1. 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

2. 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!

3. 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)

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

5. 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

6. Francesco Giacosa

7. Francesco Giacosa

8. 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) , arXiv:

9. Francesco Giacosa

10. Francesco Giacosa

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

12. 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

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

14. Results of the fit: pictorial representation
Francesco Giacosa
Results of the fit: pictorial representation
arXiv:
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

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

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

17. 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.

18. Francesco Giacosa
Part II: Baryon sector

19. 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!

20. 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

21. 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:  [hep-ph]

22. 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

23. 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)

24. 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.

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

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

27. Part III: Nonzero density
Francesco Giacosa
Part III: Nonzero density

28. 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)

29. 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

30. Nuclear matter saturation
Francesco Giacosa
Nuclear matter saturation
arXiv:

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

32. Related ‘amusing’ question: does nuclear matter binds at large Nc?
Francesco Giacosa
arXiv:
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:  [hep-ph]

33. Masses Critical densities for the mixed phase Francesco Giacosa
arXiv:

34. 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.

35. 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

36. Francesco Giacosa
Thank You
for the
attention

37. 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

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

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

40. 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 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!)

41. 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:  [hep-ph]

42. 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

43. Francesco Giacosa
Mass of the nucleon (2)

44. Francesco Giacosa