# Space-time picture of hadronic and nuclear collisions

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Space-time picture of hadronic and nuclear collisions

Space-time picture of hadronic and nuclear collisionsFrom low to high energies

1collision @ alice16.05.20082

2collision @ alice16.05.20083

Higgs?junk?It is essential to understand hadronic interactions at LHC!the structure of the underlying eventbehaviour of tot, el and diff with energy...99,9999% of event!!pp interactions at LHC are small AA systems?

...or else, no discovery!

3overviewWhat is a hadron/nucleus? What are the relevant degrees of freedom?How does a hadron interact with another hadron? What about nuclei?What is the difference of these interactions going from low to high energies?

16.05.200844motivationIt is essential to understand hadronic interactions at LHC!the structure of the underlying eventbehaviour of tot, el and diff with energy..99,9999% of events!!

...or else, no discovery!Is physics @ LHC only about discovering Higgs, SUSY??pp interactions at LHC are small AA systems?collective behaviours?thermal yields, QGP?new physics in forward directionlumps of strange matterparton saturationwhat is the reference?black holes in AA

16.05.200855why a Space-time description?intuitive (especially in the case for scattering off large nuclei)gives new insight into the dynamics of hadronic collisionsFeynman diagrams are covariant give no information about space-time dynamics of the processesdramatic change of classical space-time picture above a given critical energy!16.05.20086a space-time formulation of hadron-hadron scattering is an interesting exercise in itself because the results are partly at variance with the naive expectations that a fast hadron Lorentz-contracts. (!)

time-ordered perturbation theory:formal similarity to potential scattering close to nonrelativistic quantum mechanics

6hadrons, nuclei16.05.20087complex building blocks7

what is a hadron?strongly interacting composite subatomic particleconsists of quarksbaryons: 3 quarks, fermionmesons: quark anti-quark pair, bosonexcited states - resonancesat high enough temperatures they dissolve!

16.05.20088ududuud8

strange and strong interaction16.05.20089qqqqqqqqQuantum ChromoDynamics (QCD) fundamentalcalculable for short distance processescalculable on lattice for static situationsuseless for large distance physics, dynamics...need approximations, models, ideas!

9nuclear physics at high energiesmacroscopic volumesconditions ~early Universefree quarks and gluons?Quark-Gluon Plasma (QGP)16.05.200810

udu10

hydrodynamical pictureneed to assumeinfinitesimally small cells are locally thermalizedlarge rate of interactioncan define temperature, energy density and pressure16.05.200811

Lev Landau11thermalizationusually: particles start with an arbitrary velocity distributionequilibrate over time, maximization of entropytake the continuum limit loosing the concept of particles16.05.200812

12

Bjorken initial conditionboost invariant initial condition, adiabatical expansionthe longitudinal motion is uniform: vz=z/tgives rise to a central plateau height independent of energy!initial energy density

16.05.200813

13pictUre of a fast hadron16.05.20081414

feynmans (naive) parton modelin a frame where the hadron is moving infinitely fast, it consists of infinitely many partonsthe partons carry a fraction of the total momentum of the hadron eachthe partons are free!16.05.200815udu15how can this be?uncertainty principle!the constituent quarks caninteract via gluon exchangefluctuate into a quark-antiquark pairwhen boosting the proton, the timescales related to these fluctuations are Lorentz dilatedinteractions of quarks now take place over much larger timescales..16.05.200816

16feynman scaling16.05.200817

leading particle keep arbitrary large fraction of the initial energyflat probability distribution

~half of the energy goes into particle production

17distribution of quarks and gluons

the probatility of finding a parton (quark, gluon, heavy quark...) with momentum fraction x of the total protonnon-perturbative quantitybut dependence on resolution given by QCDuniversal quantitymeasured in ep collisionscan predict p, pp etc...16.05.200818heavy-ion collisions at RHIC!18

the reggeon approachbased on analyticity, unitarity and crossing symmetry of the S-matrixestablishes a connection between high-energy scattering and spectra of particles and resonancesTotal cross section:Reggeons: , A2, Pomeron: not confirmed (glueball..?)supercritical: P>1 dominates high energy scattering

16.05.200819

V.N. Gribov19

the reggeon approachRegge trajectory

linear interactionmotivates the string picturedescribes strong interactions at long distancesQCD perturbation theory: BFKL approximation16.05.200820

20

the hadronic fluctuationthe Fock state vector is in general

the content of the fluctuation is Lorentz frame dependentin the rest frame of the projectile: small fluctuationquark constituentsin a frame where the projectile is fast: large fluctuationFeynmans partons develop16.05.200821

a few partons...

hgggqqqq21

picture of a fast hadron16.05.200822fast partonsslow partonstarget