Outline

Preliminary measurement of the total cross section in pp collisions at √s=7 TeV

with the ALFA subdetector of ATLAS

Hasko Stenzel, JLU Giessenon behalf of the ATLAS Collaboration

ConfNote: http://cds.cern.ch/record/1740971

http://cds.cern.ch/record/1740971

• Introduction

• Experimental setup: ALFA

• Data analysis

• Differential elastic cross section

• Theoretical prediction, fits and cross-checks

• Results for σtot

• Conclusion

CERN seminar 22.07.2014 Hasko Stenzel 2

Outline

The total ppX 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:CERN seminar 22.07.2014 Hasko Stenzel 3

Introduction

0Im4 teltot f

stot

el

2

1

spppp

p1 p2

p3

p4

θ 2

242

231

pt

ppppt

At the ISR a rise of the total cross section was first observed.


Rise of σtot at ISR

S.R. Amendolia et al., Phys. Lett. B 44 (1973) 119

U. Amaldi et al., Phys. Lett. B 44 (1973) 192

Would the total cross section continue to rise with ln(s) or rather ln2(s)?

http://www.sciencedirect.com/science/article/pii/037026937390316X









http://www.sciencedirect.com/science/article/pii/0370269373903158











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):

02

2

1

161

t

eltot dt

dN

L

elinel

t

el

tot NN

dtdN

0

21

16

tot

inelel NNL

If the total inelastic yield is measured simultaneously with the elastic yield, the luminosity can be eliminated:

Luminosity-dependent methodρ taken from model extrapolation

Luminosity-independent method

If the elastic and inelastic cross sections are measured separately:

elineltot ρ-independent method

Im

Re

0

tel

el

tf

tf


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

D. Bernard et al., UA4 Collaboration, Phys. Lett. B 171 (1986) 142

tBedt

d

2

1

tdt

d

pt

dt

d ATLAS

range












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.


Experimental setup: ALFA

Elastic scattering with ATLAS-ALFA


In October 2011 ALFA had the special run 191373 with β*=90m and recorded 800k good selected elastic events used for the analysis of the total cross section and the nuclear slope B.

Roman Pot detectors at 240m from IP1 approaching the beam during special runs at high β*.

The ALFA detector in a nutshell


Special overlap detectors to measure the distance between upper and lower detectors. alignment

ALFA is a scintillating fibre tracker, 10 double-sided modules with 64 fibres in uv-geometry. Resolution ~30µm.

u fibresv fibres

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°

y*

y*

parallel-to-point focusingydet

IP Leff

• Only one pair of colliding bunches at 7 1010 p • More pilot bunches / unpaired bunches• L≈1027/cm2/s, µ ≈0.035

good t-resolution

Hit pattern at ALFA


Hit pattern in one station, before elastic event selection. Pattern shape is caused by beam opticsLeff

y=270 mLeff

x=13 m


Data Analysis

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

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)

2*pt

*

*

2221

1211

yy

y

MM

MMy

12

*

M

yy


Different reconstruction methods • subtraction method:

• local angle method:

• local subtraction:

• lattice method:

yxu ,CA

CAu MM

uu

,12,12

*

CA

CxAxx MM ,22,22

,,*

plane horizontal

241,12

237,11

237,12

241,11

,241237

,11,237241

,11*,

SSSS

SSSSSx MMMM

xMxM

CAS ,

xx MxM 122

112

*


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


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%.


Background 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)

anti-golden

Arm 1

Arm 2

golden


Background

Background fraction is 0.5 ± 0.25 %dominated by halo protons

anti-goldenVertex method


Simulation: acceptance & unfolding • Using PYTHIA8 as elastic scattering generator• Beam transport IPRP (matrix transport / MadX PTC)• Fast detector response parameterization tuned to data

Comparison of data and MC for positions at ALFA


Acceptance

Acceptance is given by geometry, mostly by vertical cuts.


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.


Unfolding resolution effects

Transition matrix from true value of t to reconstructed value of t used as input for IDS unfolding. B. Malaescu arXiv:1105.3107

http://arxiv.org/abs/arXiv:1106.3107




Impact of unfolding

Systematic uncertainty evaluated with a data-driven closure test, based on the small difference between data and MC at reconstruction level.


Reconstruction efficiency Fully data-driven method, using a tag-and-probe approach exploiting elastic back-to-back topology and high trigger efficiency.

Slightly different efficiency in the two arms material budget is different.

Arm 1 Arm 2

Efficiency εrec 0.898 0.880

Uncertainty ±0.006 ±0.009


Reconstruction efficiency

Several different topologies contribute to the inefficiency, which is mainly caused by shower developments.

4/04/14/)11(4/)02(4/34/4

4/4

NNNNNN

Nrec

Ensure ¾ events are elasticsCheck shape

Check t-independence of reconstruction efficiency.

3/4 case:2/3 of the losses

4/4


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).

Peaks observed resulting from showers in RP window and beam screen: These events are outside of acceptance and removed.

Distribution of remaining 2/4 events are fit to estimate the background contribution with BG-enhances templates.

CERN seminar 22.07.201429

Luminosity

Systematic uncertainty 2.3%

L=78.7±1.9 µb-1

Hasko Stenzel

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%


Beam optics

Hasko Stenzel

From the elastic data several constraints were recorded to fine-tune the transport matrix elements. These are obtained from correlations in the positions/angles:

12* My y

outer

inner

outer

inner

M

M

y

y

12

12

Lever arm ratio

y inner vs outer

x left vs right


Beam optics scaling factors

Hasko Stenzel

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).


beam optics fit

Small correction to optics model, 3‰ to inner triplet magnet strength.

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

Hasko Stenzel

ΔkQ1Q3[‰] Beam 1 Beam 2

2.88±0.15 3.13±0.12


Differential elastic cross section


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 eventsB: estimated backgroundεreco: reconstruction efficiencyεtrig: trigger efficiencyεDAQ: dead-time correction Lint: luminosity

int

1

L

M1

DAQtrigrecoi

ii

ii A

BN

tdt

d


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.


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.


Theoretical predictions


The elastic scattering amplitude The elastic scattering amplitude is usually expressed as a sum of the nuclear amplitude and the Coulomb amplitude:

t

tGctfC )(8 2

Im

Re

0

tel

el

tf

tf 2/BttotN e

c

itf

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.

GeV 71.0 ,t

)( 2

2

tG

2)()()(16

1 tiCN etftf

dt

d

Differential elastic cross section with

the Coulomb phase Φ.


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.

Proton dipole form factor

Coulomb phase

Coulomb

CNI

Nuc.


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


Results for σtot


Fit Results

2GeV 24.073.19

mb 3.14.95

Btot

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.

exp.

+sta

t.


theoretical/extrapolation uncertainties

• uncertainty in ρ = 0.14 ± 0.008 (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.


The electric form factor

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-Dipolevery small impact on total cross section.

2

2

GeV 71.0 ,

t

tG

Dipole:





The Coulomb phase

Alternative parameterizations were proposed by CahnR.N. Cahn, Z. Phys. C 15 (1982) 253and 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 .

E

tBt

2ln

West and Yennie:

https://cds.cern.ch/record/137742







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.

2GeV (extr.)17.0(exp.)19.0stat.)(14.073.19

mb (extr.)37.0(exp.)25.1stat.)(38.04.95

Btot

http://arxiv.org/abs/hep-ph/0007359






Cross checks (1)Comparison of different t-reconstruction methods consistent results

Using only statistical uncertainties in the fit, i.e. w/o nuisance parameters

2-GeV 05.062.19

mb 12.031.95

Btot Statistical

erroronly

Instead of unfolding the data we folded the theoretical prediction to the raw data consistent fit results


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)


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

1. fit with Ct2 term

2. fit with sqrt(t) term

3. SVN model

4. BP model

5. BSW model


Results for alternative models

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.

σtot [mb] Reference

Nominal 95.35 ±1.30 -

C 95.49 ±1.27 M.M.Block et al., Czech. J. Phys. 40 (1990) 164.

c 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) 094019.

BSW 95.53 ±1.38 C.Bourrely et al., Eur. Phys. J. C 71 (2011) 1601.

http://ccdb5fs.kek.jp/cgi-bin/img_index?8707559
























Results

Energy evolution of σtot and σel

Standard model cross section measurements by ATLAS


Energy evolution of B

Increase of B compatible with a 2nd order polynomial in ln(s).

private compilation

Parameters from: V.A.Schegelsky and M:G: Ryskin , Phys.Rev.D 85 (2012) 0940243










Comparison with TOTEM

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.

The ATLAS measurement is 3.2 mb lower than TOTEM, the difference corresponds to 1.3 σ, assuming uncorrelated uncertainties.


Further derived quantities

Elastic cross section from the integrated fit-function (nuclear part)

222

16

1

cBtot

el

2

0

mb/GeV 13474tdt

d

The observed elastic cross section inside the fiducial volume:

mb 6.00.24 el

The optical point:

mb 6.07.21 observedel


The inelastic cross section

The total inelastic cross section σinel is obtained by subtraction of the elastic cross section from the total cross section.

mb 90.03.71 inel

56

Conclusion and outlookATLAS 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.

2-GeV 3.07.19

mb 4.14.95

Btot

005.0257.0 tot

el

CERN seminar 22.07.2014 Hasko Stenzel


Back Up


Transport matrix

2

242

231

pt

ppppt

*

*

sincossin1cos

sinsincos

yy

yLy

phase advancevertical: ψ=90° horizontal ψ=185°

ALFA IPbeam transport matrix from optical functions


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.


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.


Results for 4 different methods


Systematic uncertainties for dσ/dt

Systematic shiftsused in the profile fit

iTiTiT kk nominal


Systematic uncertainties for dσ/dt

Systematic shiftsused in the profile fit

iTiTiT kk nominal


The t-spectrum Reconstructed t-spectrum for different methods before corrections.

Difference between methods understood as resulting from different resolutions inducing different unfolding corrections.


Nuisance parameters

2stat

stat

GeV 14.0

mb 38.0)(

B

tot

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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