Transcript Light scalar mesons as diquark-antidiquark bound states A

The Light Scalar Nonet, the sigma(600), and the EW Higgs
Nils A. Törnqvist
University of Helsinki
Talk at Frascati January 19-20 2006
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.
•
•
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Two recent reviews on light scalars
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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.
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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 Pwave, but further out they rearrange as 2 quark-antiquark
systems and finally as meson–meson states.
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Recent s(600) pole determinations
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BES collaboration: PL B 598 (2004) 149–158
Finds the σ pole in J/ψ →ωπ+π− at
(541±39)−i(252±42) MeV
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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
Ms=
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(a)
The two pion invariant mass distribution in D+ to ppp
decay (dominated by broad low-mass f0(600)), and
(b) the Dalitz plot (from E791).
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The invariant mass distribution in Ds to 3p
decay showing mainly f0(980) and f0(1370).
and Dalitz plot (E791).
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The D+ to K- p+p+
Dalitz plot. A broad
kappa is reported
under the dominating
K*(892) bands (E791).
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• Very recently
• I. Caprini, G. Colangelo, H. Leutwyler, Hep-ph/05123604
from Roy equation fit get
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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
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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
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Spontaneous symmetry breaking and the Mexican hat potential
Cylindrical symmetry
mp
=
Cylindrical symmetry
ms
mp = 0, ms >
0, proton mass>0
and constituent quark mass 300MeV
Chosing a vacuum breaks the symmetry spontaneously
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Tilt the potential by hand and the pion gets mass
mp > 0, ms > 0
But what tilts the potential? Another instability?
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Two coupled instabilities breaking the symmetry
If they are coupled, they can tilt each other spontaneously:
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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
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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.
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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)L x SU(2) R as in the LsM
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Compare this with the LsM for p and s in matrix representation;
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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.
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The mixing term shifts the vacuum values a little and mixes the states
And the pseudoscalar mass matrix becomes
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Diagonalizing this matrix
one gets a massive pion and a massless triplet Goldstone;
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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.
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Quark loops should mix the scalars of strong
and weak interactions and produce the mixing
term e2 proportional to quark mass?
q
higgs, WL
q
s, p
Also isospin and other global symmetries schould be violated by similar graphs
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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!
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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
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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.
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Unitarize the basic terms.
Example for contact term + resonance graphically:
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K-matrix unitarization
F.Q.Wu and B.S.Zou,
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hep-ph/0412276
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