Measurement of the total cross section from elastic scattering in $\mathit{pp}$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of the total cross section from elastic scattering in pp collisions at √

s = ^{8 TeV with the ATLAS detector}

.TheATLAS Collaboration^

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received25July2016

Receivedinrevisedform9August2016 Accepted9August2016

Availableonline16August2016 Editor:W.-D.Schlatter

A measurement ofthe total pp crosssection atthe LHC at√

s=^{8 TeV is presented.An integrated} luminosity of 500 μb⁻¹ wasaccumulated inaspecial run withhigh-β^ beamopticsto measure the differential elasticcross sectionas a functionofthe Mandelstammomentum transfervariable t. The measurementisperformedwiththe ALFAsub-detector ofATLAS. Usingafittothedifferentialelastic crosssectioninthe−^{t rangefrom0}.014 GeV²to0.1 GeV²toextrapolatet→^{0,thetotalcrosssection,} σtot(pp→^X),ismeasuredviatheopticaltheoremtobe

σtot(pp→X)=96.07±0.18(stat.)±0.85(exp.)±0.31(extr.)mb,

wherethefirsterrorisstatistical,thesecondaccountsforallexperimentalsystematicuncertaintiesand thelastisrelatedtouncertaintiesintheextrapolationt→^{0.Inaddition,theslopeofthe}exponential functiondescribing the elasticcrosssectionatsmallt isdeterminedtobe B=¹⁹.74±⁰.05(stat.)± 0.23(syst.)GeV⁻².

©^{2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Thetotalcrosssectionforproton–proton(pp)interactionschar- acterizesa fundamental process of thestrong interaction. Its en- ergy evolution hasbeen studiedat each newrange ofcentre-of- massenergiesavailable.ATLAShaspreviouslyreportedameasure- mentofthetotalcrosssection in pp collisionsat√

s=^{7 TeV[1].}

Thispaperdetailsameasurementofthetotalcrosssectionat√ s= 8 TeV using data collected in 2012. The measurement method- ology and analysis technique are very similar between the two measurements andthe technicaldetails are discussedthoroughly inRef.[1].

Bothmeasurementsrelyontheopticaltheorem:

σtot=⁴πIm[^fel(t→⁰)] ⁽¹⁾

which relates the total pp cross section σtot to the elastic- scattering amplitude extrapolated to the forward direction f_el(t→⁰),witht beingthefour-momentumtransfersquared.The totalcrosssectioncanbeextractedindifferentwaysusingtheop- ticaltheorem.ATLASusestheluminosity-dependent methodwhich requires a measurement of the luminosity in order to normalize theelasticcrosssection.Herethemeasurementbenefitsfromthe high-precisionluminositymeasurementthatATLASprovides.With thismethod, σtotisgivenbytheformula:

 E-mailaddress:atlas.publications@cern.ch.

σ_tot² =¹⁶π(^hc¯ )² 1+ρ²

dσel

dt



t→0

, (2)

where ρ represents a small correction arising from the ratio of the realto the imaginarypartof theelastic-scattering amplitude intheforwarddirectionandistakenfromglobalmodelextrapola- tions[2].

The first measurement of σtot at the LHC at 8 TeV was performed by the TOTEM Collaboration [3] using a luminosity- independent method and using data from the same LHC fill as ATLAS. At 7 TeV measurements of σtot were provided by TOTEM [4–6]andATLAS[1].Inarecentpublicationameasurementinthe Coulomb–nuclear interferenceregion atverysmallt was alsore- portedbyTOTEM[7].Theinelasticcrosssection σinelcaneitherbe derived fromthe totalandelastic crosssection measurements as inRefs.[3–6,1]at7and8 TeV,orbedetermineddirectlyfromthe measurement of the inelastic ratewithout exploitingthe optical theorem. These measurements of σinel were performed at 7 TeV by all LHC Collaborations [8–12] and recently also at13 TeV by ATLAS[13].

2. Experimentalsetup

The ATLAS detectoris described in detail elsewhere[14]. The elastic-scattering datawere recordedwith the ALFA sub-detector (AbsoluteLuminosityForATLAS)[1].ItconsistsofRomanPot(RP) tracking-detectorstationsplacedatdistancesof237 m(innersta- http://dx.doi.org/10.1016/j.physletb.2016.08.020

0370-2693/©^{2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

tion) and 241 m (outer station) on eitherside of the ATLAS in- teraction point (IP). Each station houses two vertically moveable scintillating fibre detectors which are inserted in RPs and posi- tionedclose to the beamfor data taking. Each detectorconsists of 10 modules of scintillating fibres with 64 fibres on both the frontandbacksidesofatitaniumsupportplate.Thefibresarear- rangedorthogonally ina u–v-geometry at ±^{45◦ withrespect to} they-axis.¹Thespatialresolutionofthedetectorsisabout35 μm.

Elasticscatteringeventsarerecordedintwoindependentarmsof thespectrometer.Arm1consistsoftwoupperdetectorsattheleft sideandtwolowerdetectorsattherightside,andarm2consists inverselyoftwo lowerdetectorsattheleft andtwo upperdetec- torsattherightside.Events withreconstructed tracksinallfour detectorsofanarmarereferredtoas“golden”events[1].Thede- tectorsaresupplementedwithtriggercountersconsistingofplain scintillator tiles. The detector geometryis illustrated inFig. 1 of Ref. [1]. All scintillation signals are detected by photomultipliers coupledtoa compactassemblyoffront-endelectronicsincluding the MAROC chip [15,16] for signal amplification and discrimina- tion.TheentireexperimentalsetupisdepictedinFig. 2ofRef.[1].

3. Experimentalmethod 3.1.Measurementprinciple

Thedatawererecordedinasingle runoftheLHCwithspecial beamoptics[17,18]ofβ^=^{90 m.2 Thesameopticswere usedat} 7 TeV[1]andresultina smallbeamdivergencewithparallel-to- pointfocusing intheverticalplane. The four-momentumtransfer t iscalculatedfromthescatteringangleθ^andthebeammomen- tump by:

−^t= θ^×^p2

, (3)

whereforthenominalbeammomentump=³⁹⁸⁸±^{26 GeV isas-} sumed[19] andthescatteringangleiscalculatedfromtheproton trajectoriesandbeamopticsparameters.Therelevantbeamoptics parameters are incorporated in transport matrix elements which describetheparticletrajectory fromtheinteractionpointthrough themagneticlatticeoftheLHCtotheRPs. Severalmethods were developed for the reconstruction of the scattering angle, as de- tailed in Ref. [1]. The subtractionmethod has the best resolution andisselectedasthenominalmethod.Itusesonly thetrackpo- sitions(w= {^x,y}^{)andthematrixelement M}12=√

β× β^sinψ, whereψ refers to thephase advanceof thebetatron functionat theRP:

θ_w^ = ^wA−^wC

M_12,A+^M12,C

. (4)

HereA refers tothe left sideof theIP atpositive z andC refers totherightside atnegative z.Threealternative methodsare de- fined in detail in Ref. [1]. The localangle method uses only the M₂₂ matrix element andthe track angle betweenthe inner and outerdetectors.Thelocalsubtractionmethod usesacombinationof M11 andM12 matrixelements andboth thelocalangleandtrack position. The latticemethod also uses both track parameters and reconstructsthescatteringangleby an inversionofthe transport matrix.Thealternativemethodsareusedtoimposeconstraintson thebeamopticsandtocross-checkthesubtractionmethod.

1 ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominalIP inthecentreofthedetectorandthez-axisalongthebeampipe.Thex-axispoints fromtheIPtothecentreoftheLHCringandthey-axispointsupwards.

2 Theβ-functiondeterminesthevariationofthebeamenvelopearoundthering anddependsonthefocusingpropertiesofthemagneticlattice;itsvalueattheIP isdenotedbyβ^.

3.2. Datataking

The low-luminosity, high β^ run had 108 colliding bunches withabout7×^{1010protonsperbunch,butonly3}well-separated bunchesoflowemittancewereselectedfortriggering.Precisepo- sitioningoftheRPsisachievedwithabeam-basedalignmentpro- cedure whichdetermines the positionofthe RPs withrespectto the proton beams by monitoring the rate of the LHC beam-loss monitors during the RP insertion. The data were collected with the RPs at a distance of approximately 7.5 mm from the beam centre, corresponding to 9.5 times the vertical beam width. The beam centre andwidth monitored by LHC beam position moni- tors and the ATLAS beam-spot measurement [20] were found to be stableto within 10 μm during the run. The beamemittance wasderivedfromthewidthoftheluminousregioninconjunction withthebeamoptics.Itwassupplementedbydirectmeasurement fromALFAinthe verticalplane.The luminosity-weightedaverage oftheemittanceintheverticalplanewasdeterminedtobe1.6 μm forboth beamsandbetween1.8 μmand2.5 μmforbeam 1and beam 2respectivelyinthehorizontalplane.Theemittanceuncer- taintyisabout 10%.

To trigger on elastic-scattering events a coincidence was re- quired betweenthe A- and C-sides, whereon each side at least one triggersignalinadetectorofthecorresponding armwas re- quired.Thetrigger efficiencywasdetermined fromadata stream recordedwithlooserconditionstobe99.9% withnegligibleuncer- tainty.Thedead-timefractionofthedataacquisitionsystem(DAQ) fortheselectedperiodwas 0.4%.

3.3. Trackreconstructionandalignment

A well-reconstructed elastic-scattering event consists of local tracksfromtheprotontrajectoryinallfourALFAstations.There- construction method assumes that the protons pass through the fibre detectorperpendicularly.The averagemultiplicity perdetec- tor is about23 hits, where typically 18–19are attributed tothe protontrajectory while theremaining 4–5hits aredueto beam- relatedbackground,cross-talkandelectronic noise.Tracksare re- constructedinseveralstepsfromtheoverlapareaofthehitfibres andseveralselectionsareapplied[1]inordertorejecteventswith hadronicshowerdevelopments.

The precise detector positions with respect to the circulating beamsarecrucialinputsforthereconstructionoftheprotonkine- matics.First,thedistancebetweentheupperandthelowerdetec- torsisdeterminedbytheuseofdedicatedALFAoverlapdetectors which allow simultaneous measurements ofthe same particle in theupperandlowerhalfofastation.Then,thedetectorpositions aredirectlydeterminedfromtheelastic-scatteringdata,usingthe fact that the high-β^ opticsand the azimuthal symmetry of the scattering angle result in elastic hit patterns that have an ellip- soidal shape elongated in the vertical direction. Three alignment parameters are determined foreach detector: the horizontaland vertical offsets andthe rotationangle around thebeam axis.For thehorizontaloffsetthe centreofthex-distribution istakenand therotationisobtainedfroma linearfittoaprofilehistogramof the x– y correlation. The vertical offset is obtained froma com- parison ofthe yields inthe upperand lower detectorsusing the slidingwindowtechnique[1].Theaboveproceduresprovideanin- dependentalignmentofeachALFAstation.Theverticalalignment parametersareinadditionfine-tuned,exploitingthestrongcorre- lationsbetweenpositionsoftracksmeasuredbydifferentdetectors inelasticevents.First,thepositionsmeasuredinonedetectorare extrapolatedtotheother detectorsinthesamearmusingthera- tiooftheappropriateM12matrixelements.Then,theextrapolated positionsarecomparedtothecorrespondingmeasurements –the

Fig. 1. (a)ThecorrelationbetweenthehorizontalcoordinatesontheA- andC-sides.Elastic-scatteringcandidatesafterdataquality,triggerandbunchselectionbutbefore acceptanceandbackgroundrejectioncutsareshown.Identifiedelasticeventsarerequiredtolieinsidetheellipse.(b) ThedistributiondN/dt,beforecorrections,asafunction oft inarm1comparedtothebackgroundspectrumdeterminedusinganti-goldenevents.TheresultsofasimulationoftheDPEbackgroundisalsoshownforcomparison.

average distancegives information aboutresidual misalignments.

Theresidualsobtainedforallpairsofdetectorsarecombinedwith the verticaloffset anddistance measurements ina global χ² fit, resultinginthefinalalignmentparameters.

4. Modelforelasticscatteringsimulation

Severalparameterizations are available [21–31] forthe differ- entialelasticpp crosssection.Aconventionalapproachisadopted herebytakingthefollowingsimplifiedformulae:

dσ

dt = ¹ 16π

^fN(t)+^fC(t)e^iαφ(t)² , (5) fC(t)= −8π αhc_¯ G²(t)

|t| , (6)

fN(t)= (ρ₊i)σtot

¯

hc e^−B|t|/2 , (7)

where G is the electric form factor of the proton, B the nu- clear slope, fC the Coulomb amplitude and fN the nuclear am- plitude with φ their relative phase shift. The value of ρ = Re(fel)/Im(fel)=⁰.1362±⁰.0034 is taken from a global fit to lower-energydata[2]andparameterizationsforG andφaregiven inRef.[1].Thisexpression isusedtofitthedataandextract σtot and B.

MonteCarlosimulationofelastic-scatteringeventsisperformed withPYTHIA8[32,33] version 8.186witha t-spectrum generated accordingtoEq.(5).Thesimulationisusedtocalculateacceptance andunfoldingcorrections.Inthesimulationtheangulardivergence of beams at the IP and the spread of the production vertex are settothemeasuredvalues.Elasticallyscatteredprotonsaretrans- portedfromtheinteractionpoint totheRPs nominallybymeans ofthetransportmatrix.Forstudiesofsystematicuncertaintiesthis wasalsodonebythetrackingmoduleoftheMadX[34]beamop- tics calculation program. A fast parameterization of the detector response is used in the simulation and tuned to reproduce the measured difference inpositionbetween theouter detectors and theirpositionasextrapolatedfromtheinnerdetectors.

5. Dataanalysis 5.1. Eventselection

Events are requiredto pass the trigger conditions forelastic- scattering events and have a reconstructed track in all four de- tectorsof an arm in the golden topology. The fiducialvolume is

defined by cuts on the vertical coordinate of the reconstructed track, which is required to be at least90 μm from the detector edgenearthebeamandatleast1 mm awayfromtheshadowof thebeamscreen,ineachofthefourdetectors.³Thevaluesofcuts arechosentoobtaingoodagreementbetweendataandsimulation in theposition distributions.The back-to-back topologyof elastic events isfurther exploitedto clean thesample byimposing cuts ontheleft-rightacollinearity.Thedifferencebetweentheabsolute value ofthe verticalcoordinateattheA- and C-sideis requested to be below 3 mm.Forthe horizontalcoordinate the correlation of the A- and C-sides is used. Events are selected inside an el- lipse with half-axis values of 3.5σ of the resolution determined by simulation, as illustrated in Fig. 1(a). Elastic events are con- centratedinsideanarrowellipsewithnegativeslope,whereasthe beam-halo background appears inbroad uncorrelatedbands. The most efficient selection against backgroundis obtained from the correlation between theposition inthe horizontalplane andthe localanglebetweentwostations,whereeventsoneitherside are againrequiredtobeinsideanellipseof3.5σ width.Fromaninitial sample of4.2millionelasticcandidates,3.8milliongoldenelastic eventswereselectedafterallcuts. Thet-spectrum,beforecorrec- tions,forselectedelasticeventsinonearmisshowninFig. 1(b).

5.2. Backgroundestimate

A small fraction of the events inside the selected elliptical area showninFig. 1(a)are expectedtobe background,predomi- nantlyoriginatingfromdouble-Pomeronexchange(DPE)according to simulations based on theMBR model[35]. Thebackground is estimatedwithadata-drivenmethod[1]usingeventsinthe“anti- golden” topology with two tracks in both upper or both lower detectors at the A- and C-sides. This sample is free of signal and yields an estimate of backgroundin the elastic sample with the goldentopology.Theshape ofthet-spectrumforbackground events is obtainedby flipping thesign ofthe vertical coordinate on eitherside. Theresulting backgrounddistributionis shownin Fig. 1(b).Intotal 4400backgroundevents areestimatedto be in theselectedsample,correspondingtoafractionof0.12% ofthese- lected events.Thesystematicuncertaintyisabout50%,asderived inRef.[1]fromacomparisonofdifferentmethods.

3 Thebeamscreenisaprotectionelementofthequadrupoles,whichlimitsthe acceptanceofthedetectoratlarge|^y|^.