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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 : http://cds.cern.ch/record/1740971. Outline. Introduction Experimental setup: ALFA

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  1. Preliminary measurement of the total cross section in pp collisions at √s=7 TeVwith the ALFA subdetector of ATLASHasko Stenzel, JLU Giessenon behalf ofthe ATLAS CollaborationConfNote: http://cds.cern.ch/record/1740971

  2. Outline • Introduction • Experimental setup: ALFA • Data analysis • Differential elastic cross section • Theoretical prediction, fits and cross-checks • Results for σtot • Conclusion 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: σtotdoesn’t rise faster than ln2s • Black disk limit: • Pomeranchuk theorem: • p4 • θ • p1 • p2 • p3 Hasko Stenzel

  4. Rise of σtot at ISR At the ISR a rise of the total cross section was first observed. S.R. Amendoliaet al., Phys. Lett. B 44 (1973) 119 U. Amaldiet al., Phys. Lett. B 44 (1973) 192 Would the total cross section continue to rise with ln(s) or rather ln2(s)? Hasko Stenzel

  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 Hasko Stenzel

  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 Hasko Stenzel

  7. Available measurements Atthe LHC firstmeasurementsweredoneby TOTEM: σtot = 98.6±2.2 mb (7 TeV) σtot= 101.7±2.9 mb (8 TeV) Measurementswereperformedbycosmicrayobservatories at yethigherenergies, usingairshowersandtransforming proton-aircrosssectionsinto pp crosssectionwith Glauber models. Hasko Stenzel

  8. Experimental setup: ALFA Hasko Stenzel

  9. Elastic scattering with ATLAS-ALFA Roman Pot detectorsat 240m from IP1 approachingthe beam duringspecialrunsat high β*. In October 2011 ALFA had the special run 191373 with β*=90m andrecorded 800k goodselectedelasticeventsusedfortheanalysisofthe total crosssectionandthenuclearslope B. Hasko Stenzel

  10. The ALFA detector in a nutshell ALFA is a scintillatingfibretracker, 10 double-sidedmoduleswith 64 fibres in uv-geometry. Resolution ~30µm. Special overlap detectors to measure the distance between upper and lower detectors.  alignment vfibres u fibres Hasko Stenzel

  11. parallel-to-point focusing ydet y* y* IP Leff Beam optics and properties • Special optics high β* =90m • Small emittance 2-3µm • Small divergence ~3µrad • Phase advanceofβy=90° parallel-to-point focusing • Phase advanceofβx≈180°  good t-resolution • Only one pair of colliding bunches at 7 1010p • More pilotbunches / unpairedbunches • L≈1027/cm2/s, µ≈0.035 Hasko Stenzel

  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 Hasko Stenzel

  13. Data Analysis Hasko Stenzel

  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 Hasko Stenzel

  15. Measurement of t Measureelastictrackpositionsat ALFA togetthescattering angle andtherebythe t-spectrum dσ/dt p=beam momentum, θ*=scattering angle Tocalculatethescattering angle fromthemeasuredtracks weneedthebeam optics, i.e. the transportmatrixelements. In thesimplestcase (high β*, phaseadvance 90°, parallel-to-point focusing) Hasko Stenzel

  16. Different reconstruction methods • subtractionmethod: • local angle method: • localsubtraction: • latticemethod: Hasko Stenzel

  17. Event selection • firstlevelelastictrigger • dataqualitycuts • applygeometricalacceptancecuts • applyelasticselectionbased on back-to-back topologyandbackgroundselectioncut elasticselection: y A- vs C-side backgroundrejection Hasko Stenzel

  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%. Hasko Stenzel

  19. Background • Twowaystoestimatetheirreduciblebackgroundundertheelasticpeak: • Countingevents in the anti-golden configuration(nominal method) • Reconstructingthevertexdistribution in x throughthelattice, where background appears in non Gaussian tails, fraction estimated with background templates obtained from data (for systematics) Arm 2 Arm 1 golden anti-golden Hasko Stenzel

  20. Background Vertex method anti-golden • Background fractionis 0.5 ± 0.25 % • dominatedbyhaloprotons Hasko Stenzel

  21. Simulation: acceptance & unfolding • Using PYTHIA8 aselasticscatteringgenerator • Beam transport IPRP (matrixtransport / MadX PTC) • Fast detectorresponseparameterizationtunedtodata Comparisonofdataand MC forpositions at ALFA Hasko Stenzel

  22. Acceptance Acceptanceisgivenbygeometry, mostlybyverticalcuts. Hasko Stenzel

  23. Resolution of different methods Subtractionmethodhasbyfarbestresolution, dominatedby beam divergence. All othermethodssufferfrom a poorlocal angle resolution. Hasko Stenzel

  24. Unfolding resolution effects Transition matrixfromtruevalueof t toreconstructedvalueof t usedasinputfor IDS unfolding. B. Malaescu arXiv:1105.3107 Hasko Stenzel

  25. Impact of unfolding Systematicuncertaintyevaluatedwith a data-drivenclosuretest, based on thesmalldifferencebetweendataand MC at reconstructionlevel. Hasko Stenzel

  26. Reconstruction efficiency Fullydata-drivenmethod, using a tag-and-probe approachexploitingelastic back-to-back topologyand high triggerefficiency. Slightly different efficiency in thetwoarms material budgetis different. Hasko Stenzel

  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. Hasko Stenzel

  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. HaskoStenzel

  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 Systematicuncertainty 2.3% HaskoStenzel

  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 innervsouter x leftvsright Lever arm ratio HaskoStenzel

  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*xfrom subtraction  scaling factor R(M12/M22). HaskoStenzel

  32. beam optics fit 14 constraintsarecombined in a fit ofthe relevant beam opticsparameters. Most importantarethestrengthsoftheinnertripletquadrupoles. Quadrupoles Q1,Q3 and Q2 wereproduced at different sites fit an intercalibrationoffset Thatisthesimplest but not uniquesolution effectiveoptics Small correctiontoopticsmodel, 3‰ toinnertripletmagnetstrength. HaskoStenzel

  33. Differential elasticcrosssection Hasko Stenzel

  34. The differential elastic cross section Fullycorrected t-spectra in thetwoarmsarecombinedanddividedbytheluminositytoyieldthe differential elasticcrosssection. A: acceptance(t) M: unfoldingprocedure (symbolic) N: selectedevents B: estimatedbackground εreco: reconstructionefficiency εtrig: triggerefficiency εDAQ: dead-time correction Lint: luminosity Hasko Stenzel

  35. Systematic uncertainties for dσ/dt • luminosity: ± 2.3% • beam energy: ± 0.65% • background 0.5 ± 0.25 % • optics: quadrupolestrength ± 1‰, Q5,6 -2‰ magnetmis-alignment, optics fit errors, beam transport, ALFA constraintsvariedby ± 1σ • residual crossing angle ±10 <mrad More than 500 alternative opticsmodelswereusedtoreconstructthe t-spectrumandcalculateunfolding & acceptancecorrections. Hasko Stenzel

  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 systematicuncertainties: Luminosityand beam energy. Systematicshiftsareincluded in the fit ofthe total crosssection. Hasko Stenzel

  37. Theoreticalpredictions Hasko Stenzel

  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. Hasko Stenzel

  39. Theoretical prediction The theoreticalpredictionusedto fit theelasticdataconsistsofthe Coulomb term, the Coulomb-Nuclear-Interferencetermandthe dominant Nuclearterm. Coulomb CNI Nuc. Proton dipole form factor Coulomb phase Hasko Stenzel

  40. modified χ2to account for systematics D: data, T: theoreticalprediction V: statisticalcovariancematrix δ: systematicshift k in t spectrum β: nuisanceparameterfor syst. shift k ε: t-independent normalizationuncertainty (luminosity, recoefficiency) α: nuisanceparameterfornormalizationuncertainties Hasko Stenzel

  41. Resultsforσtot Hasko Stenzel

  42. Fit Results exp.+stat. The fit includes experimental systematicuncertainties in theχ. The fit qualityisgood: χ2/Ndof=7.4/16. The fit rangeissetto –t[0.01,0.1] GeV2, wherepossibledeviationsfromexponential form ofthenuclearamplitudeareexpectedtobesmall. Hasko Stenzel

  43. theoretical/extrapolation uncertainties • uncertainty in ρ = 0.14 ± 0.008 (COMPETE) • variationoftheprotonelectric form factor • variationofthe Coulomb phase • in orderto probe possible non-exponentialcontributionstothenuclearamplitude a variationoftheupper end ofthe fit rangeiscarried out from 0.1 0.15 GeV2 , based on theoreticalconsiderations. Hasko Stenzel

  44. The electric form factor Dipole: New measurementsfrom A1 usinglow-energyelectron-proton scattering at MAMI. J.C. Bernauer et al. A1 Collaboration, arXiv:1307:6227 Largestdeviationisobservedbetween Dipole andDouble-Dipoleverysmallimpact on total crosssection. Hasko Stenzel

  45. The Coulomb phase West andYennie: Alternative parameterizationswereproposedby Cahn R.N. Cahn, Z. Phys. C 15 (1982) 253 andbyKohara et al.(KFK) A.K. Kohara, Eur. Phys. J. C 73 (2013) 2326 Phase has a smallimpact on the CNI term, whichissmallverysmallimpact on total crosssection. Hasko Stenzel

  46. Fit range dependence Nominal fit range [0.01,0.1], variationby ±0.05, asadvocatedby KMR V.A. Khoze et al., Eur. Phys. J. C 18 (2000) 167 Systematicuncertaintyisderivedfromtheendpointsofthe fit rangevariation. Hasko Stenzel

  47. Cross checks (1) Comparisonof different t-reconstructionmethods consistentresults Usingonlystatisticaluncertainties in the fit, i.e. w/o nuisanceparameters Statistical error only Insteadofunfoldingthedatawefoldedthetheoreticalpredictiontotherawdata  consistent fit results Hasko Stenzel

  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) Hasko Stenzel

  49. Alternative modelsforthenuclearamplitude • severalmodelsforthenuclearamplitudefeaturing a non-exponentialbehaviouraretested • all modelscomewithmoreparametersandareintendedtobeextendedto larger t [0.01,0.3] • restricttoparametricmodelsallowingto fit the total crosssection • fit with Ct2 term • fit withsqrt(t) term • SVN model • BP model • BSW model Hasko Stenzel

  50. Resultsfor alternative models Onlystatisticaland experimental systematicuncertainties on dσ/dtareincluded in theprofile fit. The RMS of all themodelstestedis in goodagreementwiththeassignedextrapolationuncertaintyof 0.4mb. Hasko Stenzel

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