Measurement of inelastic, single- and double-diffraction cross sections in proton-proton collisions at the LHC with ALICE

TL;DR

ALICE measures inelastic and diffractive proton–proton cross sections at 0.9, 2.76, and 7 TeV using pseudorapidity-gap signatures to separate single and double diffraction. The analysis relies on gap-based event classification, detector-driven efficiencies, and van der Meer scans to calibrate luminosity, with diffraction modeled by adjusted PYTHIA6/PHOJET (KP1/DL MX distributions) to bound systematic uncertainties. Combined with measured diffraction fractions, the study yields σINEL and σSD/σDD values that are broadly consistent with prior experiments and with theoretical models KP1, GLM, KMR, Ostapchenko, and Goulianos, thereby validating diffraction contributions at LHC energies. The results provide precise inputs for hadronic interaction models used in heavy-ion physics and cosmic-ray energy extrapolations, underpinning accurate background estimates and event characterizations at the LHC.

Abstract

Measurements of cross sections of inelastic and diffractive processes in proton--proton collisions at LHC energies were carried out with the ALICE detector. The fractions of diffractive processes in inelastic collisions were determined from a study of gaps in charged particle pseudorapidity distributions: for single diffraction (diffractive mass $M_X < 200$ GeV/$c^2$) $σ_{\rm SD}/σ_{\rm INEL} = 0.21 \pm 0.03, 0.20^{+0.07}_{-0.08}$, and $0.20^{+0.04}_{-0.07}$, respectively at centre-of-mass energies $\sqrt{s} = 0.9, 2.76$, and 7~TeV; for double diffraction (for a pseudorapidity gap $Δη> 3$) $σ_{\rm DD}/σ_{\rm INEL} = 0.11 \pm 0.03, 0.12 \pm 0.05$, and $0.12^{+0.05}_{-0.04}$, respectively at $\sqrt{s} = 0.9, 2.76$, and 7~TeV. To measure the inelastic cross section, beam properties were determined with van der Meer scans, and, using a simulation of diffraction adjusted to data, the following values were obtained: $σ_{\rm INEL} = 62.8^{+2.4}_{-4.0} (model) \pm 1.2 (lumi)$ mb at $\sqrt{s} =$ 2.76~TeV and $73.2^{+2.0}_{-4.6} (model) \pm 2.6 (lumi)$ mb at $\sqrt{s}$ = 7~TeV. The single- and double-diffractive cross sections were calculated combining relative rates of diffraction with inelastic cross sections. The results are compared to previous measurements at proton--antiproton and proton--proton colliders at lower energies, to measurements by other experiments at the LHC, and to theoretical models.

Figures (12)

• Figure 1: Lowest order Pomeron exchange graphs contributing to elastic (left), to single- (middle) and to double-diffractive (right) proton--proton scattering. $\mathbb{P}$ stands for Pomeron, p for proton and $X$ ($X_1$, $X_2$) for the diffractive system(s).
• Figure 2: Schematic rapidity ($y$) distribution of outgoing particles in elastic (left), in single- (middle), and in double-diffraction (right) events, showing the typical rapidity-gap topology.
• Figure 3: Triple-Reggeon Feynman diagram occurring in the calculation of the amplitude for single diffraction, corresponding to the dissociation of hadron b in the interaction with hadron a. (See Ref. ReggeTheory). Each of the Reggeon legs can be a Pomeron or a secondary Reggeon (e.g. $f$-trajectories), resulting in eight different combinations of Pomerons and Reggeons. In the text, we use the notation $(R_1R_2)R_3$ for the configuration shown in this figure.
• Figure 4: Diffractive-mass distributions, normalized to unity, for the SD process in pp collisions at $\sqrt{s}$ = 0.9 TeV (left) and $\sqrt{s}$ = 7 TeV (right), from Monte Carlo generators PYTHIA6 (blue histogram), PHOJET (red dashed-line histogram), and model KP1 (black line) --- used in this analysis for central-value estimate. The shaded area around the black line is delimited by (above at lower masses, below at higher masses) variation of the model KP1, multiplying the distribution by a linear function which increases the probability at the threshold mass by a factor 1.5 (keeping the value at upper-mass cut-off unchanged, and then renormalizing the distribution back to unity), and by (below at lower masses, above at higher masses) Donnachie--Landshoff parametrization DL. This represents the variation used for systematic-uncertainty estimates in the present analysis. A $1/M_X$ line is shown for comparison (magenta dotted-dashed line). At $\sqrt{s}$ = 7 TeV (right) black dashed-lines show $1/M_X^{1+2\Delta}$ distributions with $\Delta = 0.085$ and $0.1$ also used with PYTHIA8 event generator in the ATLAS measurement of inelastic cross section ATLAS_InelXS.
• Figure 5: Pseudorapidity ranges covered by FMD, SPD and VZERO (V0-L and V0-R) detectors, with an illustration of the distances $d_{\rm L}$ and $d_{\rm R}$ from the edges ($\eta_{\mathrm{L}}$ and $\eta_{\mathrm{R}}$, respectively) of the particle pseudorapidity distribution to the edges of the ALICE detector acceptance (vertical dashed lines --- for the nominal interaction point position) and the largest gap $\Delta\eta$ between adjacent tracks. The centre of the largest gap is denoted $\eta_{\rm gC}$. L and R stand for Left and Right, respectively, following the convention defined in Section \ref{['experiment']}.