NEXUShep-ph/0007198

Physics Reports 350 (2001) 93-289

Guideline: theoretical consistency

hep-ph/0102194

Phys. Rev. Lett. 86 (2001) 3506

Hajo Drescher,Fuming LiuSergej Ostapchenko,Tanguy PierogKlaus Werner

1Parton-based

Gribov-ReggeTheoryAim: connecting properly parton model and Gribov-Regge Theory

Extending work by Gribov, Kaidalov, Capella ...

Reminder (Basic QM)

22

amplitude

Elastic

T XT 2

amplitude

Inelastic

TIm2 :Unitarity 2*222

X XXTT diagramcut

Symbols: full and dashed line elastic and cut diagram

22 Ti

222

12

*22

1 Im2 TTTs

XXXs

Very useful for nucleus-nucleus

soft

hard semihard (one of three)

The elastic amplitude:

semihardsoft22 TTTT

Soft: parameterization - hard: pQCD - semihard: convolution soft/hard

Inelastic scattering in pp:

Amplitude:

Squared amplitude => interference terms: => Symbolic notation

Inelastic scattering in AB:

i

iXABXAB TT )(

Squaring amplitude sum over many interference terms

expressed via cut anduncut elementarydiagrams

full energy conservation!!

(Elastic andinelastic elem.Interactions)

We sum all terms in a class => (K). The inelastic cross section is a sum over classes:

kmkABkkkk kkxxmK

1,1},,{

0

c.s. ltopologica

),(2 )()(K

bsAB Kbds

Symbol b

= impact parameter+ nuclear coordinates

- Number of cut diagrams for kth NN pair

- Momentum fractions of elementary interactionskm

kk kk xx ,

Classes of interference terms:

Interpretation:

KKbs for on distributiy probabilit is )(),(

kmkABkkkk kkxxmK

1,1},,{

One can show:

with

K

bs K 1)(),(

serves clearly as basis to calculate (topological) cross sections

but also particle production conserving energy in both cases !!

(the only model which does so)

Consistency problem solved !!

hadrons partons Pomeron :then

definedfully Pomerons Pomerons theallfor

toaccording and and generates one

:production Particle

xxmkk kkk

• Pomeron number distribution narrower than in conv. appr.

• Considerably less multiplicity fluctuations in pp

• comparison with data: not so great

Comparing with conventional approach

Dashed: conventionalFull: new approach

2 Pomeron-Pomeron Interactions

• Shadowing• Saturation

• Diffraction• Screening

• Increasing mult. fluctuations • Solving F2-tot puzzle

One additional parameter: triple Pomeron coupling. Fixed from HERA diffractive data

Parton language:

Consider a cut Pomeron as a succession of parton emissions = parton cascade

At high energies, more and more parton cascades contribute

They overlap and interact

Energy dependence

With increasing energy, higher and higher orders have to be considered

We fix a maximal energy (so far LHC) and consider all contributing orders

Cutting diagrams

Elastic scattering:

Cut diagrams:

Reduces increaseof cross sectionwith energy(screening)

Increasesmultiplicityfluctuations

Some consequences

No effect on inclusive spectra: relative weight of diagrams 1 : -4 : 2 the three contributions cancel

Inclusive spectra

The diagrams do not cancel. The middle one is dominant. negative contribution

softening of inclusive spectra

Consider the different contributions to inclusive particle production in pp scattering at given rapidity ()

factorizable

non-factorizable

Contribution zero (complete cancellation)

inclusive cross section is factorizable

The different contributions to F2 in deep inelastic scattering (DIS) are as well factorizable:

So does this mean one can hide all these complicated diagrams in a simple measurable function f ?

with the same function f as in pp scattering

DIS from with ˆdy

incl fffd pp

YES - if one is only interested in inclusive spectra

NO - if one is interested in total cross sections:

tot = factorizable + non-factorizable diagrams

Very important!

NO - if one is interested in Monte Carlo applications

topological cross sections = factorizable + non-factorizable diagrams

Very important!

Structure function F2

Red: complete calculationBlue: calculation without Pomeron-Pomeron interactions

Littledifference

!!!!

becauseof many

cancellations

Total and elastic cross section in pp

Red: complete calculationBlue: calculation without Pomeron-Pomeron interactions

Big difference!!!

Important contributions from nonfactorizable diagrams

3 NEXUS + HydroNucleus-nucleus collisions:

particle densities are too high for independent string fragmentation

• Use NEXUS for the initial stage (0)

• Calculate energy density and velocity field at =0

• Apply hydro evolution for 0 (event by event!)

Efficient hydro code = SPHERIOC.E. Aguiar, T. Kodama

U.F. Rio de Janeiro

T. Osada,Y. HamaU. São Paulo

Coupling:O. Socolowski, KW

Nantes

Summary

Final stage: hydro-evolution

Considerable improvement of the GRT approachby considering energy conservation properly

Pomeron-Pomeron interactions are crucialbut

contribute differently for inclusive spectra and cross sections (eikonal approach does not work)