The anomalous suppression of [pi][sub 2](1670)->b[sub 1](1235)[pi] Page: 4 of 6
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3
q Qq q Q
q q Q
3Po, 3S1, 3D1 models 7r exchange model Gluon exchange
Figure 2. The OZI allowed decay of an initial meson to two final mesons in various models.
test the selection rule.
It has been pointed out that a success of the non-relativistic flux-tube breaking model,
where the created quark-antiquark pair has 3Po quantum numbers (Fig. 2), i.e. S = 1,
is the fact that 7r2 - b7r is predicted to vanish due to the selection rule [5]. Other
decay models where the created pair has S = 1, such as the non-relativistic chromo-
electric string-breaking model where the pair has 3S1 or 3D1 quantum numbers (Fig. 2) [6],
will also have this suppression. Both the 3P and 3S1 models involve a decay operator
proportional to 6 - p, with 6 the Pauli matrices and # a momentum operator.
While the flux-tube and chromo-electric string-breaking models have a qq' pair decaying
to the two final meson pairs qQ and Qq', one of which is identified with the pseudoscalar
boson, the one-pion emission model (Fig. 2) has either q - Q7r or q' -+ Q'?r. An expansion
of the axial current in the lowest order one-boson coupling to the quark or antiquark gives
a decay operator of the form 6 - p" (Eqs. 2 and 28 or ref. [7]). This means that the boson
is created from the quark with S = 1, so that the selection rule would also be valid for
lowest order one-boson emission.
We conclude that the phenomenologically successful pair-creation model for light-light
mesons (the 3Po model) [5], the chromo-electric string-breaking model (3S1 or 3D1 model),
and the lowest order one-boson emission model, which has successfully been applied to
the decay of heavy-light mesons [7,8], are consistent with the experimental decay width
of 72 - b17r.
3. Models possibly constrained by 7r2(1670) -+ b1(1235) 7r
Higher order contributions in boson emission models do contain terms that are not of
the form o - p which violate the selection rule. An example is interactions where both a
pseudoscalar boson is emitted, and a particle is exchanged between the quark and anti-
quark in the initial meson (Eqs. 13, 38 and 39 or ref. [7]). The amplitudes corresponding
to the higher order contributions can be similar in magnitude to those corresponding to
the lowest order contribution (Table 4 of ref. [7]). We hence suggest that consistency with
the small decay 7r2 -+ bi7r can be constraining for models which do not obey the selection
rule, e.g. higher order contributions in one-boson emission models, and can provide a
viability check on new decay mechanisms, e.g. the higher order contributions that were
introduced [7] to cure problems with the lowest order contribution [7,8]. Although one-
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Page, P. R. (Philip R.). The anomalous suppression of [pi][sub 2](1670)->b[sub 1](1235)[pi], article, January 1, 2002; United States. (https://digital.library.unt.edu/ark:/67531/metadc932505/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.