Evidence for hadronic deconfinement in p¯-p collisions at 1.8 TeV T. Alexopoulos,(1∗) E. W. Anderson,(2) A. T. Bujak,(3) D. D. Carmony(3) A. R. Erwin,(1) L. J. Gutay,(3) A. S. Hirsch,(3) K. S. Nelson,(1∗∗) N. T. Porile,(4) S. H. Oh,(6) R. P. Scharenberg,(3) B. K. Srivastava,(4) B. C. Stringfellow,(3) F. Turkot,(7) J. Warchol,(5) W. D. Walker(6) 2 (1) Department of Physics, University of Wisconsin, Madison, WI 53706 0 0 (2) Department of Physics, Iowa State University, Ames, Iowa 50011 2 (3) Department of Physics, Purdue University, West Lafayette, Indiana 47907 n (4) Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 a J (5) Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 8 (6) Department of Physics, Duke University, Durham, North Carolina 27706 1 (7) Fermi National Accelerator Laboratory, Batavia, Illinois 60510 1 (February 7, 2008) v 0 3 0 Abstract 1 0 We have measured deconfined hadronic volumes, 4.4 < V < 13.0 fm3, 2 produced by a one dimensional (1D) expansion. These volumes are directly 0 / proportionaltothechargedparticlepseudorapiditydensities6.75 < dN /dη < x c e 20.2. The hadronization temperature is T = 179.5 5 (syst) MeV. Using - ± p Bjorken’s 1D model, the hadronization energy density is ǫF = 1.10 0.26 ± e (stat) GeV/fm3 corresponding to an excitation of 24.8 6.2 (stat) quark- h ± : gluon degrees of freedom. v i X PACS Numbers: 12.38.Mh: 25.75.-q r a Typeset using REVTEX 1 Corresponding Author: Prof. Rolf P. Scharenberg Department of Physics 1396 Purdue University West Lafayette, IN 47907-1396 phone: (765) 494-5393 fax: (765) 494-0706 email: [email protected] The observation of high total multiplicity, high transverse energy, non jet, isotropic events [1] led Van Hove [2] and Bjorken [3] to conclude that high energy density events are produced in high energy p¯-p collisions [4]. These events have a far greater cross section than jet production. In these events the transverse energy is proportional to the number of low transverse momentum particles. This basic correspondence can be explored over a wide rangeofthechargedparticlepseudorapiditydensitydN /dη inp¯-pcollisionsatcenterofmass c energy √s = 1.8 TeV. The various measurements from the Fermilab quark-gluon plasma search experiment E-735 have already been published. In this letter, we present for the first time a coherent picture based on the relationship between the volume V, temperature T, energy density ǫ , and pions per fm3 n emitted from V. Spectra of identified particles, π, F π K, ϕ, p, p¯, Λo Λo, Ξ−, Ξ− are used to extract the V, ǫ , and n values and to determine F F the strange quark content and relative yields of the hadrons. Previously the various individual measurements did not provide an overall understand- ing of these p¯-p collisions. Prompted by the new analysis of the initial collision, we have developed a self-consistent picture of hadronic deconfinement. This letter discusses: (1) The role of parton-parton (gluon) scattering; (2) The volume at decoupling, resulting from the one dimensional longitudinal expansion; (3) The number of pions per fm3 emitted by the source; (4) The hadronization temperature of the source; (5) The hadronization energy density of the source; (6) The number of quark-gluon degrees of freedom in the source; (7) The deconfined volumes and plasma lifetimes, estimates of initial energy densities and temperatures. Experiment E-735 [5] was located at the C interaction region of the Fermi National ∅ Accelerator Laboratory (FNAL). The p¯-p interaction region was surrounded by a cylindrical drift chamber which in turn was covered by a single layer hodoscope including endcaps. This system measured the totalcharged particle multiplicity 10 < N < 200 inthe pseudorapidity c range η < 3.25. A magnetic spectrometer with tracking chambers and time of flight | | counters, provided particle identified momenta spectra in the range 0.1 < p < 1.5 GeV/c. t ◦ The spectrometer covered 0.37 < η < +1.00 with ∆ϕ 20 ( ϕ is the azimuthal angle − ∼ around the beam direction ). (1) Recently the E-735 collaboration has analyzed the charged particle multiplicity dis- tributions arising from p-p and p¯-p collisions over a range of center of mass energies 0.06 √s 1.8 TeV [6]. Results at 1.8 TeV support the presence of double (σ ) and triple (σ ) 2 3 ≤ ≤ parton interactions. These processes increase the non-single diffraction cross section (NSD) from 32 mb at √s = 0.06 TeV to 48 mb at √s = 1.8 TeV. The variation of the double ∼ ∼ encounter and triple encounter cross sections σ and σ with center of mass energy √s is 2 3 shown in Fig. 1. 2 FIGURES 40 s 35 s 1 s 2 3 30 25 ) b m 20 ( s 15 10 5 0 3 4 10 10 √s (GeV) FIG. 1. Comparison of the cross sections for single, double, and triple encounter collisions which increase σ above 32 mb as a function of √s. NSD The multiplicity distribution is made up of three contributions corresponding to single, double and triple parton-parton collisions. Our work on multiparton interactions shows that the increase in the p-p inelastic cross section with energy is nearly completely accounted for by the increase in multiparton interactions. Previously this increase in the p-p inelastic cross section was ascribed to copious minijet production [7]. As the energy is increased, a decreasing fraction of the center of mass energy appears in the NSD part of the inelastic cross section. This may be due to the decrease of the Feynman x of the partons involved in these collisions. It is thus likely that gluons become more involved with increasing energy leading to rapid thermalization [8]. (2) To measure the hadronization volume V, pion HBT (Hanbury Brown, Twiss) corre- lation measurements were made as a function of both P~ = p~ +~p the total momentum of ππ 1 2 thepionpairandof dN /dη. TheP~ momentum dependent results areshown inTableI[9]. c ππ R is the Gaussian radius parallel to the beam, τ the Gaussian lifetime, and λ the chaoticity G parameter. The lifetime τ can be viewed as a measure of the radius perpendicular to the beam [10]. The increase of R and τ with decreasing P is the characteristic signature for G ππ the expansion of the pion source [11]. The dependence of R and τ on dN /dη is shown in G c Table II [9]. A clear increase of R with dN /dη is evident. The dependence of R and τ G c G on P and dN /dη is consistent with a one dimensional (1D) longitudinal expansion of the ππ c pion source. The effect of a 1D expansion on the Bose Einstein correlation has been calcu- lated for a massless relativistic ideal gas [12]. This calculation provides correction factors ℓ and ℓ to our values of R and τ obtained from the HBT analysis. Both ℓ and ℓ are R τ G R τ a function of P and ∆η, where ∆η is the spectrometer aperture. The cylindrical volume ππ V of the pion source is V = π(ℓ τ)2 2 ℓ R where R varies with dN /dη and ℓ τ reaches τ R G G c τ an asymptotic value for the larger dN /dη values. From our data R = e+h dN /dη where c G c e = (0.0788 0.013) fm and h = (0.0730 0.011) fm and χ2/NDF = 3.09/4.00 as shown in ± ± 3 Fig. 2. We neglect e since h dN /dη is 6 to 20 times larger than e. The cylindrical volume c becomes, V = πℓ2τ2 2 ℓ h dN /dη (1) τ R c 3 2.5 ) 2 m f ( G R 1.5 1 0.5 0 0 5 10 15 20 25 30 dN /dh c FIG. 2. Dependence of the Gaussian radius R on dN /dη. The gluon diagram indicates that G c two gluons are required to form two pions. The largest measured value of τ = 0.95 fm is used to evaluate V. We estimate the ℓ factors using the extrapolation procedure (P 0) outlined in Ref. [12]. ( See in particular ππ → Fig.4 and Eq.(7) in Ref [12]). For our P values and a 1D expansion, ℓ = 1 independent ππ τ of P . For the data in Table II ℓ = 1.56. Thus V = (0.645 0.130)dN /dη fm3 and the ππ R c ± range of V is 4.4 0.9 < V< 13.0 2.6 fm3 for 6.75 < dN /dη < 20.2. c ± ± (3) We assume that for dN /dη > 6.75 the system is above the deconfinement transi- c tion. The hot thermalized system expands, cools and then hadronizes. We attribute all of the measured volume to the expansion before hadronization. We neglect the subsequent expansion of the hadronic phase. Following Bjorken’s derivation, we further assume that hydrodynamics of a massless relativistic ideal gas can describe the 1D expansion and that the observed number of pions/fm3 are proportional to the entropy density s at hadronization. To estimate the pions/fm3 emitted by the source, the Bjorken 1D boost invariant equation becomes 3/2 dN /dη c s n = (2) π ∝ A 2 T where A is the transverse area and is the proper time [13]. The collisions occur at T longitudinal coordinate z = 0 and time t = 0. Eq. (2) describes an isentropic expansion s( )/s( ) = / and 0 0 T T T T = (t2 z2)1/2 (3) T − 4 where is the initial proper time when thermalization has occurred. For a relativistic 0 T massless ideal gas above the phase transition the maximum expansion velocity, responsible for most of the longitudinal expansion, is likely to be the sound velocity, v2 = 1/3 [13]. The s expansion time t = z/v = ℓ R /v and = (3z2 z2)1/2 = √2 z. We note that is the s R G s f T − T proper time at hadronization. = √2ℓ R = √2 ℓ h dN /dη (4) f R G R c T and Eqn. (2) becomes 3/2 dN /dη 1/√2 3/2 1/√2 c n = = (5) π πτ2 2 ℓ h dN /dη πτ2 2 ℓ h R c R where 1/√2 is the effective ∆η slice. Thus n is independent of dN /dη and one obtains π c n = 1.64 0.33 (stat) pions fm−3 (6) π ± This n value indicates that the deconfinement transition occurs at a definite entropy π density. Since s n is constant we can directly evaluate n using the total number of pions π π ∝ emitted divided by the total volume for the data set in Table I. We choose the lowest P ππ value where τ = 0.95 fm, R = 1.2 fm, and ℓ = 1.43. Here the average pseudo-rapidity G R density is < dN /dη >= 14.4 and Eqns. (2) and (4) become c 3/2 dN /dη 1/√2 n = c = 1.57 0.25 (stat) pions fm−3 (7) π πτ2 2 ℓ R ± R G which has a smaller statistical error than (6). (4) The negative particle p spectrum is used to measure the temperature. A slope t parameter b−1 is obtained from a fit of the invariant cross section d2N /dy d2p to the c t function Aexp( bp ) for 0.15 p 0.45 GeV/c [14]. The b−1 value is constant to 1% for t t − ≤ ≤ ± 6.75 < dN /dη < 20.2. Transverse flow has not been seen in p-p reactions at lower energies c [15,16]. In heavy ion reactions the transverse flow is attributed to final state interactions of thehadronswhichpresumably arenotimportantinp¯-pcollisions. ThefactthatR increases G by a factor of three and b−1 remains constant to 1%, suggests that the transverse flow ± is negligible. The components σ ,σ in the NSD cross section indicate that the parton- 2 3 parton mean free paths are shorter in high energy collisions. Since gluon-gluon interactions dominate in the initial encounters, early thermalization 0.5 fm/c when T 200 MeV is likely [8]. We interpret b−1 = T = 179.5 5 MeV (syst)∼as the hadronization∼temperature. ± We neglect the expansion of the hadronic phase following hadronization i.e. decoupling is associated with hadronization. The systematic error estimate is based on possible kaon (K0) misidentification in the negative particle spectrum at low p . We have not made a s t correction for the effect of resonance decays on the negative particle p spectrum. We note t that the negative particle temperature is significantly higher than the temperature based on the spectra of idenitified pions which include resonance particle decay pions (T 168 ≃ MeV). A hadronization inverse slope parameter T can be estimated from our measurement m of the relative yields of mesons and hyperons as shown in Fig. 3, using all the events with dN /dη > 6.75. The hadron yield versus rest mass inverse slope parameters indicates 162 < c 5 T < 173 MeV. Similar T 168 MeV values, based on thermal model analyses of hadron m m yield ratios, have been seen i∼n high energy p¯p, p p, e+e− and heavy ion reactions [17]. This has been interpreted as evidence for a universal limiting temperature T for hadrons, the m Hagedorn temperature [18]. p 1 d el Yi e -1 K v 10 ti p a el R L S -2 X 10 F -3 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Mass (GeV/c2) FIG. 3. Relative meson and hyperonyields versus rest mass[19,20]. For themesons, theinverse slope parameter T = 162 5 MeV, and for the hyperons T = 173 12 MeV. m m ± ± (5) We can also use the average measured energies to estimate the hadronization energy density ǫ [19]. Since ǫ = 3/4 T s , ǫ is also constant versus dN /dη [13], F F F F c ǫ = PhFh ×(mh)⊥ ×1/√2 (8) F πτ2 2 ℓ h R × × × where (mh)⊥ = (m2h + p2t)1/2 is the average transverse mass of hadron h, Fh is a hadron abundance factor which also accounts for the neutral hadrons of each species. We have determined F for π,K,ϕ,p,n,Λ0,Ξ, etc. For τ = 0.95 fm, ℓ = 1.56, h=0.073, ǫ h R F becomes ǫ = 1.10 0.26 (stat) GeV/fm3 (9) F ± (6) We can estimate the average number n of constituents in volume V at temperature c T, for a system without boundaries [21] G(T) 1.202 (kT)3 n = V (10) c π2 h¯3 c3 where G(T) are the number of degrees of freedom (DOF). For a pion gas G(T) = 3, V = 1 fm3, and T = 179.5 MeV. The average number of pions (pion gas) in the source is n = 0.28 π 6 pions/fm3. We observe 1.57 pions/fm3, emitted from the source at temperature T = 179.5 MeV, which requires many more DOF. For a quark-gluon plasma G(T) = G (T)+G (T)+G (T) = 16+21/2 (f) where f are g q q¯ the number of quark flavors [13]. G (T) are the gluon DOF; G (T), G (T) are the quark, g q q¯ antiquark DOF. We assume that pion emission from the source can be determined by the number of constituents in the source at hadronization, that one pion is a quark antiquark (q,q¯) pair and that two gluons (2g) are required to produce two pions (see insert Fig. 2). n = n +(n +n )/2 (11) π g q q¯ Our data indicates that 6% strange quarks are present at hadronization [19,20]. Thus ∼ we use f = 2 to evaluate Eqn. (10) where V = 1 fm3 and, n = (1+2 21/64)G 16.1 T3 (GeV) (12) π g × × where G are the effective number of gluon DOF. For n = 1.57/fm3 and T = 0.1795 GeV, g π we obtain G = 10.18. The total number of DOF are, g G(T) = n +n +n = (1+21/16)G = 23.5 6 DOF (13) g q q¯ g ± nearly eight times the DOF for a pion gas. A second method for estimating the DOF is to use the energy density and temperature at hadronization. For the isentropic expansion, the energy E in the volume V at temperature T is [21] G(T) π2 k4 E = V T4 . (14) 30 h¯3 c3 For ǫ = 1.10 0.22 (stat) GeV/fm3 and T = 179.5 5 MeV, we find G(T) = 24.8 6.2 F ± ± ± (stat) quark gluon DOF, in good agreement with the DOF using the number of constituents (Eq. 13). (7) Two Lorentz contracted nucleons collide at t = 0, z = 0 and the thermalized con- stituents are assumed to emerge at . Suppose we choose = 1.0 fm/c. For a given expan- 0 0 T T sion velocity, the data determines the hadronization proper time and 1.09 < < 3.25 f f T T fm/c. For 6.75 < dN /dη < 20.2, the deconfined volumes V, determined by the data, range c between 4.4 < V < 13.0 fm3. For dN /dη > 6.75 and using G(T) from Eq. (14) c ǫ/T4 = π2/30 G(T) = 8.15 2.0(stat) (15) ± ingeneralagreement withlatticegaugecalculations [22]. Theratiooftheinitialtemperature T to the final T is T /T = ( / )1/3 and 185 < T < 266 MeV. The ratio of the initial i f i f f 0 i T T energy density ǫ to the final energy density ǫ is ǫ /ǫ = ( / )4/3 and ǫ is 1.23 < ǫ < 5.30 i f i f f 0 i i T T GeV/fm3 for 6.75 < dN /dη < 20.2. Note a different choice of would change the T and c 0 i T ǫ estimates. i In summary, the HBT analysis and the constant temperature versus dN /dη are consis- c tant with a model in which a pion source undergoes a 1D expansion with total longitudinal dimension 2 l R directly proportional to dN /dη. We have used the Bjorken 1D model to R G c analyze our data. We find that there is a unique hadronization entropy density and temper- ature at which the pions are produced independent of dN /dη. We have used phase space c 7 estimates of the average number of thermalized constituents in volume V at temperature T and the measured energy density ǫ to compute the number of DOF in the source. However, F we note that reducing the average expansion velocity from v2 = 1/3 to v2 = 1/5 reduces the DOF estimate by 30%. Then the lower limit for the DOF is 16.6 4.2, still substantially ± larger than the pion gas DOF of 3. This lower limit allows a more conservative argument that quark-gluon constituents are present in the large deconfined volumes. Our estimate of the number of DOF in the source (23.5 6, 24.8 6.2) is in general agreement with those ± ± expected for a quark-gluon plasma. The n , ǫ , and T values characterize the quark-gluon π F to hadron thermal phase transition. We expect that these hadronization conditions will be observed in p-p collisions at the CERN Large Hadron Collider where higher pseudorapid- ity density dN /dη values will produce even larger deconfined volumes and longer plasma c lifetimes. We would like to acknowledge the important support for Fermi National Laboratory experiment E-735 by J. D. Bjorken and L. M. Lederman. This work was supported in part by the United States Department of Energy and the National Science Foundation. 8 REFERENCES ∗ Current Address: Department of Physics, National Technical University of Athens, Athens, Greece. ∗∗ Current Address: Department of Physics, University of Virginia, Charlottesville, Vir- ginia. [1] UA1 collaboration, Phys. Lett. B 123 (1983) 115; Physics Letters 107B (1981) 320. [2] L. Van Hove, Phys. Lett. B 118 (1982) 138. [3] J. D. Bjorken, Fermilab Pub. 82/44-THY. [4] L. McLerran, Rev. Mod. Phys. 58 (1986) 1021. [5] E-735 proposal. 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Lett. 97B (1980) 136. [19] T. Alexopoulos, et al., (E-735 collaboration), Phys. Rev. D 46 (1992) 2773; Phys. Rev. D 48 (1993) 984. [20] T. Alexopoulos, et al., (E-735 collaboration), Z. Phys. C67 (1995) 411. [21] R. K. Pathria, Statistical Mechanics, Pergamon Press, Ltd, 1972, p 187f. [22] F. Karsch, et al., Phys. Lett. B 478 (2000) 249. 9 TABLES TABLE I. Fitted values of radius R , lifetime τ, and chaoticity λ in the Gaussian parameter- G ization with respect to q and q . Values are a function of average two-pion total momentum P t 0 ππ or average two-pion transverse momentum P . The total momentum interval containing the data t is listed in column 1. Momentum is in GeV/c. The errors are statistical. P P R (fm) τ (fm) λ P ππ ππ G t h i h i 0.2-0.5 0.404 1.20 0.05 0.95 0.06 0.24 0.01 0.369 ± ± ± 0.2-0.7 0.503 1.05 0.08 0.71 0.05 0.25 0.01 0.462 ± ± ± 0.5-1.0 0.708 0.80 0.07 0.67 0.07 0.23 0.02 0.650 ± ± ± 0.7-1.2 0.900 0.60 0.06 0.64 0.05 0.26 0.03 0.832 ± ± ± 0.9-1.7 1.175 0.58 0.06 0.53 0.07 0.26 0.02 1.087 ± ± ± >1.0 1.403 0.48 0.06 0.45 0.05 0.21 0.02 1.285 ± ± ± >1.2 1.600 0.43 0.06 0.41 0.06 0.23 0.02 1.479 ± ± ± 10