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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
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1Parton-based
Gribov-ReggeTheoryAim: connecting properly parton model and Gribov-Regge Theory
Extending work by Gribov, Kaidalov, Capella ...
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Reminder (Basic QM)
22
amplitude
Elastic
T XT 2
amplitude
Inelastic
TIm2 :Unitarity 2*222
X XXTT diagramcut
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Symbols: full and dashed line elastic and cut diagram
22 Ti
222
12
*22
1 Im2 TTTs
XXXs
Very useful for nucleus-nucleus
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soft
hard semihard (one of three)
The elastic amplitude:
semihardsoft22 TTTT
Soft: parameterization - hard: pQCD - semihard: convolution soft/hard
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Inelastic scattering in pp:
Amplitude:
Squared amplitude => interference terms: => Symbolic notation
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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)
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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:
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Interpretation:
KKbs for on distributiy probabilit is )(),(
kmkABkkkk kkxxmK
1,1},,{
One can show:
with
K
bs K 1)(),(
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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
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• 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
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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
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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
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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
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Cutting diagrams
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Elastic scattering:
Cut diagrams:
Reduces increaseof cross sectionwith energy(screening)
Increasesmultiplicityfluctuations
Some consequences
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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
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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
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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
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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!
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Structure function F2
Red: complete calculationBlue: calculation without Pomeron-Pomeron interactions
Littledifference
!!!!
becauseof many
cancellations
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Total and elastic cross section in pp
Red: complete calculationBlue: calculation without Pomeron-Pomeron interactions
Big difference!!!
Important contributions from nonfactorizable diagrams
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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
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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)