Effects of Light Scalar Mesons in eta -> 3pi decay Page: 1 of 17
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Effects of light scalar mesons in 71 - 37r decay
Abdou Abdel-Rehima *, Deirdre Blackb t, Amir H. Fariborzt 1 and Joseph Schechterd
a,d Department of Physics, Syracuse University, Syracuse, NY 13244-1130, USA,
b Jefferson Lab, 12000 Jefferson Ave., Newport News, VA 23606, USA, and
C Department of Mathematics/Science, State University of New York Institute of Technology, Utica, NY 13504-3050, USA.
(Dated: October 12, 2002)
We study the role of a possible nonet of light scalar mesons in the still interesting r, - 37 decay
process, with the primary motivation of learning more about the scalars themselves. The framework
is a conventional non-linear chiral Lagrangian of pseudoscalars and vectors, extended to include the
scalars. The parameters involving the scalars were previously obtained to fit the s-wave 77 and
rK scatterings in the region up to about 1 GeV as well as the strong decay rj' -+ rprxr. At first,
one might expect a large enhancement from diagrams including a light -(560). However there is
an amusing cancellation mechanism which prevents this from occurring- In the simplest model
there is an enhancement of about 13 per cent in the rj -4 37 decay rate due to the scalars- In
a more complicated model which includes derivative type symmetry breakers, the cancellation is
modified and the scalars contribute about 30 percent of the total decay rate (although the total is
not significantly changed). The vectors do not contribute much. Our model produces a reasonable
estimate for the related ao(980) - fo(980) mixing strength, which has been a topic of current debate.
Promising directions for future work along the present line are suggested.
There has been a revival of interest recently  in the possible existence of a broad scalar meson (sigma) with a mass
in the 560 MeV region and its corresponding nonet partners. A large number of workers - have found evidence
for the sigma in models of irr scattering even though it is partially obscured by background. Generally this state is
considered to be of exotic nature (more complicated than qq) and hence an important clue to an understanding of QCD
in its low energy non-perturbative regime. Similarly, analyses of 7r , rK and irg scattering have provided evidence
for the existence of the remaining members of a possible light scalar nonet: the tc, the ao(980) and the fo(980). In
fact, the latter two states have been well established experimentally for some time. Of course, the treatment of such
strongly interacting processes is inevitably model dependent and there are a number of different opinions as to the
correct approach . Thus it is of great interest to see whether treatments of the role of scalars in other processes
using the same models employed in the scattering processes above give consistency with experiment-
From this point of view we will study the role of possible light scalars in the interesting sj -4 3T decay. Typically
this process has been treated by chiral perturbation theory , in which the possible effects of scalars have been
amalgamated into effective contact interactions among the psudoscalars. This is probably the most effective way to
study the sj - 3r decay. However, our goal here is to learn more about the scalars so it is natural to keep them rather
than integrating them out. Also there is a possibility that a light scalar [like the o-(560)] might give an enhancement
due to closeness of its propagator to the pole [see for instance Feynman diagrams like (a) and (b) of Fig.2]. Another
reason for including light scalars explicitly is to become more familiar with the isospin violating ao(980) - fo(980)
transition which should play a role in the 'p - 3r decay and has also recently been postulated  to provide an
explanation for observations of anomalously strong ao(980) central production and the large F(o -+ fo-y)/F(o -+ ao7)
ratio. It is important to know whether the value consistent with the eta decay determination is consistent with these
T Email: firstname.lastname@example.org
t Email: email@example.com
$ Email: fariboa@sunyitedu
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Abdel-Rehim, Abdou; Black, Deirdre; Fariborz, Amir H. & Schechter, Joseph. Effects of Light Scalar Mesons in eta -> 3pi decay, article, October 1, 2002; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc741604/m1/1/: accessed January 24, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.