Measurement of the inelastic pp cross section at √s = 7 TeV with the CMS detector


A new method to measure the inelastic pp cross section has been developed based on the assumption that pile-up events are randomly distributed according to a Poisson probability. This method relies only on the accurate knowledge of the CMS tracking system and it does not depend upon a specific Monte Carlo simulation. The value of the cross section for events with at least 2 charged particles with $|\eta|<2.4$ and $p_\perp > 200 $ MeV is determined to be $ \sigma_{2-trks} = 58.7 \pm 2.0 \; (Syst) \pm 2.4 \; (Lum) \; {\rm mb} $. Using model-dependent extrapolations, the value for the total inelastic $pp$ cross section is determined to be $ \sigma_{inel}(pp) = 68.0 \pm 2.0 \; (Syst) \pm 2.4 \; (Lum) \; \pm 4 (Ext.) \; {\rm mb} $.

Approved Plots from FWD-11-001 PAS ( click on plot to get .pdf )

Figure Abbreviated Caption
Vtx_Eff_2_3_trk.gif Fraction of generated events with a given vertex track multiplicity accepted by the selection criteria $NDOF \ge 0.5$ and with either 2 (empty circles) or 3 (solid circles) reconstructed tracks. The plot shows this fraction evaluated with 2 different versions of PYTHIA.

Data_MC_Lumibins.gif Comparison data - reweighted Monte Carlo. Each plot shows, as function of luminosity, the number of events with a given value of vertices, from 1 to 11. The first 9 plots contain the data used in this analysis.

MC_data_64_05.gif Data and Monte Carlo distribution in each of the 13 luminosity bins, from 0.05~to~0.7~$\cdot 10^{30}\; {\rm cm^{-2} \; s^{-1}}$.

FInal_plots_05.gif Fraction of events with n pile-up events as a function of luminosity. The dotted line is a Poisson fit.

Sigma_chi_final_65_05_2trk.gif $\chi^2$/NDOF (top) and $\sigma(pp)$ values (bottom) for each of the fit of Figure~\ref{fig:final}. The dashed line is the result of the fit to the 9 $\sigma(pp)$ values. The fits are for events with at least 2 charged particles.

sigma_com_part.gif Comparison between the CMS results and several Monte Carlo models for events with at least 2, 3 and 4 charged particles in $abs(\eta)<2.4$ and $p_t > $ 200 MeV. Systematic uncertainties shown by the inner red error bars and luminosity uncertainty by the outer black bars. Monte Carlo predictions have a common uncertainty of $~1 $ mb

Tot_inel.gif Compilation of total inelastic $pp$ and $p\bar{p}$ cross section values. CMS analysis uncertainty is shown in dark blue while the model-dependent extrapolation is shown in light blue.

Additional approved plots for FWD-11-001 PAS

Figure Description
Vtx_vs_lumi.gif Number of vertices as a function of the bunch instantaneous luminosity.
nvertexes.gif Number of vertices during the 2010 run period
Blind2.gif The x-axis of the plot is the distance between two vertices while on the y axis it shows their combined track multiplicity. This plot shows that vertices that are closer to each other more than ∼ 0.6mm are merged together.
Uncor_plots_05.gif Uncorrected pile-up distribution. The dashed lines are a fit using a Poisson distribu- tion, see eq.1.
MC_64_564.gif Monte Carlo events fitted with a Poisson function for each value of pile-up events
MC_Sigma_chi2.gif χ2 (top) and σ values (bottom) for each of the fit of Figure 17. The dashed line is the result of the fit to the 9 σ values. The generator value of σinel = 56.2 mb is well reproduced by the measurement.

Secondary.gif Fraction of secondary vertices with and without the requirement on the transverse position of the vertex to be within 0.06 mm from the beam line.

data_over_MC_64_05.gif Ratio data over Monte Carlo in each of the 13 luminosity bins, from 0.05 to 0.7 1030 cm−2 s−1.

MC_LumiBins.gif Each of this plot shows distributions for a given luminosity interval, from 0 to 0.7 1030 cm−2 s−1. In each of the 14 plots there are 3 histograms: the theoretical Poisson pile-up distribution (assuming σinel(pp) = 65 mb), the part that has at generation at least 2 tracks, each with pt > 200 MeV in the range abs(η) < 2.4 and the reconstructed values.

Additional plots for presentations ( click on plot to get .pdf )

Figure Description
xi_models.gif Generator level $\xi$ distribution of several MC models (PYTHIA, PHOJET, SIBYLL, QGSJET, EPOS) for all events and for events with at least 2 charged particles, each with $p_t > 200$ MeV in the range $abs(\eta)< 2.4$.
CMS_manyVtx.gif CMS event with many vertices
transversecut.gif Transverse cut to remove fakes

-- NicoloCartiglia - 01-Aug-2011

Topic attachments
I Attachment History Action Size Date Who Comment
GIFgif 1_2_vtx.gif r1 manage 8.0 K 2011-08-02 - 09:39 NicoloCartiglia  
GIFgif Blind2.gif r1 manage 29.1 K 2011-08-01 - 22:26 NicoloCartiglia  
GIFgif CMS_manyVtx.gif r1 manage 162.1 K 2011-08-02 - 09:28 NicoloCartiglia  
GIFgif Data_MC_Lumibins.gif r1 manage 30.2 K 2011-08-01 - 13:22 NicoloCartiglia  
GIFgif FInal_plots_05.gif r1 manage 21.1 K 2011-08-01 - 13:28 NicoloCartiglia  
GIFgif MC_64_564.gif r1 manage 17.1 K 2011-08-01 - 22:33 NicoloCartiglia  
GIFgif MC_LumiBins.gif r1 manage 25.2 K 2011-08-02 - 09:34 NicoloCartiglia  
GIFgif MC_Sigma_chi2.gif r1 manage 10.0 K 2011-08-01 - 22:34 NicoloCartiglia  
GIFgif MC_data_64_05.gif r1 manage 26.1 K 2011-08-01 - 13:22 NicoloCartiglia  
GIFgif Secondary.gif r1 manage 8.3 K 2011-08-01 - 23:08 NicoloCartiglia  
GIFgif Sigma_chi_final_65_05_2trk.gif r1 manage 9.5 K 2011-08-01 - 13:29 NicoloCartiglia  
GIFgif Tot_inel.gif r1 manage 146.0 K 2011-08-01 - 13:48 NicoloCartiglia  
GIFgif Uncor_plots_05.gif r1 manage 16.1 K 2011-08-01 - 22:28 NicoloCartiglia  
GIFgif Vtx_Eff_2_3_trk.gif r1 manage 14.2 K 2011-08-01 - 13:09 NicoloCartiglia Fig1_gif
GIFgif Vtx_vs_lumi.gif r1 manage 12.3 K 2011-08-01 - 22:24 NicoloCartiglia  
GIFgif csi.gif r1 manage 11.0 K 2011-08-01 - 14:14 NicoloCartiglia  
GIFgif data_over_MC_64_05.gif r1 manage 29.2 K 2011-08-02 - 09:33 NicoloCartiglia  
GIFgif nvertexes.gif r1 manage 11.0 K 2011-08-01 - 22:26 NicoloCartiglia  
GIFgif sigma_com_part.gif r1 manage 10.3 K 2011-08-01 - 13:34 NicoloCartiglia  
GIFgif transversecut.gif r1 manage 17.8 K 2011-08-02 - 09:28 NicoloCartiglia  
GIFgif xi_models.gif r2 r1 manage 16.6 K 2011-08-01 - 14:01 NicoloCartiglia  
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Topic revision: r5 - 2011-08-09 - NicoloCartiglia
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