D. Toivonen, M. Tokarev

JINR, Dubna

Z-scaling&

High- pT and cumulative particle production

in pp and pA collisions at high energies

Z

XXXII International Symposium on Multiparticle Dynamics

Alushta, Crimea, Ukraine, 7 - 13 September, 2002

Content

Introduction

Z-scaling & basic principles - self-similarity, locality, fractality

Z-scaling & properties - energy and angular independence, power law

High- hadron production in pp and pD

Cumulative particle production in pA

Summary

Tp

Motivation & Goals

The numerous experimental data on high-pT hadron, direct photon and jet production obtained at U70, ISR, SpS and Tevatron reveal scaling properties in Z-presentation.

The general concept of Z-scaling is based on the fundamental symmetry principles of self-similarity, locality and fractality.

Therefore the violation of Z-scaling is suggested to use as a signature of new physics phenomena in pp, pA and AA interactions at high-pT.

To include in joint analysis new high-pT data sets to verify the properties of Z-scaling.

To perform the analysis of cumulative processes of particle production in the framework of Z-presentation.

Z-scaling & Symmetry

Self-similarity

The dropping of certain dimensional quantities or parameters out of a physical picture interaction.

Locality The momentum-energy conservation law is locally valid for interacting constituents.

Fractality The internal structure of colliding objects, interaction of their constituents and formation mechanism of real particles reveal self-similarity and are described by the power law.

The general concept of Z-scaling is based on the fundamental principles of self-similarity, locality and fractality.

Z-scaling

New presentation of experimental data revealing scaling properties

zψ(z)33σ/dpEd Tp vs..vs

*max

*R /EEx

*max||

*||F /ppx

20

2TT mpm

radial scaling variable

Feynman variable

transverse mass

(s)

sz

/

)mmMxM(xsss 2122111/2χ

1/2λ

1/2

21 δ2

δ1 )x(1)xm(1Ω

(s)|dN/dηρ(s) 0η

) (αχλx 1,21,21,2

)MMP)/(PmMq(Pλ 212122,12,11,2

1,21/22

1,221,21,2 ω)ω(μχ

)λ)/(1λ)(1λλ}(λα α, {μ 2,11,202112

1,2

)λ)/(1λλ})(λα α, {(10.5ω 2,1021-1

1,2

,)PλP(λs 22211λ

)MMP)/(Pm(m0.5λ 212121

220

12/δδα

Scaling variable Z 1x

2x1P

2P

q

is the measure of constituent interaction

is the multiplicity density of charged particles

are the momentum fractions

are the anomalous fractal dimensions,

22211χ )PχP(χs

21,δδ

is the energy of constituent sub-process

3

31

inel dq

σdEJ

ση)ρ(s,

sπψ(z)

221 )p(ps

inelσ

dN/dηη)ρ(s,

))ln(tg(0.5θ0.5η

)λy/()λz/()λz/()λy/(J 2121

min

1ψ(z)dzz

33σ/dqEd

)/λln(λ0.5y 21

Scaling function

is the collision energy is the multiplicity particle density

is the inelastic cross section is the pseudorapidity

is the rapidity

is the inclusive cross section

Normalization equation

ψ(z)1P

q

2P X

Physical meaning of and

o The scaling variable is the formation length revealing the property of a fractal measure

o The scaling function is the probability density

to form a particle with the formation length

I.Zborovsky, hep-ph/0101018I.Zborovsky et al., JINR E2-2001-41

ψ(z)

ψ(z)z

z

δε0

zz

ρ)/(msz0

21 A2

A1

-1 )x(1)x(1ε

Properties of Z-scaling

Energy independence of

Angular independence of

Power behavior,

A-dependence of ,

βzψ(z) Aαψ(z)

ψ(z)

ψ(z)

Energy independence of Z-scaling

The scaling function has the same shape

for different collision energy s

Angular independence of Z-scaling

The scaling function has the same shape

for different angles of produced particles

ψ(z)

Z-presentation and power law

The scaling function in the high- range reveals the power behavior

zψ(z)βzψ(z)

ψ(z)

Z

(a) The dependence of cross section of meson production on transverse momentum. (b) The corresponding scaling function .

- Energy independence of - Angular independence of - Power law

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.

ψ(z)

-βz~ψ(z)

33σ/dqEd

ψ(z)ψ(z)

M.TokarevYu.PanebratsevI.ZborovskyG.Skoro

JINR E2-2001-282

Z-scaling and energy dependenceof -meson production in pp collisions at high-

π p

Z

33σ/dqEd(a) The dependence of cross section of meson production on transverse momentum. (b) The corresponding scaling function .Experimental data are taken from: 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.

ψ(z)

Z-scaling and energy dependenceof -meson production in pp collisions at high-

π p

A-dependence of Z-scaling

The scaling transformations of and allow us to compare scaling functions for different nuclei

z ψ(z)

zαz A

ψαψ 1A

0.15A 0.9Aα

M.Tokarev, Yu.Panebratsev, I.Zborovsky, G.Skoro

JINR E2-99-113; Int. J. Mod. Phys. A16 (2001) 1281.

A-dependence of Z-scaling

z ψ(z) vs.T33 p σ/dpEd vs.

Z

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.

-βzψ(z)

M.TokarevYu.PanebratsevI.ZborovskyG.Skoro

JINR E2-99-113Int.J.Mod.Phys.A16 (2001) 1281

(GeV/c)p Tz

The shape of the scaling function is the same for different nuclei from D to Pb

Energy independence of Power law at high-z A-dependence of

ψ(z)

ψ(z)

Z

(a) The dependence of cross section of meson production on transverse momentum. (b) The corresponding scaling function .

- Energy independence of - Angular independence of - Power law

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.

ψ(z)

-βz~ψ(z)

33σ/dqEd

ψ(z)ψ(z)

Z-scaling and energy dependenceof -meson production in pD collisions at high-

π p

plot

The plot allows us to determine the kinematical range where the scaling can be violated .

The plot can be used as a joint kinematical and dynamic criterion to select domain where new physical phenomena can be found.

Tpz

Summary I

Results of data analysis on inclusive cross sections of high-pT charged hadron production in p-p and p-D collisions at high energies do not give indications of Z-scaling violation.

The mechanism of particle formation is described by the scaling function over a wide kinematical range.

The power law at is observed . is used to determine the kinematical region preferable to search for the scaling violation.

ψ(z)

-βzψ(z) 4.z

Tpz

Cumulative particle production in p-A & Z-scaling

The kinematical region for h-A and A-A interactions forbidden for particle production in nucleon-nucleon collision is called the cumulative region.

221

2X q)P(PM min

m),M,Mθ, s, ( q 21max

11 M,P

22 M,P

mq,

X

4-momentum conservation law &baryon, strange, charm numbers

q q ppmax

pAmax

Kinematical boundary for pion backward hemisphere production in p-A

πlabθ

π

p AX

p D Li Be Ta

0.45 0.90 3.09 3.93 37.8

0.46 0.92 3.24 4.17 69.8

0.46 0.93 3.26 4.19 78.1(GeV/c)

q πmax

0πlab 180θ

70

400

(GeV/c)

p L

33σ/dqEdψ(z)

Z

(a) The dependence of cross section of meson production on particle momentum. (b) The corresponding scaling function . Experimental data are taken from: N.A. Nikiforov et al., Phys. Rev. C22 (1980) 700. 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.

Z-scaling, cumulative and high- -meson production in pTa collisions

πp

Angular dependence of multiplicity particle density

in backward hemisphere particle production in p-A

• Li, Be, C, Al, Cu, Ta • •

00πlab 16070θ

GeV/c 400Plab

Angular dependence of

A-dependence of

A),θρ(s, lab

The ratio and at and .

A),θρ(s, lab

00πlab 160 70θ 1.5 3.5|/χ|χ LiTa

3

31

inel dq

σdEJ

σA)η,ρ(s,

sπψ(z)

0.180.1050η A0.67s|A)ρ(s,

A),χ(θA)ρ(s,A)θ,ρ(s, labA),χ(θlab

plot

The kinematical range for the process where the scaling can be violated

p-z

GeV/c 70pat GeV/c 1.9p labπ

20zz hardcum

GeV/c 400pat GeV/c 2.17p labπ

X)(160πTap 0

GeV/c 800pat GeV/c 2.25p labπ

Summary

New analysis of high-pT data on charged hadrons produced in p-p and p-D collisions were performed. The obtained results confirm the general properties of z-scaling.

Data z-presentation of backward hemisphere particle production in pA collisions was presented.

The angular dependence of multiplicity particle density

for different nuclei (Li, Be, C, Al, Cu, Ta) was found.

Comparison of scaling functions for high-pT and cumulative data sets was performed.

Available experimental data on high-pT particle spectra give no indication on z-scaling violation.

The change of fractal dimension is suggested to use as the quantitative measure of the scaling violation.

ψ(z)

p,K,π

A),θ ρ(s, lab

δ

THE END

? ?

RHIC LHC

Z violationscaling-z of signature theis jump"δ"

δ0 εzz

-βzψ(z)

π

δpp

1A2

A1

-1 })x(1)x{(1ε 21

?

D. Toivonen, M. Tokarev

JINR, Dubna

Search for Z-scaling violation

in pp and pA collisions at high energies

XVI International Seminar on High Energy Physics Problems “Relativistic Nuclear Physics & Quantum Chromodynamics”

JINR, Dubna, June 10-15, 2002

Z

D. Toivonen, M. Tokarev

JINR, Dubna

Z

XVI International Conference on Particles and Nuclei (PANIC02) Osaka, Japan, September 30 - October 4, 2002

Z-scaling, high-pT and cumulative particle production in p-A collisions at high energies