1. Nils A. Törnqvist University of Helsinki Talk at Frascati January 19-20 2006 The Light Scalar Nonet, the sigma(600), and the EW Higgs

2. Frascati. January 2006Mixing Higgs N.A. Törnqvist2 Tentative quark–antiquark mass spectrum for light mesons The states are classified according to their total spin J, relative angular momentum L, spin multiplicity 2S +1 and radial excitation n. The vertical Each box represents a flavour nonet containing the isovector meson, the two strange isodoublets, and the two isoscalar states.,

3. Frascati. January 2006Mixing Higgs N.A. Törnqvist3 Two recent reviews on light scalars

4. Frascati. January 2006Mixing Higgs N.A. Törnqvist4 Why are the scalar mesons important? The nature of the lightest scalar mesons has been controversial for over 30 years. Are they the quark-antiquark, 4-quark states or meson-meson bound states, collective excitations, or … Is the  (600) a Higgs boson of QCD? Is there necessarily a glueball among the light scalars? These are fundamental questions of great importance in QCD and particle physics. If we would understand the scalars we would probably understand nonperturbative QCD The mesons with vacuum quantum numbers are known to be crucial for a full understanding of the symmetry breaking mechanisms in QCD, and Presumably also for confinement.

5. Frascati. January 2006Mixing Higgs N.A. Törnqvist5 What is the nature of the light scalars? In the review with Frank Close we suggested: Two nonets and a glueball provide a consistent description of data on scalar mesons below 1.7 GeV. Above 1 GeV the states form a conventional quark-antiquark nonet mixed with the glueball of lattice QCD. Below 1 GeV the states also form a nonet, as implied by the attractive forces of QCD, but of a more complicated nature. Near the centre they are diquark-antidiquark in S-wave, a la Jaffe, and Maiani et al, with some quark-antiquark in P- wave, but further out they rearrange as 2 quark-antiquark systems and finally as meson–meson states.

6. Frascati. January 2006Mixing Higgs N.A. Törnqvist6

7. Frascati. January 2006Mixing Higgs N.A. Törnqvist7 Recent  (600) pole determinations

8. Frascati. January 2006Mixing Higgs N.A. Törnqvist8 BES collaboration: PL B 598 (2004) 149–158 Finds the σ pole in J/ψ →ωπ + π − at (541±39)−i(252±42) MeV

9. Frascati. January 2006Mixing Higgs N.A. Törnqvist9      M=M= Study of the Decay      with the KLOE Detector The KLOE Collaboration Phys.Lett. B 537 (2002) 21-27 (arXiv:hep-ex/0204013 Apr 2002) Sigma parameters from E791

10. Frascati. January 2006Mixing Higgs N.A. Törnqvist10 (a)The two pion invariant mass distribution in D + to  decay (dominated by broad low-mass f 0 (600)), and (b) the Dalitz plot (from E791).

11. Frascati. January 2006Mixing Higgs N.A. Törnqvist11 The invariant mass distribution in D s to 3  decay showing mainly f 0 (980) and f 0 (1370). and Dalitz plot (E791).

12. Frascati. January 2006Mixing Higgs N.A. Törnqvist12 The D + to K -     Dalitz plot. A broad kappa is reported under the dominating K*(892) bands (E791).

13. Frascati. January 2006Mixing Higgs N.A. Törnqvist13 Very recently I. Caprini, G. Colangelo, H. Leutwyler, Hep-ph/05123604 from Roy equation fit get

14. Frascati. January 2006Mixing Higgs N.A. Törnqvist14 Important things to notice in analysis of the very broad  (and  One should have an Adler zero as required by chiral symmetry near s=m   /2. This means spontaneous chiral symmetry breaking in the vacuum as in the (linear) sigma model. To fit data in detail one should furthermore have: Right analyticity behaviour (dispersion relations) at thresholds One should include all nearby thresholds (related by flavour symmetry) in a coupled channel model. One should unitarize Have (approximate) flavour symmetric couplings

15. Frascati. January 2006Mixing Higgs N.A. Törnqvist15 The U3xU3 linear sigma model with three flavours If one fixes the 6 parameters using the well known pseudoscalar masses and decay constants one predicts: A low mass  (600) at 600-650 MeV with large (600 MeV)  width, An a0 near 1030 MeV, and a very broad 700 MeV kappa near 1120 MeV

16. Frascati. January 2006Mixing Higgs N.A. Törnqvist16 Cylindrical symmetry m  = m  Cylindrical symmetry m  = 0, m  proton mass>0 and constituent quark mass 300MeV Spontaneous symmetry breaking and the Mexican hat potential Chosing a vacuum breaks the symmetry spontaneously

17. Frascati. January 2006Mixing Higgs N.A. Törnqvist17 Tilt the potential by hand and the pion gets mass m  > 0, m  > 0 But what tilts the potential? Another instability?

18. Frascati. January 2006Mixing Higgs N.A. Törnqvist18 Two coupled instabilities breaking the symmetry If they are coupled, they can tilt each other spontaneously:

19. Frascati. January 2006Mixing Higgs N.A. Törnqvist19 F>F crit F<F crit Another way to visualize an instability, An elastic vertical bar pushed by a force from above The cylindrical symmetry broken spontaneously

20. Frascati. January 2006Mixing Higgs N.A. Törnqvist20 Now hang the Mexican hat on the elastic vertical bar. This illustrates two coupled unstable systems. Now there is still cylindrical symmetry for the whole system, which includes both hat and the near vertical bar. One has one massless and one massive near-Goldstone boson.

21. Frascati. January 2006Mixing Higgs N.A. Törnqvist21 To see the anology with the L  M, write the Higgs doublet in a matrix form: NAT, PLB 619 (2005)145 and a custodial global SU(2) x SU(2) as in the L  M LR

22. Frascati. January 2006Mixing Higgs N.A. Törnqvist22 Compare this with the L  M for  and  in matrix representation;

23. Frascati. January 2006Mixing Higgs N.A. Törnqvist23 The L  M and the Higgs sector are very similar but with very different vacuum values. = Now add the two models with a small mixing term  This is like two-Higgs-doublet model, but much more down to earth.

24. Frascati. January 2006Mixing Higgs N.A. Törnqvist24 The mixing term shifts the vacuum values a little and mixes the states And the pseudoscalar mass matrix becomes

25. Frascati. January 2006Mixing Higgs N.A. Törnqvist25 Diagonalizing this matrix one gets a massive pion and a massless triplet Goldstone; The pion gets a mass through the mixing m   =  2 [V/v +v/V]. Right pion mass if  = 2.70 MeV. The Goldstone triplet is swallowed by the W and Z in the usual way, but with small corrections from the scalars. 2

26. Frascati. January 2006Mixing Higgs N.A. Törnqvist26 Quark loops should mix the scalars of strong and weak interactions and produce the mixing term  proportional to quark mass?  higgs, W q q L 2 Also isospin and other global symmetries schould be violated by similar graphs

27. Frascati. January 2006Mixing Higgs N.A. Törnqvist27 Conclusions We have one extra light scalar nonet of different nature, plus heavier conventional quark-antiquark states (and glueball). It is important to have Adler zeroes, chiral and flavour symmetry, unitarity, right analyticity and coupled channels to understand the broad scalars (  ) and the whole light nonet,  (600)  (800),f 0 (980),a 0 (980). Unitarization can generate nonperturbative extra poles! The light scalars can be understood with large [qq][qbar qbar] and meson-meson components By mixing the E-W Higgs sector and L  M the pion gets mass, and global symmetries broken? Further analyses needed!

28. Frascati. January 2006Mixing Higgs N.A. Törnqvist28

29. Frascati. January 2006Mixing Higgs N.A. Törnqvist29

30. Frascati. January 2006Mixing Higgs N.A. Törnqvist30 Adler zero in linear sigma model Example: resonance + constant contact and exchange terms cancel near s=0, Thus  scattering is very weak near threshold, but grows rapidly as one approaches the resonance Destructive interference between resonance and ”background”

31. Frascati. January 2006Mixing Higgs N.A. Törnqvist31 Correct analytic behaviour from dispersion relation It is not correct to naively analytically continue the phase space factor  (s) below threshold one then gets a spurious anomalous threshold and a spurious pole at s=0.

32. Frascati. January 2006Mixing Higgs N.A. Törnqvist32 Unitarize the basic terms. Example for contact term + resonance graphically:

33. Frascati. January 2006Mixing Higgs N.A. Törnqvist33 K-matrix unitarization F.Q.Wu and B.S.Zou, hep-ph/0412276

34. Frascati. January 2006Mixing Higgs N.A. Törnqvist34