verification of z scaling in pp collisions at rhic

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M.Tokarev ISMD2005, Kroměříž

Verification of Z scaling in pp collisions at RHIC

M. Tokarev (JINR,Dubna) & I. Zborovský (NPI, Řež)

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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±,π0,η,0,KS,K*,φ, Λ,Ξ,γ spectra) Multiplcity dependence of Z-scaling Summary

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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, pT > 0.5 GeV/c, s1/2 > 11 GeV )

Scaling variables

The scaling regularities have restricted range of validity

20

2TT mpm

*max

*R /EEx

*max||

*||F /ppx

/pkα light-cone variable

radial scaling variable

Feynman variable

transverse mass

/2(Pq)qx 2Bj Bjorken variable

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Motivation & Goals

Development of 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.

¯

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The scaling variable z depends on:

1. Reaction characteristics (A1, A2, 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)

dz

dσ

Nσ

1ψ(z)

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.

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Gross features of inclusive particle distributions for the reaction

are expressed in terms of the constituent sub-process

XmMM 121

)mMxM(xmMxMx 2221112211

Locality of the hadronic interactions at constituent level is expressed by the 4-momentum conservation law

222211

22211 )mMxM(xp)PxP(x

Locality principle

V.S.Stavinsky, A.M.Baldin,…

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Fractality principle

Principle of fractality states that variables used in description of the processes diverge in terms of resolution.

The scaling variable z = z0Ω-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

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Charged hadrons

Jets Di-Jets Direct photons

High-pT hadrons

Jets

Direct photons

D-Y lepton pairs

W ±, Z0 -bosons Heavy quarkonia

High-pT 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.

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Scaling variable Z

Ω) (dN/dη

sz

1/2

is the transverse energy of the subprocess dN/d is the multiplicity density at is resolution with respect to constituent subprocess

1/2s

and depend on x1 and x 2

1/2s

Principle of minimal resolution: Momentum fraction x1 and x2 are determined in a way to minimize the resolution with respect to all constituent subprocesses taking into account energy-momentum conservation law.

Momentum fractions x1,2 consist of dependent and independent parts (decomposition)

121,21,21,2 /δδα , α) (χλx

21

122

δ2

δ1)(xxx1 )x(1)x-(1 Ω where0,| /dxdΩ

222211

22211 )mMxM(x p)PxP (x

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Transverse energy of subprocess 1/2s

1/2χ

1/2λ

1/2 sss

transverse energy of inclusive particle

transverse energy of recoil particle

22211λ )PλP(λs

1212

22,12,11,2 MM)P(P

mMp)(Pλ

22211χ )PχP(χs

1,21/22

1,221,21,2 ω)ω(μχ

2,1

1,2021

121,2 λ-1

λ-1)λλ(λ αμ

2,1

02111,2 λ-1

λλλ) α (10.5ω

The variable z is expressed via momenta (P1 , P2 , p) and masses (M1 , M2 , m1) of colliding and produced particles and charged

particle multiplicity density (dN/d

Ω)| (dN/dη

sz

0η

1/2

1212

21

22

0 MM)P(P

)m-0.5(mλ

21 δ2

δ1 )x(1)x-(1 Ω

12 /δδα ,

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Fractal property of the scaling variable z

1x

2x1P

2P

p1

0 Ω zz has character of a fractal measure

For a given production process, the finite part z0 is ratio of

the transverse energy released in the underlying collision of

constituents and the average multiplicity density dN/d

21 δ2

δ1 )x-(1)x(1Ω

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 x1 and x2 of the incoming momenta P1 and P2.

0Ω if ) z(Ω

Z


3

31

inel dp

σdEJ

σ ) (dN/dη

sπΨ(z)

0

1Ψ(z)dz

Scaling function z

Normalization equation

1Pp

2P X

The scaling function z is probability density to produce inclusive particle

with formation length z.

33σ/dpEd

s1/2 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

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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 s1/2. 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.

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Relativistic Heavy Ion Collider, RHIC

3.83 km circumferenceTwo separated rings

120 bunches/ring106 ns bunch crossing time

A+A, p+A, p+pMaximum Beam Energy :

500 GeV for p+p200A GeV for Au+Au

LuminosityAu+Au: 2 x 1026 cm-2 s-1

p+p : 2 x 1032 cm-2 s-1 Beam polarizations

P=70%

Upton, Long Island, New York

PP2PPRHIC

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Z-scaling at RHICCharged hadron production in pp collisions from STAR

STAR confirms Z-scaling

Phys.Rev.Lett. 91 (2003) 172302

TevatronISRU70

RHIC

RHIC

Z


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)1671PHENIX confirms Z-scaling

The cross section Ed3/dp3 vs. pT.

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

→

m=135 MeV c = 251Å Br = 98.8%

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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 Ed3/dp3 vs. pT.


The scaling function (z) vs. z.

→

m=547 MeV c = 11 Ǻ Br = 38.8%

RHIC RHIC

Z


STAR measures the strange particle spectra with great improvement

in statistical errors

Transverse momentum spectra of strange particles in pp collisions at STAR

STAR collaborationM.Heinz (University of Bern)40th Rencontres de Moriond, 12-19 March, 2005, La Thuile, Italy

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

¯

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Z-scaling at RHIC K+ & KS

0-meson production in pp collisions at high-pT

Shape of Ψ(z) for K+ & KS0

F-dependence of z High-pT asymptotic of KS

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 Ed3/dp3 vs. pT

STAR Collaboration J. Adams & M. Heinz, QM’04, January, 2004, Oakland, USA (nucl-ex/0403020)

0SK

Λ

Λ

Indication on validity of Z-scaling for KS0

S→

m= 494MeV c = 2.67 cm Br = 68.6%

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Predictions based on STAR data

Z-scaling at RHIC -hyperon production in pp collisions from

STARΛ & Λ

0SK

Λ

Λ

STAR Collaboration J. Adams & M. Heinz, QM’04, January, 2004, Oakland, USA (nucl-ex/0403020)

STRANGENESS origin in anti-hyperons

The cross section Ed3/dp3 vs. pT

The scaling function (z) vs. z

F-dependence of (z)

Energy independence of (z)F-dependence of Ψ(z) Power law, (z) ~ z-→ p

m=1.12 GeV c = 7.89 cm Br = 63.9%

Λ0(uds)

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STAR Collaboration R.Witt et al., nucl-ex/0403021

RHIC can test Z-scaling at s1/2 = 50-500 GeV

Energy independence of (z) Power law, (z) ~ z-

Z-scaling at RHIC -hyperon production in pp collisions from STAR

Ξ &Ξ

STRANGENESS origin in baryons



F-dependence of (z)→ m=1.32 GeV c = 4.91 cm Br = 99.9% STAR Collaborations

B.Bezverkhny (Yale University)“Quark Matter 2005”, 4-9 August, 2005, Budapest, Hungary

Ξ-(ssd)

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Z-scaling at RHIC -meson production in pp collisions from

STAR

STAR Collaboration J.Adams et al., nucl-ex/0406003



F-dependence of (z)

STAR

→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-

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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



F-dependence of (z)

→K π m=892 MeV c ≈ 3.9 fm Br ≈100%

STAR

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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



F-dependence of (z)

→ π+ π–

m=770 MeV c = 1.3 fm Br ≈100%

STAR

Z


Z-scaling at RHIC --meson production in pp collisions at high-pT

Energy scaling (up to z ≈ 30) Power law zz (z > 4)

STAR Collaboration, O.Barannikova, QM’05, August, 2005, Budapest, Hungary PHENIX Collaboration, M. Harvey, QM’04, January, 2004, Oakland, USA

Spectra of ID’d hadrons at high pT

STAR & PHENIXSTAR & PHENIX

The scaling function (z) vs. z The cross section Ed3/dp3 vs. pT

1/2π

pT

d2 N

/dp

T d

y , (

GeV

/c)-2

RHIC confirms Z-scaling

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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

photonCompton/Annihilation process

FkγkR

kijR

γijFj

j2

kj,i,Fi

i1ji

fragdir

μ,zD)(μdzσ)(μσ μ,xfμ,xfdxdxσ

σσσ

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The cross section Ed3/dp3 vs. pT. 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.PotrebenikovaJINR E2-98-64 Comput.Phys.Com.117 (1999) 229

M.T.G.Efimovhep-ph/0209013

M.T.G.EfimovD.ToivonenSov.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 s1/2 and pT

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Z-scaling at RHIC Direct photon production in pp collisions from PHENIX

PHENIX Collaboration K.Okada, “Spin 2004”,October 11-16, 2004, Trieste, Italyhep-ex/0501066

NLO pQCD describes data within exp. errors Sensitivity of data to properties of z-presentation




RHICRHIC

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Medium produced in pp & AA collisions

Particle multiplicity <Nch> Multiplicity density dNch/d Mean transverse momentum <pT> Energy density Bj R2) dET /dy

Measured multiplicity density dNch/d in pp & pp is much more larger than dNch/d/(0.5Np) in central AA collisions at AGS, SppS and RHIC

¯

¯

Is medium produced in pp collisions at high dNch/dsimilar to nuclear medium created in central AA ? Are there general properties of particle production mechanism in pp & AA ?

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Multiplicity selection of events

low pT spectra → exponential law multiplicity evolution of hadronization “invisible” quark & gluon degrees of freedom ↔ no constituent structure

high pT spectra → power law pT evolution of hadronization constituent structure is visible

Multiplicity density dNch /dis characteristic of nuclear medium Modification of particle spectra with multiplicity density, RAA(pT) & RCP (pT) Multiplicity density ~ gluon density at small x → saturation regime (CGC, QGP)

Quarks & Gluons

Mesons & Baryons

Central Au-Au s1/2=200 GeV

RHIC & STARRHIC & STAR

pp s1/2 = 200 GeV

L.McLerran, D.Kharzeev,…

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Generalized scaling variable z

1

0

1/2

Ω)| (dN/dη

sz c

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

1/2s

and depend on x1, x2, y1/2s

Principle of minimal resolution: The momentum fractions x1 , x2 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:

0| /dxdΩ

y)(1)x(1)x-(1 Ω where0,| /dxdΩ

)x,y(xy2

2δ2

1δ1)x,y(xy1

21

21

ε

222211

22211 /y)mMxM(x p/y)PxP (x

M.T., I.Zborovsky hep-ph/0506003

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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

1/2s

W

1/2sz

1

0

1/2

Ω)dN/dη(

sz c

Ωc)dη/(dN0

W

Entropy

WS lnStatistical Thermodynamical

const. lnVRlnTcV S

const.])x(1)x(1y)(1ln[)dη/dN(lnc 2δ2

1δ10

ε S

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 .

)/zsln( 1/2S

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.

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E735 Collaboration T.Alexopoulos et al., Phys. Lett. B336 (1994) 599.

E735

c=0.25|η|<3.25

|η|<3.25

11/2

c) (dN/dηs

z Strong dependence of high pT 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 |η|<2.5

UA1 Collaboration G. Arnison et al., Phys. Lett. B118 (1982) 167.

Multiplicityindependence of Z-scalingCharged hadron production in pp collisions at Tevatron and SppS ¯ ¯

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Multiplicity independence of Z-scaling at RHIC Charged hadron spectra vs. dNch/din pp collisions from STAR

STAR Collaboration J.E.Gans, PhD Thesis, Yale University, USA (2004).

Sensitivity of cross section to multiplicity density at high pT

Self-similarity & fractality are reflected in processes with high multiplicities in pp and pp collisions at high pT

STAR

c=0.25

11/2

c) (dN/dη

sz

Independence of heat capacity c on energy and multiplicity over a wide pT range is confirmed by UA1, E735, CDF and STAR data.

¯

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Z-scaling at RHIC Multiplicity dependence ofcharged 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 ofcharged 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 <pT> dependence vs. dNch/dη and energy s1/2

¯

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Z-scaling is manifestation of principlesSelf-similarity & Fractality

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

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Summary

Z-scaling is a tool to search for new phenomena in high-pT and high multiplicity particle production in pp & pp collisions

at the RHIC, Tevatron and LHC¯

Z-scaling is specific feature of high-pT particle production

established in pp and pp collisions.

Z-scaling is observed in numerous high-pT data obtained at the U70, ISR, SppS, Tevatron and RHIC. New data on particle (h±,π,η,0,KS,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-pT 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.

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Thank You for Your Attention

We are grateful for fruitful collaboration to our colleguesYu.Panebratsev, G.Skoro, O.Rogachevsky, T.Dedovich, D.Toivonen

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Back-up slides

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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

verification of z scaling in pp collisions at rhic

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