1. Preliminary measurement of the total cross section in pp collisions at √s=7 TeV with the ALFA subdetector of ATLAS Hasko Stenzel, JLU Giessen on behalf of the ATLAS Collaboration ConfNote:

2. Outline Introduction Experimental setup: ALFA Data analysis
Differential elastic cross section
Theoretical prediction, fits and cross-checks
Results for σtot
Conclusion
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Hasko Stenzel

3. Introduction
The total ppX cross section is a fundamental quantity setting the scale for all interaction probabilities, it should be measured at each new collider or centre-of-mass energy.
The total cross section can‘t be calculated in perturbative QCD, but still can be measured, e.g. using the Optical Theorem:
A number of bounds and constraints can be placed on σtot:
Froissart-Martin bound: σtot doesn’t rise faster than ln2s
Black disk limit:
Pomeranchuk theorem: p4 θ p1 p2 p3
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4. Rise of σtot at ISR
At the ISR a rise of the total cross section was first observed.
U. Amaldi et al., Phys. Lett. B 44 (1973) 192
S.R. Amendolia et al., Phys. Lett. B 44 (1973) 119
Would the total cross section continue to rise with ln(s) or rather ln2(s)?
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5. Luminosity and total cross section
The optical theorem can be used together with the luminosity to determine the total cross section (method used by ATLAS):
Luminosity-dependent method
ρ taken from model extrapolation
If the total inelastic yield is measured simultaneously with the elastic yield, the luminosity can be eliminated:
Luminosity-independent method
If the elastic and inelastic cross sections are measured separately:
ρ-independent method
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6. The differential elastic cross section
At small |t| the cross section decreases exponentially
The nuclear slope parameter B increases with energy shrinkage of forward cone
At large |t| a diffractive minimum appears “the dip”, its position is energy dependent
At very large |t| the distribution follows a power law
At very small t the contribution from Coulomb interaction becomes important
ATLAS
range
D. Bernard et al., UA4 Collaboration, Phys. Lett. B 171 (1986) 142
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7. Available measurements
At the LHC first measurements were done by TOTEM:
σtot = 98.6±2.2 mb (7 TeV)
σtot = 101.7±2.9 mb (8 TeV)
Measurements were performed by cosmic ray observatories at yet higher energies, using air showers and transforming proton-air cross sections into pp cross section with Glauber models.
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8. Experimental setup: ALFA
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9. Elastic scattering with ATLAS-ALFA
Roman Pot detectors at 240m from IP1 approaching the beam during special runs at high β*.
In October 2011 ALFA had the special run with β*=90m and recorded 800k good selected elastic events used for the analysis of the total cross section and the nuclear slope B.
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10. The ALFA detector in a nutshell
ALFA is a scintillating fibre tracker, 10 double-sided modules with 64 fibres in uv-geometry. Resolution ~30µm.
Special overlap detectors to measure the distance between upper and lower detectors.  alignment
v fibres
u fibres
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11. Beam optics and properties
Special optics high β* =90m
Small emittance 2-3µm
Small divergence ~3µrad
Phase advance of βy=90° parallel-to-point focusing
Phase advance of βx≈180°
 good t-resolution y*
y*
parallel-to-point focusing
ydet IP
Leff
Only one pair of colliding bunches at p
More pilot bunches / unpaired bunches
L≈1027/cm2/s, µ ≈0.035
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12. Hit pattern at ALFA
Hit pattern in one station, before elastic event selection.
Pattern shape is caused by beam optics
Leffy=270 m
Leffx=13 m
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13. Data Analysis
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14. Alignment Rough centering and alignment through scraping
Offsets and rotations are obtained from elastic data
Distance measurement from OD detectors
Vertical offsets wrt beam center are obtained by assuming efficiency-corrected equal yields in upper and lower detectors
Final vertical detector positions are related one station as reference and using optics lever arm ratios to predict the positions from inner to outer detectors
Vertical position precision is ~80µm
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15. Measurement of t
Measure elastic track positions at ALFA to get the scattering angle and thereby the t-spectrum dσ/dt
p=beam momentum, θ*=scattering angle
To calculate the scattering angle from the measured tracks
we need the beam optics, i.e. the
transport matrix elements.
In the simplest case (high β*,
phase advance 90°,
parallel-to-point focusing)
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16. Different reconstruction methods
subtraction method:
local angle method:
local subtraction:
lattice method:
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17. Event selection first level elastic trigger data quality cuts
apply geometrical acceptance cuts
apply elastic selection based on back-to-back topology and background selection cut
elastic selection: y A- vs C-side
background rejection
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18. Trigger efficiency
Elastic trigger: Coincidence of A- and C-side in elastic configuration, using a local OR.
Data were also recorded with a looser trigger condition requiring any of the 8 detectors to fire: trigger efficiency = 99.96±0.01 % .
For the selected data period the DAQ life fraction was 99.7±0.01%.
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19. Background golden anti-golden
Two ways to estimate the irreducible background under the elastic peak:
Counting events in the anti-golden configuration (nominal method)
Reconstructing the vertex distribution in x through the lattice, where background appears in non Gaussian tails, fraction estimated with background templates obtained from data (for systematics)
Arm 2
Arm 1
golden
anti-golden
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20. Background Background fraction is 0.5 ± 0.25 %
Vertex method
anti-golden
Background fraction is 0.5 ± 0.25 %
dominated by halo protons
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21. Simulation: acceptance & unfolding
Using PYTHIA8 as elastic scattering generator
Beam transport IPRP (matrix transport / MadX PTC)
Fast detector response parameterization tuned to data
Comparison of data and MC for positions at ALFA
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22. Acceptance Acceptance is given by geometry, mostly by vertical cuts.
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23. Resolution of different methods
Subtraction method has by far best resolution, dominated by beam divergence.
All other methods suffer from a poor local angle resolution.
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24. Unfolding resolution effects
Transition matrix from true value of t to reconstructed value of t used as input for IDS unfolding. B. Malaescu arXiv:
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25. Impact of unfolding
Systematic uncertainty evaluated with a data-driven closure test, based on the small difference between data and MC at reconstruction level.
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26. Reconstruction efficiency
Fully data-driven method, using a tag-and-probe approach exploiting elastic back-to-back topology and high trigger efficiency.
Arm 1
Arm 2
Efficiency εrec
0.898
0.880
Uncertainty
±0.006
±0.009
Slightly different efficiency in the two arms  material budget is different.
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27. Reconstruction efficiency
Several different topologies contribute to the inefficiency, which is mainly caused by shower developments.
4/4
3/4 case:
2/3 of the losses
Ensure ¾ events are elastics
Check shape
Check t-independence of reconstruction efficiency.
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28. Reconstruction efficiency
2/4 case (≈30% of the losses): ensure these events are inside the acceptance and elastics (not background, e.g. from SD+Halo).
Distribution of remaining 2/4 events are fit to estimate the background contribution with BG-enhances templates.
Peaks observed resulting from showers in RP window and beam screen: These events are outside of acceptance and removed.
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29. Luminosity
Dedicated analysis for this low-luminosity run: Based on BCM with LUCID and vertex counting as cross-check.
Systematics:
vdM calibration 1.5%
BCM drift 0.25%
Background 0.2%
Time stability 0.7%
Consistency 1.6%
L=78.7±1.9 µb-1
Systematic uncertainty 2.3%
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30. Beam optics
From the elastic data several constraints were recorded to fine-tune the transport matrix elements. These are obtained from correlations in the positions/angles:
y inner vs outer
x left vs right
Lever arm ratio
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31. Beam optics scaling factors
A second class of constraints is obtained from correlations of the reconstructed scattering angle using different methods. These constraints are derived using design 90m optics and indicate the amount of scaling needed in order to equalize the scattering angle measurement from different methods.
Measure the difference in reconstructed scattering angle in horizontal plane between subtraction and local angle method vs Θ*x from subtraction  scaling factor R(M12/M22).
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32. beam optics fit
14 constraints are combined in a fit of the relevant beam optics parameters.
Most important are the strengths of the inner triplet quadrupoles. Quadrupoles Q1,Q3 and Q2 were produced at different sites  fit an intercalibration offset
That is the simplest but not unique solution effective optics
Small correction to optics model, 3‰ to inner triplet magnet strength.
ΔkQ1Q3[‰]
Beam 1
Beam 2
2.88±0.15
3.13±0.12
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33. Differential elastic cross section
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34. The differential elastic cross section
Fully corrected t-spectra in the two arms are combined and divided by the luminosity to yield the differential elastic cross section.
A: acceptance(t)
M: unfolding procedure (symbolic)
N: selected events
B: estimated background
εreco: reconstruction efficiency
εtrig: trigger efficiency
εDAQ: dead-time correction
Lint: luminosity
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35. Systematic uncertainties for dσ/dt
luminosity: ± 2.3%
beam energy: ± 0.65%
background 0.5 ± 0.25 %
optics: quadrupole strength ± 1‰, Q5,6 -2‰ magnet mis-alignment, optics fit errors, beam transport, ALFA constraints varied by ± 1σ
residual crossing angle ±10 <mrad
More than 500 alternative optics models were used to reconstruct the t-spectrum and calculate unfolding & acceptance corrections.
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36. Systematic uncertainties for dσ/dt
reco. eff.: ± 0.8%
emittance: ± 10%
detector resolution: ±15%
physics model for simulation: B=19.5 ± 1 GeV-2
unfolding: data driven closure test
alignment uncertainties propagated
track reconstruction cut variation
Most important experimental systematic uncertainties: Luminosity and beam energy.
Systematic shifts are included in the fit of the total cross section.
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37. Theoretical predictions
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38. The elastic scattering amplitude
The elastic scattering amplitude is usually expressed as a sum of the nuclear amplitude and the Coulomb amplitude:
The nuclear amplitude is the dominant contribution in the differential cross section with a term quadratic in σtot and an essentially exponential shape with slope B.
The Coulomb term is important at small t, but the Coulomb-nuclear interference term has a non-negligible contribution inside the accessible t-range.
Differential elastic cross section with the Coulomb phase Φ.
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39. Theoretical prediction
The theoretical prediction used to fit the elastic data consists of the Coulomb term, the Coulomb-Nuclear-Interference term and the dominant Nuclear term.
Coulomb
CNI
Nuc.
Proton dipole form factor
Coulomb phase
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40. modified χ2 to account for systematics
D: data, T: theoretical prediction
V: statistical covariance matrix
δ: systematic shift k in t spectrum
β: nuisance parameter for syst. shift k
ε: t-independent normalization uncertainty (luminosity, reco efficiency)
α: nuisance parameter for normalization uncertainties
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41. Results for σtot
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42. Fit Results
exp.+stat.
The fit includes experimental systematic uncertainties in the χ.
The fit quality is good: χ2/Ndof=7.4/16.
The fit range is set to –t[0.01,0.1] GeV2,
where possible deviations from exponential form of the nuclear amplitude are expected to be small.
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43. theoretical/extrapolation uncertainties
uncertainty in ρ = 0.14 ± (COMPETE)
variation of the proton electric form factor
variation of the Coulomb phase
in order to probe possible non-exponential contributions to the nuclear amplitude a variation of the upper end of the fit range is carried out from 0.1 0.15 GeV2 , based on theoretical considerations.
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44. The electric form factor
Dipole:
New measurements from A1 using low-energy electron-proton scattering at MAMI.
J.C. Bernauer et al. A1 Collaboration, arXiv:1307:6227
Largest deviation is observed between Dipole and Double-Dipolevery small impact on total cross section.
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45. The Coulomb phase West and Yennie:
Alternative parameterizations were proposed by Cahn
R.N. Cahn, Z. Phys. C 15 (1982) 253
and by Kohara et al.(KFK)
A.K. Kohara, Eur. Phys. J. C 73 (2013) 2326
Phase has a small impact on the CNI term, which is small very small impact on total cross section .
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46. Fit range dependence Nominal fit range [0.01,0.1],
variation by ±0.05, as advocated by KMR
V.A. Khoze et al., Eur. Phys. J. C 18 (2000) 167
Systematic uncertainty is derived from the endpoints of the fit range variation.
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47. Cross checks (1)
Comparison of different t-reconstruction methods consistent results
Using only statistical uncertainties in the fit, i.e. w/o nuisance parameters
Statistical error
only
Instead of unfolding the data we folded the theoretical prediction to the raw data  consistent fit results
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48. Cross checks (2)
Determination of the differential elastic cross section in each independent arm: consistent, even within statistical errors.
Split the run in periods (≈20 min., 80k events)  no time-structure (stat.error ≈ 0.5 mb)
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49. Alternative models for the nuclear amplitude
several models for the nuclear amplitude featuring a non-exponential behaviour are tested
all models come with more parameters and are intended to be extended to larger t [0.01,0.3]
restrict to parametric models allowing to fit the total cross section
fit with Ct2 term
fit with sqrt(t) term
SVN model
BP model
BSW model
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50. Results for alternative models
σtot [mb]
Reference
Nominal
95.35 ±1.30 -
C 𝑡 2
95.49 ±1.27
M.M.Block et al., Czech. J. Phys. 40 (1990) 164.
c −𝑡
96.03 ±1.31
O.V.Selyugin, Nucl. Phys. A 922 (2014) 180.
SVM
94.90 ±1.23
A.K.Kohara et al., Eur. Phys. J. C 73 (2013) 2326. BP
95.49 ±1.54
R.J.N.Phillips et al., Phys. Lett. B 46 (1973) 412.
D.A.Fagundes et al.,Phys. Rev. D 88 (2013)
BSW
95.53 ±1.38
C.Bourrely et al., Eur. Phys. J. C 71 (2011) 1601.
Only statistical and experimental systematic uncertainties on dσ/dt are included in the profile fit.
The RMS of all the models tested is in good agreement with the assigned extrapolation uncertainty of 0.4mb.
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51. Results Standard model cross section measurements by ATLAS
Energy evolution of σtot and σel
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52. Energy evolution of B
private compilation
Increase of B compatible with a 2nd order polynomial in ln(s).
Parameters from: V.A.Schegelsky and M:G: Ryskin , Phys.Rev.D 85 (2012)
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53. Comparison with TOTEM
The ATLAS measurement is 3.2 mb lower than TOTEM, the difference corresponds to 1.3 σ, assuming uncorrelated uncertainties.
ATLAS σtot = 95.4±1.4 mb B = 19.7 ± 0.3 GeV-2
TOTEM σtot = 98.6±2.2 mb B = 19.9 ± 0.3 GeV-2
Comparison of results using the luminosity-dependent method.
The luminosity uncertainty for ATLAS is ±2.3% and for TOTEM ±4%,
it enters in the uncertainty of σtot with a factor 0.5.
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54. Further derived quantities
Elastic cross section from the integrated fit-function (nuclear part)
The observed elastic cross section inside the fiducial volume:
The optical point:
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55. The inelastic cross section
The total inelastic cross section σinel is obtained by subtraction of the elastic cross section from the total cross section.
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56. Conclusion and outlook
ATLAS has performed a preliminary measurement of the total cross section at the LHC at √s=7 TeV from elastic scattering measured with the ALFA detector
in good agreement with previous measurements from TOTEM.
Our measurement of indicates that the black-disk limit is not reached at the LHC
We have collected in 2012 at √s=8 TeV more data with β*=90m optics and with β*=1km optics, the latter enables access to yet smaller values of t in the CNI region.
During the LHC shutdown a substantial consolidation of the ALFA detector achieved (RF protection, optimized placement of Roman Pot stations), and we are looking forward to collect more elastic and diffractive data in the LHC run 2.
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57. Back Up
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58. Transport matrix ALFA IP beam transport matrix from optical functions
phase advance
vertical: ψ=90°
horizontal ψ=185°
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59. Rescaling factors
Scaling factor based on the isotropy of elastic scattering, i.e. scattering angle distribution is flat in phi, density in x must be the same as in y.
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60. Pulls of the fit to dσ/dt
Pulls of the fit with respect to the data, taking into account fitted nuisance parameters adjusting data and theory.
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61. Results for 4 different methods
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62. Systematic uncertainties for dσ/dt
Systematic shifts
used in the profile fit
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63. Systematic uncertainties for dσ/dt
Systematic shifts
used in the profile fit
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64. The t-spectrum
Reconstructed t-spectrum for different methods before corrections.
Difference between methods understood as resulting from different resolutions inducing different unfolding corrections.
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65. Nuisance parameters
The nuisance parameters are expected with a mean value of 0 and an uncertainty of ±1.
The statistical uncertainty of the physics parameters σtot and B are obtained from simulated pseudo-experiments:
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