Departamento de Fsica Terica II' Universidad Complutense de Madrid

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Departamento de Física Teórica II.
Universidad Complutense de Madrid
ON THE NATURE OF THE LIGHT SCALAR NONET FROM
UNITARIZED CHIRAL PERTURBATION THEORY AND LARGE NC
José R. Peláez
Phys.Rev.Lett.92102001,2004
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OUTLOOK
Some light on the hadron spectroscopy has come
from unitarized Chiral Lagrangians The
paradigmatic example is meson-meson scattering
and unitarized Chiral Perturbation Theory
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OUTLOOK
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Unitarity and the Inverse Amplitude Method One
channel
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The Inverse Amplitude Method Results for one
channel
Truong, Dobado, Herrero, Pelaez
Unitarity Chiral Low energy expansion
Justified within dispersion Theory (But left
cut approximated !!)
Dynamically Generates Poles ? Resonances ?,
K, ?
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Unitarity and the Inverse Amplitude Method
Multiple channels
Oller, Oset, Peláez, PRL80(1998)3452,
PRD59,(1999)074001
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Meson-meson Scattering at one loop in Chiral
Perturbation Theory
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IAM fit to meson-meson scattering (3 syst.)
low-energy ?00-?11
????? ?00
?
???KK ?00
????? ?11
K??K? ?1/2 1
K??K? ?1/2 0
????? ?20
K??K? ?3/2 0
d???/dElab
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Complete Meson-meson Scattering in Unitarized
Chiral Perturbation Theory
First, IAM with previous ChPT parameters (we
could not compare before)
? resonant features
MINUIT fit
Incompatible sets of Data. Customarily add
systematic error
3,
IAM fit parameters compatible with ChPT !!
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OUTLOOK
INTRODUCTION Unitarization of ChPT amplitudes
generation of resonances Complete one-loop
meson-meson scattering
Simultaneous description of low energy and
resonances Fully renormalized and with parameters
compatible with ChPT.
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A. Gomez Nicola and J.R.P. PRL80(1998)3452,
PRD59,(1999)074001
Coupled channel IAM
With the full one-loop SU(3) unitarized ChPT, we
GENERATE, the following resonances, not present
in the ChPT Lagrangian, as poles in the second
Rieamann sheet
J.R.Pelaez, hep-ph/0301049. AIP
Conf.Proc.660102-115,2003 Brief review
Mod.Phys.Lett.A192879-2894,2004
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Resonance POLE POSITIONS...
Re?s ?M (MeV)
-Im?s ??/2 (MeV)
Complete IAM
Complete IAM
?
754?18
74 ?10
K
889 ?13
24?4
?
440?8
212 ?15
?
753?52
235 ?33
f0
a0
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OUTLOOK
Scalar poles found with complete and fully
renormalized UNITARIZED amplitudes with standard
ChPT parameters
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Large Nc Limit
We do not know how to obtain the Li from QCD in a
model independent way
But the QCD Li large Nc SCALING, is known
and Model Independent
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VECTOR MESONS
qqbar states
Nc
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Resonance poles in the Large N Limit
Subtlety The large Nc does not see the scale
of Li(?) but is expected to correspond
to ??500-1000 MeV
Since now we use the completely renormalized
expresions of ChPT we can choose any ? for
the large Nc scaling and we get the uncertainty
Nc
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What about the ? and the ? ?
MN/M3
?N/?3
Nc
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Resonance poles in the Large N Limit
Large dependence on ? choice for the large Nc
scaling
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Resonance poles in the Large N Limit
Another way of seeing it is with the modulus of
the amplitude
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What about the f0 and the a0 ?
Following the pole large Nc behavior is
complicated by the nearby thresholds, at least
for relatively low Nc. In addition, the a0(980)
amplitude on the real axis is more robust than
the pole position
For sufficienly high Nc they also disappear in
the continuum like the ? and ?
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Resonance poles in the Large N Limit
four quarktwo meson glueball (if I0 J0) in
this counting
What are they?
For the ? and f0 glueball interpretation also
possible. Likely some mixing. Not for ? or a0
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The imaginary part of amplitudes vanish
consistently with Imt1/Nc2
in one corner of ? space, the a0(980) still
behaves as qqbar
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Summary
Unitarized meson-meson scattering results
robust. ?, K, ?, ?, f0 and a0 poles
appear simultaneously allowing for low energy
description Suggests nonet interpretation for
light scalars
?, ?, f0 and a0 large Nc QCD behavior at odds
with dominant qqbar nature
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(H. Zheng et al. hep-ph/0411025 hep-ph/0411375
hep-ph/0412175 )
Warning for practitioners...
We use the large Nc behavior, but it is only
relevant not far from reality ? Nc3
Only qqbars survive at Nc? ...
For sufficiently large Nc, even the tiniest
admixture of qqbar could be made dominant. The
mathematics could be correct, but gives no
information about the DOMINANT component of
physical states at Nc3.