Measurement of visible cross sections in proton-lead collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV in van der Meer scans with the ALICE detector

In 2013, the Large Hadron Collider provided proton-lead and lead-proton collisions at the center-of-mass energy per nucleon pair $\sqrt{s_{\rm{NN}}}=5.02$ TeV. Van der Meer scans were performed for both configurations of colliding beams, and the cross section was measured for two reference processes, based on particle detection by the T0 and V0 detectors, with pseudo-rapidity coverage $4.6<\eta<4.9$, $-3.3<\eta<-3.0$ and $2.8<\eta<5.1$, $-3.7<\eta<-1.7$, respectively. Given the asymmetric detector acceptance, the cross section was measured separately for the two configurations. The measured visible cross sections are used to calculate the integrated luminosity of the proton-lead and lead-proton data samples, and to indirectly measure the cross section for a third, configuration-independent, reference process, based on neutron detection by the Zero Degree Calorimeters.


Introduction
Luminosity determination in ALICE (A Large Ion Collider Experiment) [1] at the LHC is based on visible cross sections measured in van der Meer (vdM) scans [2,3].The visible cross section σ vis seen by a given detector (or set of detectors) with a given trigger condition is a fraction of the total inelastic interaction cross section σ inel : σ vis = εσ inel , where ε is the fraction of inelastic events which satisfy the trigger condition.In the following, an inelastic event satisfying a given trigger condition will be referred to as a reference process.Once the reference-process cross section (σ vis ) is measured, the collider luminosity can be determined as the reference-process rate divided by σ vis .This procedure does not require the knowledge of ε.
In vdM scans the two beams are moved across each other in the transverse directions x and y.Measurement of the rate R of the reference process as a function of the beam separation ∆x, ∆y allows one to determine the luminosity L for head-on collisions of a pair of bunches with particle intensities N 1 and N 2 as where f rev is the accelerator revolution frequency and h x and h y are the effective beam widths in the two transverse directions.The effective beam widths are measured as the area below the R(∆x, 0) and R(0, ∆y) curve (scan area), respectively, each divided by the head-on rate R(0, 0).Under the assumption that the beam profiles are Gaussian, the effective width is obtained as the Gaussian standard deviation parameter (from a fit) multiplied by √ 2π.However, the Gaussian assumption is not necessary for the validity of the method.As will be shown in section 3, other functional forms can be used, as well as numerical integration of the curve.The cross section σ vis for the chosen reference process is then σ vis = R(0, 0)/L. ( In 2013, the Large Hadron Collider provided proton-lead and lead-proton collisions at the center-of-mass energy per nucleon pair √ s NN = 5.02 TeV.Van der Meer scans were performed for both configurations of colliding beams, and the cross section was measured for two reference processes.In section 2, the detectors used for the measurements are briefly described, along with the relevant machine parameters and the adopted scan procedure.In section 3, the analysis procedure is described.In section 4, the obtained results and uncertainties are presented and discussed.In section 5, the application of the vdM scan results to the measurement of the integrated luminosity is briefly discussed.In section 6, the vdM scan results are used to indirectly determine the cross section for a third reference process, based on neutron detection by the ALICE Zero Degree Calorimeters.

Experimental setup
At the ALICE experiment, two vdM-scan sessions were carried out during the 2013 proton-lead datataking campaign at the LHC.The proton beam was travelling clockwise in the first session and counterclockwise in the second session.In the following, these configurations will be referred to as p-Pb and Pb-p, respectively.
In each session, the cross section was measured for two reference processes: one is based on the V0 detector, the other on the T0 detector.A detailed description of these detectors is given in [1], and their performance is discussed in [4], [5] and [6].The V0 detector consists of two hodoscopes, with 32 scintillator tiles each, located on opposite sides of the ALICE Interaction Point (IP2), at a distance of 340 cm (V0-A) and 90 cm (V0-C) along the beam axis, covering the pseudo-rapidity (η) ranges 2.8 < η < 5.1 and −3.7 < η < −1.7, respectively.In the p-Pb configuration the proton beam is travelling in the direction from V0-A to V0-C.The T0 detector consists of two arrays of 12 Cherenkov counters each, located on opposite sides of IP2, at a distance of 370 cm (T0-A) and 70 cm (T0-C) along the beam  axis, covering the pseudo-rapidity ranges 4.6 < η < 4.9 and −3.3 < η < −3.0, respectively.In the p-Pb configuration the proton beam is travelling in the direction from T0-A to T0-C.
The V0-based trigger condition, chosen as the reference process, requires at least one hit in each detector hodoscope, i.e. on both sides of IP2.As discussed in [7], the efficiency of such a selection is larger than 99% for non single-diffractive p-Pb collisions.A similar trigger condition defines the T0-based reference process, with the additional condition that the longitudinal coordinate of the interaction vertex, evaluated by the trigger electronics via the difference of arrival times in the two arrays (measured with a resolution of 20 ps), lies in the range |z| < 30 cm (where z = 0 is the nominal IP2 position).This online cut aims to reject the background from beam-gas and beam-satellite interactions.The cut value of 30 cm is much larger than the r.m.s.longitudinal size of the interaction region (≃ 6 cm), making signal loss induced by the cut negligible (<10 −5 ).Since the two LHC beams have the same magnetic rigidity and different projectile mass, the energy per nucleon of lead ions (1.58 TeV) differs from that of protons (4 TeV).Hence, the p-Pb (Pb-p) collision center-of-mass frame is shifted by 0.47 (-0.47) units of rapidity with respect to the ALICE frame.Due to this shift and the asymmetric setup of both detectors, there is no reason to expect identical cross sections for the p-Pb and Pb-p configurations.Therefore, the results obtained in the two scan sessions are not combined.
In the p-Pb (Pb-p) scan session the proton beam consisted of 272 bunches, while the Pb beam consisted of 338 (314) bunches.In the p-Pb (Pb-p) scan session 264 (244) bunch pairs per LHC orbit were colliding at IP2.For both beams and sessions, the minimum spacing between two consecutive bunches was 200 ns.The reference-process rates were recorded (and the cross section measured) separately for each colliding bunch pair.For each session, two independent measurements per bunch pair were performed by repeating the (horizontal and vertical) scan pair twice: from negative to positive separation and then in the opposite direction.The maximum beam separation during the scan was about 0.15 mm, corresponding to about six times the RMS of the transverse beam profile.In both sessions, the β * value1 in IP2 was 0.8 m.The current in the ALICE solenoid (dipole) was 30 kA (6 kA), corresponding to a field strength of 0.5 T (0.7 T).In both sessions, the proton and lead bunch intensities were on the order of 10 10 p/bunch and 10 8 Pb/bunch, as shown in figure 1.While the proton bunch intensity is reasonably constant across bunches, large variations are seen for the lead bunches.The structure of such variations as a function of the bunch position can be explained by different sensitivities to losses in the injection chain [8].
The bunch-intensity measurement is provided for both scan sessions by the LHC instrumentation [9]: a DC current transformer (DCCT), measuring the total beam intensity, and a fast beam current transformer (fBCT), measuring the relative bunch populations.The measured beam intensity is corrected by the fraction of ghost and satellite charge2 .The measurement of ghost charge is provided by the LHCb collaboration, via the rate of beam-gas collisions occurring in nominally empty bunch slots, as described in [11].The obtained ghost-charge correction factor to the bunch-intensity product N 1 N 2 is 0.991±0.001(0.986±0.002) for the p-Pb (Pb-p) session.The bunch intensity is further corrected by the fraction of satellite charge measured by the LHC Longitudinal Density Monitor (LDM), which measures synchrotron radiation photons emitted by the beams [12].The obtained satellite-charge correction factor to the bunch-intensity product N 1 N 2 is 0.998±0.004(0.996±0.001) for the p-Pb (Pb-p) session.This correction is implemented by multiplying the N 1 N 2 product by both the ghost-and satellite-charge factors.

Data analysis
An example of the measured raw rate for one typical pair of colliding bunches during the p-Pb scan is shown in figure 2 for both the T0-and the V0-based processes.
Three corrections are applied to the measured raw rate for each of the two reference processes.
First, the contamination by beam-satellite and beam-gas interactions in the V0 rate is removed using the detector timing capabilities.The background is identified via the sum and difference of arrival times in the two V0 arrays from offline analysis of the data collected during the scan.The arrival times are obtained by averaging over the signal times of all hits of each array.The background contamination is measured as the fraction of events in which the sum and difference of times lie outside of a window of ±4 ns around the values expected for beam-beam collisions (figure 3).The measurement is performed for each separation value and the corresponding raw rate is corrected by the obtained fraction.The background contamination in the V0-triggered sample is about 0.5-1% at zero separation and about 20-40% at a separation corresponding to five times the beam RMS.This procedure has negligible effect (< 0.1%) when applied to the T0 rates, due to the vertex cut in the T0 trigger logic described in section 2.  on the two V0 arrays.The left plot was obtained at zero beam separation; the right plot was obtained at a beam separation of 0.12 mm, roughly corresponding to five times the RMS of the beam profile.Events lying inside the area within the continuous lines are flagged as beam-beam interactions.
In order to study a possible contamination of the trigger rate by the intrinsic noise counts of the detectors, the rate of both trigger signals in absence of beam was measured and found to be zero.The rate in empty bunch slots with beam circulating was also measured and found to be zero for T0.For V0, a nonzero rate is measured up to the fourth empty bunch slot after a filled slot.Since the minimum spacing between filled slots is eight slots, such an after-pulsing effect does not affect the measurement of the rate in colliding slots.
Second, the probability of multiple interactions in the same bunch crossing (pileup) is taken into account according to Poisson statistics.The trigger rate R is smaller than the rate of visible interactions by a factor [1 − exp (−µ vis )]/µ vis , where µ vis = -ln(1 − R/ f rev ) is the average number of visible interactions occurring in one bunch crossing.The pileup-corrected rate for bunch crossing i, R PU,i , is thus given by where R BB,i is the background-corrected rate.In both scan sessions, the maximum value of µ vis during the scan for the V0 (T0) reference process is about 0.05 (0.03), leading to a maximum correction of about 2.5% (1.5%).
The third correction takes into account that the luminosity decreases with time (as can be seen in figure 2) due to the beam-intensity decay and to the growth of emittances.In order to correct for this effect, the evolution of the head-on luminosity in time is parameterised via a fit to the rates at zero separation measured before, after and in-between scans.The decay rate is satisfactorily described by an exponential function.Figure 4 shows an example of such a fit.The obtained fit parameters are used to normalize all rates of a given scan pair to an arbitrary reference time, chosen to lie between the horizontal and vertical scans.
An example of the obtained correction factors as a function of the beam separation is shown in figure 5.
The corrected rates obtained with the above-described procedure are used to compute the effective beam widths h x and h y .This is done with both a fit and a numerical method.For the fit method, it was found that a Gaussian (or double-Gaussian) function does not describe satisfactorily the measured shapes, while     reasonable values of χ 2 per degree of freedom (χ 2 /nd f ≃ 1 on average, and typically χ 2 /nd f < 2) are obtained by using a modified Gaussian function and a similar one for R(0, ∆y).An example of the quality of the fit is shown in figure 6.In the fit approach, the scan area and the head-on rate R(0, 0) are obtained from the fit parameters.In the numerical method, the scan area is obtained as the sum of all rates multiplied by the step size, and R(0, 0) is the measured rate at zero separation.The effective beam widths and head-on rates obtained with the two methods agree within 0.5%.Since the effective beam widths are independent of the process used to measure them, a consistency check is performed by computing the ratio of the h x h y quantities of equation 1, obtained with T0 and V0, for each colliding bunch.The results are shown in figure 7.For both scan sessions, the bunch-averaged value of the ratios is compatible with unity within 0.2%.
The measured beam widths are corrected by a length-scale calibration factor.This correction aims to fine tune the conversion factor (known with limited precision) between the current in the steering magnets and the beam displacement.The calibration is performed in a dedicated run, where the two beams are moved simultaneously in the same direction in steps of equal size; the changes in the interaction vertex position provide a measurement of the actual beam displacement, which is used to extract a correction factor to the nominal displacement scale.The displacement of the vertex position is measured using data from the ALICE Inner Tracking System [13] and Time Projection Chamber [14].This is shown in figure 8, left, for the horizontal length-scale calibration run.For each step, the vertex position and its uncertainty are obtained from a Gaussian fit to the vertex distribution.The length-scale correction factor is obtained as the slope parameter of a linear fit to the measured vertex displacement as a function of the nominal displacement (figure 8, right).Since this correction affects the global beam-displacement scale, all measured beam widths are multiplied by the correction factors 0.98±0.01for the horizontal scale and 1.02±0.01for the vertical scale.
The cross section for each colliding bunch pair and reference process is calculated according to eq. 1 and 2 from the measured bunch intensities, beam widths and head-on rates.As there are two measured head-on rates per scan pair (one from the vertical and one from the horizontal scan), the arithmetic mean of the two is used, after checking that the two values are compatible within statistical uncertainties.1: Cross section for the V0-and T0-based reference process in two p-Pb vdM scans, as obtained with the numerical and fit methods.The weighted average between the numerical results of the two scans, retained as the final result, is also reported.The quoted uncertainties are statistical.
The measured cross sections (obtained with the numerical method) for the T0-and V0-based processes during the first scan of the p-Pb and Pb-p sessions are shown in figure 9 for all the colliding bunch pairs, as a function of the product of the colliding bunch intensities (N 1 N 2 ).No dependence of the results on N 1 N 2 is observed.For the p-Pb session, fluctuations beyond the statistical uncertainties are observed, and accounted for as a source of systematic uncertainty (see section 4).

Results and systematic uncertainties
For both processes and scan sessions the weighted average of results from all colliding bunch pairs is computed, for each scan and method.The results for all scans and methods are summarised in tables 1 and 2. The numerical and fit method agree to better than 0.3% for all scans.The numerical result is preferred, because it implies a weaker assumption on the scan shape and to be consistent with earlier ALICE results in pp and Pb-Pb collisions [4,15].For each session, the weighted average of the results of the two performed scans is retained as the final result.The differences between the two methods and between different scans in the same session are taken into account in the evaluation of the systematic uncertainties.
The sources of systematic uncertainty considered are listed below; unless otherwise specified, the quoted uncertainties apply to both the T0 and the V0 cross-section measurements.
-Transverse correlations: the formalism of equation 1 assumes complete factorisation of the beam profiles in the two transverse directions, such that the beam overlap region is fully described by  the h x h y quantity.Luminosity measurements at the LHC [11,16] have shown that factorisation can be broken at a non-negligible level.In previous studies [16,17,18], the bias arising from such an effect was quantified by comparing the results obtained with the standard analysis method with those obtained from a correlated two-dimensional double-Gaussian fit to the data.The same method was applied to this analysis, using the fitting function defined in [18].As already observed for the one-dimensional case, the double-Gaussian function provides a rather poor description of the data, with χ 2 /nd f ranging from ≃ 140/32 to ≃ 1200/32 across scans and bunches.A better agreement (χ 2 /nd f ranging from ≃ 20/32 to ≃ 800/32) is found if the standard double-Gaussian function is modified by dropping the requirement that the coefficients of both Gaussian functions be positive (unconstrained double-Gaussian).The bunch-by-bunch difference between the cross section obtained with the unconstrained two-dimensional double-Gaussian (DG2D) fit model and that obtained with the one-dimensional fit model of Eq. 4 (gPol6) shows a two-fold behaviour, depending on how well the scan shape is reproduced by the DG2D fit.For fits with relatively small χ 2 /nd f , the difference fluctuates by at most ≃ 1% around zero and shows no dependence on χ 2 /nd f .For fits with large χ 2 /nd f , the difference is large (up to ≃ 5%) and systematically negative, and it exhibits a strong dependence on χ 2 /nd f , its magnitude increasing linearly with χ 2 /nd f .The negative difference values observed in the high-χ 2 /nd f region, as well as their trend as a function of χ 2 /nd f , are identically observed when comparing the results of a one-dimensional double-Gaussian (DG1D) fit with those of the gPol6 fit.Hence, they are not interpreted as the effect of transverse correlations, but rather as a fit-model bias occurring when the scan shape is not well reproduced by the double-Gaussian fit.Such an interpretation is supported by the previously-cited studies [11,16,17], where it is reported that the presence of transverse correlation systematically leads to positive discrepancies between the two-dimensional and the one-dimensional fit.For bunches in the small-χ 2 /nd f region, where no fit bias is expected, the transverse correlation uncertainty is evaluated as the full envelope of the bunch-by-bunch difference between the DG2D and the gPo6 fit result.Operationally, the small-χ 2 /nd f region is defined as the one where there is no correlation between the DG2D-gPol6 difference and the value of χ 2 /nd f .The threshold χ 2 /nd f value corresponding to such a definition varies slightly across scans and luminometers, ranging from 58/32 to 105/32.For both the p-Pb and Pb-p scan sessions, the full envelope is at most 2.2% across scans and luminometers (Fig. 10), hence such a value is retained as uncertainty.For bunches in the large-χ 2 /nd f region the uncertainty could not be evaluated with the above-described method, due to the double-Gaussian fit bias.If these bunches are affected by transverse correlations in a different way than the small-χ 2 /nd f bunches, they may in principle bias the measured, bunch-averaged, cross section.In order to quantify a possible bias, the average cross sections obtained from the two sub-sets of bunches are compared.They are found to be consistent within 1.3% (0.6%) for the p-Pb (Pb-p) scan session.These values are assigned as additional uncertainty, leading to a total transverse-correlation uncertainty of 2.6% (2.3%) for the p-Pb (Pb-p) cross sections.
-Bunch-by-bunch consistency: an uncertainty of 1.6% is assigned to the results of the p-Pb session.
It is obtained from the RMS of the distribution of the cross section measured for all colliding bunch pairs, after subtracting in quadrature the bunch-averaged statistical uncertainty.For the Pb-p session the RMS is smaller than the average statistical uncertainty, hence no systematic uncertainty is assigned.
-Scan-to-scan consistency: the difference between the first and second scan in the same session (0.5% for the p-Pb scans and 1.5% for the Pb-p scans) is retained as a systematic uncertainty.
-Length-scale calibration: 1.5%, from the quadratic sum of the statistical uncertainties on the horizontal and vertical scale factors reported in section 3.
-Background subtraction: in order to evaluate a possible bias arising from beam-beam events identified as beam-gas by the cut described in section 3, the analysis has been repeated by increasing the width of the window for beam-beam events from 8 to 14 ns: for the V0 cross section, a difference of 0.45% is found and added to the systematic uncertainty for both configurations.The difference is negligible (≪ 0.1%) for the T0 cross section.
-Method dependence: 0.3% for both scan sessions, quantified via the maximum difference between the results obtained with the numerical and the fit method (tables 1 and 2).
-Beam centering: the measurement of R(0, 0) can be affected by a non-optimal alignment of the two beams in the head-on position.Such misalignment is quantified, for the x and y directions, via the µ parameter of eq. 4. For about half of the scans, the value of µ is compatible with zero; for the first horizontal and the second vertical p-Pb scan, and for the first horizontal Pb-p scan, it reaches up to 2.5 µm.The effect of such misalignment on the measured head-on rates was estimated using eq. 4 and the obtained fit parameters: the resulting systematic uncertainty on the cross-section measurement is 0.3% (0.2%) for the p-Pb (Pb-p) configuration.
-Trigger dependence of the measured beam widths: 0.2% for both sessions, from the bunchaveraged difference between the h x h y quantities measured with T0 and V0 (figure 7).
-Luminosity-decay correction: when varying the luminosity decay parameters within their uncertainties, a negligible (< 0.1%) effect on the measured cross section is observed.
-Bunch intensity: the uncertainty on the bunch-intensity product N 1 N 2 arising from the DCCT calibration [19] is 0.46% (0.54%) for the p-Pb (Pb-p) scan session; given the very large fraction of colliding over circulating bunches, the uncertainty on the relative bunch populations has negligible effect on the cross section measurement [20].
-Orbit drift: possible variations of the reference orbit during the scan may lead to a difference between the nominal and the real beam separation.In order to quantify a possible bias, the data from the LHC Beam Position Monitors (BPM) [21] in various locations along the ring are used to extrapolate, with the YASP steering program [22], the transverse coordinates of the reference orbit of the two beams at IP2, for each scan step.The (small) observed variations in the orbit are used to correct the separation values, and the cross section is re-calculated: a difference of 0.4% (0.1%) is found for the p-Pb (Pb-p) configuration results.
-Beam-beam deflection: due to their electric charge, the two beams exert a repulsive force upon each other [23].Such repulsion results in a beam separation slightly different than its nominal value.The variations of the beam separation are calculated using the MAD-X [24] code: the effect on the measured cross section (partially correlated between the p-Pb and Pb-p sessions) is found to be 0.2% (0.3%) for the p-Pb (Pb-p) scan, in the same direction for the two fills.
-Ghost and satellite charge: the uncertainty on the LHCb ghost-charge measurement [11] propagates to an uncertainty of 0.1% (0.2%) on the p-Pb (Pb-p) cross-section measurement; the uncertainty in the LDM satellite-charge measurement [12] propagates to an uncertainty of 0.04% (0.1%) on the p-Pb (Pb-p) cross-section measurement.
-Dynamic β * : due to their electric charge, the two colliding beams (de-)focus each other in a separation-dependent way, which alters the measured scan shape.Calculations [25] are used to estimate the variations of β * with the separation, according to the prescription given in [17]; the effect on the measured cross section (partially correlated between the p-Pb and Pb-p sessions) is found to be ≤ 0.1% for all p-Pb and Pb-p scans.
Summing in quadrature all the above-mentioned uncertainties (summarised in table 3), one gets a total systematic uncertainty of 3.5% for the p-Pb cross sections and 3.2% for the Pb-p cross sections.The uncertainty applies in the same way to the T0 and V0 cross sections, since the only non-common term is the background subtraction, which becomes negligible in the quadratic sum.
All uncertainties are systematic.
The length-scale calibration and background-subtraction uncertainties are fully correlated between the p-Pb and Pb-p results, leading to a total correlated uncertainty between the two measurements of 1.5% for T0 and 1.6% for V0.

Comparison between V0-and T0-based luminosities
The visible cross sections measured in the vdM scans are used to determine the integrated luminosity for the data collected in the 2013 proton-lead run [26,27,28,29].The luminosity is measured independently via the V0 or the T0 trigger counts, corrected for pileup and for background contamination in the same way as done for the vdM scan data, divided by the corresponding cross sections.
The data sample is divided in several smaller datasets (runs).The integrated luminosity corresponding to each run is computed using both reference processes, and the results are compared.Figure 11 shows the   ratio of the integrated luminosity obtained with T0 to the one obtained with V0, as a function of the run number, for the p-Pb and Pb-p running modes.Although the overall agreement is satisfactory, fluctuations of about 1% around unity are seen in the run-by-run ratio; since these fluctuations are significantly larger than the tiny statistical uncertainties, a 1% additional systematic uncertainty is considered in the computation of the integrated luminosity uncertainty (table 3).

Measurement of the ZDC trigger cross section
The ALICE Zero Degree Calorimeter system (ZDC) [30] is composed of two neutron (ZN) and two proton (ZP) calorimeters, as well as two small electromagnetic calorimeters (ZEM).The two ZNs (ZNA and ZNC) are located on opposite sides of IP2, 112.5 m away from the interaction point.Each ZN is placed at zero degrees with respect to the ALICE z axis and is used to detect neutral particles at pseudorapidities |η| > 8.8.The ZNs were used to measure the cross section for neutron emission in Pb-Pb collisions at the LHC [31].A similar study is foreseen in p-Pb collisions.For this purpose, data have been collected with a trigger condition requiring a signal in the ZN located on the Pb remnant side (i.e.ZNA for p-Pb, ZNC for Pb-p).In this paragraph, the measured T0 and V0 cross sections are used to  4: Ratio of the ZDC to the reference process rates and ZDC cross sections resulting from such ratios, for all reference processes and beam configurations.The systematic uncertainties are split into correlated and uncorrelated components between the p-Pb and the Pb-p sessions.
determine indirectly the cross section for events satisfying such a trigger condition.Since the trigger condition is symmetric with respect to the swapping of the proton and lead beams, one expects the cross section to be the same in the p-Pb and Pb-p configurations.Thus, such a measurement provides a consistency check for the analysis of data from the two sessions.
The ZDC trigger cross section is calculated from the measured T0 and V0 cross sections, rescaled by the ratio of the ZDC trigger rate to the rate of the two reference processes, as measured during the two vdM scan sessions.All rates are corrected for background and pileup.The ratios and the resulting cross sections for the ZDC trigger are reported in table 4. The results obtained in the two fills are compatible within the uncorrelated uncertainties.The results obtained with T0 and V0 are also compatible.Thus, all results are combined to get σ ZDC = 2.22 b ± 0.01 b (stat) ± 0.06 b (syst).

Conclusions
Van der Meer scans were done for proton-lead collisions at √ s NN = 5.02 TeV at the LHC.The cross section was measured for two reference processes, based on particle detection by the T0 (4.6 < η < 4.9 and −3.3 < η < −3.0) and V0 (2.8 < η < 5.1 and −3.7 < η < −1.7) detectors.For the p-Pb configuration (proton beam travelling clockwise), the cross-section uncertainty is 3.5% and the results are: σ V0 = 2.09 b ± 0.07 b (syst), σ T0 = 1.59 b ± 0.06 b (syst).For the Pb-p configuration (proton beam trav- elling counter-clockwise), the cross-section uncertainty is 3.2% and the results are: σ V0 = 2.12 b ± 0.07 b (syst), σ T0 = 1.59 b ± 0.05 b (syst).The two reference processes were independently used for the lumi- nosity determination in the 2013 proton-lead run at the LHC.The luminosities measured via the two processes differ by at most 1% throughout the whole data-taking period; with such value quadratically added to the reference process cross section uncertainties, a total uncertainty on the luminosity measurement of 3.7% (3.4%) for the p-Pb (Pb-p) configuration is obtained.Finally, the measured reference cross sections were used to indirectly determine the cross section for a third, configuration-independent, reference process, based on neutron detection by the Zero Degree Calorimeter: σ ZDC = 2.22 b ± 0.01 b (stat) ± 0.06 b (syst).

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment; the CERN accelerator teams for the outstanding performance of the LHC complex, for availability and excellent support in carrying out vdM scans and for providing the bunch intensity and other crucial measurements; the LHCb collaboration, for providing the ghost charge measurements; everyone in the LHC Luminosity Calibration and Monitoring Working group, for many useful and stimulating discussions.The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration.The ALICE Collaboration acknowledges the following funding agencies for their support

Fig. 1 :
Fig. 1: (Colour online) Bunch intensities N 1 and N 2 for all colliding bunches, for an arbitrary timestamp during the p-Pb (left) and Pb-p (right) scan sessions.

Fig. 2 :
Fig.2:(Colour online) Raw rate of the T0 (left) and V0 (right) process for a typical colliding bunch pair, as a function of time, during the p-Pb scan session.In each plot, the first (second) bell-shaped structure corresponds to the beam separation in the horizontal (vertical) direction being varied from negative to positive values.The third (fourth) bell-shaped structure corresponds to the beam separation in the horizontal (vertical) direction being varied from positive to negative values.

Fig. 3 :
Fig.3: (Colour online) Correlation between the sum and difference of arrival times (relative to the bunch crossing) on the two V0 arrays.The left plot was obtained at zero beam separation; the right plot was obtained at a beam separation of 0.12 mm, roughly corresponding to five times the RMS of the beam profile.Events lying inside the area within the continuous lines are flagged as beam-beam interactions.

Fig. 4 :
Fig. 4: (Colour online) Background-and pileup-corrected head-on rates of the T0 (left) and V0 (right) reference process as a function of time for one interacting bunch crossing in the p-Pb scan session.The solid red curve is an exponential fit to the data points.

Fig. 5 :
Fig. 5: (Colour online) Background (R BB /R raw ), pileup (R PU /R BB ) and luminosity decay (R DC /R PU ) correction factors to the T0 (left) and V0 (right) rates as a function of the beam separation for one typical pair of colliding bunches during the first p-Pb vertical scan.Due to the different size of the background correction factor for T0 and V0, the two figures have different vertical scales.

Fig. 6 :
Fig. 6: (Colour online) Rates of the T0 (left) and V0 (right) reference process as a function of beam separation for one typical pair of colliding bunches in the first vertical p-Pb scan.The solid red curve is a fit according to eq. 4.

Fig. 7 :Fig. 8 :
Fig.7: (Colour online) Ratio between the h x h y quantities obtained (via numerical method) with the T0 and V0 reference processes in the p-Pb (left) and Pb-p (right) scan session, as a function of the colliding bunch pair ID number.The solid red lines are zero-order-polynomial fits to the data.

Fig. 9 :
Fig. 9: (Colour online) Cross sections for the T0 and V0 processes measured in the first scan of the p-Pb (left) and Pb-p (right) sessions, as a function of the product of the intensities of the colliding bunch pair.The results are obtained with the numerical method.Only the statistical uncertainties are shown.Method σ V0 [b] σ T0 [b]

Fig. 10 :
Fig. 10:Relative difference between the cross section obtained with the two-dimensional DG2D and the one-dimensional gPol6 fit models, as a function of the χ 2 /nd f value of the two-dimensional fit, for χ 2 /nd f < 105/32.Left: results for V0 in the first p-Pb scan.Right: results for V0 in the first Pb-p scan.

Fig. 11 :
Fig. 11: Ratio of T0-to V0-based integrated luminosities as a function of run number for the p-Pb (left) and Pb-p (right) data taking.The tiny statistical uncertainties are covered by the data-point markers.

Table 2 :
Cross section for the V0-and T0-based reference process in two Pb-p vdM scans, as obtained with the numerical and fit methods.The weighted average between the numerical results of the two scans, retained as the final result, is also reported.The quoted uncertainties are statistical.

Table 3 :
Relative uncertainties on the measurement of the T0 and V0 reference process cross section in p-Pb and Pb-p collisions.