INFN - Laboratori Nazionali di Frascati, May 1995
From: The Second DAFNE Physics Handbook
Chapter 9: One Photon Initiated Processes
Eds. L. Maiani, G. Pancheri, N. Paver
Supported by the INFN, by the EC under the HCM contract number CHRX-CT920026 and by the authors home institutions.
cm S.I. Eidelman
mm Budker Institute of Nuclear Physics Novosibirsk 630090, RUSSIA
cm
Radiative decays of the low-lying vector mesons are very
interesting for tests of the quark model, SU(3), Vector Dominance Model
(see the review in [1]). We present below a brief review of the
experimental situation with the decays 
where V and P stand for a vector and pseudoscalar meson
respectively and related to them so called conversion decays in which
a real photon is replaced by a virtual one producing a lepton pair
(electron or muon one).
The decay mode 
has
traditionally been studied using coherent 
production on
nuclear targets (Primakoff effect). Actually observed in this case is
the reaction 
and to obtain
the radiation width one has to extract the contribution of the
inverse process 
. The extraction
procedure requires separation of the Coulomb and nuclear parts and is
therefore model dependent. At high energies the extraction of radiative
widths becomes less sensitive to the phenonemology of the nuclear models
employed in the analysis. This is probably the reason accounting for the
discrepancy between the first measurement performed with the 
momentum of 22.7 GeV/c [2] and later experiments at much higher energy
around 200 GeV [3-5].The experimental values of the widths obtained as
well as the world average one [6] are shown in Table 1.
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Table 1
The radiative width of the neutral 
meson was
studied in one experiment only which had been performed with the ND
detector at the 
collider VEPP-2M at Novosibirsk [7]. The value
of the width is obtained from the analysis of Dalitz plots of a three
photon final state arising from the reaction 
.
Since both 
and 
-mesons contribute, one has
to take into account their interference. Although the contribution of
the 
decay is statistically
significant, it is not possible to distinguish between the constructive
and destructive 
interference using the experimental data
only. One has to additionally consider other data. The quark model and
isospin invariance predict the same values of partial widths for charged
and neutral 
. The value 824
16 keV obtained for the
destructive 
interference is in obvious disagreeement with
the above value 68
7 keV for the 
. Another confirmation
for the constructive case comes from the analysis of the ratio 
.
For destructive interference it is 0.157 
0.011 in disagreement
with the value 0.089 
0.010 obtained from the reaction 
[8] in which 
interference vanishes.
For the constructive interference the value from 
data is 80.099
0.007 consistent with the hadroproduction data. Thus the whole
bulk of the data favors the constructive 
interference and
one obtains
Although the value of 
is higher than that of 
,
their difference is statistically insignificant (less than 2
standard deviations) not contradicting their expected equality.
Further improvement of the accuracy can be achieved at 
and
at VEPP-2M. In addition to the measurement of the radiative width of
the 
one can think of an exotic way of observing both
and
decays studying
and
decays. The idea is to
look for a 
decay followed by a
decay. Simple estimations show that the
expected probability of such a decay is about 
which makes
it observable at the level of luminosities expected at 
.
The value of 
is consistent
with the previous measurements (see [6]) and has much better accuracy.
Note also that the value itself changed significantly
because recent Novosibirsk measurements [9,10] of the 
-meson
total width resulted in the new average value of 8.43 
0.10 MeV [6].
This value is much lower than a previous one 9.8 
0.3 MeV [11]
and should be taken into account since the value of
is a basis for theoretical
predictions of the radiative widths.
The problem of 
interference is also very
important when one studies 
decays into 
.
Until recently there were two measurements only: one is diffractive
photoproduction of vector mesons from a complex-nucleus target using
the tagged photon beam at Cornell [12] and another one is the ND measurement
at VEPP-2M [7]. In both cases the authors could not find the unique solution
from their data only and presented both solutions for the values of
the radiative widths in keV shown in Table 2.
However, the results for the constructive interference seem more preferable
since they agree with the quark model satisfactorily explaining all
radiative decays.
Table 2
These difficulties seem to be avoided in a recent experiment
of the GAMS collaboration which studied decays of 
produced
in the charge-exchange reaction 
[13].
By choosing a region of sufficiently high momentum transfers the
authors suppress the effects of 
interference and
present a model-independent value
or
which solves the ambiguity above and supports the constructive interference.
Decays of the 
-meson into 
and 
were studied in several experiments. The first experiments on
hadro- or photoproduction of the 
-mesons [14,15] were followed by
more precise from Orsay [16,17] and Novosibirsk [18,19] 
colliders. The current accuracy of the branching ratios is determined by
the dedicated high statistics experiment with at VEPP-2M [19].
One should also mention an only existing experiment on the decay
performed by the ND group [20] who placed
an upper limit
The current experimental situation is summarized in Table 3 presenting the world average values of the branching ratios [6]. Note also a recent theoretical paper discussing possible relations between the discussed radiation widths and QCD anomalies [21].2 cm Table 3
An obvious consequence of the radiative decays is the existence
of conversion decays. A transition
form factor F(
) arising in the vertex provides information on the
meson structure (see the comprehensive review [22] discussing
predictions for 
dependence in different theoretical models). In
conversion decays one can study a range of 
from 
up to
where 
, 
and 
are masses of lepton, vector
and pseudoscalar respectively. Experimental information on such decays
is rather scarce, the branching ratios of three such decays only have been
measured, see Table 4, which agree with the estimations based on the
experimental values of the corresponding radiative width [23] and
lattice calculations [24].
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Table 4
The transition form factor was
studied in [22] using 60 observed 
events. In
general, one can also obtain information on the transition form factors
from the reactions 
and, under some additional assumptions, from the Dalitz decays like
as
well as from the two photon production of 
and 
.
Each of the processes mentioned above gives 
in some range of
. The available experimental information qualitatively does not
contradict the predictions of Vector Dominance, but much higher
statistics is needed for the consistent picture of vector to
pseudoscalar transitions [6,22,28]. One can hope for substantial
improvement of the situation after new series of experiments at VEPP-2M
with the CMD-2 [29] and SND [30] detectors and 
.
REFERENCES
-factory, Frascati, 1991, p. 451.
Physics Handbook,
1993, V.II, p. 499.
-factory, Frascati, 1991, p. 605.