ISMD'07, August 4-9, 2007, Berkeley, USA 1 High-p T Spectra from RHIC & QCD test of z-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  Motivation & goals  z-Scaling (ideas, definitions, properties,…)  RHIC high-p T data & z presentation  QCD test of z-scaling  Conclusions Contents

ISMD'07, August 4-9, 2007, Berkeley, USA 3 Motivations & Goals Development of a universal phenomenological description of high-p T 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-p T particle production and predictions for LHC. –

ISMD'07, August 4-9, 2007, Berkeley, USA 4 Principles & Symmetries  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,…)  ……. Guiding principles to discover new laws in Nature  C,P,T  Lorenz covariance  ……. nano -9 pico -12 femto -15 = 1 fermi atto -18 zepto fm ~ 0.2 /MeV RHIC ~50 GeV ~ 10^-3 fm Tevatron ~500 GeV ~ 10^-4 fm LHC ~5000 GeV ~ 10^-5 fm

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 interactions of their constituents (partons, quarks and gluons,...).  Gross features of an inclusive particle distribution can be described in terms of the kinematic characteristics of the corresponding constituent subprocesses (V.S. Stavinsky 1979).

ISMD'07, August 4-9, 2007, Berkeley, USA 6 Self-similarity principle  Self-similarity of hadron interactions reflects a property that hadron 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 interaction of the constituents is an ensemble of mutually similar individual sub-processes.  These properties are common to various interactions of hadrons and nuclei at high energies.

ISMD'07, August 4-9, 2007, Berkeley, USA 7 Constituent subprocess m 1 π+ π+ π- π- K + K - p - Λ0 Λ0 γ m 2 m n -m p mπmπ m Λ -m p m K m p m K -m p 0  (x 1 M 1 ) + (x 2 M 2 )  m 1 /y 1  + (x 1 M 1 +x 2 M 2 +m 2 /y 2 ) (x 1 P 1 +x 2 P 2 –p/y 1 ) 2 = (x 1 M 1 +x 2 M 2 +m 2 /y 2 ) 2 is subject to the kinematic condition: 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

ISMD'07, August 4-9, 2007, Berkeley, USA 8 Scaling variable z and  depend on x 1, x 2, y Principle of minimal resolution: The momentum fractions x 1, x 2 and y are determined in a way to minimize the resolution   of the fractal measure z with respect to all constituent subprocesses taking into account the energy – momentum conservation:  is transverse kinetic energy of the constituent subprocess consumed on production of m 1 & m 2  Ω -1 is minimal resolution at which the subprocess can be singled out of the inclusive reaction  dN ch /dη| 0 is 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) M.T. & I.Zborovsky Phys.At.Nucl.70,1294(2007) Phys.Rev.D75,094008(2007)

ISMD'07, August 4-9, 2007, Berkeley, USA 9 Ω & momentum fractions x 1, x 2, y 1, y 2 Principle of minimal resolution: The momentum fractions x 1, x 2 and y 1, y 2 are determined in a way to minimize the resolution Ω -1 of 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 m 1 & m 2 energy consumed for the inclusive particle m 1 energy consumed for the recoil particle m 2 The variable z is expressed via momenta (P 1, P 2, p) and masses (M 1, M 2, m 1 ) of colliding and produced particles and multiplicity particle density (dN ch /d    Decomposition:

ISMD'07, August 4-9, 2007, Berkeley, USA 11 Scaling function  z  Normalization equation The scaling function  z  is probability density to produce the inclusive particle with the formation length z. s 1/2 is the collision energy dN/d  is the pseudorapidity multiplicity density   inel  is the inelastic cross section is the inclusive cross section J is the corresponding Jacobian           The variable z is expressed via momenta (P 1, P 2, p) and masses (M 1, M 2, m 1 ) of colliding and produced particles and multiplicity particle density (dN ch /d    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 12 Normalization equation The scaling function  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 of the 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 production was investigated 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. The variable z is 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) (s 1/2 > 20 GeV)  Angular independence of Ψ(z) (θ cms >3-5 0,..)  Power law, Ψ(z) ~ z -β (z >4)  Multiplicity independence of Ψ(z) (dN ch /dη= )  Flavor independence of Ψ(z) (π,K,…) M.T., I.Zborovsky Phys.At.Nucl. 70,1294(2007) Phys.Rev. D75,094008(2007) 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.

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

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

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

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

ISMD'07, August 4-9, 2007, Berkeley, USA 19 θ 0 Spectra of π mesons in pp  Angular independence of Ψ(z) strong sensitivity to m 2 & ε: m 1 =m 2 =m π  Power behavior of Ψ(z) for z > 4 ISR BS B.Alper et al., Nucl.Phys.B100, 237(1975)

ISMD'07, August 4-9, 2007, Berkeley, USA 20 θ 0 Spectra of K mesons in pp  Angular independence of Ψ(z) strong sensitivity to m 2 & ε: m 1 =m 2 =m K  Power behavior of Ψ(z) for z > 4  RHIC data are compatible with data from ISR ISR & RHIC STAR BS B.Alper et al., Nucl.Phys.B100, 237(1975) CHLM M.G.Albrow et al., Nucl.Phys.B56, 333(1973) BS British-Scandinavian CHLM CERN-Holland-Lund-Manchester CP CHICAGO-PRINCETON (CRONIN) SPEC D.Jaffe

ISMD'07, August 4-9, 2007, Berkeley, USA 21 Multiplicity dependence of pp spectra Why is it interesting ? Measured multiplicity density dN ch /d  in pp & pp is much more larger than dN ch /d  /(0.5N p ) in central AA collisions at AGS, SppS, and RHIC ¯ ¯  Multiplicity density is a characteristic of medium (, ε Bj )  Regulator of modification of particle spectrum (high p T )  Search for sensitive indicators of phase transition

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

ISMD'07, August 4-9, 2007, Berkeley, USA 23 K S 0 Spectra vs. Multiplicity  Multiplicity independence of Ψ(z)  Power behavior of Ψ(z) for z > 4  RHIC (STAR) data confirm Tevatron data (E735) STAR & RHIC M.T., I.Zborovsky Phys.At.Nucl. 70,1294(2007) Phys.Rev. D75,094008(2007) STAR nucl-ex/ B.I.Abelev et al., PRC (2007)

ISMD'07, August 4-9, 2007, Berkeley, USA 24 Λ Spectra vs. Multiplicity  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 & RHIC STAR nucl-ex/ B.I.Abelev et al., PRC (2007)

ISMD'07, August 4-9, 2007, Berkeley, USA 25 π,K,Λ,.. Spectra vs. Flavor FNAL, ISR & RHIC PHENIX Particle ratio is flat vs. p T  Flavor independence of Ψ(z)  Power behavior of Ψ(z) for z > 4  More convincing confirmation is needed ω/π 0 = 0.81± 0.02±0.07 η/π 0 = 0.48± 0.02±0.02 K S 0 /π 0 = 0.45±0.01±0.05 p T >2-3 GeV/c nucl-ex/ pp

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, μ R, μ F, μ H, are partially under control.  Correct extrapolation in low and high (x,p T ) 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 NLO QCD ingredients  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 · p T, c = 0.5, 1., 2. – Renormalization μ R – Factorization μ F – Hadronization μ H  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 · p T, c = 0.5,1,2 – Renormalization μ R – Factorization μ F – Hadronization μ H

ISMD'07, August 4-9, 2007, Berkeley, USA 28 h ± NLO QCD spectra in z-presentation  Strong dependence of spectra on energy s 1/2 at high p T  Sensitivity to PDFs & FFs  Sensitivity to μ R, μ F, μ H scales  NLO QCD results are in agreement with exp. data  Different extrapolation of spectra predicted by NLO QCD and z-scaling

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

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

ISMD'07, August 4-9, 2007, Berkeley, USA 31 Conclusions (I)  New analysis of FNAL, ISR, and RHIC data on high-p T hadron spectra in the framework of z-scaling is performed.  Properties of z-presentation are confirmed.  STAR data on multiplicity dependence of K S 0 & Λ spectra in pp 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-p T 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. p T & multiplicity The ratio of multiplicity binned p T spectra to multiplicity- integrated spectra scaled by mean multiplicity for each bin for K S 0 and Λ is sensitive to dN ch /dη for high p T (R pp > 10) STAR B.I.Abelev et al., PRC (2007) KS0KS0

ISMD'07, August 4-9, 2007, Berkeley, USA 35 Scaling analysis in high energy interactions z-Scaling: it provides universal description of inclusive particle cross sections over a wide kinematical region (central+fragmentation region, p T > 0.5 GeV/c, s 1/2 > 10 GeV ) Scaling variables light-cone variable radial scaling variable Feynman variable transverse mass Bjorken variable  These scaling regularities have restricted range of validity  Violation of the scaling laws can be indication of new physics KNO variable