M.F.M. Lutz

On meson resonances and chiral symmetry

Abstract We study meson resonances with quantum numbers J P =1 + in terms of the chiral SU(3) Lagrangian. At leading order a parameter-free prediction is obtained for the scattering of Goldstone bosons off vector mesons with J P =1 − once we insist on approximate crossing symmetry of the unitarized scattering amplitude. A resonance spectrum arises that is remarkably close to the empirical pattern. In particular, we find that the strangeness-zero resonances h 1 (1380), f 1 (1285) and b 1 (1235) are formed due to strong K K μ and K K μ channels. This leads to large coupling constants of those resonances to the latter states.

Scattering of vector mesons off nucleons

Abstract We construct a relativistic and unitary approach to ‘high’ energy pion– and photon–nucleon reactions taking the πN , πΔ , ρN , ωN , ηN , KΛ , KΣ final states into account. Our scheme dynamically generates the s - and d -wave nucleon resonances N (1535), N (1650) and N (1520) and isobar resonances Δ (1620) and Δ (1700) in terms of quasi-local interaction vertices. The description of photon-induced processes is based on a generalized vector-meson dominance assumption which directly relates the electromagnetic quasi-local four-point interaction vertices to the corresponding vertices involving the ρ and ω fields. We obtain a satisfactory description of the elastic and inelastic pion– and photon–nucleon scattering data in the channels considered. The resulting s -wave ρ – and ω –nucleon scattering amplitudes are presented. Using these amplitudes we compute the leading density modification of the ρ and ω energy distributions in nuclear matter. We find a repulsive energy shift for the ω meson at small nuclear density but predict considerable strength in resonance–hole like ω -meson modes. Compared to previous calculations our result for the ρ -meson spectral function shows a significantly smaller in-medium effect. This reflects a fairly small coupling strength of the N (1520) resonance to the ρN channel.

Open charm meson resonances with negative strangeness

Abstract We study heavy-light meson resonances with quantum numbers JP=0+ and JP=1+ in terms of the non-linear chiral SU(3) Lagrangian. Adjusting the free parameters that arise at subleading order to reproduce the mass of the D(2420) resonance as well as the new states established recently by the BaBar, CLEO and BELLE Collaborations we obtain refined masses for the anti-triplet and sextet states. Bound states of antikaons at the D(1867) and D(2008) mesons are predicted at 2352 MeV (JP=0+) and 2416 MeV (JP=1+). In addition we anticipate a narrow scalar state of mass 2389 MeV with (I,S)=( 1 2 ,0) .

On charm baryon resonances and chiral symmetry

Abstract We study heavy-light baryon resonances with quantum numbers J P = 1 2 − in terms of the non-linear chiral SU(3) Lagrangian. Within the χ –BS(3) approach a parameter-free leading order prediction is obtained for the scattering of Goldstone bosons off heavy-light baryon resonances with J P = 1 2 + . The three states Λ c 1 (2593), Λ c 0 (2880) and Ξ c 1 (2790) discovered by the CLEO Collaboration are recovered. We suggest the existence of resonance states that form an anti-quindecimplet, two sextet and two anti-triplet representations of the SU(3) group. In particular, narrow states with anomalous isospin ( I ) and strangeness ( S ) quantum numbers (I,S)=( 1 2 ,+1) are anticipated.

From pion nucleon scattering to vector mesons in nuclear matter

Abstract We construct a relativistic and unitary approach to ‘high’ energy pion nucleon scattering taking into account the inelastic πΔ, ρ N , ω N , K Σ, K Λ and η N channels [1]. Our scheme dynamically generates the s- and d-wave nucleon and isobar resonances N *(1535), N *(1650), N *(1520), N *(1700), Δ*(1620) and Δ*(1700). We also describe the ρ- and ω-nucleon scattering amplitudes which in turn provide the leading density modification of the ρ and ω mass distribution in nuclear matter. We find repulsive mass shifts for both vector mesons at small nuclear density but predict considerable strength in low energy resonance-hole like vector meson modes.

Self consistent and covariant propagation of pions, nucleon and isobar resonances in cold nuclear matter

Abstract We evaluate the in-medium spectral functions for pions, nucleon and isobar resonances in a self consistent and covariant manner. The calculations are based on a recently developed formulation which leads to predictions in terms of the pion–nucleon scattering phase shifts and a set of Migdal parameters describing important short range correlation effects. We do not observe significant softening of pion modes if we insist on reasonable isobar resonance properties but predict a considerable broadening of the N ( 1440 ) and N ( 1520 ) resonances in nuclear matter. Contrasted results are obtained for the s-wave N ( 1535 ) and N ( 1650 ) resonances which are affected by a nuclear environment very little. The properties of slowly moving isobars in nuclear matter are found to depend very sensitively on a soft form factor in the π N N vertex, which is not controlled by the πN scattering data.

Resonances in QCD

Abstract We report on the EMMI Rapid Reaction Task Force meeting ‘ Resonances in QCD ’, which took place at GSI October 12–14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: • What is needed to understand the physics of resonances in QCD? • Where does QCD lead us to expect resonances with exotic quantum numbers? • What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up , down and strange quark content were considered. For heavy–light and heavy–heavy meson systems, those with charm quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.

Chiral Symmetry, Strangeness and Resonances

We review the important role played by the chiral SU(3) symmetry in predicting the properties of antikaons and hyperon resonances in cold nuclear matter. Objects of crucial importance are the meson-baryon scattering amplitudes obtained within the chiral coupled-channel effective field theory. The formation of baryon resonances as implied by chiral coupled-channel dynamics is discussed. Results for antikaon and hyperon-resonance spectral functions are presented for isospin symmetric and asymmetric matter.

On the convergence of the chiral expansion for the baryon ground-state masses

Abstract We study the chiral expansion of the baryon octet and decuplet masses in the isospin limit. It is illustrated that a chiral expansion of the one-loop contributions is rapidly converging up to quark masses that generously encompasses the mass of the physical strange quark. We express the successive orders in terms of physical meson and baryon masses. In addition, owing to specific correlations amongst the chiral moments, we suggest a reordering of terms that make the convergence properties more manifest. Explicit expressions up to chiral order five are derived for all baryon masses at the one-loop level. The baryon masses obtained do not depend on the renormalization scale. Our scheme is tested against QCD lattice data, where the low-energy parameters are systematically correlated by large- N c sum rules. A reproduction of the baryon masses from PACS-CS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC is achieved for ensembles with pion and kaon masses smaller than 600 MeV. Predictions for baryon masses on ensembles from CLS as well as all low-energy constants that enter the baryon masses at N3LO are made.

The associated photoproduction of positive kaons and π0Λ or πΣ pairs in the region of the Σ(1385) and Λ(1405) resonances

The