Z
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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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±,π0,η,0,KS,K*,φ, Λ,Ξ,γ spectra) Multiplcity dependence of Z-scaling Summary
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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, 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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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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 = 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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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
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M.Tokarev ISMD2005, Kroměříž
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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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 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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
Z-scaling at RHICCharged hadron production in pp collisions from STAR
STAR confirms Z-scaling
Phys.Rev.Lett. 91 (2003) 172302
TevatronISRU70
RHIC
RHIC
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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)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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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 Ed3/dp3 vs. pT.
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.
→
m=547 MeV c = 11 Ǻ Br = 38.8%
RHIC RHIC
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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
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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
The cross section Ed3/dp3 vs. pT
The scaling function (z) vs. z
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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M.Tokarev ISMD2005, Kroměříž
Z-scaling at RHIC -meson production in pp collisions from
STAR
STAR Collaboration J.Adams et al., nucl-ex/0406003
The cross section Ed3/dp3 vs. pT
The scaling function (z) vs. z
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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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 Ed3/dp3 vs. pT
The scaling function (z) vs. z
F-dependence of (z)
→K π m=892 MeV c ≈ 3.9 fm Br ≈100%
STAR
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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 Ed3/dp3 vs. pT
The scaling function (z) vs. z
F-dependence of (z)
→ π+ π–
m=770 MeV c = 1.3 fm Br ≈100%
STAR
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M.Tokarev ISMD2005, Kroměříž
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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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
photonCompton/Annihilation process
FkγkR
kijR
γijFj
j2
kj,i,Fi
i1ji
fragdir
μ,zD)(μdzσ)(μσ μ,xfμ,xfdxdxσ
σσσ
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M.Tokarev ISMD2005, Kroměříž
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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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, Italyhep-ex/0501066
NLO pQCD describes data within exp. errors Sensitivity of data to properties of z-presentation
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 > 5.
The scaling function (z) vs. z
RHICRHIC
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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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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
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
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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M.Tokarev ISMD2005, Kroměříž
Back-up slides
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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