Evolution of minimum-bias parton fragmentation in nuclear collisions CENPA 9, Universit of Washington, Seattle, WA 99 E-mail: trainor@hausdorf.npl.washington.edu Hard components of p t spectra can be identified with minimum-bias parton fragmentation in nuclear collisions. Minimum-bias fragment distributions (FDs) can be calculated b folding a power-law parton energ spectrum with parametrized fragmentation functions (FFs) derived from e + -e and p- p collisions. Alterations to FFs due to parton energ loss or medium modification in Au-Au collisions are modeled b adjusting FF parametrizations consistent with rescaling QCD splitting functions. The parton spectrum is constrained b comparison with a p-p p t spectrum hard component. The reference for all nuclear collisions is the FD derived from in-vacuum e + -e FFs. Relative to that reference the hard component for p-p and peripheral Au-Au collisions is found to be strongl suppressed for smaller fragment momenta. At a specific point on centralit the Au-Au hard component transitions to enhancement at smaller momenta and suppression at larger momenta, consistent with FDs derived from medium-modified e + -e FFs. High-pT Phsics at LHC -9 Februar - 9 Prague, Czech Republic Speaker. c Copright owned bhe author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/
. Introduction RHIC collisions are commonl described in terms of two themes: hdrodnamic (hdro) evolution of a thermalized bulk medium and energ loss of energetic partons (hard probes) in that medium. Hdro is thought to dominate p t spectra below GeV/c, parton fragmentation is expected above GeV/c, and quark coalescence is thought to dominate the intermediate p t interval. Recent studies of spectrum and correlation structure have revealed interesting new aspects of RHIC collisions. Number and p t angular correlations in the final state contain minijet structures (minimum-bias parton fragmentation) [,,,,,, ]. Two-component analsis of p-p and Au-Au spectra reveals a corresponding hard component interpreted as a minimum-bias fragment distribution, suggesting that jet phenomena extend down to. GeV/c hadron momentum [, 9]. Minijets (well described in p-p collisions b PYTHIA/HIJING []) are observed to dominate the transverse dnamics of nuclear collisions at energies above s NN GeV. The term minijets can be applied collectivelo hadron fragments from the minimum-bias scattered-parton spectrum averaged over a given A-A or N-N event ensemble. Minijets provide unbiased access to fragment distribution structure down to a small cutoff energ for scattered partons (those partons fragmenting to charged hadrons) and to the smallest detectable fragment momenta (. GeV/c). In this analsis minijets are studied in the form of p t -spectrum hard components isolated via the two-component spectrum model. Measured hard components are compared with calculated fragment distributions obtained b folding parton spectra with fragmentation-function ensembles. Parton spectrum parameters and modifications to fragmentation functions in more-central Au-Au collisions are inferred []. The goal is a comprehensive QCD description of all nuclear collisions.. Two-component spectrum model The two-component model of p-p spectra [] is the starting point for the fragmentation analsis described here. The two-component (soft+hard) model was first obtained from a Talor-series expansion on observed event multiplicit ˆn ch ( corrected n ch ) of spectra for several multiplicit classes. The soft component was subsequentl interpreted as longitudinal projectile-nucleon fragmentation, the hard component as transverse scattered-parton fragmentation. The two-component model applies to two-particle correlations on (, ) as well as their D projections onto p t or. The two-component spectrum model for p-p collisions with corrected soft and hard multiplicities n s +n h = n ch is dn ch ( ˆn ch ) = S ( )+ n h( ˆn ch ) n s ( ˆn ch ) d n s ( ˆn ch ) H ( ), (.) where soft component S ( ) is the Talor series constant, and hard component H ( ) is the coefficient of the term linear in ˆn ch, both normalized to unit integral. S ( ) is a Lév distribution on m t, H ( ) is a Gaussian plus QCD power-law tail on transverse rapidit = ln{(m t + p t )/m }. To compare with A-A spectra we define S pp = (/ )dn s /d with reference model n s S and similarl for H pp n h H. The two-term Talor series exhausts all significant p-p spectrum structure. Fig. (first panel) shows spectra for ten multiplicit classes from GeV non-single diffractive (NSD) p-p collisions []. The asmptotic limit for ˆn ch (dash-dotted curve) is S. The
spectra are normalized b soft-component multiplicit n s. Fig. (second panel) shows the twocomponent algebraic model Eq. (.) with unit-normal model functions S and H defined in [, 9]. Hard-component coefficient n h /n s scales as α ˆn ch. Factor α =. is the average value for most ˆn ch classes. The spectrum data in the first panel are described to the statistical limits. /n s / dn ch /d - nˆ ch =. S /n s / dn ch /d - S. H /n s / dn ch /d S ( )....... H pp /n s.. [n h (.)/n h (nˆ ch )] H pp ( ;nˆ ch ) - p t (GeV/c). H ( ) - Figure : First: spectra from s NN = GeV p-p collisions for ten multiplicities, Second: Corresponding two-component model, Third: Corresponding hard components, Fourth: Hard components normalized to NSD p-p collisions. Figure (third panel) shows hard components H pp /n s for ten multiplicit classes obtained b subtracting fixed soft component S from the ten NSD p-p spectra normalized to n s. The shape is Gaussian independent of multiplicit []. Fig. (fourth panel) shows hard components H pp from the third panel scaled b factors n h (.)/n h ( ˆn ch ) to obtain the mean hard component for NSD p-p collisions. The dash-dotted curve is.h [. (α =.)( ˆn ch =.)(n s =.) []]. The exponential tail represents the QCD power law p n QCD t. The spectrum hard component is interpreted as a minimum-bias fragment distribution dominated b minijets jets from those partons (gluons) with at least the minimum energ required to produce charge-neutral combinations of charged hadrons. Equivalent structure appears in two-particle correlations on (, ) [, ]. The corresponding two-component model for per-participant-pair A-A spectra is n part dn ch d = S NN ( )+ν H AA ( ;ν) (.) = S NN ( )+ν r AA ( ;ν)h NN ( ), where S NN ( S pp ) is the soft component and H AA is the A-A hard component (with reference H NN H pp ) integrating respectivelo multiplicities n s and n h in one unit of pseudorapidit η [, 9]. Ratio r AA = H AA /H NN is an alternative to nuclear modification factor R AA. Centralit measure ν n binar /n participant estimates the Glauber-model mean nucleon path length. We are interested in the evolution of hard component (fragment distribution) H AA or ratio r AA with A-A centralit.. Fragmentation functions e + -e (e-e) fragmentation functions (FFs) have been parametrized accuratel over the full kinematic region relevant to nuclear collisions. e-e light-quark and gluon fragmentation functions D xx (x,q ) D xx (, ) (xx is the FF context: e-e, p-p, A-A) are accuratel described above energ scale (dijet energ) Q GeV b a two-parameter beta distribution β(u; p, q) on normalized rapidit u []. Fragment rapidit for unidentified hadrons is = ln[(e + p)/m π ], and parton
rapidit = ln(q/m π ). Parameters (p,q) var slowl and linearl with above GeV and can be extrapolated down to Q GeV based on dijet multiplicit data. Fig. (first panel) shows measured FFs for three energ scales from HERA/LEP [, ]. The in the axis label indicates dijet n ch densities. The vertical lines at right denote values. The curves are determined bhe β(p,q) parametrization with min. (p t. GeV/c, left vertical line) and describe data to their error limits over the entire fragment momentum range. Fig. (second panel) shows the FF ensemble (inclusive light quarks fragment to inclusive hadrons) vs energ scale Q as a surface plot []. The dashed curve is the locus of modes the maximum points of the FFs. Between the dash-dotted lines the sstem is determined b FF data. Between the dash-dotted and dotted lines the parametrization is constrained onl b dijet multiplicities. dn ch /d TASSO, GeV e + -e s = 9 GeV OPAL dn ch /d MB GeV Q = s (GeV) p-p CDF GeV E jj E jet (GeV) Figure : First: Fragmentation functions (FFs) from e + -e collisions for three energies with β -distribution parametrizations (solid curves), Second: Full e + -e FF parametrization on parton rapidit, Third: FFs from p- p collisions for several dijet energies, Fourth: Full p- p FF parameterization on parton rapidit. Figure (third panel) shows FF data from p- p collisions at FNAL (samples from the full data set) []. The solid curves guide the ee. There is a significant sstematic difference between p-p and e-e FFs. The dotted line represents the lower limit for e-e FFs. The sstematic gap for all parton energies is apparent min for p-p collisions is. (. GeV/c) instead of. (. GeV/c). The CDF FFs also reveal a sstematic amplitude saturation or suppression at larger parton energies compared to LEP sstematics. The curve labeled MB is the hard-component reference from NSD p-p collisions []. Fig. (fourth panel) shows a surface plot of the p-p FF ensemble []. The surface represents the e-e FF parametrization modified b introducing cutoff factor g cut () = tanh{( )/ξ } >, (.) with ξ. determined bhe CDF FF data []. The modified FFs have not been rescaled to recover the initial e-e parton energ. The cutoff function thus represents real fragment and energ loss from p-p relative to e-e FFs. The difference implies that FFs are not universal. Figure (first panel) shows parametrized beta FFs for five e-e energ scales. The Q = GeV scale is associated with minijets as explained below. Such curves provide a complete description of e-e FFs at energ scales relevant to nuclear collisions. Fig. (second panel) shows light-quark dijet multiplicit sstematics from the same beta parametrization. The solid points correspond to the FFs in the first panel. The open circles represent multiplicities from medium modification of those FFs in central Au-Au collisions at GeV, as described in Sec.. The in-medium shift of FFs to smaller fragment momenta requires more fragments to satisf parton-energ conservation. The sstematics of quark and gluon jets coincide for energ scales Q = E jet < GeV ( < ).
dn ch /d GeV dijet energ 9 n ch E jet (GeV) e-e FFs no E-loss E-loss dn ch /d GeV dijet energ n ch E jet (GeV) p-p FFs e-e reference CDF Figure : First: Parametrized e + -e FFs for five dijet energies, Second: Corresponding dijet multiplicities for in-vacuum (solid points) and in-medium (open points) FFs, Third: Parametrized p- p FFs for five dijet energies compared to CDF data (points) [], Fourth: Corresponding dijet multiplicities for p-p FFs (solid points) and published values (open points [, ]). Figure (third panel) shows e-e beta FFs for five parton energies [] modified bhe g cut factor to describe p-p FFs. The deviation from e-e FFs is indicated bhe two dotted lines []. The CDF data (points) are from []. Fig. (fourth panel) shows multiplicit sstematics (solid points) for p-p (i.e., modified e-e) FFs from the parametrization. The solid curve represents unmodified e-e FFs as a reference. There is substantial reduction of p-p FF multiplicities due to the cutoff. Also plotted are CDF FF multiplicities from reconstructed jets (open triangles [] and open circles []). Comparison of Fig. second and fourth panels reveals that dijet multiplicities (and chargedparticle energ integrals) are strongl suppressed in p-p collisions compared to equivalent FFs in e-e collisions. p-p jet multiplicities are reduced b -%. FFs are apparentl modified in p-p collisions as well as A-A collisions. At Q = GeV (minijets) there is a three-fold dijet multiplicit reduction for p-p relative to e-e collisions.. Parton spectrum model A model for the parton p t spectrum resulting from minimum-bias scattering into an η acceptance near projectile mid-rapidit can be parametrized as p t dσ di jet dp t = f cut (p t ) A p t p n QCD t dσ di jet d = f cut ( )A max exp{ (n QCD ) }, (.) which defines QCD exponent n QCD, with ln( p t /m π ). The cutoff factor f cut ( ) = {tanh[( cut )/ξ cut ]+}/ (.) represents in this analsis the minimum parton momentum which leads to detectable charged hadrons as neutral pairs (i.e., local charge ordering). Parton spectrum and cutoff parameters are determined via FD comparisons with p-p and Au-Au spectrum hard components. Fig. (semilog and linear formats) shows the parton spectrum (solid curve) inferred from a p-p spectrum hard component []. cut and A max are well-defined bhe p-p hard component, and n QCD is defined b Au-Au spectrum hard components extending to larger. The dotted curve in the first panel is an ab-initio pqcd calculation [9]. The linear plot (second panel) indicates
dσ dijet / d (mb) - mb mb. mb pqcd p t. dσ dijet / d (mb) E jet (GeV) mb. mb dσ dijet / dp t [mb/(gev/c)] - KLL p t. UA p t (GeV/c) Figure : First: Parton spectra inferred from this analsis for p-p collisions (solid curve) and central Au-Au collisions (dash-dotted curve) compared to an ab-initio pqcd theor result (bold dotted curve [9]), Second: Parton spectra from this analsis in a linear plot, Third: Parton spectrum from reconstructed jets (UA, solid points []) compared to theor (dashed curve []) and this analsis (solid curve, note factor ). the narrowness of the spectrum, with effective mean energ near GeV (minijets). Fig. (third panel) compares the spectrum defined in this analsis (solid curve, and note the factor ) with GeV UA jet cross-section data obtained b event-wise jet reconstruction []. The UA spectrum integral is mb []. The spectrum from this analsis integrates to. ±. mb with well-defined cutoff GeV which agrees well with pqcd theor (e.g., []). The KLL parametrization /p t mb/(gev/c) (dashed line) integrates to. mb above GeV/c [].. Fragment distributions from a QCD folding integral The folding integral used to obtain fragment distributions (FDs) in this analsis is d n h ddη ε(δη, η) d D xx (, ) dσ di jet, (.) σ NSD η d where D xx (, ) is the dijet FF ensemble from a source collision sstem (xx = e-e, p-p, A-A, in-medium or in-vacuum), and dσ di jet /d is the minimum-bias parton spectrum []. Hadron spectrum hard component d n h /ddη as defined represents the fragment ield from scattered parton pairs into one unit of η. Efficienc factor ε. (for a single dijet and one unit of η) includes the probabilithat the second jet also falls within η acceptance δ η and accounts for losses from jets near the acceptance boundar. η is the effective π η interval for scattered partons. σ NSD ( mb for s NN = GeV) is the cross section for NSD p-p collisions. Fig. (first panel) shows the integrand D ee (, ) dσ di jet d of the folding integral in Eq. (.) incorporating unmodified FFs from e-e collisions with lower bound at min. (p t. GeV/c) (dotted line). The plot z axis is logarithmic to show structure over the entire distribution support. Fig. (second panel) shows the corresponding FD (solid curve). The parton spectrum parameters determined from the p-p hard component are retained. The solid curve is the correct answer for an FD describing inclusive hadrons from inclusive partons produced b free parton scattering from p-p collisions, which is not observed in real nuclear collisions. The dash-dotted curve represents the hard-component model inferred from p-p collisions []. The FD from e-e FFs lies well above the measured p-p hard component for hadron p t < GeV/c ( <.), and the mode is shifted
down to. GeV/c. The correct e-e FD strongl disagrees with the relevant part of the p-p p t spectrum the hard component. Despite the strong disagreement the e-e FD is the correct reference for nuclear collisions, as demonstrated below. / d n h /ddη - - p (GeV/c) (/) d n h /ddη - - p (GeV/c) e. Figure : First: pqcd folding-integral argument for e + -e FFs, Second: Corresponding fragment distribution (solid curve) and p-p hard-component reference (dash-dotted curve), Third: Folding-integral argument for p- p FFs, Fourth: Corresponding fragment distribution(solid curve) compared to p-p hard-component data (points). Dotted curves correspond to ±% change in parton spectrum cutoff energ about GeV. Fig. (third panel) shows a surface plot of integrand D pp (, ) dσ di jet d, incorporating e-e FFs based on the LEP parametrization but modified bhe FF cutoff function inferred from p- p collisions. The main difference from e-e FFs is that the lower bound of p-p FFs is raised to min. (p t. GeV/c from. GeV/c). Fig. (fourth panel) shows the corresponding FD H NN vac (integration of the third panel over ) as the solid curve. The mode of the FD is GeV/c. The dash-dotted curve is a Gaussian-plus-tail model function, and the solid points are hardcomponent data from p-p collisions []. That comparison determines parton spectrum parameters cut =. (E cut GeV), A max and exponent n QCD =.. The p-p data are well-described b the pqcd folding integral. This procedure establishes an absolute quantitative relationship among parametrized parton spectrum, measured FFs and measured spectrum hard components over all p t, not just a restricted interval (e.g., above GeV/c).. Parton energ loss and medium-modified FDs The hpothesis of parton energ loss in a thermalized bulk medium is of central importance at RHIC. In some models the medium is opaque to most hard-scattered partons onl a small fraction emerge as correlated fragments. But minijet sstematics suggest no parton loss to thermalization. In this section I adopt a pqcd-inspired minimal model of FF modification (Borghini-Wiedemann or BW) [], with no loss of parton energo a medium or scattered partons to thermalization. Figure (first panel) illustrates the BW model of FF modification (cf. Fig. of []). Invacuum e-e FFs for Q = and GeV from the beta parametrization are shown as dashed and solid curves respectivel []. Whereas the BW model was expressed on ξ p FFs are plotted here on fragment rapidit. The relation is ξ p = ln(p jet /p) = ln( p jet /m π ) ln(p/m π ), with energ scale Q = p jet. The practical consequence of the BW energ-loss mechanism is a momentum-conserving rescaling of FFs on x p, with ξ p = ln(/x p ). Small densit reductions at larger fragment momenta (smaller ξ p ) are compensated b much larger increases at smaller momenta. The largest changes (central Au-Au) correspond to an inferred % leading-parton fractional energ loss. We model the BW modification simpl b changing parameter q in β(u; p, q)
b q, which accuratel reproduces the BW result. The modified FFs are the dash-dotted and dotted curves []. Fig. (second panel) shows the modified e-e FF ensemble with FF modes shifted to smaller fragment rapidities. No energ is lost from FFs in this model. dn ch /d GeV GeV TASSO GeV OPAL GeV vac med vac med = ln[(e + p)/m π ] E jet (GeV) / d n h /ddη - - p (GeV/c) / d n h /ddη - - p (GeV/c) Figure : First: e + -e FFs for two energies unmodified (solid and dashed curves) and modified according to a rescaling procedure [] (dash-dotted and dotted curves) to emulate parton energ loss, Second: e + - e FF ensemble modified according to [], Third: Medium-modified FD from e + -e FFs (solid curve) compared to in-vacuum e + -e FD (dotted curve) Fourth: Medium-modified FD from p- p FFs (solid curve) compared to in-vacuum FD (dotted curve). Figure (third panel) shows H ee med (solid curve), the FD obtained b inserting e-e in-medium FFs from the second panel into Eq. (.) and integrating over parton rapidit. The dotted curve is the H ee vac reference from in-vacuum e-e FFs. The dash-dotted curve is again the Gaussian-plustail p-p hard component H GG reference. The mode of H ee med is. GeV/c. Fig. (fourth panel) shows results for p-p FFs. Major differences between p-p and e-e FDs appear below p t GeV/c (.). Conventional comparisons with theor (e.g., data vs NLO FDs) tpicall do not extend below GeV/c []. The large difference between the two sstems below GeV/c reveals that the small-p t region, conventionall assigned to hdro phenomena, ma be of central importance for understanding fragmentation evolution in A-A collisions.. Fragment evolution with centralit in Au-Au collisions We have established a sstem to combine measured FFs and a parametrized pqcd parton spectrum to produce calculated fragment distributions FD xx for comparison with measured spectrum hard components H xx. Conventional comparisons emplo a ratio measure. Two questions emerge: what is the validit of the ratio definition, and what should be the reference for such a ratio. The conventional spectrum ratio at RHIC is R AA, defined in the first line of R AA ν S NN( )+ν H AA ( ;ν) S NN ( )+H NN ( ) ν + H NN S NN r AA at =. In that definition the terms in numerator and denominator are normalized per participant pair n part /, so the prefactor is /ν rather than /n binar. Fig. (first panel) illustrates problems with that measure. Hard-component evolution with centralit, the main object of this analsis, is described b ratio r AA H AA /H NN. The second line of Eq. (.) gives the limiting value of R AA near where the H NN /S NN ratio is tpicall /. r AA is thus suppressed b a large factor (.)
in just the interval where fragmentation details are most important. The p-p data (dots) illustrate suppression of even statistical fluctuations. All information is lost. R AA = /ν /n part ρ AA / ρ NN / ν GeV Au-Au pions GeV p-p pqcd r AA = H AA / H NN -% pions GeV Au-Au -% GeV p-p pqcd r xx = FD med / FD vac ~. r eernn q =. r AA (-%) r xx = FD med / FD vac ~. q =. r AA (-%) r en Figure : First: Conventional spectrum-ratio measure R AA, illustrating strong suppression of spectrum information below GeV/c ( = ), Second: Hard-component ratio r AA illustrating restoration of suppressed structure at small, Third: Comparison of calculated FD ratios to measured r AA for central Au-Au collisions, Fourth: Comparison of novel FD ratio r en to measured r AA for central Au-Au collisions. Figure (second panel) shows ratio r AA based on hard-component reference H NN set equal to Gaussian model H GG = n h H from []. Evolution of suppression and enhancement is dramaticall more accessible. The p-p data and the most peripheral Au-Au data agree with the N-N reference (r AA = ) above =. but deviate significantl from H GG below that point. For the Au-Au collisions in this figure ν n bin /n part values for five centralities are.9,.,.9,.,., where ν. is N-N collisions and ν is b = Au-Au collisions [9]. From ν =.9 to ν =. there is a dramatic change in the hard component. At the transition point ν. n part = (out of ) and n bin = (out of ). Figure (third panel) shows calculated FD ratios r xx = FD xx med /FD xx vac with xx = e-e (dash-dotted curve, e-e FFs) or N-N (dashed curve, p-p FFs) []. The solid curve is the measured r AA from central (-%) Au-Au collisions at GeV [9]. q. for H ee med and H NN med (in-medium FFs) was adjusted to obtain the correct large- suppression for -% central Au-Au. The reference for r AA is hard-component model function H GG. The dotted curve is a reference ratio obtained b shifting H GG on b. (negative boost) [9]. The simple negative-boost model does not describe the Au-Au data. But the e-e and N-N ratios also do not describe the data. Figure (fourth panel) introduces a novel concept. Instead of comparing the calculated inmedium FD for N-N collisions averaged within A-A collisions with the in-vacuum FD for isolated N-N collisions, or similarl comparing e-e with e-e as in the third panel, the in-medium FD for e-e is compared with the in-vacuum FD for N-N b defining ratio r en = FD ee med FD NN vac. (.) Calculated r en describes the measured r AA well over the entire fragment momentum range. We conclude that FD NN vac is not the correct reference. The proper in-vacuum reference for all sstems is an FD from e-e FFs, not p-p FFs. We define FD ratios r xx = FD xx /FD ee vac with xx = ee, NN, AA and = med or vac to be compared with equivalent spectrum hard components H xx. Figure (first panel) shows ratios redefined in terms of the ee-vac reference: H pp (p-p data points), H AA (peripheral Au-Au data solid curve) and calculated H ee med (dash-dotted curve) 9
and H NN vac (dashed curve) all divided b reference H ee vac. The strong suppression of p-p and peripheral Au-Au data apparent at smaller results from the cutoff of p-p FFs noted above. The comparison is linear rather than logarithmic, as in Fig., and is thus more differential. r xx = H xx / H ee-vac........ r ee Au-Au -% p t (GeV/c) GeV p-p ν <. r xx = H xx / H ee-vac........ r ee -% r NN p t (GeV/c) GeV Au-Au ν >. ν <. -% H AA - H ee-med p t (GeV/c) H NN-vac H GG GeV p-p pions GeV Au-Au p-p Gaussian ref. p-p FD in vacuum e-e FD in medium - Figure : First: FD ratios relative to an ee-vacuum reference for Au-Au collisions below the sharp transition, Second: FD ratios relative to an ee-vacuum reference for Au-Au collisions above the sharp transition revealing major changes in FD structure, Third: Hard-component evolution in central Au-Au collisions vs centralit. Large increases in fragment ield at smaller (p t < GeV/c) accompan suppression at large. Figure (second panel) shows measured H AA /H ee vac for more-central Au-Au collisions (solid curves) above a transition point on centralit at ν.. The main difference is partial restoration of the suppressed region at smaller and suppression at larger. The latter has been the major observation at RHIC for jet-related modification (high-p t suppression, jet quenching []). Apparent from this analsis is the accompaning ver large increase in fragment ield below GeV/c, still strongl correlated with the parent parton []. Also notable is the substantial gap between the peripheral data and the four more-central spectra [9]. Changes in fragmentation depend ver strongl on centralit near the transition point. It is remarkable that the trend at GeV/c corresponds closelo the trend at. GeV/c. Calculated FD ratio r ee (dash-dotted curve) corresponds to a parton spectrum cutoff shifted down to. GeV from GeV for p-p collisions, as shown in Fig. (first and second panels). The shift ma result from an increased hadron densit of states []. Figure (third panel) shows spectrum hard components H AA (solid curves) for five centralities from GeV Au-Au collisions [9]. The hard components of spectra scale proportional to n binar, as expected for parton scattering and fragmentation in A-A collisions (jets). The points are hard-component data from GeV NSD p-p collisions []. The dash-dotted curve is the standard Gaussian+tail model function H GG. Calculated FDs are also shown. The dashed curve is H NN vac, and the upper dotted curve is H ee med with q =., which nominall corresponds to the mostcentral Au-Au curve (-%). The parton spectrum cutoff for H ee med has been reduced from GeV ( =.) to. GeV ( =.) to match the central Au-Au hard component near =. The dotted curves labeled and (Au-Au centralities) are H ee med with cutoff parameters = ξ reduced to accommodate the data below =.. H pp, H AA and ratios based on the e-e in-vacuum reference are thus well described b pqcd FD ratio data from. to GeV/c [].
. Discussion This analsis establishes a quantitative correspondence between calculated pqcd FDs and measured spectrum hard components H xx over the entire fragment p t range and parton spectrum. We obtain direct access to medium-modified FFs and the underling parton spectrum. In p-p and in peripheral Au-Au collisions below a transition point at ν. the underling power-law parton spectrum terminates near GeV. Hard component H pp or H AA is strongl suppressed at smaller (jet bases excluded from the acceptance) corresponding to p- p FFs. The suppression mechanism ma be hard-pomeron (color singlet) exchange in N-N collisions leading to color connections different in p-p than in e-e collisions (which produce q- q color dipoles). Above the transition point: ) Measured H AA is strongl enhanced at smaller (FF bases partiall restored) but suppressed at larger (so-called jet quenching ), as observed in [9]. ) Corresponding calculated FDs can be generated b incorporating a medium-modified e-e FF scenario simple rescaling of e-e splitting functions which implies a three-fold increase in jet multiplicit compared to p- p FFs. ) The parton spectrum cutoff is reduced, b up to % in central Au-Au collisions impling a % increase in the jet cross section and minijet production. Evolution of H AA corresponds to two-particle correlations on (, ) []. Observed spectrum hard-component sstematics indicate that no partons are absorbed or lost to thermalization (no opaque core is formed). All scattered partons predicted b a pqcd differential cross section produce jet-correlated hadrons in the final state. The minimum-bias jet fragment ield in central Au-Au collisions full accounts for the increase of collision multiplicit beond participant scaling (soft component). There is also no indication from correlations, spectrum structure or integrated p t that parton spectra extend down to GeV as suggested b saturation-scale arguments [9, ]. 9. Summar Two-component decomposition of hadron spectra from p-p and Au-Au collisions isolates minimum-bias parton fragment distributions as spectrum hard components (H xx ) which can be estimated theoreticall b folding measured fragmentation functions (FFs) with a pqcd parton spectrum to produce calculated fragment distributions (FDs). In this analsis accurate parameterizations of p- p ande + -e FFs for a large range of parton energies are folded with a power-law parton spectrum with cutoff to produce calculated FDs which are compared with measured spectrum hard components from p-p collisions and from Au-Au collisions for several centralities. Comparisons reveal that FFs in p-p collisions are strongl suppressed for smaller fragment momenta (jet base suppressed). The suppression is possibl related to hard-pomeron exchange and resulting color-field deviations from q- q. Comparisons further indicate that above a specific Au- Au centralit (transition point) there is evolution toward e-e FFs as an asmptotic limit (jet base partiall restored). FFs are modified consistent with alteration of parton splitting. No partons are lost to absorption or thermalization (no opaque core ), and no significant parton energ is lost from integrated FFs. Perturbative QCD describes parton scattering and fragmentation in nuclear collisions over a large kinematic domain, and minijets dominate collision dnamics in all cases. The most dramatic alteration of parton fragmentation in A-A collisions occurs below p t = GeV/c.
This work was supported in part bhe Office of Science of the U.S. DoE under grant DE- FG-9ER References [] R. J. Porter and T. A. Trainor (STAR Collaboration), J. Phs. Conf. Ser., 9 (), hep-ph/. [] R. J. Porter and T. A. Trainor (STAR Collaboration), PoS C FRNC, (). [] J. Adams et al. (STAR Collaboration), Phs. Rev. C, 9 (). [] Q. J. Liu, D. J. Prindle and T. A. Trainor, Phs. Lett. B, 9 (). [] J. Adams et al. (STAR Collaboration), J. Phs. G: Nucl. Part. Phs., L (). [] J. Adams et al. (STAR Collaboration), J. Phs. G, (). [] M. Daugherit (STAR Collaboration), J. Phs. G, 9 (). [] J. Adams et al. (STAR Collaboration), Phs. Rev. D, (). [9] T. A. Trainor, Int. J. Mod. Phs. E, 99 (), arxiv:.. [] X. N. Wang, Phs. Rev. D, R9 (99); X. N. Wang and M. Gulass, Phs. Rev. D, (99). [] T. A. Trainor, arxiv:9.. [] T. A. Trainor and D. T. Kettler, Phs. Rev. D, (). [] W. Braunschweig et al. (TASSO Collaboration), Z. Phs. C, (99). [] M. Z. Akraw et al. (OPAL Collaboration) Phs. Lett. B,, (99). [] D. Acosta et al. (CDF Collaboration), Phs. Rev. D, (). [] K. Goulianos (CDF Collaboration), Proceedings of the QCD and high energ hadronic interactions, XXXII Rencontres de Moriond, Les Arces, France, March -9, 99, FERMILAB-CONF-9--E. [] D. Acosta et al. (CDF Collaboration), Phs. Rev. Lett. 9, (). [] A. Safonov (CDF Collaboration), Proceedings of the International Euroconference in Quantum Chromodnamics, Montpellier, France, Jul -, 999, CDF Note, October, 999. [9] F. Cooper, E. Mottola and G. C. Naak, Phs. Lett. B, (). [] C. Albajar et al. (UA Collaboration), Nucl. Phs. B 9, (9). [] I. Sarcevic, S. D. Ellis and P. Carruthers, Phs. Rev. D, (99). [] K. Kajantie, P. V. Landshoff and J. Lindfors, Phs. Rev. Lett. 9, (9). [] N. Borghini and U. A. Wiedemann, hep-ph/. [] A. Adare et al. (PHENIX Collaboration), Phs. Rev. D, (). [] C. Adler et al. (STAR Collaboration), Phs. Rev. Lett. 9, (). [] K. J. Eskola, K. Kajantie, P. V. Ruuskanen and K. Tuominen, Nucl. Phs. B, 9 ().