Transport Theoretical Studies of Hadron Attenuation in Nuclear DIS T. Falter, W. Cassing,, K. Gallmeister,, U. Mosel Contents: Motivation Model Results Summary & Outlook
Motivation elementary en reaction confinement reaction products hadronize long before they reach the detector estimation of formation time via hadronic radius (r h = 0.5 fm)? r h c time dilatation: t f = γ
ea reactions at HERMES interactions with (cold) nuclear medium during t f space-time picture of hadronization & prehadronic interactions l f lessons for more complex heavy-ion collisions jet supression at RHIC partonic energy loss in QGP (pre-)hadronic FSI talk by K. Gallmeister
Model γa, ea reaction splitted into 2 parts : γ * N X using PYTHIA & FRITIOF additional consideration of binding energies Fermi motion Pauli blocking coherence length effects propagation of final state X within BUU transport model consideration of elastic and inelastic scattering (coupled channels)
hadronic structure of the photon & event classes direct photon interactions: DIS QCD Compton photon-gluon fusion resolved photon interactions: diffractive VMD VMD GVMD
hadronic structure of the photon W=5 GeV σ i /σ tot (γ*n) 0.2 VMD GVMD direct 0.0 0.1 1 10 Q 2 [GeV 2 ]
shadowing of the vector meson component coherence length: distance that γ travels as a vector meson fluctuation l V = k V kγ 1 2ν Q 2 + m 2 V coherence length > mean free path inside nucleus density of nucleons participating in the production process reduced influences reactions triggered by the vector meson component (e.g. γ N ρ 0 N) a eff [fm -3 ] 84 Kr ν=17.9 GeV b [fm] 0.12 0.10 0.08 0.06 0.04 0.02-8 -6-4 -2 0 2 4 6 Q 2 =0.9 GeV 2 l ρ =4.7fm 8-8 -6-4 -2 0 2 4 6 8 z [fm]
hard interactions (e.g. direct γ*n reaction) excitation of hadronic strings fragmentation according to the Lund model = production point of color neutral prehadron
dn/dz h [a.u.] general approach in transport model 7 6 5 4 3 2 1 0 0.3 0.2 0.1 0.0 string fragments very fast into color-neutral prehadrons t p = 0 prehadrons need formation time t f = γ h to build up hadronic wave function prehadronic cross section σ determined by constituent quark model HERMES kinematics 0.2 ρ 0 0.5 φ 0.2 z h π 0 K + σ b = #q orig 3 σm = #q orig 2 0 leading quark 1 leading quark 2 leading quarks 3 leading quarks 0.2 p K - σ b σ m
effective cross section of nucleon debris σ eff [mb] 200 180 160 140 120 100 80 ν = 25 GeV Q 2 = 10 GeV 2 60 =0.5 fm/c 40 = fm/c 20 Ref. [Cio02] 0 0 1 2 3 4 5 6 t [fm/c] comparison with gluon bremsstrahlung model C. Ciofi degli Atti and B. Z. Kopeliovich, Eur. Phys. J. A 17, 133 (2003).
starting time of (pre-)hadronic FSI t [fm/c] Comparison with Lund estimate A. Bialas and M.Gyulassy,, NPB 291 (1987) 793 22 20 18 16 14 12 10 8 6 4 2 <t p > <t f > <t FSI > <t f > Bialas =0.5 fm/c 0 0.0 0.2 z h =E h /ν
DIS of complex nuclei leading prehadrons (= target-, beam remnants) can undergo FSI directly after γ * N interaction hadrons that solely contain quarks from string fragmentation start to interact after FSI production of new particles redistribution of energy
BUU transport model for each particle species i (i = N, R, Y, π, ρ,, K, ) exists a Boltzmann-Uehling-Uhlenbeckhlenbeck equation: µ t +( ~ph) ~r ( ~r H) ~p f i (~r, ~p, t) =I coll [f 1,...,f i,...,f M ] f i : phase space density H : Hamilton function q H = (µ + Us) 2 + ~p 2 collision integral accounts for changes in f i due to 2 particle collisions: creation, annihilation, elastic scattering (Pauli blocking for fermions) mean field for baryons set of BUU equations coupled via I coll and mean field products of γ * A reaction need not be created in primary γ * N reaction
Results HERMES: look for CT in incoherent ρ 0 electroproduction off 14 N ν 10 20GeV, Q 2 0.5 5GeV 2 diffractive V production: γ*n ρ 0 N size of initially produced qq pair is expected to decrease with increasing Q 2 early stage of evolution: small qq pair interacts mainly via its color dipole moment: σ qq ~ diameter 2 large energies: qq frozen in small sized configuration while passing nucleus effects nuclear transparency ratio: T A = σ γ A ρ 0 A Aσ γ p ρ 0 p
Comparison with Hydrogen data σ(γ*p ρ 0 p) [µb] 100 10 1 0.1 x30 x10 x4 x1 <Q 2 >=3 GeV 2 1000 coherent production <Q 2 >=1.3 GeV 2 <Q 2 >=2.3 GeV 2 <Q 2 >=4.0 GeV 2 dσ/dt σ(γ*a ρ 0 X) [µb/gev 2 ] 100 10 1 0.1 x10 1 H (HERMES) 14 N (HERMES) 5 10 15 20 25 30 W [GeV] 0.0 0.1 0.2 0.3 0.5 t-t max [GeV 2 ] experimental t-cut: t > 0.09 GeV 2 to get rid of coherent ρ 0 production: γ * A ρ 0 A
BUU & Glauber theory agree with experiment 14 N 0.2 HERMES E665 T A BUU Glauber 84 Kr 0.2 0.0 1 10 100 l ρ [fm] no CT in both calculations only coherence length effects
hadron attenuation in DIS off nuclei multiplicity ratio: µ Nh (z h,p T,ν) R h M(z h,p T, ν) = N e (ν) µ Nh (z h,p T,ν) N e (ν) A Experiments: EMC: 100-200 GeV µ-beam on HERMES: 27.6 GeV e + -beam on 14 Jefferson Lab: 5.4 GeV e - -beam on 12 C, D z h = E h ν on 64 Cu 14 N, 20 Ne, 84 Kr C, 56 Fe, 208 Pb attenuation due to partonic energy loss (X.N. Wang et al., F. Arleo) (pre)hadronic absorption (A. Accardi et al.) + rescaling of fragmentation function (B. Kopeliovich et al., T. Falter et al.)
DIS off proton HERMES ν = 2.5 24 GeV, Q 2 > 1 GeV 2, W > 2 GeV red curves: : calculation w/o cuts on hadron kinematics and assuming 4π-detector 10 1 0.1 0.01 π - π + 10 1 0.1 0.01 dn h /(N e dz h ) 0.1 0.01 1E-3 K - K + 0.1 0.01 1E-3 1 0.1 0.01 1E-3 0.2 p default PYTHIA HERMES Tuning HERMES 0.2 p 0.01 1E-3 1E-4 1E-5 z h
charged hadron production in DIS off 84 Kr at HERMES including all experimental cuts accounting for angular acceptance of HERMES detector average kinematic variables from simulation: 30 <ν> [GeV] 25 20 15 10 <ν> <Q 2 > 2 1 <Q 2 > [GeV 2 ] <z> 0.2 <z> <Q 2 > 2 1 <Q 2 > [GeV 2 ] 0.0 0.2 z=e h /ν 8 10121416182022 ν [GeV]
multiplicity ratio of charged hadrons w/o prehadronic FSI R 1.1 0.9 0.7 0.5 HERMES 84 Kr = 0 = 0.1 fm/c = 0.3 fm/c = 0.5 fm/c = fm/c = 1.5 fm/c 0.0 0.2 z 8 10 12 14 16 18 20 22 ν [GeV] prehadronic interactions needed
charged hadrons with prehadronic interactions 1.1 14 N 0.9 0.7 = 0. = 0.1 fm/c = 0.5 fm/c = fm/c R h M 1.1 0.9 HERMES 84 Kr = 0.3 fm/c = 1.5 fm/c 0.7 0.5 0.2 z h 8 10 12 14 16 18 20 22 ν [GeV] > 0.5 fm/c compatible with pa data at AGS energies
influence of detector geometry (τ( f = 0.5 fm/c) R h 1.1 0.9 0.7 0.0 0.2 z 84 Kr with geometrical detector acceptance w/o geometrical detector acceptance 8 10 12 14 16 18 20 22 ν [GeV] needs to be accounted for at z h < important for integrated spectra
p T -spectrum of charged hadrons (τ( f = 0.5 fm/c) 1.5 R h M 1.4 1.3 1.2 1.1 84 Kr <k T >=0.5 GeV <k T >= GeV (default) <k T >=1.5 GeV HERMES strong increase at high p T >1 GeV Cronin effect? 0.9 0.7 0.01 0.1 1 p 2 T [GeV2 ] from calculations: : <k< T > A = <k< T > N, i.e. not Cronin!
R h M 1.2 π + π - K + K - 1.2 p attenuation of identified hadrons (τ( f = 0.5 fm/c) 0.2 z h p 20 20 Ne Ne 4 8 12 16 20 24 ν [GeV] R h M 1.2 π + π - π 0 K + K - 1.2 p 0.2 z h p HERMES 84 84 Kr Kr BUU absorption 8 12 16 20 24 ν [GeV]
double-hadron attenuation (τ( f = 0.5 fm/c) leading hadron z 1 > 0.5 subleading hadron z 2 < z 1 R 2 (z 2 )= ³ N2 (z 2 ) N 1 A ³ N2 (z 2 ) N 1 D R 2 (z 2 ) 1.2 1.1 0.9 0.7 1.2 1.1 0.9 0.7 14 N HERMES [no (+,-)] (preliminary) 84 Kr 0.1 0.2 0.3 z 2
HERMES @ 12 GeV ( = 0.5 fm/c) model also works at lower energies 14 N 0.9 84 Kr 0.9 R h M 0.7 h + BUU h - BUU h + HERMES (preliminary) h - HERMES (preliminary) 0.7 0.5 h + BUU h - BUU h + HERMES (preliminary) h - HERMES (preliminary) 0.9 0.9 0.7 π + BUU π - BUU π + HERMES (preliminary) π - HERMES (preliminary) 0.7 0.5 π + BUU π - BUU π + HERMES (preliminary) π - HERMES (preliminary) 0.2 3 4 5 6 7 8 9 0.2 3 4 5 6 7 8 9 z h ν [GeV] z h ν [GeV]
Jefferson Lab ( = 0.5 fm/c) CLAS detector larger geometrical acceptance detects more secondary particles from FSI CEBAF lower energy strong effect of Fermi-motion motion R h M 1.2 1.2 1.2 1.2 1.2 1.2 1.2 12 C 56 Fe 208 Pb 0.2 z h π + π - π 0 K + K - K 0 K 0 2.5 3.0 3.5 4.0 ν [GeV]
model for γ and e induced reactions at GeV energies combines: qm coherence in entrance channel sophisticated event generation coupled channel transport description of FSI can decribe coherence length effects in exclusive ρ 0 production most features observed in hadron attenuation works also for: γ and e reactions in resonance region same parameter set πa, pa and AA reactions future plans: Summary & Outlook talk by K. Gallmeister consistent event generation AND space-time picture by PYTHIA analysis of future JLab experiments, ultra-peripheral HIC at HERMES energies