The luminosity values shown have been calibrated with van-der-Meer beam-separation scan data. The error on the luminosity is estimated to be 11%, dominated by the uncertainty in the beam intensities.

The total time of stable beams during these fills is 41.8 hours. The total delivered (recorded) luminosity is 142.5 nb⁻¹ (138.9 nb⁻¹). The luminosity values given have been calibrated with van-der-Meer beam-separation scan data. The error on the luminosity is estimated to be 11%, dominated by the uncertainty in the beam intensities.

First Plot: Rate of events in LHC Fill 1005 with at least one charged primary particle with pT>0.5 GeV/c, |eta|<0.8, versus UTC time (solid markers). Also shown is the raw rate of events with at least one track in this acceptance range (dashed line). The correction factor applied to the raw rate to obtain the charged particle rate is 1.04 +\- 0.017. Error bars represent the statistical uncertainty, the colored bands include both the systematic and statistical uncertainties.

Second Plot: The instantaneous luminosity derived from counting of events with at least one charged primary particle (pT>0.5 GeV/c, |eta|<0.8) for LHC Fill 1005 as a function of UTC time. Pythia MC09 was used for the acceptance and cross-section models after the correction for tracking, vertex and trigger efficiencies. Error bars represent the statistical uncertainty, the colored bands include both the systematic and statistical uncertainties. The systematic uncertainties account for the correction procedure and the dependence on the Monte Carlo models used for the acceptance and cross-sections by comparing the results obtained with Pythia MC09 and Phojet.

Third Plot: The instantaneous luminosity derived from counting of events with at least one charged primary particle (pT>0.5 GeV/c, |eta|<0.8) for LHC Fill 1005 as a function of UTC time (black points) compared with the Van der Meer calibrated ATLAS luminosity measurement (blue triangles). Pythia MC09 was used for the acceptance and cross-section models for the charged particle analysis. Error bars represent the statistical uncertainty, the colored bands include both the systematic and statistical uncertainties. The systematic uncertainties on the charged particle method account for the correction procedure and the dependence on the Monte Carlo models used for the acceptance and cross-sections by comparing the results obtained with Pythia MC09 and Phojet.

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First Plot: Rate of events in LHC Fill 1089 with at least one charged primary particle (p_T > 0.5 GeV, |η| < 0.8) versus UTC time for recorded events (black open circles), and corrected for pile-up (red filled circles). The pile-up correction (μ-correction) was performed as detailed in Equation 2 of ATLAS-CONF-2010-060. The error bars include the statistical uncertainty and the 1.7% uncertainty on the track to particle correction factor of 1.04. This fill corresponds to four ATLAS runs, therefore periods in between runs are empty, as well as the period of the van der Meer scan and periods when the Inner Detector was not fully operational.

Second Plot: The cross section measured in LHC Fill 1089 for events with at least one charged primary particle (p_T > 0.5 GeV, |η| < 0.8) versus UTC time. The error bars include the statistical uncertainty and the 1.7% uncertainty on the track to particle correction factor of 1.04. The average cross-section is 42.3 ± 0.7 (stat. + sys.) mb. The scale uncertainty of 11% in the luminosity used to calculate the cross section from the event rate is not included. This fill corresponds to four ATLAS runs, therefore periods in between runs are empty, as well as the period of the van der Meer scan and periods when the Inner Detector was not fully operational.

For details on the event selection see also ATLAS-CONF-2010-101.

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(a) The horizontal luminous centroid during a horizontal vdM scan moves in the same direction as the beam with the narrower horizontal width. If the beam profiles (and therefore the luminosity distribution) are Gaussian then one would see only linear motion of the luminous centroid. The deviation from linearity requires the single beam profiles to be modelled as something more complicated. The density distribution of each bunch is modelled by the non-factorisable sum of three 3-D gaussians, the parameters of which are tuned to reproduce the evolution of the luminous centroid observed in the data. This model provides a satisfactory description of the data except at the largest beam separation. (b) The vertical luminous centroid position during a horizontal vdM scan would be constant if there were no transverse correlation in the single beam profiles (and therefore neither in the luminosity distribution). The density distribution of each bunch is modelled by the non-factorisable sum of three 3-D gaussians, the parameters of which are tuned to reproduce the evolution of the luminous centroid observed in the data. This model provides a satisfactory description of the data. Note that a simulation in which the individual beam profiles are modelled by 3-D single gaussians could also describe these data if one or both of the beams had some degree of transverse correlation.

(a) The horizontal luminous widthd uring a horizontal vdM scan wouldn ot vary if each individual beam profile were modelled by a 3-D single Gaussian. The increase in luminous width with separation (and then decrease again at large separations) requires a more complicated model. The density distribution of each bunch is modelled by the non-factorisable sum of three 3-D gaussians, the parameters of which are tuned to reproduce the evolution of the luminous centroid observed in the data. This model is able to provide the qualitative features needed for describing the observed variation in width.

(b) The vertical luminous width during a horizontal vdM scan will vary if there is some non-linear transverse correlation in at least one of the beams. The variation in width points to non-factorisation effects in the transverse beam distribution. The density distribution of each bunch is modelled by the non-factorisable sum of three 3-D gaussians, the parameters of which are tuned to reproduce the evolution of the luminous centroid observed in the data. This model provides a satisfactory description of the data.

(a) The horizontal luminous width during a horizontal vdM scan would not vary if each individual beam profile were modelled by a 3-D single Gaussian. The increase in luminous width with separation (and then decrease again at large separations) requires a more complicated model. However unlike the data from the July vdM scan session (Figure 2), in November the luminosity distribution width initially decreases as a function of separation before increasing again at large separation. The double (or triple) Gaussian model is insufficient to describe these observations.

The three grey curves show the results of three simulations in which the density distribution of each bunch is modelled by 3-D double gaussians in each case with slightly varying parameter choices, but in each the two beams are identical. A double Gaussian (gDG) is the non-factorisable sum of two normalised 3-D single Gaussians (gA and gB) in which gA is weighted by a parameter, f , the fraction and gB by 1 - f . The first grey curve (a straight horizontal line) is the case when the horizontal widths of Gaussians A and B are equal. The second, in which the horizontal luminous width continues increasing with separation, is the case when the horizontal width of Gaussian A is greater than that of B. The third grey line, in which the horizontal luminous width increases initially with separation and then starts decreasing is the case in which the width of Gaussian B is greater than that of A. Note that for each curve the vertical width of Gaussian B is greater than the vertical width of Gaussian A.

A model for the density distribution of each bunch which does describe the data satisfactorily is the non-factorisable sum of two 3-D supergaussians (double supergaussian), the parameters of which are tuned to reproduce the evolution of the luminous centroid observed in the data. In one dimension a supergaussian is an extension of a single Gaussian and has the form gSG(x) = A.exp(-0.5*(|x-mu|/sigma)**(2+epsilon)) where A is a normalisation constant, mu is the mean, sigma is the width and epsilon is a small number. In the case epsilon=0, the sthe single Gaussian distribution is recovered. The supergaussian provides an acceptable parameterisation of the data except at the largest beam separation.

(b) Any variation of vertical luminous width during a horizontal scan is indicative of non-factorisation of the luminosity distribution. Figure 2(b) showed data from the July 2012 scan session and showed significant variation in luminous width with separation. Figure 3(b) shows data from November and it is observed that the variation is much less. This suggests that the vdM formalism used to calibrate the luminosity is likely to hold better in November than in July.

The data is compared to a simulation in which the density distribution of each bunch is modelled by the non-factorisable sum of two 3-D supergaussians, the parameters of which are tuned to reproduce the evolution of the luminous centroid observed in the data. The model provides an acceptable parameterisation of data except at the largest beam separation. In this case (unlike for (a)) a simulation using double Gaussian beam profiles would have also been able to describe the data.