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M. Tokarev * & I. Zborovsky **

H igh - p T S pectra from RHIC & Q C D test of z -S caling * Joint Institute for Nuclear Research, Dubna, Russia ** Nuclear Physics Institute, Ř e ž near Prague, Czech Republic. M. Tokarev * & I. Zborovsky **. Contents. Motivation & goals

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M. Tokarev * & I. Zborovsky **

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  1. High-pT Spectra from RHIC & QCDtestofz-Scaling *Joint Institute for Nuclear Research, Dubna, Russia **Nuclear Physics Institute, Řež near Prague,Czech Republic M. Tokarev* & I. Zborovsky** ISMD'07, August 4-9, 2007, Berkeley, USA

  2. Contents • Motivation &goals • z-Scaling (ideas, definitions, properties,…) • RHIChigh-pT data&zpresentation • QCDtest ofz-scaling • Conclusions ISMD'07, August 4-9, 2007, Berkeley, USA

  3. Motivations & Goals • Development of a universal phenomenological description • of high-pT particle production in inclusive reactions to search for: • - new physics phenomena in elementary processes (quark compositeness, fractal space-time, extra dimensions, ...) • - signatures of exotic state of nuclear matter (phase transitions, quark-gluon plasma, …) • - complementary restrictions for theory (nonperturbative QCD effects, Standard Model, ...). • Analysis of new pp experimental data obtained at RHIC • to verify z-scaling observed at U70, ISR, SppS, and Tevatron • in high-pT particle production and predictions for LHC. – ISMD'07, August 4-9, 2007, Berkeley, USA

  4. Principles & Symmetries • C,P,T • Lorenz covariance • ……. • Relativity (special, general, scale,…) • Gauge invariance (U(1), SU(2), SU(3),…) • Self-similarity (hydro & aerodynamics, point explosions, critical phenomena,...) • Fractality (scale dependence,…) • Locality (constituent level of interactions,…) • ……. nano -9 pico -12 femto -15 = 1 fermi atto -18 zepto -21 1 fm ~ 0.2 /MeV RHIC ~50 GeV ~ 10^-3 fm Tevatron ~500 GeV ~ 10^-4 fm LHC ~5000 GeV ~ 10^-5 fm Guiding principles to discover new laws in Nature ISMD'07, August 4-9, 2007, Berkeley, USA

  5. Locality in inclusive reactions • Locality of hadron interactions: at sufficiently high energies hadrons and nuclei interact via interactionsoftheir constituents (partons, quarks and gluons,...). • Gross features of an inclusive particle distribution can be described in termsof thekinematiccharacteristics of the corresponding constituentsubprocesses (V.S. Stavinsky 1979). ISMD'07, August 4-9, 2007, Berkeley, USA

  6. Self-similarity principle • Self-similarity of hadron interactions reflects a property thathadron constituents, their interactions, and formation of the produced particles are similar. • The self-similarity is connected with dropping of certain dimensional quantities out of the description of physical phenomena. • Multiple interactionof theconstituents is an ensemble of mutually similar individual sub-processes. • These propertiesare common to various interactions of hadronsand nuclei at high energies. ISMD'07, August 4-9, 2007, Berkeley, USA

  7. Hadron/nucleus collisions at a constituent level M.T. & I.Zborovsky Part.Nucl.Lett.312(2006) PRD75,094008(2007) inclusive particle colliding object colliding object recoil particle Constituent subprocess • (x1M1) + (x2M2 ) Þ (m1/y1) + (x1M1+x2M2+m2 /y2) is subject to the kinematic condition: (x1P1+x2P2 –p/y1)2 = (x1M1+x2M2+m2/y2)2 ISMD'07, August 4-9, 2007, Berkeley, USA

  8. andWdepend on x1, x2, y Scaling variable z M.T. & I.Zborovsky Phys.At.Nucl.70,1294(2007) Phys.Rev.D75,094008(2007) • is transverse kinetic energy of the constituent subprocess consumed on production of m1 & m2 • Ω-1 is minimal resolution at which the subprocess can be singled out of the inclusive reaction • dNch /dη|0is multiplicity density of charged particles at η= 0 • c is a parameter interpreted as “heat capacity” of the created medium • m is arbitrary normalization (we fix it at the value of nucleon mass) ISMD'07, August 4-9, 2007, Berkeley, USA Principle of minimal resolution: The momentum fractions x1, x2 and y are determined in a way to minimize the resolution W-1 of the fractal measure z with respect to all constituent subprocesses taking into account the energy – momentum conservation:

  9. Ω&momentumfractions x1, x2, y1, y2 Principle of minimal resolution: The momentum fractions x1, x2 and y1, y2are determined in a way to minimize the resolution Ω-1of the fractal measure z with respect to all constituent sub-processes taking into account momentum conservation: Kinematic condition: ISMD'07, August 4-9, 2007, Berkeley, USA

  10. Transverse kinetic energy consumed on production of m1 & m2 energy consumed for the recoilparticle m2 energy consumed for the inclusive particle m1 Decomposition: ISMD'07, August 4-9, 2007, Berkeley, USA The variable z is expressed via momenta (P1 , P2 , p) and masses (M1 , M2 , m1) of colliding and produced particles and multiplicity particle density (dNch/dh| h=0).

  11. Scaling function Y(z) s1/2is the collision energy dN/dhis the pseudorapidity multiplicity density sinelis the inelastic cross section Jis the corresponding Jacobian is the inclusive cross section The variable z and the function Ψ(z) are expressed via momenta and masses of the colliding and produced particles, multiplicity density,and inclusive cross section. ISMD'07, August 4-9, 2007, Berkeley, USA The variable z is expressed via momenta (P1 , P2 , p) and masses (M1 , M2 , m1) of colliding and produced particles and multiplicity particle density (dNch/dh| h=0). Normalization equation The scaling function Y(z) is probability density to produce the inclusive particle with the formation length z.

  12. Normalization equation The scaling function Y(z) is probability density to produce the inclusive particle with the corresponding fractal measure z. ISMD'07, August 4-9, 2007, Berkeley, USA

  13. Fractality of hadron matter • Fractality is a specific feature connected with sub-structure ofthe interacting objects (hadrons and nuclei). Fractal compositeness includes sub-structure of hadron constituents over a wide scale range. • Fractality of soft processes concerning the multiparticle productionwasinvestigated by many authors (A.Bialas, R.Peshchanski, I.Dremin, E.DeWolf,…). • Fractality in hard processes regards fractal structure of the colliding objects and fractal character of particle formation. This aspect was specifically built into the definition of the scaling variable z. • Thevariablezis a fractal measure • which can be attributed to any inclusive reaction. ISMD'07, August 4-9, 2007, Berkeley, USA

  14. Properties of z-presentation in pp • Energy independence of Ψ(z) (s1/2 > 20GeV) • Angular independence of Ψ(z) (θcms>3-50,..) • Power law, Ψ(z) ~ z-β(z >4) • Multiplicity independence of Ψ(z) (dNch/dη=1.5-26.) • Flavor independence of Ψ(z) (π,K,…) These properties reflect self-similarity, locality, and fractality of the hadron interaction at constituent level. It concerns the structure of the colliding objects, interactions of their constituents, and fragmentation process. M.T., I.Zborovsky Phys.At.Nucl. 70,1294(2007) Phys.Rev. D75,094008(2007) ISMD'07, August 4-9, 2007, Berkeley, USA

  15. Spectra of charged hadrons in pp FNAL, ISR & RHIC STAR • Energy independence of Ψ(z) • Power behavior of Ψ(z) for z>4 • RHIC data are compatible with data from FNAL, ISR STAR J.Adams et al., PRL91, 172302(2003) ISMD'07, August 4-9, 2007, Berkeley, USA

  16. Spectra of π mesons in pp FNAL, ISR & RHIC STAR • Energy independence of Ψ(z) • Power behavior of Ψ(z) for z > 4 • RHIC data are compatible with data from FNAL, ISR STAR J.Adams et al., PL B637, 161 (2005) ISMD'07, August 4-9, 2007, Berkeley, USA

  17. Spectra of K mesons in pp FNAL, ISR & RHIC STAR STAR B.I.Abelev et l., PRC75 064901(2007) • Energy independence of Ψ(z) • Power behavior of Ψ(z) for z > 4 • RHIC data are compatible with data from FNAL, ISR R.Witt & STAR J.Phys.G31, S863, (2005) ISMD'07, August 4-9, 2007, Berkeley, USA

  18. Spectra of antiprotons in pp FNAL, ISR & RHIC STAR • Energy independence of Ψ(z) • Power behavior of Ψ(z) for z > 4 • RHIC data are compatible with data from FNAL, ISR STAR J.Adams et al., PL B616, 8 (2005) ISMD'07, August 4-9, 2007, Berkeley, USA

  19. θ0 Spectra of π mesons in pp ISR • Angular independence of Ψ(z) strong sensitivity to m2 & ε: m1=m2=mπ • Power behavior of Ψ(z) for z > 4 BS B.Alper et al., Nucl.Phys.B100, 237(1975) ISMD'07, August 4-9, 2007, Berkeley, USA

  20. θ0 Spectra of K mesons in pp ISR &RHIC BS British-Scandinavian CHLM CERN-Holland-Lund-Manchester CP CHICAGO-PRINCETON (CRONIN) SPEC D.Jaffe STAR BS B.Alper et al., Nucl.Phys.B100, 237(1975) • Angular independence of Ψ(z) strong sensitivity to m2 & ε: m1=m2=mK • Power behavior of Ψ(z) for z > 4 • RHIC data are compatible with data from ISR CHLM M.G.Albrow et al., Nucl.Phys.B56, 333(1973) ISMD'07, August 4-9, 2007, Berkeley, USA

  21. Measured multiplicity density dNch/dh inpp & ppis much more larger than dNch/dh/(0.5Np) in centralAAcollisions at AGS, SppS, and RHIC ¯ ¯ Multiplicity dependence of pp spectra Why is it interesting ? • Multiplicity density is a characteristic of medium (<pT>, εBj) • Regulator of modification of particle spectrum (high pT ) • Search for sensitive indicators of phase transition ISMD'07, August 4-9, 2007, Berkeley, USA

  22. z-Scaling & Entropy S Experimentally measurable quantities: σ, s1/2, N, dN/dη, … Model dependent quantities: T, p, V, c, μ, … Wis proportional to all parton and hadron configurations of he colliding system which can contribute to production of the inclusive particle with mass m1 and momentum p1 • The quantitiescanddNch/dη|0have physical meaning of “heat capacity” and “temperature” of the produced medium. • EntropySof the system depends on the resolutionΩ-1. • Maximal entropyS  minimal resolutionΩ-1. ISMD'07, August 4-9, 2007, Berkeley, USA

  23. KS0 Spectra vs. Multiplicity STAR &RHIC STAR nucl-ex/0403020 B.I.Abelev et al., PRC75 064901(2007) • Multiplicity independence of Ψ(z) • Power behavior of Ψ(z) for z > 4 • RHIC (STAR) data confirm Tevatron data (E735) M.T., I.Zborovsky Phys.At.Nucl. 70,1294(2007) Phys.Rev. D75,094008(2007) ISMD'07, August 4-9, 2007, Berkeley, USA

  24. Λ Spectra vs. Multiplicity STAR &RHIC • Multiplicity independence of Ψ(z) sensitivity to “heat capacity” c • Power behavior of Ψ(z) for z > 4 • RHIC data allow to fix the value of c STAR nucl-ex/0403020 B.I.Abelev et al., PRC75 064901(2007) ISMD'07, August 4-9, 2007, Berkeley, USA

  25. PHENIX π,K,Λ,.. Spectra vs. Flavor FNAL, ISR &RHIC Particle ratio is flat vs. pT pp ω/π0 = 0.81± 0.02±0.07 η/π0 = 0.48± 0.02±0.02 KS0 /π0= 0.45±0.01±0.05 pT >2-3 GeV/c nucl-ex/0702046 • Flavor independence ofΨ(z) • Power behavior ofΨ(z)for z > 4 • More convincing confirmation is needed ISMD'07, August 4-9, 2007, Berkeley, USA

  26. QCD test of z-scaling • QCD is basic theory for calculations of hadron interactions in terms of quarks and gluons. • Perturbative expansion is under control (LO, NLO, ...). • Non-perturbative effects – PDFs, FFs, μR, μF, μH, are partially under control. • Correct extrapolation in low and high (x,pT) range is restricted by available data (e+e–, DIS,…). • Additional constraints on PDFs and FFs are needed to confirm their universality (gluons, flavor, …). • Soft regime (multiple interactions, … ). • A lot of data are analyzed in framework of z–presentation. • New confirmations from RHIC and Tevatron are obtained. • Can NLO QCD describe z-scaling in soft and hard regime ? • ….. Hadron interaction at a constituent level ISMD'07, August 4-9, 2007, Berkeley, USA

  27. NLOQCDingredients • NLO QCD hadron production code (h±,π,K,…) F.Aversa, P.Chiappetta, M.Greco, J.Ph.Guillet • Parton Distribution Functions CTEQ5m – H.L.Lai et al., Pumplin et al., MRST99 – A.D.Martin, R.G.Roberts, W.J.Stirling, R.S.Thorne • Fragmentation Functions KKP–B.A.Kniehl, G.Kramer, B.Potter BKK – J.Binnewies, B.A.Kniehl, G.Kramer • Scales μ = c · pT, c = 0.5, 1., 2. – Renormalization μR – Factorization μF – Hadronization μH • NLO QCD hadron production code (h±,π,K,…) F.Aversa, P.Chiappetta, M.Greco, J.Ph.Guillet (PLB210,225(1988);B211,465(1988);NPB327,105(1989)) • Parton Distribution Functions CTEQ5m – H.L.Lai et al., Pumplin et al., MRST99 – A.D.Martin, R.G.Roberts, W.J.Stirling, R.S.Thorne (Eur.Phys.J.C14,133(2000)) • Fragmentation Functions KKP–B.A.Kniehl, G.Kramer, B.Potter BKK – J.Binnewies, B.A.Kniehl, G.Kramer • Scales μ = c · pT, c = 0.5,1,2 – Renormalization μR – Factorization μF – Hadronization μH ISMD'07, August 4-9, 2007, Berkeley, USA

  28. h ± NLOQCDspectra in z-presentation • Strong dependence of spectra on energys1/2at high pT • Sensitivity toPDFs &FFs • Sensitivity toμR, μF, μHscales • NLOQCDresults are in agreement with exp. data • Different extrapolation of spectra predicted by NLOQCDand z-scaling ISMD'07, August 4-9, 2007, Berkeley, USA

  29. π± NLOQCDspectra in z-presentation • Features of π and h± spectra are similar • Available data are in agreement with NLOQCD • z-presentation of NLO QCDcalculated results indicates deviation from asymptotic behavior of Ψ(z) predicted by z-scaling ISMD'07, August 4-9, 2007, Berkeley, USA

  30. K± NLOQCD spectra in z-presentation • Features of K and h±,π spectra are similar • Available data are in agreement with NLOQCD • Asymptotic behavior of the scaling function Ψ(z) is not reproduced by NLO QCDevolution of spectra ISMD'07, August 4-9, 2007, Berkeley, USA

  31. Conclusions (I) • New analysis of FNAL, ISR, and RHIC data on high-pT hadron spectra in the framework of z-scaling is performed. • Properties of z-presentation are confirmed. • STARdata on multiplicity dependence of KS0& Λspectrainpp collisions give new insight on “heat capacity” c and fractal dimension ε. • z-Scaling is tested by NLO QCD: - Self-similar features of particle production dictated by z-scaling give restriction on the asymptotic behavior of inclusive spectra in high-pT region. - They are not reproduced by NLO QCD evolution of spectra with available PDFs and FFs in TeV energy range. ISMD'07, August 4-9, 2007, Berkeley, USA

  32. Conclusions (II) • z-scaling in pp collisions is a regularity which reflects self-similarity, locality, and fractality of the hadron interactions at a constituent level. It concerns the structure of colliding objects, interactions of their constituents, and fragmentation process. • New experimental data on particle spectra over a wide range of collision energy, transverse momenta, production angle, and multiplicity density in pp collisions allow us to search for new phenomena in extreme conditions at RHIC. ISMD'07, August 4-9, 2007, Berkeley, USA

  33. Thank You for Your Attention ISMD'07, August 4-9, 2007, Berkeley, USA

  34. Spectra ratio vs. pT & multiplicity KS0 STAR B.I.Abelev et al., PRC75 064901(2007) The ratio of multiplicity binned pT spectra to multiplicity- integrated spectra scaled by mean multiplicity for each bin for KS0 and Λ is sensitive to dNch/dη for high pT (Rpp > 10) ISMD'07, August 4-9, 2007, Berkeley, USA

  35. Scaling analysis in high energy interactions transverse mass Feynman variable Scaling variables radial scaling variable light-cone variable Bjorken variable KNO variable • These scaling regularities have restricted range of validity • Violation of the scaling laws can be indication of new physics z-Scaling: it provides universal description of inclusive particle cross sections over a wide kinematical region (central+fragmentation region, pT > 0.5 GeV/c, s1/2 > 10 GeV ) ISMD'07, August 4-9, 2007, Berkeley, USA

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