A year after publishing first results on proton–proton elastic scattering at a centre-of-mass energy of 7 TeV at the LHC, the TOTEM collaboration now has new measurements based on the analysis of data collected in October 2011. These latest results extend the measurement of the differential elastic cross-section to smaller values of |t|, the four-momentum transfer squared. They also allow a new determination of the elastic and total proton–proton (pp) cross-sections.
TOTEM, which stands for “TOTal cross-section, Elastic scattering and diffraction dissociation Measurement”, is optimized for making precise measurements of particles that emerge from collisions in the forward direction, close to the direction of the LHC beams. This allows it to probe physics that is not easily accessed by other LHC experiments, in particular elastic pp scattering down to small values of |t|. It detects protons scattered at small angles by using silicon detectors in Roman Pots – movable insertions in the beam pipe that allow the detectors to be brought closer to the beam (CERN Courier September 2009 p19).
The first measurement of the differential elastic cross-section dσ/dt by TOTEM covered a range 0.36 < |t| < 2.5 GeV2, revealing features similar to those first observed at CERN’s Intersecting Storage Rings in the 1970s: a peak at low |t| with an exponential decrease leading to a pronounced dip, followed by a rounded peak that falls away as a power law (CERN Courier October 2011 p37). With the data taken in 2011, the collaboration has now extended the measurements down to 0.005 GeV2 – corresponding to scattering angles of some 20 µrad – enabling the observation of 91% of the elastic cross-section and further exploration of the exponential slope of dσ/dt at small |t|.
For these measurements, the Roman Pot detectors had to approach close to the beam centre – to a distance of around five times the transverse size of the beam – during a dedicated run in which the LHC beams were deliberately left relatively wide and straight as they collided, rather than being “squeezed” for maximum luminosity. This involved running the LHC with magnet settings such that the β function, which describes the envelope of the beam oscillations, had a value of β* – the distance to the point where the beam is twice as wide as at the interaction point – of 90 m.
The results show that the slope of dσ/dt remains constant down to 0.005 GeV2, so that an exponential fit with only one constant B = (19.9±0.3) GeV–2 describes all of the range 0.005 < |t| < 0.2 GeV2 (TOTEM collaboration 2012). The small error on B – a result of the high precision of the measurement and the large range of the fit – allows a precise extrapolation over the non-visible cross-section (the remaining 9%) to t = 0. Taken with the luminosity measured by the CMS experiment at the same interaction point, this gives an elastic pp cross-section of 25.4±1.1 mb at a centre-of-mass energy of 7 TeV and, using the optical theorem, yields a value for the total pp cross-section of 98.6±2.2 mb. In addition, the difference between the total and elastic cross-sections gives a precise indirect measurement of the fully inclusive inelastic cross-section, with no dependence on Monte Carlo models, notably in the low-mass extrapolation region.
The measurements are being repeated this year at a centre-of-mass energy of 8 TeV. In addition, the machine optics for a still larger β* of 500–1000 m is being developed, which will enable TOTEM to reach a value of |t| as small as 0.0005 GeV2. This is where the Coulomb and hadronic contributions to the differential cross-sections are about equal, allowing the study of Coulomb-hadronic interference and the determination of the ρ parameter (the ratio of the real to imaginary part of the forward hadronic scattering amplitude). The collaboration is also studying the possibilities for measurements of pp elastic scattering at high values of |t| because these could reveal further diffractive minima, as predicted by some models.