Results on Total and Elastic Cross Sections in Proton-Proton Collisions at s √ = 200 GeV Obtained with the STAR Detector at RHIC
RRESULTS ON TOTAL AND ELASTIC CROSS SECTIONS INPROTON-PROTON COLLISIONS AT √ s = 200 GeV OBTAINED WITH THESTAR DETECTOR AT RHIC For the STAR CollaborationB. Pawlik
Institute of Nuclear Physics PAN, Radzikowskiego 152,31-342 Cracow, Poland
W. Guryn
Brookhaven National Laboratory, Department of PhysicsUpton, NY 119735000, USA
We report the first results on differential, total and elastic cross sections in proton-proton colli-sions at the Relativistic Heavy Ion Collider (RHIC) at √ s = 200 GeV. The data were obtainedwith the Roman Pot Detector subsystem of the STAR experiment. The data used for thisanalysis cover the four-momentum transfer squared ( t ) range 0 . ≤ | t | ≤ .
135 (GeV/c) .The Roman Pot system was placed downstream of the STAR detector. During the datataking the Roman Pots were moved to 8 σ y , the vertical distance of from the beam center.They were operated during standard data taking procedure. The results include values of theexponential slope parameter (B), elastic cross section ( σ el ) and the total cross section ( σ tot )obtained by extrapolation of the elastic differential cross section ( dσ/dt ) to the optical pointat t = 0 (GeV/c) . The detector setup and analysis procedure are reviewed. All results arecompared with the world data. Presented at EDS Blois 2019The 18th Conference on Elastic and Diffractive ScatteringQuy Nhon, Vietnam,June 2328, 2019
Results presented here are based on data collected with pp2pp Roman Pots part of the STARdetector at RHIC. The Roman Pots ( RPs ) setup Fig. 1 consisted of four stations with two ofthem (
W1,W2 ) placed at ∼ ∼ IP ) and other two ( E1,E2 ) symmetrically upstream, (East) from IP . Each RP station consistsof two Roman Pots ( one above and the other below beam line) each equipped with package of 4silicon strip detector (Si) planes, two planes for measuring X and the other two for Y positionsof the particle track. The scintillation counter placed behind Si planes and read by two PMTswas used to trigger on candidate events. Candidate event had to fulfill the trigger condition,from here referred to as RP ET , requiring presence of the signal in at least one Roman Pot( RP ) on each side of IP . a r X i v : . [ h e p - e x ] M a y igure 1 – The layout of Roman Pots system at STAR (left) and example of reconstructed points configurationfor elastic event detected in arm EDWU (right) .Figure 2 – Acceptance as function four-momentum transfer t (left), West-East co-linearity ∆ θ Y vs ∆ θ X (right). Data were taken with nominal beam conditions β ∗ = 0 . m , luminosity ≈ · cm − sec − .There were approximately 6.7 millions events fulfilling trigger condition RP_ET recorded for inte-grated luminosity 1.8pb − . The geometrical acceptance was constrained by the closest possibleapproach of the detector to the beam and, the aperture of the beam line elements (DX magnet)in front of the detector. The closest achieved distance of the first strip was ∼
30 mm correspond-ing to minimum four-momentum transfer | t min | (cid:39) . The aperture of DX magnet setsthe maximum achievable four-momentum transfer | t max | ≈ . The detector acceptanceas function of four-momentum transfer | t | is shown in fig.2. All events collected with trigger
RP_ET underwent reconstruction procedure. First, in all RPsin each detector Si plane clusters - continuous set of strips with signal above threshold - wereformed. Next, clusters found in two X-planes were matched by comparing their positions x and x and finding the pair with minimum distance ∆ x c = | x − x | smaller then 200 µm (twice Sidetector strip pitch). Analogous procedure was repeated for two Y-planes. Unmatched clusters,f any, were considered as detector noise or random background and were neglected. Pairs ofclusters matched in x and y-plane defined space points X RP and Y RP coordinates of the protontrack. These were used to calculate the local angles θ x and θ Y in (x,z) and (y,z) planes as: θ X = X RP − X RP Z RP − Z RP and θ Y = Y RP − Y RP Z RP − Z RP (1)where subscripts RPs(RPs) denote RP stations 1(2) at same side of IP and Z RP ( Z RP ) are z-positions of the stations. For small scattering angles in this experiment, to a good approximationthe four-momentum transfer t was calculated with formula: t = − p · θ = − p · ( θ X + θ Y ) (2)where p is proton momentum, θ = (cid:113) θ X + θ Y scattering angle and θ X , θ Y calculated as in eq.1.The RPs system was positioned and aligned with respect to nominal beam trajectory, hence theangles θ X and θ Y provide direct measurement of the projections of scattering angle θ on (x,z)and (y,z) plane, respectively. The hardware trigger requiring signal in at least one RP on each side of IP was very inclusive.The clean pattern indicating elastic scattering ( see right sub-figure in fig.1 ) is presence of twoback to back protons in the event. This requires signal only in top RP1 and/or RP2 at one sideof IP and only in bottom RP1 and/or RP2 on the other side. Calculation of the track directionangles (eq.1) requires points in two stations on the each side of IP.The data sample used to obtain this results consist only of events with four reconstructedpoints, four points ( ) events, and fulfilling West-East co-linearity condition:∆ θ = (cid:113) ( θ W estX − θ EastX ) + ( θ W estY − θ EastY ) < · σ θ (3)with σ θ = 255 µ rad was dominated by the beam angular divergence ( ∼ µ rad for each beam).The kinematic range of four-momentum transfer t versus azimuth angle φ for this sample ( ) is shown in fig.3.For the 4PT-COL events, scattering angles at the IP θ ∗ X , θ ∗ Y were obtained from the linearfit using four X RP and Y RP points. The four-momentum transfer t for those events was thencalculated using Eq.2, where local angles θ X , θ Y were replaced respectively with θ ∗ X , θ ∗ Y .Additionally geometrical cut was imposed to reduce background by staying away from ac-ceptance boundaries and maintain relatively flat, slow varying acceptance corrections (see datalabeled as ET-4RP-COL-GEO in fig.2). It was required that the scattered proton angle θ and azimuth angle φ obey following limits:79 . [deg] < | φ | < . [deg] . [mrad] < θ < . [mrad] (4) The beam line elements and all RP detectors were implemented in detail in Geant4 [7] basedMonte Carlo application. The events were generated according to standard formula for the elasticscattering differential cross section with the slope B = 14 . − , the parameter ρ =0.128 andWest-Yennie Coulomb phase. The beam angular divergence and the interaction point IP position uncertainty were included in the generator.The experimental differential distributions dN/dt was corrected using “bin by bin” methodwith the formula : (cid:18) dNdt (cid:19) DAT Acorrected = (cid:18) dNdt (cid:19) DAT Areconstructed × ( dN/dt ) MCgenerated ( dN/dt ) MCreconstructed (5) igure 3 – Four momentum transfer | t | vs azimuth angle φ for accepted ET co-linear events with four reconstructedpoints ( ) (left), and (right) background contribution estimate based on comparison of West-East co-linearity∆ θ for DATA and Monte-Carlo samples of events within GEO limits (4). where ( dN/dt ) MCgenerated and ( dN/dt ) MCreconstructed are true MC distribution and reconstructed basedon MC event sample which passed the same reconstruction procedure and selection criteria asthose applied for experimental data. The corrections obtained this way account for limitedgeometrical acceptance, effects of the scattering angle reconstruction resolution ( t smearing )and impact of the secondary scattering of the final state proton off the material on the way from IP to detector Si planes. The corrected differential cross section ( dσ/dt ) was fitted with standard formula , , : dσ el dt = 1 + ρ π (¯ hc ) · σ tot · e − B | t | (6)with ρ =0.128 from COMPETE model. The Coulomb and interference terms were neglectedas their contribution in the fit range 0.045 < − t < is negligibly small within thisexperiment’s precision. The data and fit results are shown in Fig.4.The total cross section σ tot was calculated using the optical theorem as : σ tot = 16 π (¯ hc ) ρ · dσ el dt | t =0 (7)and the total elastic cross section σ el was obtained by integrating fitted formula (6) over whole t range, the elastic cross section integrated within the t-acceptance of this measurement ( σ detel )is also quoted. The inelastic cross section is simply result of subtraction σ inel = σ tot − σ el . Allresults with their statistical and systematic uncertainties are shown in table 1. The elastic differential cross section in pp scattering was measured with Roman Pots systemof the STAR experiment at RHIC in t range 0.045 < − t < at √ s =200 GeV. Inthis t range the cross section is well described by exponential exp ( − B · t ) with the slope B = igure 4 – Top panel: pp elastic differential cross-section dσ/dt fitted with exponential A · exp ( − Bt ); Bottompanel: Residuals (Data - Fit)/Data. Table 1: Results summary. Quantity Statistical Systematic uncertaintiesname units Value uncertainty beam-tilt luminosity ρ full dσ el /dt | t =0 [mb/GeV ] 139.53 ± +1 . − .
83 +10 . − . n/a +10 . − . B [GeV − ] 14.32 ± +0 . − . n/a n/a +0 . − . σ el [mb] 9.74 ± +0 . − .
04 +0 . − . n/a +0 . − . σ detel [mb] 3.63 ± +0 . − .
01 +0 . − . n/a +0 . − . σ tot [mb] 51.81 ± +0 . − .
61 +1 . − .
90 +0 . − .
40 +1 . − . σ inel [mb] 42.07 ± +0 . − .
61 +2 . − .
99 +0 . − .
40 +2 . − . ± +0 . − . ) GeV − , in brackets full systematic errors are given. The elastic cross sectionintegrated within detector acceptance σ detel = 3.63 ± +0 . − . ) mb, extrapolation of this measuredcross section over undetected ( 60%) t region results in value of the total elastic cross section σ el =9.74 ± +0 . − . )mb. Using optical theorem we found the value of total pp scattering crosssection σ tot =51.81 ± +1 . − . ). Figure 5 – Comparison of the STAR result on σ tot , σ el and σ inel (left) and B-slope (right) with the world data oncross sections and B-slopes , , , , , , , , COMPETE prediction for σ tot and σ inel are displayed. The results obtained with STAR are compared with the world data in Fig.5. We found theycompare well and follow COMPETE prediction of dependence of cross section on √ s . Acknowledgments
This work was partly supported by the National Science Center of Poland under grant numberUMO-2015/18/M/ST2/00162.
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