Nils A. Törnqvist University of Helsinki

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

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

3. Two recent reviews on light scalars Mixing Higgs N.A. Törnqvist

4. 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 s(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. Mixing Higgs N.A. Törnqvist

5. 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-antiquarkin P-wave, but further out they rearrange as 2 quark-antiquark systems and finally as meson–meson states. Mixing Higgs N.A. Törnqvist

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7. Recent s(600) pole determinations Mixing Higgs N.A. Törnqvist

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

9. Ms= f(1020)p0p0g Study of the Decay f(1020)p0p0g with the KLOE Detector The KLOE Collaboration Phys.Lett. B 537 (2002) 21-27 (arXiv:hep-ex/0204013 Apr 2002) Sigma parameters from E791 Mixing Higgs N.A. Törnqvist

10. The two pion invariant mass distribution in D+ to pppdecay (dominated by broad low-massf0(600)), and (b) the Dalitz plot (from E791). Mixing Higgs N.A. Törnqvist

11. The invariant mass distributionin Ds to 3pdecay showingmainly f0(980) and f0(1370). and Dalitz plot(E791). Mixing Higgs N.A. Törnqvist

12. The D+to K-p+p+ Dalitz plot. A broad kappa is reported under the dominating K*(892) bands (E791). Mixing Higgs N.A. Törnqvist

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

14. Important things to notice in analysis of the very broad s(600) (and k(800)) • One should have an Adler zero as required by chiral symmetry near s=mp2/2. 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 Mixing Higgs N.A. Törnqvist

15. 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 s(600) at 600-650 MeV with large (600 MeV) pp width, An a0 near 1030 MeV, and a very broad 700 MeV kappa near 1120 MeV Mixing Higgs N.A. Törnqvist

16. Spontaneous symmetry breaking and the Mexican hat potential Cylindrical symmetry mp = ms Cylindrical symmetry mp = 0, ms > 0, proton mass>0 and constituent quark mass 300MeV Chosing a vacuum breaks the symmetry spontaneously Mixing Higgs N.A. Törnqvist

17. Tilt the potential by hand and the pion gets mass mp > 0, ms > 0 But what tilts the potential? Another instability? Mixing Higgs N.A. Törnqvist

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

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

20. 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. Mixing Higgs N.A. Törnqvist

21. To see the anology with the LsM, 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 LsM L R Mixing Higgs N.A. Törnqvist

22. Compare this with the LsM for p and s in matrix representation; Mixing Higgs N.A. Törnqvist

23. The LsM and the Higgs sector are very similar but with very different vacuum values. = Now add the two models with a small mixing term e This is like two-Higgs-doublet model, but much more down to earth. Mixing Higgs N.A. Törnqvist

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

25. Diagonalizing this matrix one gets a massive pion and a massless triplet Goldstone; 2 The pion gets a mass through the mixing mp= e2[V/v +v/V]. Right pion mass if e = 2.70 MeV. The Goldstone triplet is swallowed by the W and Z in the usual way, but with small corrections from the scalars. Mixing Higgs N.A. Törnqvist

26. Quark loops should mix the scalars of strong and weak interactions and produce the mixingterm e proportional to quark mass? 2 q higgs, W L s, p q Also isospin and other global symmetries schould be violated by similar graphs Mixing Higgs N.A. Törnqvist

27. 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 (s, k) and the whole light nonet, s(600) k(800),f0(980),a0(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 LsM the pion gets mass, and global symmetries broken? Further analyses needed! Mixing Higgs N.A. Törnqvist

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

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

32. Unitarize the basic terms.Example for contact term + resonance graphically: Mixing Higgs N.A. Törnqvist

33. K-matrix unitarizationF.Q.Wu and B.S.Zou, hep-ph/0412276 Mixing Higgs N.A. Törnqvist

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