TOTEM’s luminosity-independent cross-sections

The TOTEM collaboration has published the first luminosity-independent measurement of the total proton–proton cross-section at a centre-of-mass energy of 7 TeV. This is based on the experiment’s simultaneous studies of both inelastic and elastic scattering in proton collisions at the LHC.

The TOTEM (TOTal cross-section, Elastic scattering and diffraction dissociation Measurement) experiment, which co-habits the intersection region at Point 5 (IP5) with the CMS experiment, is optimized for making precise measurements of particles that emerge from collisions close to the non-interacting beam particles. To study elastic proton–proton (pp) collisions, in which the interacting protons simply change direction slightly, the experiment uses silicon detectors in Roman Pots, which can bring the detectors close to the beam line. For inelastic collisions, where new particles are created, two charged-particle telescopes, T1 and T2, come into play. T1 is based on cathode-strip chambers in two “arms” at about 9 m from IP5; T2 employs gas electron-multiplier (GEM) chambers, in this case in two arms at around 13.5 m from IP5.

The measurements at 7 TeV in the centre of mass are based on data recorded in October 2011 with a special setting of the LHC in which the beams were not squeezed for high luminosity but were left relatively wide and straight. With the Roman Pot detectors moved close to the beam, the TOTEM collaboration measured the differential elastic cross-section, dσ/dt, down to values of the four-momentum transfer squared, |t| < 0.005 GeV². Using the luminosity at IP5 as measured by CMS then gave a value for the elastic pp cross-section, σ_el = 25.4±1.1 mb ( TOTEM collaboration 2013a). Using the optical theorem, which relates dσ/dt at t=0 to σ_tot, the measurement of dσ/dt also provided a value of the total cross-section, σ_tot, and indirectly, for the inelastic cross-section, as σ_inel= σ_tot – σ_el. This yielded σ_inel = 73.2±1.4 mb.

To measure σ_inel more directly, the collaboration has analysed events that have at least one charged particle in the T2 telescope. After applying several corrections and, again, the luminosity from CMS, they arrive at a final result of σ_inel = 73.7±3.4 mb (TOTEM collaboration 2013b).

The excellent agreement between this value for σ_inel and the one determined from dσ/dt confirms that the collaboration understands well the systematic uncertainties and corrections used in the analysis and allows them to extract still more information from the data. In particular, as the elastic and inelastic data were collected simultaneously, the optical theorem allows the rates to be combined without the need to know the luminosity. This gives luminosity-independent values of σ_el = 25.1±1.1 mb, σ_inel = 72.9±1.5 mb and σ_tot = 98.0±2.5 mb (TOTEM collaboration 2013c). Using the optical theorem in a complementary way also allows TOTEM to determine the luminosity and in this case the collaboration finds values that are in excellent agreement with those measured by CMS.