Measurements of Ξ − and Ξ ¯ ¯ ¯ ¯ + production in proton-proton interactions at s NN − − − − √ = 17.3 GeV in the NA61/SHINE experiment
NA61/SHINE Collaboration, A. Aduszkiewicz, E.V. Andronov, T. Antićić, V. Babkin, M. Baszczyk, S. Bhosale, A. Blondel, M. Bogomilov, A. Brandin, A. Bravar, W. Bryliński, J. Brzychczyk, M. Buryakov, O. Busygina, A. Bzdak, H. Cherif, M. Ćirković, M. Csanad, J. Cybowska, T. Czopowicz, A. Damyanova, N. Davis, M. Deliyergiyev, M. Deveaux, A. Dmitriev, W. Dominik, P. Dorosz, J. Dumarchez, R. Engel, G.A. Feofilov, L. Fields, Z. Fodor, A. Garibov, M. Gaździcki, O. Golosov, V. Golovatyuk, M. Golubeva, K. Grebieszkow, F. Guber, A. Haesler, S.N. Igolkin, S. Ilieva, A. Ivashkin, S.R. Johnson, K. Kadija, N. Kargin, E. Kashirin, M. Kiełbowicz, V.A. Kireyeu, V. Klochkov, V.I. Kolesnikov, D. Kolev, A. Korzenev, V.N. Kovalenko, S. Kowalski, M. Koziel, A. Krasnoperov, W. Kucewicz, M. Kuich, A. Kurepin, D. Larsen, A. László, T.V. Lazareva, M. Lewicki, K. Łojek, V.V. Lyubushkin, M. Maćkowiak-Pawłowska, Z. Majka, B. Maksiak, A.I. Malakhov, A. Marcinek, A.D. Marino, K. Marton, H.-J. Mathes, T. Matulewicz, V. Matveev, G.L. Melkumov, A.O. Merzlaya, B. Messerly, Ł. Mik, S. Morozov, S. Mrówczyński, Y. Nagai, M. Naskręt, V. Ozvenchuk, V. Paolone, O. Petukhov, R. Płaneta, P. Podlaski, B.A. Popov, B. Porfy, M. Posiadała-Zezula, D.S. Prokhorova, D. Pszczel, S. Puławski, J. Puzović, M. Ravonel, R. Renfordt, D. Röhrich, et al. (38 additional authors not shown)
EEUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
Submitted to: EPJ C CERN-EP-2020-102June 4, 2020
Measurements of Ξ − and Ξ + production inproton-proton interactions at √ s N N = in the NA61 / SHINE experiment
The NA61 / SHINE Collaboration
The production of Ξ (1321) − and Ξ (1321) + hyperons in inelastic p + p interactions is studiedin a fixed target experiment at a beam momentum of 158 GeV / c . Double di ff erential distribu-tions in rapidity y and transverse momentum p T are obtained from a sample of 33M inelasticevents. They allow to extrapolate the spectra to full phase space and to determine the meanmultiplicity of both Ξ − and Ξ + . The rapidity and transverse momentum spectra are com-pared to transport model predictions. The Ξ − mean multiplicity in inelastic p + p interactionsat 158 GeV / c is used to quantify the strangeness enhancement in A + A collisions at the samecentre-of-mass energy per nucleon pair. c (cid:13) / SHINE Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license. a r X i v : . [ nu c l - e x ] J un Introduction
Hyperons are made up of one or more strange valence quarks. In p + p interactions the initial state hasno constituent strange quarks. Thus, hyperons are excellent probes of the dynamics of p + p interactions.As a result hyperon production has been studied in a long series of experiments on elementary p + pinteractions as well as proton-nucleus and nucleus-nucleus collisions. Nevertheless, the experimental dataon hyperon production in p + p interactions are incomplete, and their interpretation is all but conclusive. Atthe same time rather impressive e ff orts have been invested into studies of hyperon production in nucleus-nucleus interactions, because strangeness carrying particles are expected to have di ff erent characteristicswhen produced in hadron-hadron and nucleus-nucleus collisions. These di ff erences increase with thestrangeness content of the particle. Thus hyperons containing two or three strange quarks are especiallyimportant. This subject has been first brought up in connection with the search for the Quark GluonPlasma, a ”deconfined” state of matter in high energy nucleus-nucleus interactions [1]. The authorspredict an enhanced production of strange particles, especially of doubly strange hyperons. In this context"enhanced" means that the multiplicity normalized to the number of nucleons participating in the collisionis significantly greater in central A + A than in inelastic p + p collision at the same centre-of-mass energyper nucleon pair ( √ s NN ).In the absence of reliable results on elementary production cross sections of hyperons, however, suchclaims are often based on assumptions as e.g. the validity of an elementary reference extracted fromhadron-nucleus data. A number of complex nuclear e ff ects enter here which are di ffi cult to control quan-titatively. This is why NA61 / SHINE has embarked upon a systematic study of hyperon production inan experimental programme which covers hadron-proton, hadron-nucleus, and nucleus-nucleus colli-sions [2–5]. These fixed target measurements employ the same detector and beam momenta from 13to 158 GeV / c per nucleon.This publication presents measurements of Ξ − and Ξ + hyperon production in inelastic p + p interactionsat 158 GeV / c corresponding to √ s NN = / SHINE detector
NA61 / SHINE is a fixed target experiment employing a large acceptance hadron spectrometer situated inthe North Area H2 beam-line of the CERN SPS [6]. A schematic layout is shown in Fig. 1. The maincomponents of the detection system are four large volume Time Projection Chambers (TPC). Two of them,called Vertex TPCs (VTPC-1, VTPC-2), are located downstream of the target inside superconductingmagnets with combined maximum bending power of 9 Tm. The MTPCs and two walls of pixel Time-of-Flight (ToF-L / R) detectors are placed symmetrically to the beamline downstream of the magnets. AGAP TPC between VTPC-1 and VTPC-2 improves the acceptance for high-momentum forward-goingtracks.A secondary beam of positively charged hadrons at a momentum of 158 GeV / c was used to collect the datafor the analysis presented in this paper. This beam was produced by 400 GeV / c protons on a Be-target.The primary protons were extracted from the SPS in a slow extraction mode with a flat-top of 10 seconds.Protons produced together with other particles in the Be-target constitute the secondary hadron beam.The former are identified by two Cherenkov counters, a CEDAR [7] (either CEDAR-W or CEDAR-N)2
13 m ToF-LToF-R PSDToF-FMTPC-RMTPC-LVTPC-2VTPC-1 Vertex magnetsTarget GAPTPCBeam S4 S5
S2S1BPD-1 BPD-2 BPD-3V1V1V0THCCEDAR zxy p Figure 1: (Color online) Schematic layout of the NA61 / SHINE experiment at the CERN SPS (horizontal cut, notto scale). The orientation of the NA61 / SHINE coordinate system is shown on the picture. The nominal beamdirection is along the z axis. The magnetic field bends charged particle trajectories in the x - z plane. The electrondrift direction in the TPCs is along the y (vertical) axis. and a threshold counter (THC). A selection based on signals from the Cherenkov counters allowed toidentify the protons in the beam with a purity of about 99% [8]. The beam momentum and intensitywas adjusted by proper settings of the H2 beamline magnets and collimators. The current settings in thebending magnets have a precision of approximately 0.5%. Individual beam particles are detected by aset of scintillation counters. Their trajectories are precisely measured by three beam position detectors(BPD-1, BPD-2, BPD-3) [6].A cylindrical target vessel of 20.29 cm length and 3 cm diameter was situated upstream of the entrancewindow of VTPC-1 (centre of the target z = -580 cm in the NA61 / SHINE coordinate system, where z = Inelastic p + p events were selected using the following criteria:(i) no o ff -time beam particle detected within a time window of ± µ s around the time of the triggerparticle, 3ii) beam particle trajectory measured in at least three planes out of four of BPD-1 and BPD-2 and inboth planes of BPD-3,(iii) the primary interaction vertex fit converged,(iv) z position of the interaction vertex (fitted using the beam trajectory and TPC tracks) not farther awaythan 20 cm from the center of the LHT,(v) events with a single, positively charged track with laboratory momentum close to the beam momen-tum (see Ref. [8]) are rejected, which eliminates most of the elastic scattering reactions.The data sample used in this paper was registered in 2009, 2010 and 2011. After the above selection ofinelastic events it is reduced to 33 millions. Ξ reconstruction method Particle trajectories (tracks) were reconstructed using an appropriate selection of TPC-clusters. The cor-responding momenta were calculated on the basis of the trajectories and the magnetic field values alongthe trajectory. Fits provided the momentum vectors at the main interaction vertex and at the first measuredpoint. The Λ (here and in the following the line of arguments holds also for the anti-particles) candidatesare found by pairing tracks with appropriate mass and charge assignments. The corresponding particlesare tracked backwards through the NA61 / SHINE magnetic field from the first track point, which is re-quired to lie in one of the VTPCs. This backtracking is performed in 2 cm steps in the z (beam) direction.At each step the separation in the transverse coordinates x and y is evaluated and the minimum is searchedfor. A pair is considered a Λ candidate if the distances in the x and y directions at the minimum are bothbelow 1 cm. Using the distances at the two neighbouring space points around the found minimum thepoint of closest approach is found by interpolation. This point is the first approximation of the Λ decaypoint. Its position together with the momenta of the particles at this point are used as input for a 9 param-eter fit using the Levenberg-Marquardt procedure [9]. It provides the momentum vectors of both decayparticles and the final coordinates of the Λ decay point.To find the Ξ candidates, all Λ candidates are combined with charged pion tracks of appropriate chargesign. A Ξ candidate fitting procedure with 13 parameters [9] is applied, using as parameters the decayposition of the Λ candidate, the momentum vectors of both Λ decay particles, the momentum vectorsof the daughter particles, and finally the z position of the Ξ decay point. The x and y coordinates ofthe Ξ decay position are not subject of the minimization, as they are calculated using the fit results andmomentum conservation. This procedure yields the decay position and the momentum vector of the Ξ candidate. Ξ candidates Several cuts are applied to track parameters and decay topologies in order to minimize the combinatorialbackground and to maximize the signal to background ratio. They represent a compromise between thesize of the hyperon signal and the signal to background ratios in the various invariant mass distributions(see Section 6). 4o ensure good track quality and well defined momenta tracks are accepted only if they have at least 10clusters in either VTPC-1 or VTPC-2. The identification of charged pions and protons is based on thespecific energy loss (d E / d x ) recorded in the TPCs for the corresponding tracks. The appropriate massis assigned, if the energy loss is within a ± σ d E / d x window around the expectation value given by aBethe–Bloch parametrization adjusted to the d E / d x measurements.A rapidity dependent cut is applied on the distance between the primary and the secondary Ξ vertex. Itsvalues are shown in Table 1. Rapidity values in the paper are given in the centre-of-mass frame. Addi-tionally, the decay vertex of the Λ is requested to be located downstream in z from the Ξ decay vertex.Also a mass window of ±
15 MeV around the nominal PDG value [10] is applied in the invariant mass dis-tribution of the Λ candidates to improve the selection of the Ξ candidates. The combinatorial backgroundunder the Ξ signal in the invariant mass distribution (see Section 6), formed by tracks originating from themain vertex is reduced by applying a cut on the distance of closest approach (DCA) of the Ξ trajectory atthe z position of the main vertex. Since the DCA resolution is approximately twice better in y than in x directions, the cut is implemented as: (cid:113) ( bx Ξ ) + ( b y Ξ / . < Ξ originatesfrom a displaced vertex. Thus the background is further reduced by requiring that the DCA of the extrap-olated daughter track at the z position of the main vertex is (cid:113)(cid:16) bx dau g hter (cid:17) + ( b y dau g hter / . > Table 1: Ξ distance cut between primary and secondary vertex in the z (beam) direction for di ff erent rapidities. Ξ rapidity y < − . − . < y < .
75 0 . < y < .
25 1 . < y minimum decay length 0 cm 5 cm 12 cm 20 cm For each Ξ candidate the invariant mass was calculated assuming the Λ and pion masses for the re-constructed candidate daughter particles in suitably selected ( y - p T ) bins. A careful evaluation of thecombinatorial background allows to determine the number of Ξ − and Ξ + in each bin. The correspondingprocedure consists of a fit of a signal and background function to the experimental distribution using χ minimization. The signal is described by the Lorentzian function: L ( m ) = π Γ ( m − m Ξ ) + ( Γ ) , (1)where m Ξ is the center of the distribution and Γ is a parameter specifying the width. The background isparametrized by a 2nd order polynomial (3th and 4th order polynomial for the estimation of the systematicuncertainty - see Section 8). The fit is performed over the mass range from 1.29 to 1.38 GeV. It isimportant to note that the extracted yield varies smoothly, when extending the mass range, and stabilizes5eyond the above mentioned mass interval. The parameters describing the background were fixed usingthis interval. The signal is then determined by subtracting the background function from the experimentalinvariant mass spectrum. In order to limit the propagation of statistical background fluctuations into thesignal, the mass range for this extraction is restricted to the base width of the hyperon mass distribution asgiven by the Lorentzian function with an additional extension of ±
12 MeV. Figure 2 shows the invariantmass distribution of Ξ − and Ξ + candidates for the central rapidity bin and transverse momenta around0.5 GeV / c . The black, blue, and magenta lines show the combined, background and signal fit functions,respectively. E n t r i e s - πΛ M( m=1322±1 MeV Γ =3.50 ±0.01 MeV ) (GeV) + πΛ M(1.26 1.28 1.3 1.32 1.34 1.36 1.38 E n t r i e s m=1322±1 MeV Γ =3.83 ±0.03 MeV Figure 2: (Color online)
Left:
The Λ π − invariant mass spectrum of Ξ − candidates for rapidity y between -0.25 and0.25 and transverse momentum p T from 0.4 to 0.6 GeV / c . Magenta line represents the fitted Lorentzian function andblue one shows the fitted background, black line represents their sum. The vertical solid gray line shows the nominalPDG Ξ mass, dashed lines show the integration range used. Right:
Analogous Λ π + invariant mass spectrum of Ξ + candidates. The extracted mass ( m Ξ = ± m Ξ = . ± .
07 MeV) [10]. The fitted widths are close to expectations as given by the analysis of in-elastic p + p interactions generated by E pos Ξ reconstruction procedures. In order to determine the true numbers of charged hyperons produced in inelastic p + p interactions a setof corrections was applied to the extracted raw results.The triggered and accepted events comprise interactions with the target vessel and other material in thevicinity of the target. To estimate the fraction of those events about 10% of the data were collectedwithout the liquid hydrogen in the target vessel. The signal extraction procedure described in Section 6was applied to these events (1.3 millions events was selected), and the resulting suitably normalized yieldswere subtracted from the results of the analysis of the data sample with full target vessel. This correctionwas applied for each ( y , p T ) bin. The normalization of the empty target data was based on the fitted vertex z distribution. The ratio of the numbers of events with the fitted vertex outside of the target (in the rangefrom -400 cm to -200 cm) was calculated for full and empty target data and used subsequently as thenormalization factor [8, 11]. 6 detailed Monte-Carlo simulation is performed to quantify the losses due to acceptance limitations,detector ine ffi ciencies, reconstruction shortcomings, analysis cuts, and re-interactions in the target. Thissimulation used complete events produced by the E pos / SHINE apparatus. They are then reconstructed with thesame software as used for real events. Numerous variables are confirmed to be similar to data, suchas residual distributions, widths of mass peaks, track multiplicities and their di ff erential distributions,number of events with no tracks in the detector, as well the cut variables and others. The reconstructedMonte-Carlo events are then analyzed in the same way as the experimental data.A correction factor is computed for each ( y , p T ) bin: C F = n MC g enerated / n MCrec , (2)where n MCrec is the number of reconstructed, selected and identified Ξ s normalized to the number of an-alyzed events, and n MC g enerated is the number of Ξ s generated by E pos C F in order to determine the true Ξ − and Ξ + yields. These correction factors also include the branchingfraction of the decay into the non–measured in NA61 / SHINE channels (99.887% of the Ξ hyperons decayinto registered channels).The contribution of Ω decays to the Ξ yield in the final state is neglected. Typically the multiplicity of Ω s is approximately a factor of 10 lower than the Ξ multiplicity (at pp 7 TeV collisions [14]). The smallbranching fraction of Ω decays into charged Ξ s and the small Ω production probability imply that itscontribution is significantly below 1%.Additionally, analysis in rapidity and lifetime bins was performed. Obtained Ξ − and Ξ + lifetimes areconsistent with the PDG ones: τ PGD = . × − s and τ PGD = . × − s for Ξ − and Ξ + ,respectively. The resulting τ/τ PDG ratio as a function of center of mass rapidity is shown in Fig. 3.
Possible systematic biases of final results (spectra and mean multiplicities) are due to imperfectness ofthe Monte Carlo procedure - physics models and detector response simulation - used to calculate thecorrection factors.To determine the magnitude of the di ff erent sources of possible biases several tests were done:(i) Methods of event selection.Not all events which have tracks stemming from interactions of o ff -time beam particles are removed.A possible bias due to this e ff ect was estimated by changing by ± µ s the width of the time windowin which no second beam particle is allowed with respect to the nominal value of ± µ s. Themaximum di ff erence of the results was taken as the bias due to the selection. It was estimated to be2-4%.Another source of a possible bias are losses of inelastic events due to the interaction trigger. The S4detector trigger condition selects mainly inelastic interactions and vetoes elastic scattering events.However, it will miss some of the inelastic events. To estimate the possible loss of Ξ s, simulations7 - - P D G t / t - X + X Figure 3: (Color online) Measured lifetime ratio τ/τ
PDG for Ξ − (blue squares) and Ξ + (red circles) as a function ofcenter of mass rapidity. Only statistical uncertainties are shown. were done with and without the S4 trigger condition. The di ff erence between these two results wastaken as another contribution to the systematic uncertainty. The bias due to the interaction triggerwas calculated as the di ff erence between these two results and it is 3-6(ii) Methods of Ξ − and Ξ + candidates selection.To estimate the bias related to the Ξ − and Ξ + candidate selection the following cut parameters werevaried independently: the distance cut between primary and secondary vertex was changed by ± ± Ξ s in the x and y direction at the main vertex z position was changed from (cid:113) ( bx Ξ ) + ( b y Ξ / . < (cid:113) ( bx Ξ ) + ( b y Ξ / . < Ξ ) daughter track to the main vertex was changed from (cid:113)(cid:16) bx dau g hter (cid:17) + ( b y dau g hter / . > Ξ yields by a change of ±
12 MeVwith respect to the nominal integration range yielded a possible bias of 2-7%.The systematic uncertainty was calculated as the square root of the sum of squares of the describedpossible biases assuming that they are uncorrelated. The uncertainties are estimated for each ( y - p T ) binseparately. 8 Experimental results
This section presents results on inclusive Ξ − and Ξ + hyperons spectra in inelastic p + p interactions atbeam momentum 158 GeV / c . The spectra refer to hyperons produced by strong interaction processes. Double di ff erential hyperon yields constitute the basic result of this paper. The Ξ − ( Ξ + ) yields are deter-mined in 6 (4) rapidity and between 4 (4) and 8 (7) transverse momentum bins. The former are 0.5 unitsand the latter 0.2 GeV / c wide. The resulting ( y , p T ) yields are presented in Fig. 4 as function of p T . Thetransverse momentum spectra can be described by the exponential function [15, 16]: d nd p T d y = S c p T T + m T exp (cid:18) − m T − mT (cid:19) , (3)where m is the Ξ mass. The yields S and the inverse slope parameters T are determined by fittingthe function to the data points in each rapidity bin. The resulting inverse slope parameters are listedin Table 4. The p T spectra from successive rapidity intervals are scaled by appropriate factors for bettervisibility. Statistical uncertainties are smaller than the symbol size, shaded bands correspond to systematicuncertainties. Tables 2 and 3 list the numerical values of the results shown in Fig. 4. (GeV/c) T p0 0.5 1 1.5 2 2.5 ( / G e V / c ) T n / d y dp d - - - - -
10 110 -1.0 » y · +X at 158 GeV/c - X fi p+p -0.5 » y · +X at 158 GeV/c - X fi p+p » y · +X at 158 GeV/c - X fi p+p » y · +X at 158 GeV/c - X fi p+p » y · +X at 158 GeV/c - X fi p+p » y · +X at 158 GeV/c - X fi p+p (GeV/c) T p0 0.5 1 1.5 2 2.5 ( / G e V / c ) T n / d y dp d - - - - -
10 110 -0.5 » y · +X at 158 GeV/c + X fi p+p » y · +X at 158 GeV/c + X fi p+p » y · +X at 158 GeV/c + X fi p+p » y · +X at 158 GeV/c + X fi p+p Figure 4: (Color online) Transverse momentum spectra in rapidity slices of Ξ − ( left ) and Ξ + ( right ) produced ininelastic p + p interactions at 158 GeV / c . Rapidity values given in the legends correspond to the middle of thecorresponding interval. Statistical uncertainties are smaller than the marker size, shaded bands show systematicuncertainties. Spectra are scaled by the given factors for better separation. able 2: Numerical values of double-di ff erential spectra of Ξ − produced in inelastic p + p interactions at 158 GeV / c beam momentum. Rapidity and transverse momentum values correspond to the middle of the presented bin. Firstvalue is the particle multiplicity, second represents the statistical uncertainty and third one corresponds to theestimated systematic uncertainty. Ξ − : d nd y d p T × − (1 / GeV / c ) p T (GeV / c ) y = -1.0 y = -0.5 y = ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± p T (GeV / c ) y = y = y = ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Rapidity distributions were then obtained by summing the measured transverse momentum spectra andextrapolating them into the unmeasured regions using the fitted functions given by Eq. 3. The resultingrapidity distributions are shown in Fig. 5. The statistical uncertainties are smaller than the symbol size.They were calculated as the square root of the sum of the squares of the statistical uncertainties of thecontributing bins. The systematic uncertainties (shaded bands) were calculated as square root of squaresof systematic uncertainty as described in Sec. 8 and half of the extrapolated yield. The numerical valuesof rapidity yields and their errors are listed in Table 4.Gaussian functions were fitted to the rapidity distributions and used to extrapolate into the unmeasuredregions. The extrapolation factors for Ξ + and Ξ − are 1.24 and 1.33, respectively. Summing the data pointsand the extrapolated yield add up to the mean multiplicities (cid:104) Ξ − (cid:105) = (3.3 ± ± × − and (cid:104) Ξ + (cid:105) = (7.9 ± ± × − . The Gaussian function used to determine the multiplicity is a rather arbitrarychoice. To study the uncertainty introduced by this choice the same extrapolation factors were computedfor the events generated by the two models mentioned in Sec. 10. The extrapolation factors obtainedfrom the two models di ff er by only 5% and their shapes agree within uncertainties with the one of theexperimental data. Thus the already assigned systematic error of 50% of the extrapolated yield is largecompared to the uncertainty due to the function used for extrapolation, and no additional uncertainty wasadded. 10 able 3: Numerical values of double-di ff erential spectra of Ξ + produced in inelastic p + p interactions at 158 GeV / c beam momentum. Rapidity and transverse momentum values correspond to the middle of the presented bin. Firstvalue is the particle multiplicity, second represents the statistical uncertainty and third one corresponds to theestimated systematic uncertainty. Ξ + : d nd y d p T × − (1 / GeV / c ) p T (GeV / c ) y = -0.5 y = y = y = ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± y3 − − − dn / d y - Ξ + Ξ p+p at 158 GeV/c ×10 -4 Figure 5: (Color online) Rapidity spectra of Ξ − (blue squares) and Ξ + (red circles) produced in inelastic p + p interac-tions at 158 GeV / c . Statistical uncertainties are smaller than the marker size, shaded bands correspond to systematicuncertainties of the measurements. Curves depict Gaussian fits used to determine total mean multiplicities. In Fig. 6 we compare the rapidity densities ( dn / d y ) at mid-rapidity of Ξ − and Ξ + in inelastic p + p interac-tions at √ s NN = . √ s NN =
200 GeV [17]and from CMS at the CERN LHC measured at √ s NN = Ξ + yield is almost11 able 4: Numerical values of rapidity spectra of Ξ − and Ξ + produced in inelastic p + p interactions at 158 GeV / c beam momentum and fitted inverse slope parameter T (see eq. 3). Rapidity values correspond to the middle of thepresented bin. First value is the multiplicity, second represents the statistical uncertainty and third one correspondsto the estimated systematic uncertainty. y Ξ − : dnd y × − Ξ − : T (MeV) Ξ + : dnd y × − Ξ + : T (MeV)-1.0 7.53 ± ± ± ±
11 - --0.5 9.19 ± ± ± ±
10 3.08 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
11 1.42 ± ± ± ± ± ± ± ±
15 - - two times smaller than Ξ − yield. This di ff erence vanishes already in the STAR data at 200 GeV and isnegligible beyond. / baryon ratios The production ratio of doubly strange anti-hyperons and hyperons is of special interest since simplestring models predict values close to unity because both Ξ − and Ξ + stem from the pair production pro-cess. The double di ff erential data presented in the previous subsection are therefore presented in the formof ratios (systematic errors were calculated with the procedure of Sec. 8 and not from the systematicuncertainties of the yields which may be correlated). The Ξ − / Ξ + ratios as function of rapidity and trans-verse momentum are listed in Table 5. The ratio of the rapidity spectra are listed in Table 6 and drawnin Fig. 9(c). We observe little variation with a tendency for a weak maximum around 400 MeV / c in p T and y = (cid:68) Ξ + (cid:69) / (cid:10) Ξ − (cid:11) = ± ± Ξ + production. Table 5: The Ξ + / Ξ − ratio in inelastic p + p interactions at 158 GeV / c beam momentum. Rapidity and transversemomentum values correspond to the middle of the presented bin. First value is the particle ratio, second representsthe statistical uncertainty and third one corresponds to the estimated systematic uncertainty. Ξ + / Ξ − p T (GeV / c ) y = -0.5 y = y = y = ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± able 6: Ratio of p T integrated yields versus rapidity of Ξ + and Ξ − produced in inelastic p + p interactions at158 GeV / c beam momentum. Rapidity values correspond to the middle of the presented bin. First value is the ratio,second represents the statistical uncertainty and third one corresponds to the estimated systematic uncertainty. y Ξ + / Ξ − -0.5 0.341 ± ± ± ± ± ± ± ± (GeV) NN s1 ) » dn / d y ( y - - - - +X - Xfi p+p +X + Xfi p+p SPS RHIC LHC
Figure 6: (Color online) Mid-rapidity densities (dn / d y ) of Ξ − (full symbols) and Ξ + (open symbols) measured ininelastic p + p interactions as a function of centre-of-mass energy √ s NN . The systematic and statistical uncertaintiesare smaller than the symbol size. The data are compared to results from STAR at the BNL RHIC measured at √ s NN =
200 GeV [17] and from CMS at the CERN LHC measured at √ s NN = The predicted enhancement of strangeness production in nucleus-nucleus collisions (per participatingnucleon) relative to proton-proton reactions was established experimentally 30 years ago [19, 20]. It wasalso found that this enhancement is increasing with the strangeness content of the studied particle [21,22].This subsection discusses the system size dependence of the strangeness enhancement in A + A collisions.The strangeness enhancement factor E for a given particle species is defined as: E = (cid:104) N W (cid:105) dn / d y ( A + A ) dn / d y ( p + p ) , (4)13here (cid:104) N W (cid:105) is the number of wounded nucleons in the collision [23]. At SPS energies and above thenumber of wounded nucleons is close to or equal to the number of participating nucleons.The Ξ mean multiplicities measured by NA61 / SHINE in inelastic p + p interactions are used to calculatethe enhancement factors of Ξ s observed in centrality selected Pb + Pb, in semi-central C + C, and in Si + Sicollisions as measured by NA49 [24] at the CERN SPS. The results for mid-rapidity densities are shownin Fig. 7 ( left ) as a function of (cid:104) N W (cid:105) . The enhancement factor increases approximately linearly from 3.5in C + C to 9 in central Pb + Pb collisions. This result is compared to data from the NA57 experiment at theSPS [22], the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) [25] and the ALICE exper-iment at the Large Hadron Collider (LHC) [26]. The published enhancement factor reported by NA57 atthe CERN SPS was computed using p + Be instead of inelastic p + p interactions. Since strangeness produc-tion is already slightly enhanced in p + A collisions [27], this is not a proper reference. With the advent ofthe NA61 / SHINE results on Ξ production in p + p interactions a new baseline reference becomes availableand it is used here for the recalculation of the enhancement observed in the NA57 p + Be and A + A data.The agreement between the enhancement factors calculated using the NA49 and the NA57 A + A (p + Be)data is satisfactory. The STAR data show a slightly lower enhancement, but the enhancement observed byALICE is significantly lower. Figure 7 ( right ) shows the rapidity densities dn / d y of Ξ + at mid-rapidityper mean number of wounded nucleons divided by the corresponding values for inelastic p + p collisionsas a function of (cid:104) N W (cid:105) . Apart from a slightly flatter rise the overall picture remains unchanged. æ W N Æ ] - X [ y = E NA49 (NA61/SHINE p+p)NA57 (NA61/SHINE p+p)STARALICE (GeV) NN s 17.317.32002760 æ W N Æ ] + X [ y = E NA57 (NA61/SHINE p+p)STARALICE (GeV) NN s 17.32002760 Figure 7: (Color online) The strangeness enhancement E at the mid-rapidity as a function of average number ofwounded nucleons (cid:104) N W (cid:105) calculated as a ratio of rapidity density for Ξ − production ( left ) and Ξ + production ( right )in nucleus-nucleus interactions per (cid:104) N W (cid:105) divided by the corresponding value for p + p interactions (see Eq. 4). Redcircles – NA49 Pb + Pb at 158 A GeV [24], blue squares - NA57 p + Be, p + Pb and Pb-Pb at the same center-of-massenergy √ s NN = + Au at √ s NN =
200 GeV [25], gray diamonds -ALICE Pb + Pb at √ s NN = The NA61 / SHINE data on charged Ξ production in inelastic p + p interactions are important for the un-derstanding of multi-strange particle production in elementary hadron interactions. In particular, thenew NA61 / SHINE results constitute essential input for theoretical concepts needed for the modellingof elementary hadron interactions and of more complex reactions involving nuclei like p + A and A + Acollisions.In this section the experimental results of NA61 / SHINE are compared with predictions of the follow-ing microscopic models: E pos qmd mpt mash hsd [37,38]. In E pos the reaction proceeds from the excitation of strings according to Gribov-Regge the-ory to string fragmentation into hadrons. Ur qmd starts with a hadron cascade on the basis of elementarycross sections for resonance production which either decay (mostly at low energies) or are converted intostrings which fragment into hadrons (mostly at high energies). A mpt uses the heavy ion jet interactiongenerator (H ijing ) for generating the initial conditions, Zhang’s parton cascade for modeling partonic scat-terings, the Lund string fragmentation model or a quark coalescence model for hadronization. S mash usesthe hadronic transport approach where the free parameters of the string excitation and decay are tuned tomatch the experimental measurements in elementary proton–proton collisions. P hsd is a microscopic o ff -shell transport approach that consistently describes the full evolution of a relativistic heavy-ion collisionfrom the initial hard scatterings and string formation through the dynamical deconfinement phase transi-tion to the quark-gluon plasma as well as hadronization and the subsequent interactions in the hadronicphase. The model predictions are compared with the NA61 / SHINE data in figs. 8 and 9. E pos Ξ − and Ξ + rapidity spectra but fails on the shape of the transverse momentum dis-tribution. The comparison of the Ur qmd / SHINE measurements revealsmajor discrepancies for the Ξ + hyperons. The model output describes almost perfectly the rapidity andtransverse momentum spectra of Ξ − but strongly overestimates Ξ + yields. Consequently also the ratio of Ξ + to Ξ − cannot be described by the Ur qmd model, see Fig. 9(c). The A mpt , S mash and P hsd models failin the description of both transverse momentum spectra and rapidity distributions. A mpt overestimatesthe Ξ − and Ξ + multiplicities while S mash underestimates them, both failing to describe the ratio. P hsd underestimates the Ξ − yields and overestimates Ξ + . Obviously P hsd also fails to describe the ratio. E pos di ff ers from the Ur qmd , A mpt , S mash and P hsd models in its treatment of Pomeron-Pomeron interactionsand of the valence quark remnants at the string ends.The statistical Hadron Resonance Gas Models (HGM) can be used to predict particle multiplicities in el-ementary and nucleus-nucleus collisions once parameters like the chemical freeze-out temperature T chem ,the baryochemical potential µ B and strangeness saturation parameter are fixed by fits of selected meanmultiplicities of hadrons. In Ref. [39] the HGM results for (cid:10) Ξ − (cid:11) and (cid:68) Ξ + (cid:69) multiplicities were calculatedfor two versions of the model fits. The first one, called fit B, allowed for strangeness deviation from theequilibrium introducing the free parameter γ S . In the second fit, called A, the parameter γ S was replacedby the mean number of strange quark pairs (cid:104) s ¯ s (cid:105) . The mean multiplicities of Ξ and Ω hyperons wereexcluded from the fit B and the mean multiplicity of φ meson from the fit A. Table 7 shows the HGMpredictions based on the fits A and B together with the experimental mean multiplicities of Ξ − and Ξ + produced in inelastic p + p interactions at 158 GeV / c . The measurements are close to the HGM results forthe fit A which excludes mean multiplicity of φ meson. The resulting yield of s ¯ s quark pairs is about twotimes lower than the equilibrium one. 15 (GeV/c) T p0 0.5 1 1.5 2 ( / G e V / c ) T n / d y dp d - · NA61/SHINEEPOS 1.99UrQMD 3.4AMPT 1.26SMASH 1.6PHSD [-0.25,0.25) ˛ y - X (GeV/c) T p0 0.5 1 1.5 2 ( / G e V / c ) T n / d y dp d - · NA61/SHINEEPOS 1.99UrQMD 3.4AMPT 1.26SMASH 1.6PHSD [-0.25,0.25) ˛ y + X Figure 8: (Color online) Transverse momentum spectra at mid-rapidity of Ξ − ( left ) and Ξ + ( right ) produced ininelastic p + p interactions at 158 GeV / c . Rapidity range is included in the legends. Shaded bands show system-atic uncertainties. Ur qmd pos mpt mash hsd [37, 38]predictions are shown as magenta, blue, black, gray and green lines, respectively. y2 - dn / d y - · NA61/SHINEEPOS 1.99UrQMD 3.4AMPT 1.26SMASH 1.6PHSD - X (a) y2 - dn / d y - · NA61/SHINEEPOS 1.99UrQMD 3.4AMPT 1.26SMASH 1.6PHSD + X (b) y2 - ) - X ) / dnd y ( + X dn / d y ( NA61/SHINEEPOS 1.99UrQMD 3.4AMPT 1.26SMASH 1.6PHSD (c)
Figure 9: (Color online) Rapidity spectra of Ξ − ( left ), Ξ + ( middle ) and Ξ + / Ξ − ratio ( right ) measured in inelasticp + p interactions at 158 GeV / c . Shaded bands show systematic uncertainties. Ur qmd pos mpt mash hsd [37, 38] predictions are shown as magenta, blue, black, gray andgreen lines, respectively.
11 Summary
Measurements of Ξ − and Ξ + spectra in inelastic p + p interactions at 158 GeV / c were performed by theNA61 / SHINE experiment at the CERN SPS. These measurements were compared with the results ob-tained at higher energies, and it was shown that the mid-rapidity Ξ − /Ξ + ratio in p + p at √ s NN = / SHINE results were also comparedwith the measurements in A + A collisions at the same energy. The ratio of rapidity densities dn / d y of Ξ − measured in nucleus-nucleus collisions and inelastic p + p collisions at 158 A GeV, when normalised tothe same averaged number of wounded nucleons (cid:104) N W (cid:105) , rises rapidly from p + p towards peripheral Pb + Pb16 able 7: The mean multiplicity of Ξ − and Ξ + hyperons produced in inelastic p + p interactions at 158 GeV / c comparedto theoretical multiplicities obtained within Hadron Gas Models [39]. (cid:104) Ξ − (cid:105) × − (cid:104) Ξ + (cid:105) × − NA61 / SHINE 3.3 ± ± ± ± φ ) [39] 2.85 9.18HGM, Canonical Ensemble, fit B (with φ ) [39] 1.10 3.88collisions. This strangeness enhancement was found to decrease with increasing centre-of-mass energy.Furthermore, the NA61 / SHINE results were compared with Ur qmd , E pos , A mpt , S mash and P hsd modelpredictions. It was concluded that the E pos string model provides the best description of the NA61 / SHINEmeasurements. Finally, the mean multiplicities of Ξ − and Ξ + hyperons were compared with predictionsof the Hadron Gas Model. It turned out that the HGM predictions are very close to the experimentalresults when the φ meson is excluded from the HGM fit. Acknowledgments
We would like to thank the CERN EP, BE, HSE and EN Departments for the strong support of NA61 / SHINE.This work was supported by the Hungarian Scientific Research Fund (grant NKFIH 123842 / / N-CERN / /
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A. Aduszkiewicz , E.V. Andronov , T. Anti´ci´c , V. Babkin , M. Baszczyk , S. Bhosale ,A. Blondel , M. Bogomilov , A. Brandin , A. Bravar , W. Bryli´nski , J. Brzychczyk ,M. Buryakov , O. Busygina , A. Bzdak , H. Cherif , M. ´Cirkovi´c , M. Csanad ,J. Cybowska , T. Czopowicz , , A. Damyanova , N. Davis , M. Deliyergiyev , M. Deveaux ,A. Dmitriev , W. Dominik , P. Dorosz , J. Dumarchez , R. Engel , G.A. Feofilov , L. Fields ,Z. Fodor , , A. Garibov , M. Ga´zdzicki , , O. Golosov , V. Golovatyuk , M. Golubeva ,K. Grebieszkow , F. Guber , A. Haesler , S.N. Igolkin , S. Ilieva , A. Ivashkin , S.R. Johnson ,K. Kadija , N. Kargin , E. Kashirin , M. Kiełbowicz , V.A. Kireyeu , V. Klochkov ,V.I. Kolesnikov , D. Kolev , A. Korzenev , V.N. Kovalenko , S. Kowalski , M. Koziel ,A. Krasnoperov , W. Kucewicz , M. Kuich , A. Kurepin , D. Larsen , A. László , T.V. Lazareva ,M. Lewicki , K. Łojek , V.V. Lyubushkin , M. Ma´ckowiak-Pawłowska , Z. Majka , B. Maksiak ,A.I. Malakhov , A. Marcinek , A.D. Marino , K. Marton , H.-J. Mathes , T. Matulewicz ,V. Matveev , G.L. Melkumov , A.O. Merzlaya , B. Messerly , Ł. Mik , S. Morozov , ,S. Mrówczy´nski , Y. Nagai , M. Naskr ˛et , V. Ozvenchuk , V. Paolone , O. Petukhov ,R. Płaneta , P. Podlaski , B.A. Popov , , B. Porfy , M. Posiadała-Zezula , D.S. Prokhorova ,D. Pszczel , S. Puławski , J. Puzovi´c , M. Ravonel , R. Renfordt , D. Röhrich , E. Rondio ,M. Roth , B.T. Rumberger , M. Rumyantsev , A. Rustamov , , M. Rybczynski , A. Rybicki ,A. Sadovsky , K. Schmidt , I. Selyuzhenkov , A.Yu. Seryakov , P. Seyboth , M. Słodkowski ,P. Staszel , G. Stefanek , J. Stepaniak , M. Strikhanov , H. Ströbele , T. Šuša , A. Taranenko ,A. Tefelska , D. Tefelski , V. Tereshchenko , A. Toia , R. Tsenov , L. Turko , R. Ulrich ,M. Unger , D. Uzhva , F.F. Valiev , D. Veberiˇc , V.V. Vechernin , A. Wickremasinghe , ,Z. Włodarczyk , K. Wojcik , O. Wyszy´nski , E.D. Zimmerman , and R. Zwaska National Nuclear Research Center, Baku, Azerbaijan Faculty of Physics, University of Sofia, Sofia, Bulgaria Ru ¯der Boškovi´c Institute, Zagreb, Croatia LPNHE, University of Paris VI and VII, Paris, France Karlsruhe Institute of Technology, Karlsruhe, Germany University of Frankfurt, Frankfurt, Germany Wigner Research Centre for Physics of the Hungarian Academy of Sciences, Budapest, Hungary University of Bergen, Bergen, Norway Jan Kochanowski University in Kielce, Poland Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland National Centre for Nuclear Research, Warsaw, Poland Jagiellonian University, Cracow, Poland AGH - University of Science and Technology, Cracow, Poland University of Silesia, Katowice, Poland University of Warsaw, Warsaw, Poland University of Wrocław, Wrocław, Poland Warsaw University of Technology, Warsaw, Poland Institute for Nuclear Research, Moscow, Russia Joint Institute for Nuclear Research, Dubna, Russia National Research Nuclear University (Moscow Engineering Physics Institute), Moscow, Russia St. Petersburg State University, St. Petersburg, Russia University of Belgrade, Belgrade, Serbia 20 University of Geneva, Geneva, Switzerland Fermilab, Batavia, USA University of Colorado, Boulder, USA26