1. I=1 heavy-light tetraquarks and the Υ(mS) → Υ(nS)ππ puzzle Francisco Fernández Instituto de Física Fundamental y Matemáticas University of Salamanca

2. Multiquark structures in heavy- light meson systems Meson structure is a few-body problem

3. Outline ► Motivations ► the model ► D sJ mesons ► The Υ(mS) → Υ(nS)ππ puzzle

4. Motivations

5. Why four quarks configuration? qqqq  cs  J π =0 +,1 + L=0 L=1 P( s )=-1 − → → P(qq)=+1 − −

6. Open charm sector

7. the model

8. Constituent Quark Model Generalization to heavy flavours of the original SU(2) F model developed in J. Phys. G19 2013 (1993) Basic ingredients Chiral symmetry is spontaneously broken at some momentum scale provinding a constituent quark mass M(q 2 ) for the ligth quarks As a consecuence light constituent quarks exchange Goldstone bosons Both light and heavy quarks interacts besides by gluon exchange Finally both type of quarks are confined by a two body linear potential screened at large distancies due to pair creation Details can be found in J. of Phys. G: Nucl. Part Phys. 31 1-26

9. Constituent Quark Model N-N interaction –F. Fernández, A. Valcarce, U. Straub, A. Faessler. J. Phys. G19, 2013 (1993) –A. Valcarce, A. Faessler, F. Fernández. Physics Letters B345, 367 (1995) –D.R. Entem, F. Fernández, A. Valcarce. Phys. Rev. C62 034002 (2000) –B. Juliá-Diaz, J. Haidenbauer, A. Valcarce, and F. Fernández. Physical Review C 65, 034001, (2002) Baryon spectrum –H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 64, 058201, (2001) –H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 63, 035207 (2001) Meson spectrum. –L.A. Blanco, F. Fernández, A. Valcarce. Phys. Rev. C59, 428 (1999) –J. Vijande, F. Fernández, A. Valcarce. J. Phys. G31, (2005) http://web.usal.es/~gfn/menu_i.htm

10. Deuteron NN phase shifts Triton

11. qq system 

12. The QCD OGE diagram with point-like quarks gives Constituent Quark Model Ligth quarks Solve the Schrödinger equation in the two- and four-body systems Nonrelativistic approximation Heavy quarks

13. Meson spectra (I) Light I=1

14. Meson spectra (II) Light I=0

15. Meson spectra (III) Kaons

16. Meson spectra (IV) Charmonium

17. Meson spectra (VI) Bottomonium

18. qqqq system 

19. Numerical techniques x y z The two-body problem is solved using the Numerov algorithm. The four-body problem (two particles and two antiparticles) is solved by means of a variational method. Three main difficulties: Non-trivial color structure. Symmetry properties in the radial wave function (Pauli Principle) Two- and four-body mixing. r +

20. Non-trivial color structure. Four-Body formalism 1 2! We expand the radial wave function in terms of generalized gaussians with -Well defined permutation properties (SS, AA, AS, SA). - L= 0 (relative angular momenta l i  0) - Positive parity Symmetry properties in the radial wave function (Pauli Principle)

21. x y z Four-Body configurations. Tetraquarks structures Two color singlets with different symmetry.

22. We solve the tetraquark system using a variational method expanding the radial part of the wave function in terms of generalized gaussian (GG) defined as: The radial wave function defined in this way has L=0 But each generalized gaussian contains an infinite number of relative angular momentum.

23. Four-Body configurations. Two- and four-body mixing

25. D sJ mesons

26. D SJ * (2317) BaBar: PRL 90, 242001 (2003) Narrow peak in D S  0. J P =0 + I=0 favored. Width consistent with the detector resolution, less than 10 MeV. Mass near 2317 MeV, 40 MeV below DK threshold.

27. D SJ (2460) Narrow peak in D * S  0, and also observed in D S . J P =1 + favored. Width consistent with the detector resolution, less than 8 MeV. Mass close to 2460 MeV, below D * K threshold. CLEO: PRD 68, 032002 (2003)

28. Open charm sector

31. ←

32. The Υ(mS) → Υ(nS)ππ puzzle

33. Most of the tetraquark resonances are coupled to pairs qq  Isolate resonances ? qbqb  qcqc  They exist? I=1 Heavy light tetraquarks

34. qbqb 10,06 GeV.  qcqc 3,66 GeV. 

35. Υ(mS) → Υ(nS)ππ X(qbqb)  →

36. Υ(1S) 9,460 GeV. Υ(2S) 10,023 GeV Υ(3S) 10,335 GeV. Υ(4S) 10,580 GeV. →

37. Υ(2S) →Υ(1S)ππ Υ(3S) →Υ(1S)ππ Υ(3S) →Υ(2S)ππ

38. Guo et al NPA 761 269m X =10.08 GeV. qbqb 10,06 GeV. 

39. hep-ph/0601120

41. ←

42. SUMMARY We have analyzed the meson spectra using two- and four-quark states within a model which has also been applied to the NN interaction and the hadron phenomenology. We have observed that to describe the open-charmed heavy-light meson sector (D and D S ) it is necessary to go beyond the conventional quark-antiquark models including other components, as for instance four quark components. We have shown that they are several indication of isolated I=1 tetraquark resonances J. Vijande, A. Valcarce University of Salamanca

43. End

44. H. VogelFPCP 200644 Dipion Transitions in cc _ CLEO-c Y(4260) →  J  BaBar X(3872) →  J  CLEO-c  (3770) →  J  BES  (3682) →  J   (3682)  (3770) X(3872) Y(4260) compare with hep-ex/0602034 PRD 71 (2005) 071103 PRL 96(2006) 082004 hep-ex/9909038 →

46. Most of the mesons fits nicely in a pattern where they have quantum numbers of quark-antiquark bound states. However this simple and succesfull picture is difficult to apply to the J π =0 + scalar meson sector. Apparently scalar are different Motivations