Processes involving nucleons in a chiral approach Francesco Giacosa in collaboration with Susanna Gallas, Anja Habersetzer, Walaa Eshraim, Denis Parganlija, Stanislaus Janowski, Achim Heinz, K. Teilab, and Dirk Rischke J. W. Goethe University, Frankfurt am Main and Gy. Wolf, P. Kovacs, Inst..for Particle and Nuclear Physics, Wigner Research Center for Physics, Budapest (Hungary) G. Pagliara, University and INFN of Ferrara (Italy) XXV HADES Collaboration Meeting Exploring Dense Matter at SIS 18 Energies, GSI Darmstadt, 21th November 2012

Francesco Giacosa Motivation Development of a a (chirally symmetric) model for mesons and baryons including (axial-)vector d.o.f. Study of the model for T = μ =0 (spectroscopy in vacuum) (decay, scattering lengths,…) Second goal: properties at nonzero T and μ (Condensates and masses in thermal/matter medium,…) Interrelation between these two aspects!

Francesco Giacosa Fields of the model: Quark-antiquark mesons: scalar, pseudoscalar, vector and axial-vector quarkonia. Additional mesons: The scalar and the pseudoscalar glueballs Baryons: nucleon doublet and its partner (in the so-called mirror assignment) How to construct the model: (Global) Chiral symmetry: SUR(Nf)xSUL(Nf)xUV(1) Retain operators of fourth order (dilatation invariance)

Part I: The mesonic Lagrangian Francesco Giacosa Part I: The mesonic Lagrangian

Meson sector 4Nf +2 fields For Nf = 2 there are 18 mesons Francesco Giacosa Meson sector 4Nf +2 fields For Nf = 2 there are 18 mesons 16 quark-antiquark fields + 2 glueballs For Nf = 3 there are 38 mesons 36 quark-antiquark fields + 2 glueballs 2

Francesco Giacosa

Francesco Giacosa

An important ongoing work: Francesco Giacosa An important ongoing work: the calculation of the full mixing problem in the I=J=0 sector is ongoing: Our result within the Nf=2 case was: Details in S. Janowski, D. Parganlija, F.G., D. Rischke, Phys.Rev. D84 (2011) 054007, arXiv:1103.3238

Francesco Giacosa

Francesco Giacosa

Model of QCD – eLSM with scalar Glueball Chiral symmetry Dilatation invariance [S. Janowski, D. Parganlija, F. Giacosa, D. H. Rischke, Phys. Rev. D84, 054007 (2011)] [D. Parganlija, P. Kovacs, G. Wolf , F. Giacosa, D. H. Rischke, arXiv:1208.0585 [hep-ph] (2012)] 11

Basic features: Perform Spontaneous Symmetry Breaking (SSB): Francesco Giacosa Basic features: Perform Spontaneous Symmetry Breaking (SSB): Explicit symmetry breaking terms: Parameter c: axial anomaly and eta-prime mass

Results of the fit (11 parameters, 21 exp. quantities) Francesco Giacosa Results of the fit (11 parameters, 21 exp. quantities) arXiv:1208.0585 Errorr from PDG or 5%. Scalar-isoscalar sector not included

Results of the fit: pictorial representation Francesco Giacosa Results of the fit: pictorial representation arXiv:1208.0585 Overall phenomenology is good. Scalar mesons a0(1450) and K0(1430) above 1 GeV and are quark-antiquark states.. Importance of the (axial-)vector mesons Axial-vector mesons as (predominantly) quark-antiquark states

One consequence of the fit: the rho mass Francesco Giacosa One consequence of the fit: the rho mass

A new field: the pseudoscalar glueball Francesco Giacosa A new field: the pseudoscalar glueball 1208.6474 PANDA/FAIR will be able to scan the energy above 2.5 GeV Details in: W. Eshraim, S. Janowski, F.G:, D. Rischke, arxiv: 1208.6474 (submitted to Phys. Rev. D). W. Eschraim, S. Janowski, K. Neuschwander, A. Peters, F.G., Acta Phys. Pol. B, Prc. Suppl. 5/4, arxiv: 1209.3976

Nf = 2 with „frozen“ glueball: done! Francesco Giacosa What we did up to now in the meson sector and what we will be doing… Nf = 2 with „frozen“ glueball: done! Nf = 2 with active glueball ( ): done! Nf = 3 with „frozen“ glueball ( ): done!. Nf = 3 with pseudoscalar glueball: done! Nf = 3 with active glueball ( ): ongoing. Inclusion of weak bosons and tau decay: ongoing. Generalization to Nf = 4: ongoing. Molecular or tetraquark nonet: planned. Study at nonzero temperature (with dilepton emission): planned.

Francesco Giacosa Part II: Baryon sector

Francesco Giacosa Baryon sector Nf = 2 only Nucleon and its chiral partner; chiral symmetry and dilatation invariance (Axial-)vector mesons are included Mirror assignment: (C. De Tar and T. Kunihiro, PRD 39 (1989) 2805) A chirally invariant mass-term is possible!

Francesco Giacosa Mass of the nucleon parameterizes the contribution which does not stem from the quark condensate Crucial also at nonzero temperature and density also in the so-called quarkyonic phase: L. McLerran, R. Pisarski Nucl.Phys.A796:83-100,2007

Axial coupling constants Francesco Giacosa Axial coupling constants Without vector and axial-vector mesons: cannot be described without vector d.o.f. However, with (axial-)vector mesons are introduced the axial couplings are modified. A description of the axial couplings is then possible. Result for m0: S. Gallas, F.G, D. Rischke, Phys.Rev.D82:014004,2010.  e-Print: arXiv:0907.5084 [hep-ph]

Pion-nulceon scattering lengths Francesco Giacosa Pion-nulceon scattering lengths Large theoretical uncertainty due to the scalar-isosocalar sector Importance of both vector mesons and mirror assignment in order to get these results

There is indeed a problem yet for N*=N(1535) Francesco Giacosa There is indeed a problem yet for N*=N(1535) When using N*=N(1650) one gets: An enlarged mixing scenario with 4 nucleon fields is planned: N(940), N(1440), N(1535), N(1650)

Present status of baryon phenomenology in the vacuum Francesco Giacosa Present status of baryon phenomenology in the vacuum Nf = 2: done ! (enlarged mixing scenario is planned) Nf = 2 with inclusion of the delta-resonance: ongoing! Nucleon-nucleon scattering: ongoing. Nucleon-nucleon processes with eta and omega productions: ongoing. Nf = 3 extension: planned.

What we are studying rigth now… Francesco Giacosa What we are studying rigth now…

Other processes with nucleons are possible. Francesco Giacosa Other processes with nucleons are possible. Example: pseudoscalar glueball

Part III: Nonzero density Francesco Giacosa Part III: Nonzero density

Basic considerations for nonzero density Francesco Giacosa Basic considerations for nonzero density The σ-field of our model is associated with the resonance f0(1370) …and not with the lightest scalar resonance f0(500). The question is: what is f0(500) and, more in general, what are the scalar states below 1 GeV? A good phenomenology (masses and decays) is achieved when interpreting the light scalar states as tetraquarks: (bound states of a diquark and an anti-diquark)

Back to nucleons: Where does m0 comes from? Francesco Giacosa Back to nucleons: Where does m0 comes from? Tetraquark New field dilaton m0 originates form the tetraquark and the gluon condensates. Note, also, a tetraquark exchange naturally arises in nucleon-nucleon interactions

Nuclear matter saturation Francesco Giacosa Nuclear matter saturation arXiv:1105.5003

An important test: Compressibility Francesco Giacosa An important test: Compressibility Saturation: ok. Compressibility: K is about 200 MeV (in agreement with experiment) arXiv:1105.5003

Related ‘amusing’ question: does nuclear matter binds at large Nc? Francesco Giacosa arXiv:1105.5003 Thus, the tetraquark plays an important role for the stability of nuclear matter. Related ‘amusing’ question: does nuclear matter binds at large Nc?   As soon as the lightest scalar f0(500) is not a quarkonium, nuclear matter ceases to exist already for Nc=4. Luca Bonanno and F.G., Nucl.Phys.A859:49-62,2011.  arXiv:1102.3367 [hep-ph]

Masses Critical densities for the mixed phase Francesco Giacosa arXiv:1105.5003

Present status and projects Francesco Giacosa Present status and projects Nf=2 and inclusion of the tetraquark as the lightest scalar state : done. Non-homogeneous phases: ongoing. Nf = 3 (all baryons and mesons): planned. Finite temperature and finite density: full QCD phase: planned.

Francesco Giacosa Summary and outllook Chiral model (eLsM) for hadrons based on dilatation invariance Important role of (axial-)vector mesons in all phenomenology Scalar quarkonia and glueball above 1 GeV (effects in the medium) Contribution to the nucleon mass which does not stem fro the chiral condensate (but from the tetraquark and glueball condensates) Nf=3 (ongoing) and Nf=4, additional tetraquark states, weak decays,… Systematic studies of the phase diagram of QCD

Francesco Giacosa Thank You for the attention

Examples of invariants Francesco Giacosa Examples of invariants The reason is: dilatation invariance of the interaction terms and finiteness of potential Note that we are not imposing renormalizability! A low-energy theory of QCD does not need to be renormalizable. Large-Nc arguments allow to neglect some, but not all higher order diagrams

M < 1 GeV 1 GeV < M < 1.8 GeV Francesco Giacosa Scalar Quest M < 1 GeV 1 GeV < M < 1.8 GeV Too many resonances than expected from quark-antiquark states

M < 1 GeV Tetraquark interpretation Francesco Giacosa Scalar Quest M < 1 GeV Tetraquark interpretation

Indeed, mixing will occur, thus the scenario changes slightly as: Francesco Giacosa Scalar Quest Indeed, mixing will occur, thus the scenario changes slightly as: M < 1 GeV 1 GeV < M < 1.8 GeV Not the chiral partner of pion! Chiral partner of pion! These are predominantly tetraquarks (but not only!) These are predominantly quarkonia (with glueball-intrusion) (but not only!)

Tetraquark: outlook and short excursus at nonzero T Francesco Giacosa Tetraquark: outlook and short excursus at nonzero T A possibility is to interpret the light scalar states below 1 GeV [f0(600), k(800), f0(980) and a0(980)] as diquark-antidiquark objects: these are the Jaffe’s tetraquarks. The Nf=3 case is an outlook. Mixing of these tetraquark-quarkonioa takes place. Black et al, Phys. Rev. D 64 (2001), F.G., Phys.Rev.D 75,(2007) For Nf=2 only one tetraquark survives. In this case we studied a simplified system at nonzero T. Increasing of mixing: Tc decreases First order softened Cross-over obtained for g large enough Achim Heinz, Stefan Strube, F.G., Dirk H. Rischke Phys.Rev.D79:037502,2009; arXiv:0805.1134 [hep-ph]

Digression: 3 scenarios for the ρ-meson at nonzero T Francesco Giacosa Digression: 3 scenarios for the ρ-meson at nonzero T Ma1 Mρ Mρ In our case: Mρ We expect case A to hold; small drop of the masses in the medium T Case A: G0-term dominates T Ma1 Case B: the two terms have similar contributions Ma1 Mρ Mρ T T Case B: both terms are similar Case C: the condensate dominates

Francesco Giacosa Mass of the nucleon (2)

Francesco Giacosa