Volume 102B, number 4 PHYSICS LETTERS 18 June 1981

STUDY OF THE ELECTROMAGNETIC TRANSITION FORM-FACTOR

I N t o ~ l t 0 1 t + J t - D E C A Y

R.I. DZHELYADIN, S.V. GOLOVKIN, A.S. KONSTANTINOV, V.F. KONSTANTINOV, V.P. KUBAROVSKI, L.G. LANDSBERG, V.A. MUKHIN, V.F. OBRAZTSOV, T.I. PETRUNINA, Yu.D. PROKOSHKIN, V.A. VIKTOROV and A.M. ZAITSEV Institute for High Energy Physics, Serpukhov, USSR

Received 6 April 1981

Sixty events of the rare electromagnetic decay to ~ zre,u+,u - have been detected. The branching ratio for this decay been obtained to be BR(to ~ ~r°t~+~ -) = (9.6 +- 2.3) X 10 -s . The effective mass spect rum for m u o n pairs has been measured and the electromagnetic transi t ion form-factor for the vertex tour °, Fro( m2/a#; m~o) = (1 - m~#/A2) -1 , has been determined, A = (0.65 -+ 0.03) GeV/c 2. The results are compared with the vector-meson dominance model.

This paper presents new experimental data on the meson decay into a n o and a muon pair

o~ -~ r r OU+ /~ - (1)

observed earlier [1]. The main purpose of the further study of process (1)was to measure the transition form- factor which defines the corr° vertex structure.

The binary reaction

Ir-p ~ wn (2)

served as a source of monoenergetic u~ mesons. The re- action, which is well studied in our energy range [2], provides rather favourable background conditions for the experiment [ 1]. The measurements have performed with the "Lepton-G" spectrometer exposed to the 2 5 - 33 GeV/e pion beam of the 70 GeV IHEP accelerator. The description of the apparatus is given in the prev- ious papers [1,3-6] , as well as the measurement pro- cedure and the data processing. During the experiment 5 X 1011 ~r- passed through the set-up target, yielding 107 6o from reaction (1).

The events of decay (1)have been selected after ana- lysis of the exclusive reaction

r r - p -+ rrO la + g - n . (3) L_, 27

Particles have been identified in the f'mal state as was

20

10

400 600 800 1000 1200

Fig. 1. ~r°/z+#--mass spect rum for the events with m2uu < 0.4 GeW2/c 4. The peak corresponds to decay (1). The arrow points to the table value o f the to mass. N is the number of events per 40 MeV/c 2 bin. The outer and inner histograms correspond to the threshold 7 energies equal to 1 GeV and 1.4 GeV, respec- tively.

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Volume 102B, number 4 PHYSICS LETTERS 18 June 1981

done earlier [1]. Fig. 1 shows the effective 7r0/~+/a - mass distribution for events of type (3). To reduce the background the following selection has been applied:

2 < 0.4 GeV2/c 4. This kinematical region was used muu further for investigation of the form-factor.

The mass spectrum shows a distinct peak corre- sponding to decay (1). After subtraction of the non- resonant background (11%) and the 3% background from co -* ~r07r+Tr - , ~r -+ -+/a -+ processes (pion decay in flight before the 3' detector and the absorber [2,3] ) and p -+ lr0/a+/a - , the peak contains 60 +- 9 events of decay (1). After normalization the branching ratio BR(w -+ rr0/~+/~ - ) = P (w ~ 7r0/a+/a-)/P(w ~ all) has

been found:

B R ( w -~ ~/a+ta - ) = (9.6 + 2.3) × 10 - 5 (4)

(here and below both statistical and systematical errors have been taken into account).

To def'me the electromagnetic transition form-fac- tor of the vertex corr 0 we studied the spectrum for muon pair masses muu in decay (1). This was done in the same way as earlier for the decay 77 ~/a+/a- 3' [6]. The spectrum is described by the formula [7,8]

dP(Wdmi°/+ta - ) a F(w-+ rrO ~ )~l + 2 m___~2u "~ =~n- m2 u ~ m2u }

4m2 ~1[2 2 2

U . m 2 - m 2 o /

4_2 ~2 3/2 rnwm#la 1 2 . 2 2 - IF,.o(muu, m~ro )1 • (5) 2 ( m - m Zo)2J

The transition form-factor of the vertex wTr 0, Fro × 2 2 _ 2 _ 2 . 2 _ 2 • (muu ;m~o ) -F to (q 1 - muu, q2 - m~o ), xs normal-

1zeal: Fw(0; m~6) = 1. It is usually parametrized in a pole approximation:

2 . 2 _ 2 2 - 1 - muu /A ) : r e . o ) - (1 (6) IFtol 2 values obtained in the present work are

given in fig. 2. They were defined as the ratio of the measured muon pair spectrum to the one, Monte- Carlo calculated with formula (5), for which IFw[ = 1, taking the set-up efficiency into account. The calcu- lated spectrum was normalized on the total number of w mesons produced on the set-up target in reac- tion (2).

loo

:5.

E

10

/ /

/ / /

/ /

/

'V o o.i I I I J

0.2 0.3 0.4

[Gev',c']

Fig. 2. The data on the electromagnetic transition form-factor for the vertex ~ r °. The points are the experimental values

2 2 12 for IFo~(mu~; mTro) . Curve I is the result of fitting the ex- perimental data by the pole formula IFwl 2 = K(1 - m~#/A2) 2 with A = 0.65 GeV/c 2 . Coefficient K takes into account lhe experimental normalizatiorl uncertainty. Curve 2 is the predic- tion of the model [9] with a modified p propagator. Curve 3 has been calculated with the vector-meson dominance model.

To fit the experimental form-factor values (fig. 2) pole formula (6) has been used. The characteristic mass A has been found to be:

A = (0.65 + 0.03) GeV/c 2 . (7)

The form-factor slope at zero value of the time-like momentum, q2 = 0, amounts to dFto/dq 2 = A - 2 = (2.4 + 0.2) GeV-2c 4.

The vector-meson dominance model describes the transition form-factor by the contribution of the p pole only. In this case AVD M = m O . Such value differs from the measured one by four standard deviations. In the range of large masses muu the form-factor rises faster than it is predicted by the VDM (fig. 2).

The co~r 0 transition form-factor was analysed in paper [9] with the dispersion method taking into ac- count the intermediate lrlr -states (3'* -* rrlr ~ lr0~). As it follows from the unitary relation the amplitude

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Volume 102B, number 4 PHYSICS LETTERS 18 June 1981

of the reaction lrzr ~ lr0eo contributes to the form- factor. In accordance with VDM this amplitude was parametrized by introducing the p pole in s-, t- and u-channels. This resulted in some modification of the p mesOn propagator in the transition form-factor. The calculations with this model are presented in fig. 2. The obtained curve lies somewhat nearer to the ex- perimental points than the predictions of a simple VDM. However, the disagreement between theory and experiment is still noticeable.

In conclusion we would like to thank A.I. Vainstein, M.I. Vysotski, V.I. Zakharov, I.Yu. Kobsarev and M.A. Shifman for the discussion of the experimental results.

References

[1] V.A. Viktorov et al., Yad. Fiz. 29 (1979) 1513; Phys. Lett. 84B (1979) 143.

[2] W.D. Apel et al., Yad. Fiz. 31 (1980) 31; Lett. Nuovo Cimento 25 (1980) 493.

[31 Yu. B. Bushnin et al., preprint IHEP 80-57, Serpukhov (1980).

[4] Yu.B. Bushnin et al., Yad. Fiz. 28 (1978) 1507; Phys. Lett. 79B (1978) 147.

[5] V.A. Viktorov et al., Pis'ma Zh. Eksp. Teor. Fiz. 30 (1979) 387;Phys Lett. 88B (1979) 379.

[6] V.A. Viktorov et al., Yad. Fiz. 32 (1980) 998, 1002, 1005; Phys. Lett. 94B (1980) 548.

[7] C.H. Lai and G. Qugg, Preprint FN-296, Fermilab USA (1976).

[8] V.F. Obraztsov, preprint IHEP 79-115, Serpukhov (1979). [9] G. Kopp, Phys. Rev. D10 (1974) 932.

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