1. Helmholtz International Center for Helmholtz International Center for FAIR Effective Theories for Hadrons Stefan Leupold Institut für Theoretische Physik, Justus-Liebig-Universität Giessen

2. Helmholtz International Center for March 6, 2008Stefan Leupold2 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 D s 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

3. Helmholtz International Center for March 6, 2008Stefan Leupold3 HIC for FAIR opportunity: glueball spectrum consider resonance decay R → A + B  problem of lattice QCD for light enough quarks, i.e. for m A + m B < m R : 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

4. Helmholtz International Center for March 6, 2008Stefan Leupold4 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

5. Helmholtz International Center for March 6, 2008Stefan Leupold5 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

6. Helmholtz International Center for March 6, 2008Stefan Leupold6 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)

7. Helmholtz International Center for March 6, 2008Stefan Leupold7 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

8. Helmholtz International Center for March 6, 2008Stefan Leupold8 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 + p → 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

9. Helmholtz International Center for March 6, 2008Stefan Leupold9 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,...)

10. Helmholtz International Center for March 6, 2008Stefan Leupold10 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,…)

11. Helmholtz International Center for March 6, 2008Stefan Leupold11 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