Measurement of the Inelastic Proton-Proton Cross Section at $\sqrt{s} = 13$ TeV with the ATLAS Detector at the LHC

This Letter presents a measurement of the inelastic proton-proton cross section using 60 $\mu$b$^{-1}$ of $pp$ collisions at a center-of-mass energy $\sqrt{s}$ of $13$ TeV with the ATLAS detector at the LHC. Inelastic interactions are selected using rings of plastic scintillators in the forward region ($2.07<|\eta|<3.86$) of the detector. A cross section of $68.1\pm 1.4$ mb is measured in the fiducial region $\xi=M_X^2/s>10^{-6}$, where $M_X$ is the larger invariant mass of the two hadronic systems separated by the largest rapidity gap in the event. In this $\xi$ range the scintillators are highly efficient. For diffractive events this corresponds to cases where at least one proton dissociates to a system with $M_X>13$ GeV. The measured cross section is compared with a range of theoretical predictions. When extrapolated to the full phase space, a cross-section of $78.1 \pm 2.9$ mb is measured, consistent with the inelastic cross section increasing with center-of-mass energy.

The fiducial region of the measurement is determined using MC simulation. In each generated event, the largest rapidity gap between any two final-state hadrons is used to define the boundary between two collections of hadrons. These collections define the dissociation systems in an event-generator-independent manner. The invariant mass of each collection is calculated, and the larger of the two masses, denoted M X , is used to define ξ = M 2 X /s. The variable ξ is constrained to be > 6 × 10 −9 by the elastic limit of m 2 p /s where m p is the proton mass. This measurement is restricted to ξ > 10 −6 , the region in which the event selection efficiency exceeds 50%.
Two samples of data events passing the MBTS trigger requirements are selected: an inclusive sample and a single-sided sample. The inclusive selection requires at least two MBTS counters with a charge above 0.15 pC (n MBTS ≥ 2). This threshold is chosen to be well above the electronic noise level of the counters. Requiring two hits rather than one substantially reduces background due to collision-induced radiation and activation. To constrain the diffractive component of the cross section and reduce the uncertainty in extrapolation to σ inel , an additional single-sided selection is defined, requiring hits in at least two counters on one side of the detector and no hits on the other. In the data, 4,159,074 events pass the inclusive selection and 442,192 events pass the single-sided selection.
The fiducial cross section is determined by where N is the number of observed events passing the inclusive selection, N BG is the number of background events, trig and sel are factors accounting for the trigger and event selection efficiencies, 1− f ξ<10 −6 accounts for the migration of events with ξ < 10 −6 into the fiducial region, and L is the integrated luminosity of the sample.
Sources of background include interactions between the beam and residual gas in the beam pipe; interactions between the beam and collimators upstream of the detector, which can send charged particles through the detector parallel to the beam; collision-induced radiation; and activation backgrounds. Backgrounds from cosmic rays and instrumental noise are negligible. The mean number of pp collisions in the same LHC bunch crossing was 2.3 × 10 −3 for the recorded dataset. Thus, the contribution from multiple collisions are also negligible. The beam-related background components are extracted from single-beam events and dominate the total background. They are normalized by scaling the number of selected singlebeam events by a factor of 37/4 × 2, accounting for the 37 colliding pairs of bunches and 4 bunches producing the single-beam data in this run. The factor of 2 accounts for the presence of two colliding bunches. The number of protons per bunch producing these single-beam events agrees with that in the colliding bunches to within 10%. The radiation and activation-induced backgrounds are implicitly part of this background estimate. Double-counting of these components is removed using estimates from empty events. The total background contributions to the inclusive and single-sided data samples are determined to be 1.2% and 5.8% respectively. The classification of single-sided events as double-sided due to noise or other backgrounds is estimated to be below 0.1%. A systematic uncertainty of 50% is assigned to the background based on studies of the background composition and the relative contributions of the background components. This uncertainty is treated as fully correlated between the single-sided and inclusive selections.
The trigger efficiency for events passing the inclusive selection, trig , is measured with respect to events selected with the LUCID detector after subtracting the background. A trigger efficiency of 99.7% (97.4%) is measured for the inclusive (single-sided) event sample. In both cases the statistical uncertainty is below 0.1%. The efficiency is also measured with events selected by the LHCf detector and agrees within ±0.3% with the LUCID determination. This difference is taken as a systematic uncertainty.
The ratio of the number of events passing the single-sided event selection to the number passing the inclusive selection (R SS ) is used to adjust, for each model, the fractional contribution of the single-and double-diffractive dissociative cross section (σ SD + σ DD ) to the inelastic cross section, f D = (σ SD + σ DD )/σ inel [12]. The measured value is R SS = 10.4% with a total uncertainty of ±0.4%. The dominant systematic uncertainty arises from the background subtraction in the single-sided sample. For each MC model, f D is varied until it matches the observed R SS value in data. The data uncertainty is used to set the error in the constrained f D for each model. An additional uncertainty in the ratio of single-to doublediffractive events is determined by taking the diffractive events to be entirely SD or to be evenly divided between SD and DD.
Using this method, the fitted f D in the Pythia8 samples is between 25% and 31%, depending on the model (the default value is 28%). For the QGSJet-II (Epos LHC) model the fitted f D is 35% (37%), differing significantly from the default value of 21% (28%). The observed R SS and the MC predictions of its dependence on f D are shown in Figure 1. The fitted f D is used when determining the acceptance corrections sel and f ξ<10 −6 for each model.  In Figure 2 the n MBTS distributions in data are compared to the ones from MC simulated samples utilizing the fitted f D values for both the inclusive and single-sided selections. The estimated background is subtracted from the measured distribution, and the trigger efficiency measured in data is applied to the simulation. The data distributions and MC simulation are peaked at high multiplicity values. In the singlesided case, n MBTS = 12 corresponds to hits in all counters on one side of the detector. The data agree best with the DL models, particularly in the low-n MBTS range. The MBR-based distribution provides a slightly worse description of the data. The Pythia8 sample using the SS model does not describe data well in the low-multiplicity region. Epos LHC and QGSJet-II also do not describe the data well, particularly in the single-sided hit multiplicity distribution. Therefore, the Pythia8 DL model with ε = 0.085 is chosen as the nominal MC model for the sel and f ξ<10 −6 corrections, and only the DL and MBR models are considered for systematic uncertainties related to the MC corrections.
The event selection efficiency, sel , depends upon the MBTS counter sensitivity. This sensitivity is tested using isolated charged particles, reconstructed as ID tracks in the region 2.07 < |η| < 2.5 where the coverages of the MBTS and ID overlap. Over the full coverage of the MBTS counters, the calorimeter is used to measure the counter efficiency with respect to particles that deposit sufficient energy in the calorimeter to seed a topological energy cluster [38]. Differences between the efficiencies in data and MC simulation are accounted for by adjusting the MBTS charge threshold in MC simulation until the simulated efficiencies match those observed in the data. The residual uncertainty in the counter efficiency after these corrections is ±0.5% for the outer and ±1.0% for the inner counters. Additionally, an uncertainty arising from the knowledge of the material in front of the MBTS detector is estimated using MC samples with an increased amount of material in front of the MBTS. Based on the MC samples, the uncertainty in the efficiency measurement due to modeling of hadronization and the underlying event is estimated to be  negligible.
After adjusting the counter charge threshold, sel is determined from the nominal Pythia8 DL MC, using the fitted f D corresponding to this model, to be 99.34% with a statistical uncertainty of ±0.03%. The uncertainty in the MBTS counter efficiencies results in only a ±0.1% uncertainty in the overall event selection efficiency, because many counters are hit in typical events. In addition, an uncertainty of ±0.2% in sel arises from the knowledge of the material in front of the MBTS.
The fraction of events passing the inclusive selection with ξ < 10 −6 represents an additional background component in the fiducial cross-section measurement. It is determined using the same Pythia8 DL MC to be f ξ<10 −6 = (1.37 ± 0.05)%, where the uncertainty is statistical.
Because the efficiency and migration corrections are correlated, they are combined in a single correction factor, C MC = (1 − f ξ<10 −6 )/ sel , for which systematic uncertainties are assessed. The systematic uncertainties include the counter efficiency variations, the impact of the material uncertainty, the uncertainty in the fitted value of f D , and the variation in C MC found by comparing the Pythia8 DL and MBR models. Of these sources of uncertainty, the last is most important at ±0.5%. The value of C MC is (99.3 ± 0.5)%. The uncertainty also implicitly contains an uncertainty due to the CD contribution, since this is included in only some of the models.
The uncertainty in the integrated luminosity is ±1.9%. It is derived, following a methodology similar to that detailed in Refs. [39,40], from a calibration of the luminosity scale using x-y beam-separation scans performed in August 2015. This calibration uncertainty is slightly smaller than what has been reported in Ref.
[41] because the low-luminosity dataset used in this letter is not affected by the uncertainties related to high-luminosity runs. The extrapolation to σ inel uses constraints from previous ATLAS measurements to minimize the model dependence of the component that falls outside the fiducial region. σ inel can be written as .
The Pythia8 DL and Pythia8 MBR MC samples are used to assess the systematic uncertainty in the MCderived ratio of cross sections in Eq. (2), which is determined to be 1.015 ± 0.081 3 . These models also agree with the measurement of σ 7 TeV (ξ < 5 × 10 −6 ) to within 2σ.
This and other inelastic cross-section measurements are compared to several Monte Carlo models in Figure 3. Additional predictions range between 76.6 and 81.6 mb [42][43][44][45][46]. Compared to the measurement with the ALFA detector at √ s = 7 TeV the cross section is higher by (9 ± 4)%.
In summary, a measurement of the inelastic cross section in 60 µb −1 of proton-proton collision data at √ s = 13 TeV collected with the ATLAS detector at the LHC is presented. The measurement is performed in a fiducial region ξ > 10 −6 , and the result is extrapolated to the inelastic cross section using measurements at √ s = 7 TeV. The measured cross section agrees well with a variety of theoretical predictions and is consistent with the inelastic cross section increasing with center-of-mass energy, as observed at lower energies.