1. Z M.Tokarev ISMD2005, Kroměříž Verification of Z scaling in pp collisions at RHIC M. Tokarev (JINR,Dubna ) & I. Zborovský (NPI, Řež)

2. Z M.Tokarev ISMD2005, Kroměříž Outline  Introduction (motivation and goals)  Z-scaling & ideas and definitions  Properties of the scaling function  (z)  Z-scaling in pp collisions at RHIC (analysis of h ±,π 0,η,  0,K S,K *,φ, Λ,Ξ,γ spectra)  Multiplcity dependence of Z-scaling  Summary ¯ ¯

3. Z M.Tokarev ISMD2005, Kroměříž 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 > 11 GeV ) Scaling variables The scaling regularities have restricted range of validity light-cone variable radial scaling variable Feynman variable transverse mass Bjorken variable

4. Z M.Tokarev ISMD2005, Kroměříž Motivation & Goals Development of 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. ¯

5. Z M.Tokarev ISMD2005, Kroměříž T he scaling variable z depends on: 1. Reaction characteristics (A 1, A 2,  s) 2. Characteristics of the inclusive particle (m, E,  ) 3. Dynamical characteristics of the interaction (dN/d ,...) 4. Structural characteristics of the interacting objects (      ε) Self-similarity in inclusive particle production at high energies The self-similarity parameter z is specific dimensionless combination of quantities which characterize particle production in high energy inclusive reactions. It depends on momenta and masses of the colliding and inclusive particles, multiplicity density and fractal dimensions of the interacting objects. Search for self-similar solutions (inclusive cross sections) expressed via a scaling function Ψ(z). Self-similarity principle The self-similarity is property connected with dropping of certain dimensional quantities out of description of physical phenomena. Self-similarity parameters are constructed as combinations of these quantities.

6. Z M.Tokarev ISMD2005, Kroměříž Gross features of inclusive particle distributions for the reaction are expressed in terms of the constituent sub-process Locality of the hadronic interactions at constituent level is expressed by the 4-momentum conservation law Momentum fractions and are determined in a way to minimize the resolution of the fractal measure. Locality principle V.S.Stavinsky, A.M.Baldin,…

7. Z M.Tokarev ISMD2005, Kroměříž Fractality principle Principle of fractality states that variables used in description of the processes diverge in terms of resolution. The scaling variable z = z 0 Ω -1 is fractal measure depending on the resolution    with respect to all constituent subprocesses in which the inclusive particle with the momentum p can be produced. p z(Ω)→∞ for Ω→0 Fractality in soft processes: A.Bialas, R.Peschanski, A.Bershadskii, I.M.Dremin, E.De Wolf, V.Khoze, W.Kittel, … We consider structural particles (hadrons, nuclei,…) as fractal objects revealing structure at small scales

8. Z M.Tokarev ISMD2005, Kroměříž Charged hadrons   JetsDi-Jets Direct photons High-p T hadrons Jets Direct photons D-Y lepton pairs W ±, Z 0 -bosons Heavy quarkonia High-p T regime is well controled by pQCD Self-similarity, locality and fractality in hard processes Phys. Rev. D54 (1996) 5548. Phys. Rev. C59 (1999) 2227. Int. J. Mod. Phys. A15 (2000) 3495. J.Phys.G:Nucl.Part.Phys.26(2000)1671. Int. J. Mod. Phys. A16 (2001) 1281. Acta Physica Slovaca 54 (2004) 321. Sov.J.Nucl.Phys. 67 (2004) 583. Sov.J.Nucl.Phys. 68 (2005) 404.

9. Z M.Tokarev ISMD2005, Kroměříž Scaling variable Z  is the transverse energy of the subprocess  dN/d  is the multiplicity density at      is resolution with respect to constituent subprocess and  depend on x 1 and x 2 Principle of minimal resolution: Momentum fraction x 1 and x 2 are determined in a way to minimize the resolution   with respect to all constituent subprocesses taking into account energy-momentum conservation law. Momentum fractions x 1,2 consist of  dependent and independent parts (  decomposition)

10. Z M.Tokarev ISMD2005, Kroměříž Transverse energy of subprocess transverse energy of inclusive particle transverse energy of recoil particle 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 charged particle multiplicity density (dN/d   

11. Z M.Tokarev ISMD2005, Kroměříž Fractal property of the scaling variable z has character of a fractal measure For a given production process, the finite part z 0 is ratio of the transverse energy released in the underlying collision of constituents and the average multiplicity density dN/d   The divergent part   describes resolution at which the collision of the constituents can be singled out of this process.    and    are anomalous fractal dimensions of the colliding objects (hadrons or nuclei). is relative number of all initial configurations containing the constituents which carry the fractions x 1 and x 2 of the incoming momenta P 1 and P 2.

12. Z M.Tokarev ISMD2005, Kroměříž Scaling function  z  Normalization equation The scaling function  z  is probability density to produce inclusive particle with formation length z. s 1/2 is the colliding energy dN/d  (s) is the pseudorapidity multiplicity density   inel (s)  is the inelastic cross section is the inclusive cross section J is the corresponding Jacobian

13. Z M.Tokarev ISMD2005, Kroměříž Properties of z-presentation of experimental data Confirmation of these properties is possible at RHIC, Tevatron and LHC  Energy independence of  (z)  Angular independence of  (z)  Power behavior  (z) ~ z -   A-dependence of  (z)  F-dependence of  (z)  Multiplicity independence of Ψ(z) The scaling function reveals power asymptotic regime. The scaling function has same shape for different s 1/2. The scaling function has same shape for different  . The scaling function has same shape for different nuclei. Same asymptotics of the scaling function for different secondaries. Same shape of Ψ(z) for different multiplicities.

14. Z M.Tokarev ISMD2005, Kroměříž Relativistic Heavy Ion Collider, RHIC 3.83 km circumference Two separated rings 120 bunches/ring 106 ns bunch crossing time A+A, p+A, p+p Maximum Beam Energy : 500 GeV for p+p 200A GeV for Au+Au Luminosity Au+Au: 2 x 10 26 cm -2 s -1 p+p : 2 x 10 32 cm -2 s -1 Beam polarizations P=70% Upton, Long Island, New York PP2PP RHIC

15. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC Charged hadron production in pp collisions from STAR STAR confirms Z-scaling Phys.Rev.Lett. 91 (2003) 172302 RHIC Tevatron ISR U70 RHIC Z-scaling at RHIC& Non-single diffractive data from STAR Charged hadron production in pp collisions

16. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC   -meson production in pp collisions from PHENIX PHENIX Collaboration S.S.Adler et al., Phys.Rev.Lett. 91(2003)241803 ISR RHIC ISR RHIC M.T., Dedovich, O.Rogachevsky J.Phys.G:Nucl.Part. Phys.26(2000)1671 PHENIX confirms Z-scaling The cross section Ed 3  /dp 3 vs. p T. Energy independence of  (z) is observed up to z ≈ 30. Power law  (z) ~ z -  is observed for z > 4. The scaling function  (z) vs. z. PHENIX   →  (135 MeV/c2, 251Å, 98.8%),    →  m=135 MeV c  = 251Å Br = 98.8% S.S.Adler et al., PRL 91 (2003) 241803 H.Büschening, DNP-Chicago, Oct.2004. D.d’Enterria, Hard Probes, Ericeira, Portugal, Nov.7, 2004 D.d’Enterria H.Büschening, Hard Probes, Portugal, Nov.8, 2004

17. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC  -meson production in pp collisions from PHEINX PHENIX Collaboration D.d’Enterria, Hard Probes’04, November, 2004, Ericeira, Portugal M.T., T.Dedovich, O.Rogachevsky J.Phys.G:Nucl.Part. Phys.26(2000)1671 PHENIX confirms Z-scaling The cross section Ed 3  /dp 3 vs. p T. Energy independence of  (z) is observed up to z ≈ 20. Power law  (z) ~ z -  is observed for z > 4. The scaling function  (z) vs. z. RHIC PHENIX  (547 MeV/c2, 11Å, 39.2%),  →  m=547 MeV c  = 11 Ǻ Br = 38.8% RHIC PHENIX Collaboration H.Hiejima, QM’04, January, 2004, Oakland, USA

18. Z M.Tokarev ISMD2005, Kroměříž STAR measures the strange particle spectra with great improvement in statistical errors Transverse momentum spectra of strange particles in pp collisions at STAR Figure1. Invariant p T spectra for  and   +   for the top 5% central Au-Au data and p-p minbias. The p-p data is scaled by a factor of 10 for clarity. STAR collaboration M.Heinz (University of Bern) 40 th Rencontres de Moriond, 12-19 March, 2005, La Thuile, Italy H. Cines Yale University for the STAR Collaborations “Quark Matter 2005”, 4-9 August, 2005, Budapest, Hungary  Mechanism of strange mesons and baryons production in pp collisions  s & s PDF’s and FF’s  pp data are baseline for understanding of particle production in nuclear medium ¯

19. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC K + & K S 0 - meson production in pp collisions at high-p T  Shape of Ψ(z) for K + & K S 0  F-dependence of  z   High-p T asymptotic of K S 0 Experimental data: J.W. Cronin et.al., Phys. Rev. D11 (1975) 3105. D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. D.E. Jaffe et al., Phys. Rev. D40 (1989) 2777. B.Alper et al., Nucl. Phys. B87 (1975) 19.  (z) vs. z Ed 3  /dp 3 vs. p T STAR Collaboration J. Adams & M. Heinz, QM’04, January, 2004, Oakland, USA (nucl-ex/0403020) RHIC Indication on validity of Z-scaling for K S 0 K S 0 →  +  - (494 MeV/c2, 2.7cm, 68.6%)  S  →     m= 494MeV c  = 2.67 cm Br = 68.6%

20. Z M.Tokarev ISMD2005, Kroměříž M.Tokarev T.Dedovich O.Rogachevsky J.Phys.G:Nucl.Part. Phys.26(2000)1671 Predictions based on STAR data Z-scaling at RHIC   -hyperon production in pp collisions from STAR STAR Collaboration J. Adams & M. Heinz, QM’04, January, 2004, Oakland, USA (nucl-ex/0403020) STRANGENESS origin in anti-hyperons The cross section Ed 3  /dp 3 vs. p T The scaling function  (z) vs. z F-dependence of  (z) Energy independence of  (z) F-dependence of Ψ(z) Power law,  (z) ~ z -     p    GeV/c2, 7.9cm, 63.9%),    → p   m=1.12 GeV c  = 7.89 cm Br = 63.9% Λ 0 (uds)

21. Z M.Tokarev ISMD2005, Kroměříž STAR Collaboration R.Witt et al., nucl-ex/0403021 RHIC can test Z-scaling at s 1/2 = 50-500 GeV Energy independence of  (z) Power law,  (z) ~ z -  Z-scaling at RHIC   -hyperon production in pp collisions from STAR STRANGENESS origin in baryons The cross section Ed 3  /dp 3 vs. p T The scaling function  (z) vs. z F-dependence of  (z) Ξ - →  - (1.32 GeV/c2, 4.9cm, 99.9%)   →   m=1.32 GeV c  = 4.91 cm Br = 99.9% B.Bezverkhny, Yale University (for the STAR Collaborations) “Quark Matter 2005”, 4-9 August, 2005, Budapest, Hungary STAR Collaborations B.Bezverkhny (Yale University) “Quark Matter 2005”, 4-9 August, 2005, Budapest, Hungary Ξ - (ssd)

22. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC  -meson production in pp collisions from STAR STAR Collaboration J.Adams et al., nucl-ex/0406003 M.Tokarev T.Dedovich O.Rogachevsky J.Phys.G:Nucl.Part. Phys.26(2000)1671 The cross section Ed 3  /dp 3 vs. p T The scaling function  (z) vs. z F-dependence of  (z) STAR  →K + K - (1.02 GeV/c2, 280fm, 49.1%)  →K + K – m=1.02 GeV c  = 44 fm Br = 49.1%  (ss) ¯ Predictions based on STAR data STRANGENESS origin in  meson Energy independence of  (z) F-dependence of Ψ(z) Power law,  (z) ~ z - 

23. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC   -meson production in pp collisions from STAR STAR Collaboration J.Adams et al., nucl-ex/0412019 Energy independence of  (z) F-dependence of Ψ(z) Power law,  (z) ~ z -  RHIC can verify Z-scaling Origin of vector mesons The cross section Ed 3  /dp 3 vs. p T The scaling function  (z) vs. z F-dependence of  (z)   →K π m=892 MeV c  ≈ 3.9 fm Br ≈ 100% STAR

24. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC   -meson production in pp collisions from STAR STAR Collaboration J.Adams et al., Phys. Rev. Lett. 92 (2004) 092301 Energy independence of  (z) F-dependence of Ψ(z) Power law,  (z) ~ z -  RHIC can verify Z-scaling  Origin of vector mesons  Probe of nuclear matter The cross section Ed 3  /dp 3 vs. p T The scaling function  (z) vs. z F-dependence of  (z)   → π + π – m=770 MeV c  = 1.3 fm Br ≈ 100% STAR

25. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC  - -meson production in pp collisions at high-p T  Energy scaling (up to z ≈ 30)  Power law  z  z  (z > 4) The scaling function  (z) vs. z. Experimental data: J.W. Cronin et.al., Phys. Rev. D11 (1975) 3105. D. Antreasyan et al., Phys. Rev. D19 (1979) 764. V.V. Abramov et al., Sov. J. Nucl. Phys. 41 (1985) 357. D.E. Jaffe et al., Phys. Rev. D40 (1989) 2777. The cross section Ed 3  /dp 3 vs. p T. STAR Collaboration, O.Barannikova, QM’05, August, 2005, Budapest, Hungary PHENIX Collaboration, M. Harvey, QM’04, January, 2004, Oakland, USA RHIC +, K+, P+, K+, P  -, K -, P Spectra of ID’d hadrons at high p T STAR & PHENIX The scaling function  (z) vs. zThe cross section Ed 3  /dp 3 vs. p T 1/2πp T d 2 N/dp T dy, (GeV/c) -2 RHIC confirms Z-scaling

26. Z M.Tokarev ISMD2005, Kroměříž Direct photon production  Parton Distribution & Fragmentation Functions are taken from DIS & e + e -  Deviation from NLO QCD fit to data is signature of new physics Fragmentation Process photon Direct Process photon Compton/Annihilation process

27. Z M.Tokarev ISMD2005, Kroměříž The cross section Ed 3  /dp 3 vs. p T.The scaling function  (z) vs. z.  Energy independence of  (z)  Power law,  (z) ~ z -  Z-scaling at SppS and Tevatron in Run I,II Direct photon production in pp collisions ¯ ¯ M.T. E.Potrebenikova JINR E2-98-64 Comput.Phys.Com. 117 (1999) 229 M.T. G.Efimov hep-ph/0209013 M.T. G.Efimov D.Toivonen Sov.J.Nuc.Phys. 67 (2004) 583 Don Lincoln (for the DØ & CDF collaborations) “XXV Physics in Collision 2005”, 6-9 July, 2005, Prague, Czech Republic  Energy dependence of spectra  Power law, slope parameter depends on s 1/2 and p T

28. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC Direct photon production in pp collisions from PHENIX PHENIX Collaboration K.Okada, “Spin 2004”, October 11-16, 2004, Trieste, Italy hep-ex/0501066 ISR RHIC ISR RHIC M.T., Dedovich, O.Rogachevsky J.Phys.G:Nucl.Part. Phys.26(2000)1671  NLO pQCD describes data within exp. errors  Sensitivity of data to properties of z-presentation The cross section Ed 3  /dp 3 vs. p T Energy independence of  (z) is observed up to z ≈ 30. Power law  (z) ~ z -  is observed for z > 5. The scaling function  (z) vs. z PHENIX RHIC

29. Z M.Tokarev ISMD2005, Kroměříž Medium produced in pp & AA collisions  Particle multiplicity  Multiplicity density dN ch /d   Mean transverse momentum  Energy density  Bj  R 2  ) dE T /dy 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 ¯ ¯  Is medium produced in pp collisions at high dN ch /d  similar to nuclear medium created in central AA ?  Are there general properties of particle production mechanism in pp & AA ?

30. Z M.Tokarev ISMD2005, Kroměříž Multiplicity selection of events  low p T spectra → exponential law  multiplicity evolution of hadronization  “invisible” quark & gluon degrees of freedom ↔ no constituent structure  high p T spectra → power law  p T evolution of hadronization  constituent structure is visible  Multiplicity density dN ch /d  is characteristic of nuclear medium  Modification of particle spectra with multiplicity density, R AA (p T ) & R CP (p T )  Multiplicity density ~ gluon density at small x → saturation regime (CGC, QGP) Quarks & Gluons Mesons & Baryons Central Au-Au s 1/2 =200 GeV RHIC & STAR pp s 1/2 = 200 GeV L.McLerran, D.Kharzeev,…

31. Z M.Tokarev ISMD2005, Kroměříž Generalized scaling variable z  is minimal transverse energy of the subprocess  dN/d  is the multiplicity density at      is resolution with respect to constituent subprocesses  y is momentum fraction of secondary parton carried out by inclusive particle 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: M.T., I.Zborovsky hep-ph/0506003

32. Z M.Tokarev ISMD2005, Kroměříž Scaling variable z & entropy S  is minimal transverse energy of the subprocess  dN/d   is multiplicity density at      is fractal resolution with respect to constituent subprocesses  W is relative number of all configurations in the colliding system from which the inclusive particle with the momentum p can be produced Entropy Statistical Thermodynamical  The quantities c and dN/dη| 0 have physical meaning of “heat capacity” and “temperature” of medium, respectively.  Entropy of medium decreases with increasing resolution Ω -1. The specific heat calculated from multifractal analysis of hadron and nucleus interactions can be used as a universal characteristic of the multiple production. A.Bershadskii, Physica A253 (1998) 23.

33. Z M.Tokarev ISMD2005, Kroměříž  Strong multiplicity dependence of high p T spectrum  Sensitivity of  (z) to parameter c: z ~ (dN/dη) –c E735 Collaboration T.Alexopoulos et al., Phys. Lett. B336 (1994) 599. E735 c=0.25 |η|<3.25  Strong dependence of high p T spectra on multiplicity  Sensitivity of  (z) to the resolution Ω -1 : z ~ Ω –1  Sensitivity of  (z) to heat capacity c: z ~ (dN/dη) – c CDF c=0.25 CDF Collaboration D.Acosta et al., Phys. Rev. D65 (2002) 072005. UA1 c=0.25 |η|<2.5 UA1 Collaboration G. Arnison et al., Phys. Lett. B118 (1982) 167. Multiplicity  independence of Z-scaling  Charged hadron production in pp collisions at Tevatron and SppS ¯ ¯

34. Z M.Tokarev ISMD2005, Kroměříž Multiplicity independence of Z-scaling at RHIC Charged hadron spectra vs. dN ch /d  in pp collisions from STAR STAR Collaboration J.E.Gans, PhD Thesis, Yale University, USA (2004).  Sensitivity of cross section to multiplicity density at high p T  Self-similarity & fractality are reflected in processes with high multiplicities in pp and pp collisions at high p T M.T., I.Zborovsky hep-ph/0506003 STAR c=0.25 Independence of heat capacity c on energy and multiplicity over a wide p T range is confirmed by UA1, E735, CDF and STAR data. ¯

35. Z M.Tokarev ISMD2005, Kroměříž Z-scaling at RHIC Multiplicity dependence of  charged hadron spectra in pp collisions E735 Collaboration, T.Alexopoulos et al., Phys. Lett. B336 (1994) 599. STAR Collaboration, J.E.Gans, PhD Thesis, Yale University, USA (2004). Z-scaling at RHIC Multiplicity dependence of  charged hadron spectra in pp collisions  The same asymptotics for pp & pp at low z  Coincidence of Ψ(z) in the overlapping range  Power law, Ψ(z) ~ z –β, at high z  dependence vs. dN ch /dη and energy s 1/2 ¯  The same asymptotics for pp & pp at low z  Coincidence of Ψ(z) in the overlapping range  Power law, Ψ(z) ~ z –β, at high z  z-p T plot & kinematical region to search for new physics  dependence vs. multiplicity dN/dη and energy s 1/2 ¯

36. Z M.Tokarev ISMD2005, Kroměříž STAR preliminary   spectrum A.Suaide RHIC Z-scaling is manifestation of principles Self-similarity & Fractality Translation & Dilatation Structure of colliding objects (hadrons and nuclei), constituent interactions and mechanism of particle formation reveal self-similarity and fractality over a wide scale range. Established properties could give new constraints on phenomenological models and mechanisms of particle production. pp data is a reference for search for new physics phenomena in hadron and nucleus interactions at high energies. ? ? substructure collective phenomena

37. Z M.Tokarev ISMD2005, Kroměříž Summary Z-scaling is a tool to search for new phenomena in high-p T and high multiplicity particle production in pp & pp collisions at the RHIC, Tevatron and LHC ¯ Z-scaling is specific feature of high-p T particle production established in pp and pp collisions. Z-scaling is observed in numerous high-p T data obtained at the U70, ISR, SppS, Tevatron and RHIC. New data on particle (h ±,π,η,  0,K S,K *,φ, Λ, Ξ,γ) spectra obtained in pp collisions at RHIC were analyzed. Confirmation of Z-scaling is obtained. Multiplicity independence of Z-scaling is established. Predictions of high-p T particle cross sections at RHIC energies are presented. ¯ ¯ Z-scaling gives possibility to study self-similarity and fractality and search for new symmetries related to structure of particles and space-time at small scales.

38. Z M.Tokarev ISMD2005, Kroměříž Thank You for Your Attention We are grateful for fruitful collaboration to our collegues Yu.Panebratsev, G.Skoro, O.Rogachevsky, T.Dedovich, D.Toivonen

39. Z M.Tokarev ISMD2005, Kroměříž Back-up slides

40. Z M.Tokarev ISMD2005, Kroměříž Don Lincoln (for the DØ & CDF collaborations) “XXV Physics in Collision 2005”, 6-9 July, 2005, Prague, Czech Republic Jets at Tevatron in Run II CDF & D0 confirm Z-scaling M. T. T. Dedovich Int. J. Mod. Phys. A15 (2000) 3495 CDF & D0 data are described by NLO QCD very well