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Helmholtz International Center for FAIR
Effective Theories for Hadrons
Stefan Leupold
Institut für Theoretische Physik, Justus-Liebig-Universität Giessen
March 6, 2008 Stefan Leupold 2
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r Understanding the spectrum of hadrons
Selection of key questions:
How can we understand the masses of hadrons and their decay pattern?
Are there hadrons which solely/dominantly consist out of gluons (glueballs)?
Do some/many hadrons have a hadronic substructure (“hadron molecules”)?
e.g. experimental Ds spectrum qualitative input from QCD: quarks and gluons form hadrons
quantitative: challenging
experiment: PANDA
complementary approaches (relevant for PANDA):
Lattice QCD ↔ Dyson-Schwinger Equations ↔ Effective Field Theory
March 6, 2008 Stefan Leupold 3
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r HIC for FAIR opportunity: glueball spectrum
consider resonance decay R → A + B problem of lattice QCD for light enough quarks,
i.e. for mA + mB < mR :
correlator yields lightest state in spectrum two-particle state A + B instead of resonance state R
way out: Lüscher’s phase shift analysis in finite box with variable box size numerically expensive need for effective field theory in HIC for FAIR
prediction from lattice QCD: glueball masses but: so far only gluons, no quarks in calculation necessary improvements: include quarks, i.e.
mixing with mesons (next slide)
states become resonances deal with finite width
March 6, 2008 Stefan Leupold 4
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r Mixing of glueballs with mesons
complementary to lattice QCD: Dyson-Schwinger (DS) equations
for quark-gluon n-point functions (quantum correlations)
input for Bethe-Salpeter equation for glueballs and mesons
mixing of glueballs and mesons microscopic understanding
(relevant degrees of freedom,...)
gluon propagator from lattice and from DS:
difficult for lattice QCD and Dyson-Schwinger: treatment of intermediate hadron-hadron states Effective Field Theory
March 6, 2008 Stefan Leupold 5
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r Structure of resonances
Resonances decay into other “final-state” hadrons
Influence of hadrons and their interactions on resonance properties?
Examples for extreme cases: Resonance is dominantly quark-antiquark Resonance is formed by attractive interactions between hadrons
hadron molecule → fig.
HIC for FAIR opportunity and challenge: develop sophisticated approach for description of final-state hadrons and their interactions effective field theory = systematic approach unknown coupling constants from fit to data or from lattice QCD
March 6, 2008 Stefan Leupold 6
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r Axial-vector states as hadron molecules
axial-vectors decay into vectors + pseudoscalars, attractive interaction! strong enough to generate axial-vectors dynamically
(see also poster on PANDA theory)
March 6, 2008 Stefan Leupold 7
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r Structure of resonances
Resonances decay into other “final-state” hadrons
Influence of hadrons and their interactions on resonance properties?
Examples for extreme cases: Resonance is dominantly quark-antiquark Resonance is formed by attractive interactions between hadrons
hadron molecule → poster
HIC for FAIR opportunity and challenge: develop sophisticated approach for description of final-state hadrons and their interactions effective field theory = systematic approach unknown coupling constants from fit to data or from lattice QCD
March 6, 2008 Stefan Leupold 8
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r Cross relation to CBM
effective theories can yield input for unknown cross sections necessary for transport in particular important for dedicated probes, e.g. dileptons, charm, ...
(e.g. N + → resonance → N + dilepton)
in addition: systematic treatment of in-medium modifications changes induce changes:
↔
selfconsistent approaches coupled integral equations
under development by several Hessian groups, but incoherent efforts: Weinhold/Friman (GSI): dynamics of pion-nucleon-Delta Post/Mosel/Leupold (JLU): rho meson in nuclear medium Riek/Knoll (GSI): omega meson in nuclear medium Röder/Ruppert/Rischke (FFM): mesons at finite temperature Leupold (JLU): how to satisfy conservation laws
March 6, 2008 Stefan Leupold 9
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r HIC for FAIR: Opportunities and challenges
Synergy for numerically and conceptually challenging developments
understanding the spectrum of hadrons(PANDA)
Effective Field Theory(final state interactions, hadron molecules,...)
lattice QCD(spectrum, coupling constants,...)
Dyson-Schwinger(microscopic understanding, mixing,...)
coherent starting point for
in-medium modifications
(selfconsistency,...)
March 6, 2008 Stefan Leupold 10
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r Backup slide: Effective field theories for hadrons
Systematic approach (instead of arbitrary model building) principles of scattering theory and effective field theory:
exact unitarity and analyticity, i.e. use of Bethe-Salpeter equation
coupled-channel dynamics (Lutz, Kolomeitsev, ...) systematic power counting
extension of chiral perturbation theory to include (at least) vector mesons and Delta decuplet
currently developed (e.g. Lutz/Leupold, arXiv:0801.3821 [nucl-th])
Goal: disentangle hadronic rescattering effects from “elementary” resonances (quark-antiquark, glueball,…)
March 6, 2008 Stefan Leupold 11
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full analyticity (dispersion relations) requires serious treatment of left-hand cuts from t- and u-channels
coupled integral equations
get unknown coupling constants from lattice QCD e.g. three-point functions for vector mesons (V-V-V) numerically challenging
Backup slide: Shopping list