nils a. törnqvist university of helsinki

Nils A. Törnqvist University of Helsinki

Talk at Frascati January 19-20 2006

The Light Scalar Nonet, the sigma(600), and the EW Higgs

Frascati. January 2006 Mixing Higgs N.A. Törnqvist 2

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.

• • ,


Two recent reviews on light scalars


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.


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.


Recent (600) pole determinations


BES collaboration: PL B 598 (2004) 149–158 Finds the σ pole in J/ψ →ωπ+π− at

(541±39)−i(252±42) MeV


M=

Study of the Decay with the KLOE DetectorThe KLOE CollaborationPhys.Lett. B 537 (2002) 21-27(arXiv:hep-ex/0204013 Apr 2002)

Sigma parameters from E791


(a) The two pion invariant mass distribution in D+ to

decay (dominated by broad low-mass f0(600)), and

(b) the Dalitz plot (from E791).


The invariant mass distribution in Ds to 3 decay showing mainly f0(980) and

f0(1370). and Dalitz plot (E791).


The D+ to K- Dalitz plot. A broad kappa is reported under the dominating K*(892) bands (E791).


• Very recently• I. Caprini, G. Colangelo, H. Leutwyler, Hep-ph/05123604

from Roy equation fit get


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


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


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


Tilt the potential by hand and the pion gets mass

m > 0, m> 0

But what tilts the potential? Another instability?


Two coupled instabilities breaking the symmetry

If they are coupled, they can tilt each other spontaneously:


F>FcritF<Fcrit

Another way to visualize an instability,

An elastic vertical bar pushed by a force from above

The cylindrical symmetry broken spontaneously


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.


To see the anology with the LM, 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 LML R


Compare this with the LM for and in matrix representation;


The LM 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.


The mixing term shifts the vacuum values a little and mixes the states

And the pseudoscalar mass matrix becomes


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


Quark loops should mix the scalars of strong and weak interactions and produce the

mixingterm proportional to quark mass?

higgs, W

q

q

L

2

Also isospin and other global symmetries schould be violated by similar graphs


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),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 LM the pion gets mass,

and global symmetries broken?

Further analyses needed!


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”


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.


Unitarize the basic terms.Example for contact term + resonance graphically:


K-matrix unitarization

F.Q.Wu and B.S.Zou, hep-ph/0412276

nils a. törnqvist university of helsinki

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