms are easily visible.

Measurements of elastic scattering can be linked to other processes occurring on hadronic proton–proton interactions. This relationship allowed researchers to calculate several other basic parameters, such as the total proton–proton cross section (σ_tot) and the ratio of the real vs 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 σ_tot and ρ measurement together with other measurements of these quantities and predictions as a function of the centre-of-mass energy. The new total cross section measurement, which is the most precise one at high energies, confirms the trend of σ_tot increase with centre-of-mass energy. The measurement of ρ, which disagrees with pre-LHC theoretical expectations, suggests that either the increase of σ_tot with centre-of-mass energy will eventually slow down, or that the hadronic interactions of protons and anti-protons remain different at high centre-of-mass energies.

ATLAS physicists are now looking ahead to LHC Run 3, where a final special run is planned at the highest energies to complete the ALFA programme.

Learn more

• Measurement of the total cross section and ρ-parameter from elastic scattering in proton–proton collisions at 13 TeV with the ATLAS detector (STDM-2018-08)
• ICHEP 2022 presentation by Hasko Stenzel: Forward proton measurements with ATLAS
• Counting collisions with ALFA, ATLAS Physics Briefing, July 2014
• See also the full lists of ATLAS Conference Notes and ATLAS Physics Papers.