Effects of Light Scalar Mesons in eta -> 3pi decay Page: 3 of 17
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
value  r (ri - 7-+- o)e = 267 25 eV. The extra effects included involve both the implicitly integrated-out
heavier meson exchanges and partial unitarization to one loop order. One might expect a two loop calculation in
the chiral perturbation scheme to be valuable but this may involve too many unknown parameters at the present
stage- A dispersion approach using the Gasser-Leutwyler result as a subtraction gave an improved estimate 
F (--* w+7-wo) = 209 20 eV, which still seems too small.
A possible source of ambiguity arises from the determination of the coefficient of the driving scalar density interaction
in Eq.(2). This is determined from the K0 - K+ mass difference, which in turn has two components
m2(K0) - n2(K+) = [m2(K0) - m2(K+)] kmass + [m2(K0) - m2(K+)]j (3)
corresponding to the quark mass differences and the virtual photon emission and reabsorption diagrams respectively.
The latter is given in the chiral limit by m2(w0) - m2(w+) according to Dashen's theorem  and the reasonable
assumption that the photon contribution saturates the pion mass difference. A number of authors  have argued
that there are important corrections to Dashen's theorem which have the effect of boosting the rj -* 37 decay rate.
If one questions Dashen's theorem it is natural to also question Sutherland's result, which deals with the direct
electromagnetic contribution to 77 -> 37 . An investigation of this point yielded  the estimate that there was only
about a 2% change arising from this, although it decreased rather than raised the rate.
Still another point which may repay further investigation concerns the possible subtleties arising from 77 - rj' mixing.
An understanding of the 17' --+ 3w process, for example. might clarify this point. This process has been treated by
some authors ,  in the literature but has received only a fraction of the attention given 7 37 .
In the present paper we will focus on learning more about the putative nonet of light scalar mesons by studying
their contribution to r< -* 3w.
II. CHIRAL SYMMETRY RESULTS TO LOWEST ORDER
For comparison, we first present the well-known results when only the terms present in the lowest order chiral
Lagrangian of pseudoscalars are kept.
FO = F Tr (OUOuUt) + 6'Tr [M (U + Ut)] + ln detY) (4)
where the last term [see Eq.(A14) and comments there] supplies mass to the SU(3) singlet state and Mk4 is defined in
(A11). Fitting LLO to the experimental masses determines 6' = Frn/8.
The j - w+7o amplitude receives, in this approximation, contributions from diagrams (a), (b) and (c) of Fig.1,
which are given in Eq.(Bl) (with the non leading corrections deleted). To a reasonable approximation which displays
the key dependences these sum up to the lowest order result for the 7 -+ 7r+r-ora amplitude
Mo+-(E1, E2, E3) 1 l6t ycosoP(1 - ,). (5)
Here El is the 7r' energy in the 7 restframe and y is the dimensionless parameter in Eq.(A11) which measures the
isospin violation in the quark mass matrix. Assuming Dashen's theorem, Eq.(4) yields
8S'y = F; (mo - m2, - m1 o + m+), (6)
which allows us to solve for y. Furthermore Q, is the "nonstrange-strange" pseudoscalar mixing angle defined in
Eq.(A15); it is generally taken to be about 371. It is related to the "octet-singlet" angle, 0 by
cos9P - cosO - vhsino ()
Then Eq.(5) agrees with Eq. (1.14) of  except that they neglected 77 - 7j' mixing by replacing cosO, -+ 1/0' in
what was denoted the current algebra formula. The matrix element for l - 3r0 is given in general by
Mooo = Mo+-(EiE2,Es) + Mo+-(E2,E E3)+Mo+-(E3,E2,E). 8
Here’s what’s next.
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
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/m1/3/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.