In-medium Hadrons Properties, Interaction and Formation

1
In-medium Hadrons Properties, Interaction and
Formation

• L. Alvarez-Ruso, Thomas Falter, Kai Gallmeister,
  T. Leitner,
• Ulrich Mosel, Pascal Mühlich

2
Why study in-medium hadrons?

• In-medium properties may signal exotic states of
  nuclear matter (e.g. QGP, chirally restored
  phase)
• ?need baseline effects in normal nuclear matter
• Mesons in medium can give infos on meson-nucleon
  interactions through selfenergies
• Nucleus as a microdetector
• access to production- and formation-times in
  quark-fragmentation, color transparency

3
Experiments

• Observe outgoing nucleons, mesons, photons,
  dileptons, ...
• A A GSI, AGS, SPS, RHIC, LHC
• p A COSY
• ? A GSI (HADES)
• ?() A MAMI, ELSA, JLAB, HERMES incoherent
  photo- and electroproduction of hadrons on nuclei
  from 100 MeV (MAMI, ELSA) over few GeV (JLAB) to
  20 GeV (HERMES)
• ? A in LBL neutrino experiments
• Need to understand connection between in-medium
  property and final observable!

4
In-medium changes experiment 2000
explained by spectral change of ? meson in dense,
(hot) matter

• Evidence for QGP at CERN Invariant
  (ee-) mass spectrum

• Total photoabsorption cross section

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In-medium changes experiment 2003Jet Quenching

• evidence for QGP at RHIC

• Related Photonuclear Effect at HERMES

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Hadron Properties in Medium Theory

• QCD Sum Rules for Vector Mesons
• Hadronic Models
• Connection with Experiment

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QCD Sum Rule

• Compare spectral function in time-like region
  with OPE of current-correlator for space-like
  distances

• Lhs dominated by soft scale m?
• Rhs separates hard scale Q2 from soft scale
  (condensates)

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? spectral function in medium
QCDSR-allowed (?,m) at saturation density
QCD Sum Rules provide constraints, but do not fix
in-medium hadron props
Leupold et al, Phys.Rev.C582939-2957,1998
Need hadronic model
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Medium Effects

• on baryon resonances
• Fermi-motion ?
  ?
• meson decay ? ?
  
• N ? N meson
  (Pauli blocking)
• collisional broadening ? ?
• NN ? NN
• quenching
  reduction of
• NN ? NN
  meson yield
• N-propagation, self energy mass /
  width

• on mesons
• absorption/rescattering
• modified meson-meson interaction
• partial chiral symmetry restoration ?

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Rho meson in matterResonance-hole model

• Transverse

• Longitudinal

Post et al., 2004
D13(1520) and ? (2?) strongly mixed
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Observables Theoretical Method

1. Calculate hadronic properties in equilibrium
   nuclear matter
2. Calculate elementary production cross section, in
   vacuo and in matter, formation times determined
   by resonance lifetimes or string-fragmentation
   times
3. Propagate produced particles out from production
   to detector, including all FSI and CC effects.

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Theoretical Method for FSI (and ISI) BUU CC
Transport Model

• Off-shell CCBUU Equation for spectral phase
  space density

with

1. In-medium changes can be modelled in H
   (selfenergies) and in Icoll (reaction rates,
   form. times, prehadron cross sections)
2. Experimental acceptance can be simulated event by
   event

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Consequences of in-medium change

• Broad ? spectral function explains
• Absence of nucleon resonances in total
  photoabsorption cross sections on nuclei
• D13(1520) couples to ?,
• ? broad with strength at low
• masses ? opens phase-space
• for decay of D13
• Dilepton spectra in URHICs

free D13
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In-medium effects

QE
?
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Nucleon Knockout at
wo FSI
w FSI
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? in Medium
Theory P. Muehlich et al
? m -0.15 ?/?0 put in by hand
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? in Medium
transverse
Very little mass change from hadronic resonance-ho
le models Collisional broadening ¼ 60-70 MeV
from t? approx with K-matrix parameters
longitudinal
Inelastic width ? transparency
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Nuclear Transparency for ?
Depends crucially on inelastic ? Method to
measure ?_inel
P. Muehlich, U. Mosel Nucl. Phys. A (2006) In
press. E? 1.5 GeV
Crucial Input inelastic omega-N cross section
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Formation times

• At low energies, resonance regime
• tf lifetime of resonance ? N hadron
• At high energies, QCD regime,
• tf from string-fragmentation

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Transparency at high energies determined by quark
fragmentation
Hermes condition ? 14 GeV, Q2 2.5 GeV2
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Prehadron cross sections
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EMC and Hermes Transparency
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Attenuation of Identified Hadrons
Red absorption only Blue with CC and
rescattering

• Essential to know what happens to hadrons
• after attenuation
• distinguish between energy-loss
• and absorption

T. Falter et al., PRC
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JLAB 5 GeV 12 GeV
CLAS acceptance corrected
Strong nuclear effects Fermi motion, stronger
overpopulation of low z
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Summary - Conclusions

• Essential problem link of in-medium props to
  observables ? FSI must be part of theory
• Models of attenuation have to describe not only
  that leading hadrons disappear, but also where
  they go ? separate energy loss from absorption
• In-medium changes seem to be established
• CERES, NA60, TAPS/CB, Photoabs., hadron
  attenuation
• Transport is now reliable for a wide class of
  reactions

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Why study in-medium hadrons?

• Interior of stars depends on properties of
  hadrons at high density

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Why study in-medium hadrons?

• Density may restore symmetries of QCD
• Drop of condensates
• Degeneracy of chiral partnersm? /to m?

T
?
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Gold-plated Observables
explained by spectral change of ? meson in
dense/hot matter ?
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Theoretical Method for FSI BUU CC transport model

• Same Method for Same Physics
• Photonuclear reactions ? A
• Hadronic reactions ?,p A
• Heavy-ion reactions A A
• Resonance and Continuum Region treated
• Resonance Decays from data
• Continuum Decays from String Fragmentation

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Observables

• Experiment
• weak ISI ? ? best to reach nuclear interior,
• but entrance formfactors often not well known,
  
• ? like ?, because of shadowing
• FSI
• Hadronic, e.g. ? ! KK- difficult
• Semihadronic, e.g. ? ! ?0 ? possible
• Electromagnetic, e.g. ? ! ee- best

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Observables Theoretical Method

• Entrance Channel
• For Photons Quantum Coherence Shadowing
• Primary Production
• Resonance Decay or String-Fragmentation (PYTHIA)
• Exit Channel
• Incoherent Final State Interactions (Absorption
  Scattering Side-Feeding), Propagation with
  self-energies and interactions through resonances
  or fragmentation, coupled channels!? products of
  gA reaction need not be created in
  primary gN reaction

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Production and Formation Times? 14 GeV, Q2
2.5 GeV2
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With prehadronic FSI
Formation times in restframe ¼ 0.5 fm
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Transparency

Attenuation involves powers of L and L2
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Color Transparency (?)

• Glauber

• CBUU

T. Falter et al, Phys.Rev.C67054606,2003
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Off-shell Transport
? in-medium mass
Can be derived from Kadanoff-Baym eqs. (Leupold
Cassing), drives particles back to mass-shell
when they leave the nucleus
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? Photo-Production on nuclei

• S11(1535)
• small in-medium
• change for p0,
• sizeable momen-
• tum dependence
• of self-energy.

J. Lehr et al, Phys.Rev.C68044601,2003
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? in Medium

• ? ! ? ?0 (TAPS_at_ELSA)

Background from 2?0 ! 4 ?,one escapes with p(?)
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Photo-pion production on nuclei

• TAPS Data on p0 production

Theory Lehr et al
Data Krusche et al, Eur.Phys.J.A22347-351,2004

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Chiral Symmetry Restoration

• Expected s-p degenerate in chiral limit
• ? shift of s -gt 2? strength to lower masses

Connection to Observables??
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Chiral Symmetry Restoration2?0 Production on
Nuclei

• Expected s-p degenerate
• in chiral limit ? shift of s -gt 2? strength
• to lower masses

TAPS data, E? 400 500 MeV
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FSI on 2? in Nuclei
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Expecteds-p degenerate in chiral limit ? shift
of s strength to lower masses
2? production sites
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Nucleus as MicrodetectorHigh Energy ? Production
Processes

• Diffractive VMD-Event
• Main contribution to
• exclusive ?0-production
• Deep inleastic scattering,
• Jets
• How long does it take to form a hadron?

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2?0 Production on Nuclei
P. Muehlich et al, Nucl.Phys.A703393-408,2002
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2?0 Production on Nuclei

• Chiral symmetry restoration??

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Neutrino-nucleus scattering

• Fermi motion
• Pauli blocking
• Nuclear binding
• In-medium D width

1. Elementary reactions
2. In-medium modifications of the elementary cross
   sections
3. Propagation of the final state X FSI

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Nucleon knockout

• Enhancement due to secondary interactions
• ( , , )

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pT Spectra
Cronin ???
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Without prehadronic FSI

• charged hadrons

prehadronic interactions needed
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Jlab at 12 GeV
CLAS acceptance modelled
T. Falter, PhD thesis, Giessen, 2004
C Fe Pb
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Introduction

• Neutrino nucleus interactions are relevant for
• Oscillation experiments systematic uncertainties
• Hadron structure
• In-medium modifications
• Experiments MINERnA, FINeSSE with a high
  intensity n beam

• neutrino fluxes
• backgrounds
• detector responses

• nucleon axial form factor
• N-R axial transitions
• strangeness in the nucleon spin

• form factors
• spectral functions
• nuclear correlations

Understanding nuclear effects is essential for
the interpretation of the data and represents
both a challenge and an opportunity
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Inclusive cross section
D
QE
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Pion production