1. The role of the tetraquark at nonzero temperature Francesco Giacosa in collaboration with A. Heinz, S. Strüber, D. H. Rischke ITP, Goethe University, Frankfurt am Main Hadrons@Fias- 26/6/08

2. Outline Scalar mesons below and above 1 GeV at zero T Light scalar mesons (< 1 GeV) as tetraquark states and tetraquark-quarkonia mixing A chiral model with pions, light scalar quark-antiquark and tetraquark states Description of the model at zero T, quark and tetraquark condensates and mixing Results at nonzero temperature Order of the phase transition, behavior of the condensates and mixing angle, role interchange Francesco Giacosa Scalar Quest

3. Part I Spectroscopy in the vacuum

4. M < 1 GeV 1 GeV < M < 1.8 GeV Too many resonances than expected from quark-antiquark states Francesco Giacosa Scalar Quest Scalar resonances below 1.8 GeV reported by PDG:

5. M < 1 GeV interpretation Francesco Giacosa Scalar Quest Assignment has problems!!! Francesco Giacosa Scalar Quest Chiral partner of  ?

6. List of Problems Masses: degeneracy of and Strong coupling of to The scalar quarkonia are p-wave states (L = S = 1), thus expected to be heavier than 1 GeV as tensor and axial-vector mesons Some Lattice results find Large behavior of light scalar not compatible with quarkonia Francesco Giacosa Scalar Quest from: Prelovsek et al., Phys. Rev. D 70 (2004), Burch et al., Phys. Rev. D 73 (2006) from: Pelaez, Phys. Rev. Lett. (2004), Pelaez and Rios, hep-ph/0610397

7. Francesco Giacosa Scalar Quest The light scalars are interpeted as tetraquark state An example of „good diquark” is: A tetraquark is the bound state of two diquarks Idea of Jaffe ( R.L. Jaffe, Phys. Rev. D 15 (1977) ) : Example: (and not )

8. M < 1 GeV Tetraquark interpretation Francesco Giacosa Scalar Quest It is not the chiral partner of  !

9. M > 1 GeV interpretation Francesco Giacosa Scalar Quest Mixing among the isoscalars is expected Francesco Giacosa Scalar Quest Chiral partner of  !

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

11. Francesco Giacosa Scalar Quest Part II A chiral model with tetraquark

12. Francesco Giacosa Scalar Quest How does this scenario affect finite temperature behavior? We study this issue in the SU(2) limit within a simple model: Mixing shall play a crucial role:

13. Francesco Giacosa Scalar Quest A simple chiral model with tetraquark It emerges as an SU(2) limit of the SU(3) case (A. Heinz, S. Strüber, F. G. and D. H. Rischke: arXiv:0805.1134 [hep-ph] ) ( F.G., Phys.Rev.D75:054007,2007 )

14. Francesco Giacosa Scalar Quest One must therefore diagonalize the model introducing the mass eigenstates

15. Francesco Giacosa Scalar Quest That is, the fields H and S, corresponding to the two physical resonances, are introduced in order to diagonalize the potential:

16. Francesco Giacosa Scalar Quest Part III Results at nonzero T

17. Francesco Giacosa Scalar Quest We study this model at nonzero T by using the CJT formalism In the Hartree approximation. (Only double-bubble diagrams are taken into account ) Details in: A. Heinz, S. Strüber, F. G. and D. H. Rischke: arXiv:0805.1134 [hep-ph]

18. Francesco Giacosa Scalar Quest

19. 0805.1134 [hep-ph]

20. Francesco Giacosa Scalar Quest Quark condensate (order parameter) as function of T for different values of g for M S = 1.0 GeV Increasing of g (mixing): 1)T c decreases 2)First order softened 3)Cross-over obtained for g large enough

21. Francesco Giacosa Scalar Quest Similar discussion as before 0805.1134 [hep-ph]

22. Francesco Giacosa Scalar Quest We now turn to one specific case: We study for this set of parameters all the temperature-dependent quantitites: masses, mixing angle and condensates.

23. Francesco Giacosa Scalar Quest Finite Temperature behavior of quark and tetraquark condensates: This property depends on the characteristics of the model. However, It does not influence other quantities 0805.1134 [hep-ph]

24. Francesco Giacosa Scalar Quest Finite Temperature behavior of masses and angles: Two ‘critical temperatures’: The mixing angle grows with T up to the Maximal value. Then, it changes sign at T s and becomes negative. ( Second change at higher T) 0805.1134 [hep-ph]

25. Francesco Giacosa Scalar Quest Summary and outlook Spectroscopy of light scalars at zero T: if the light scalars are not quark- antiquark, how does chiral restoration change? Description of a model with pions, scalar quark-antiquark and tetraquark. Mixing at zero T: f 0 (600) is predominantly tetraquark and f 0 (1370) pred. quark-antiquark Tetraquark-quarkonium mixing implies: (i) decreasing of the critical temperature, (ii) softer first order, and, if the mixing is large enough, cross over. The latter can be obtained also for a mass of the chiral partner above 1 GeV The mixing increases with T. At a certain T s the mixing angle is maximal and a role interchange takes place. Then, chiral restoration takes place in the standard form. This was the first step! One shall go further and include more resonances.

26. Thank you very much Francesco Giacosa Scalar Quest

27. g=2 GeV. Ts>Tc

28. Francesco Giacosa Scalar Quest GeV lightest predicted glueball Lattice: Morningstar (1999)

29. Result for the mixed states: Obtained upon fit to the known results of PDG Francesco Giacosa Scalar Quest has the largest gluonic amount!!! F.G. et al, Phys.Rev.D72:094006, 2005 ( hep-ph/0509247) F.G. et al, Phys.Lett.B622:277-285,2005 ( hep-ph/0504033 ) F.G. et al, Phys.Rev.C71:025202,2005 ( hep-ph/0408085 )

30. Compatible with a dominant: Francesco Giacosa Scsalar Quest

31. Francesco Giacosa Scalar Quest Strong decays of a tetraquark state: Subdominant P P [4q] S P P Dominant [4q] S Previous works and motivations Original paper: Jaffe, Phys. Rev. D 15 (1977), Revival in: Maiani et al, Phys. Rev. Lett. (2004) Experimental study: D. V. Bugg, EPJC47 (2006) Systematic evaluation of amplitudes: my work Phys.Rev.D74:014028,2006

32. Francesco Giacosa Scalar Quest I studied the strong decays with a hadronic model (never see quarks and gluons, only hadrons) Nonet of pseduoscalar states: Nonet of scalar tetraquark states: The phys. resonances result from mixing

33. Francesco Giacosa Scalar Quest Write the flavor, P, C invariant interaction Lagrangian for the scalar 4q decays: P P Dominant [4q] S Sumdominant P P [4q] S The trace structure corresponds to the microscopic diagrams:

34. Scalar tetraquark and quarkonia states can mix Black et al, Phys. Rev. D 64 (2001), F.G., Phys.Rev.D 75,(2007) Extension of the model: ; consider scalar and pseudoscalar quarkonia meson and scalar tetraquark states Francesco Giacosa Scalar Quest Spontaneous symmetry breaking takes place, but no need to specify the potential. The pions emerge as Golstone bosons.. Going further: tetraquark-quarkonia mixing

35. Francesco Giacosa Scalar Quest decay mixing tq-condensate

36. Francesco Giacosa Scalar Quest One relates the tetraquark-decay parameters to the mixing strenght by using the decay widths of PDG; then, one can evaluate the mixing: Result in the isovector sector The mixing is small !!!

37. Francesco Giacosa Scalar Quest Consider flavor: 3 antisymmetric combinations Under SU(3)-flavor the 3 diquarks behave like antiquarks:

38. Francesco Giacosa Scalar Quest We have the correspondences: and: Compose a diquark and an antidiquark: full 4-q nonet Example:

39. Francesco Giacosa Scalar Quest A tetraquark condensate is generated:

40. Francesco Giacosa Scalar Quest