Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks/QFT_HEP_Beylin_2010l.pdf Äàòà èçìåíåíèÿ: Mon Sep 6 21:36:57 2010 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:49:15 2012 Êîäèðîâêà:

Gauge model of quark-meson interactions and the Higgs status of scalar mesons

V.Beylin, V.Kuksa, G.Vereshkov (Southern Federal University)

QFT ­ HEP, 2010, Moscow, Golitsyno

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An exact low energy hadron theory should be nonperturbative effective Lagrangian approach
· Effective Lagrangians from fundamental theory (QCD) (local or nonlocal theory) J.Gasser,H.Leutwyler;
M.Volkov with collaborators; M.Ivanov with collaborators;

· Phenomenological Lagrangians from dynamical symmetries LM theory of meson-meson and quark-meson interactions
M.Scadron with collaborators

· Vector mesons can be added as the gauge fields
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QCD

SUL(2)x SUR(2)

· Bosonization procedure (Volkov, Radzhabov, 2006) · NJL-type model with constituent quarks, mq300 MeV, gluon substructures are included · Dynamically generated masses · EM and strong interactions are described by the gauge (vector) fields · Quark level -model (QM) hadronlevel (NM)
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One of the simplest gauge approach is based on the group
U0(1) x U(1) x SU(2)
· · · · · · · Linear sigma model is extended by the gauge and quark-meson interactions. The model is renormalizable. EM and strong interactions are insensitive to the chirality, it should be localized only the diagonal sum of the global chiral group, SUL(2)x SUR(2) VDM is naturally realized in the gauge way; physical , , ­ the mixed initial gauge fields Tree-level masses are produced by the Higgs mechanism The remained Higgs degrees of freedom can be associated with the scalar mesons (isotriplet a0(980), isosinglet f0(980)) -meson (f0(600)) properties followed from the model structure
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The initial model Lagrangian

Vacuum shifts are: < >= v, < H1 >=12(v1, 0), < H2 >=12(0, v2). The gauge fields masses

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In a tree approximation the vector boson physical states

Pion-quark-vector bosons interaction part of the physical Lagrangian with the universal vector fields couplings

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The set of tree mixing parameters:

c

,

s

=

cos, sin

-meson has a small isotriplet admixture ~ sin <<1 This contribution can be omitted in calculations
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There are basic relations in the model

From vector meson decays widths

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Radiative decays of light vector bosons at the tree level and

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Differential width has the form

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Spectrum of photons in

^+^-

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: with the replacement

Due to loop contributions
can increase up to

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Processes via quark loops

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Imaginary part of the quark loop can be:
a) kept as nonzero value ­ the constituent quark deconfinement occurs only in the NPT internal hadron vacuum? Mq=(170-180) MeV; b) set to zero "by hand" ("naÎve approximation" ­ see M.Volkov et al; M.Scadron et al;...) Mq=(280-290) MeV; c) eliminated by special procedure to provide the quark confinement (M.Volkov et al; M.Ivanov et al, 2009;) Mq=(280-290) MeV for some fixed value of parameter =260 MeV - is a cutoff scale for the amplitude in -representation; it defines the integration over the "common length" for the amplitude; It is some universal scale for the quark propagation inside the hadron (?)
1



0

d dx dy...F (qi 2 , mi2 , x, y,... )
0 0

1

1



2


0

d dx dy...F (qi 2 , mi2 , x, y, ... )
0 0

1

1

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Due to isotopic structure of -, -, - interaction with the constituent quarks

=0.091±0.003 MeV
for the "infrared confinement" scheme with Mq=(280-290) MeV and =260 MeV; very close result for Mq=(170-180) MeV and =210 MeV

Indeed, /mq 0.9 ­ 1.2

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"NaÎve" system of equation for characteristic hadron masses

Here, mG ­ mass of the same "gluon" component of meson and baryon structure ­ in the effective models -meson (f0(600)) can be interpreted as a scalar excitation of NPT vacuum with a mass ~ mG. From the system it follows mq 170 MeV and mG 435 MeV
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for mq=175 MeV In the exact chiral limit (corresponding to axial anomaly term) the width is 7.63 eV. For mq=300 MeV =7.91 eV The experimental width is in the interval 7.22 eV 8.33 eV.
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The Goldberger-Treiman relation fixes qq and qq couplings in the CL the width does not depend on the quark mass.

But:
a) the G-T relation accuracy is ~3-4%; b) mixing can be noticeable; c) loop corrections can decrease the qq-coupling ­ the 2% decreasing is sufficient to provide an agreement with the data.

for mq =175 MeV (no imaginary part, with corrections from G-T relations) =7.63 eV for mq=175 MeV with the "infrared confinement" procedure, but =100 MeV only!
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Effective couplings

g g

, mod

= 14.5 1/GeV (mq = 175 MeV, =250 MeV); = 17.7 1/GeV (mq = 280 MeV, =280 MeV); =16.4 1/GeV (mq = 300 MeV, =280 MeV);

, mod , mod

g

g g g g g
, mod , exp , mod , exp

, exp

= (15-17) 1/GeV

= = = =

0.743 1/GeV (mq = 280 MeV, =280 MeV ) 0.723 ± 0.037 1/GeV 0.278 1/GeV (mq = 280 MeV) 0.276 1/GeV /mq = 0.9 ­ 1.2
(see also M.K. Volkov et al, 1996, 2000)
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For zero mixing angles, and (it corresponds to exact charged scalar combinations arise after the spontaneous breaking isotriplet structure (slightly broken by the small mixing with the singlet vector fields) - a0(980)? Two isotriplets arise: and

), two

Pion-scalar interaction part

is close to zero for is suppressed but observable

is damped

Residual global SU(2) symmetry in the scalar sector takes place approximately

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decay can be effectively considered There are four types of loops

+

There is a mixing =0 ·cos+f0·sin, the angle defines
· ·
· :

- and f0-couplings, if =0

g

=0;

f0 and a0 do not interact with quarks directly, if =0;
the f0- and a0-masses are equal, if =0.

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The decay amplitude has gauge invariance form, all divergencies are cancelled
M ~ [gµ (k1k2)-k1µ k2]·(Mq-loop + M-loop +Ma Results for the decay width ( )
·
exp
0

-loop

)

= (1 ­ 5) KeV

In the "naÎve" approximation (Im M=0) ( )mod = (3 ­ 5) KeV for mq =280 MeV, g =(m^2 ­ m^2)/2f beyond the CL, m =

450 ±50 MeV

· ( )mod = (2.5 ­ 5) KeV for mq =175 MeV, if g a free parameter, (0.5 - 1.5) of the CL, m = 600 ­ 800 MeV
·

·

Im M is small for any case gaa 1/3 of g (CL value)
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·In the approach of "infrared confinement" (when the poles of amplitude are excluded by the special integration procedure) In this case for various

mq and m values

mq =175 MeV: for =(260 ­ 300) MeV, m =500 - 800 MeV ( )
mod

= (4 ­ 6) KeV

mq =280 MeV: for =260 MeV, m =450 - 550 MeV ( )
mod

= (1.5 ­ 2.5) KeV and f0

All used parameters are in agreement with and

g



=m^2 /2f (in the CL)

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f0 , a0

from two-quark structure of the mesons. ?

f0, a0 as qq-states from constituent quarks - do not agree with 2 decays
M. Napsuciale, 2002

2 decays of scalar mesons in the gauge model via meson loops (f0, f0a0a0, f0, a0 vertices) and quarks in two-loops ­ 4-quark and gluon components?
The model should be generalized to gauge SU(3) x SU(3) Higgs sector masses and couplings, scalar mesons scalar mesons decays

axial vectors, K-mesons

This dominant decay can be described by the symmetry allowed term in the model Lagrangian
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Conclusions
· · · · · · · · The gauge renormalizable generalization of -model with the VDM at the tree level is considered. Higgs mechanism for meson masses, effective couplings from experiment data. Scalar mesons (a0,f0) are generated by the Higgs degrees of freedom (a vacuum nature of scalars). Tree-level radiative decays of light vector mesons are well described. Consituent quark loops define (,) decays in a good agreement with data, various approaches to avoid deconfinement are used. , decays are considered in details: the values m = 450-550 Mev and mq = 280 MeV are preferred. Effective vertices g, g, g are in agreement with data. From the scalar sector structure it follows: the degeneracy of a0,f0 in mass; an observable suppression of a0 , the smallness of two-quark component in a0,f0 mesons, and f0 agree with data. So, the gauge quantum field approach + the Higgs mechanism lead to the effective quark-meson model with scalar mesons as a vacuum fields; radiative and hadronic decay modes of vector and scalar mesons are well described. SU(3) chiral extension will be done to include all possible scalar, vector and axial mesons in this scheme.
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