LETT:ERE AL NUOYO CIMENT0 VOL. 16, N. 1 1 Maggie 1 9 7 6

Comment on A n o m a l o u s Lepton Product ion in e+-e - Avn lh i la t l on (*).

S. IWAO

Departme~t o] Physics, College o] Liberal Arts, Kanazawa University - Kanazawa

M. SHAKO

Data Processing Center, Kanazawa University - Kanazawa

(rieevuto il 7 Gennaio 1976)

Recently, anomalous lepton productions cross-sections in e+e - annihilation (1)

(1) e + + e--> e • ~* + ;~ 2 undetected particles

were reported in the range of total e.m. energies 3 to 7.4 GeV (most of them are observed at, or above, 4 GeV). The momentum distribution of decay leprous in units of ( p - - - -0.65 GeV/e)/(pm~x--0.65 GeV/e) (2) w~s also given for all the observed events. If a single phase volume is used in the fit the most probable answer is a three-body decay of each event. As pointed out by the authors these events may be interpreted ~s i) a three-body decay of heavy leprous, ii) a three-body decay of new (charmed) pseudo- scalar or scalar mesons and iii) a two-body decay of new (charmed) or axial vector nlesons.

The purpose of this paper is to examine whether one of these possibilities or a cer- tain combination of these alternatives is possible.

Firstly, if the events are due to the heavy lepton pair production and to their succes- sive decays, the production crosssection should be explained in the framework of quantum electrodynamics (QED). In this case the total heavy lepton pair production cross- section will be several times larger than that for the process (1), owing to the un iden t i fled decays, such as meson p~irs in ~ssociation with three final leptons for each deeply. Including all such processes we can safely use the ~-e universality so that our crude guess stated above may not be changed appreciably, unless more than four body decays

(*) The w o r k is s u p p o r t e d i n p a r t b y t h e 1975 Sciea t i f ia R e s e a r c h F u n d of t h e M i n i s t r y of E d u c a t i o n . (1) M . L . PERL, G. S. ABRAMS, ~_. M. BOYARSKI, M. BREIDENBACtI, D. D. BRIGGS, F. BULOS, W. CItI- NOWSKu J . W. DAKIN, G. J . FELDSIAN, C. J~. FRIEDBERG, D. FRYBERGER, G. GOLDI~ABER, G. HANSON, F . B. HEILE, B. JE&N-MARIE, J . ~t~. KADYK, R . 1=[. LARSEN, A. M. LITKE, D. LUKE, B. A. ]JULY, V . LOTtt, D . LYON, C. C. MOREItOUSE, J . M. PATERSON, F. M. PIERRE, T. P . PUN, P . A. RAPI1)IS, B. RICHTER, B . SADOULET, R . F . SCItWITTERS, XV. T,~NENRA.~5]~I, G. H . TRILLING, F. VANNUCOI, J . S. WttITAKER, F. C. WINKEL.~IANN aa(~ J . E. W I s s : P h y s . Rev. Le f t . , 35, 1489 (1975). (~) B. RICHTER: Exper imen t s at S P E A R , a t a l k de l i ve r ed a t t h e r e s e a r c h mee t i l l g he ld a t R I F P , K y o t o ( N o v e m b e r 1975).

29

~0 S. IWAO and ~ . SHAKO

dominate anomalously over the three-body decays. In order to apply QED to our problem, we should include the effect of radiative correction, since it is expected to be nonnegligible at such a high energy (a).

The QED prediction for the cross-section of pair production of heavy leptons

(2) c + + e--+ U++ U-

up to order a a may be obtained as (a)

(3) ,~(e+e-+U+u =) = ~o(e+e--~ U+U-)(~ + ~,.o.(-~) + ~,.o.(-~,) + ~.~.(n~o) +

+ ~,.~.(,~) + ~,.o.(~)) + ~'n~(~e) + ~=~(,~),

where 6~.r and (~T.p.(m~) are vertex correction and vacuum polarization contributions, respectively, relative to the lowest-order cross-section a o due to the virtual-photon-lepton interactions for leptons with mass m i , am~(m~) is the cross-section due to the anomalous magnetic moment, and a o may be given by

(4) ~o(e+e- + v + u -) = ~ , + - - z T ~ I I + s + s~ /"

In deriving eq. (3) the two-photon exchange contribution can be omitted, since we restrict the calculation to a situation which is charge symmetric for heavy leptons. We shall refer for the explicit forms of other terms to the original paper (3). The peak of the cross-section will be estimated roughly from eq. (4). If we neglect the terms proportional to my, the peak position is given at s~= m~(1 + ~/~) .

In the numerical work we assume m u = 1.9 GeV. The a~(m~) is of the order of _~ 10 -~ pb, while am~(m~) is less than 1 pb in the range of energies considered. We found that these contributions are negligible. The result of our calculation is shown in table I. The virtual-photon effect mainly comes from the vertex corrections where we put the virtual-photon mass to one-hundredth of electron mass. The s-dependence of each term may be seen from the table.

The main observation of this analysis is that the observed peak cross-section for process (1) is about 20 pb, while we find 3.5 nb for it in process (2). Even if we multi- ply the former by a factor of, say, 7 as a correction for unobserved (or other) modes, we still need a factor 25 in order to get complete agreement. This casts some doubt on the heavy-lepton interpretation for the observed anomalous events. If they are really due to the heavy leptons we need a large form-factor suppression. This requires a large breaking of QED for such an object.

On the other hand, if we stand on the conservative point of view, we can assume that the observed events are mixtures of two- and three-body decays of charmed mesons with various spins. This aspect, however, has some difficulty in explaining the so-called Drell ratio and presumably the observed complicated spectra obtained by e+-e - col- lissions (~). Based on the earlier information for process (1), ALTAnELLI et al. (~) pointed out that the charmed meson with j v = 1- would be the possible source of it. HAYA- SHI et al . (s) pointed out that j r = 1 + could be an another source from their rea-

(a) F. A. BERENDS, K. J. F. GAEMERS and R. GASTMANS: Nucl. Phys. , 57B, 381 (1973). (') G. ALTARELLI, N. GABIBBO aR(1 L. MAIANI: Phys. Rev. Left. , 35, 635 (1975). (s) ~ . ~-IAYASI~'tI, T. ISIt2WATA, S. IWAO, M. SHAKO and S. TAKESH1TA: preprint , HPICK-015, submitted for publicat ion (September 1975).

COMMENT ON ANOMALOUS LEPTON PRODUCTION IN e+-e - ANNIHILATION 31

TABLE I . - The total, the lowest-order cross-sections (in n b ) and the radiative corrections (in %) to the latter ]or di~erent values o] the beam energy, Etot= 2E (in G e V ) .

r a d i a t i v e c o r r e c t i o n s ( % )

E t o t ( G e V ) ~tot ( n b ) a o ( n b ) dv.c.(m~e) bv.c.(m~) dv.p.(m~) dv.p.(m~) dv.p.(m~)

3 . 9 2 4 2 . 1 5 2 . 0 7 2 5 . 6 - - 2 2 . 8 1 .13 - - 0 . 3 8 0 . 3 0

4 . 2 9 6 3 . 4 0 3 . 0 5 2 6 . 3 - 16 .0 1 .14 - - 0 . 2 9 0 . 3 2

4 . 5 4 4 3 . 5 2 3 .11 2 6 . 7 - - 15 .0 1 .15 - - 0 . 2 4 0 . 3 3

4 . 6 6 8 3 . 5 0 3 . 0 8 2 6 . 9 14 .7 1 .15 - - 0 . 2 2 0 . 3 3

5 . 1 6 4 3 . 2 2 2 . 8 0 2 7 . 7 - - 14 .0 1 .17 - - 0 . 1 6 0 . 3 5

5 . 7 8 4 2 . 7 7 2 . 3 8 2 8 . 6 - - 13 .7 1 .19 - - 0 . 1 ] 0 . 3 6

6 . 4 0 4 2 . 3 5 2 .01 2 9 . 4 - - 13 .5 1 .20 - - 0 . 0 8 0 . 3 8

7 . 0 2 4 2 .01 1 .70 3 0 . 2 - - 13 .3 1 .22 - - 0 . 0 5 0 . 3 9

7 . 6 4 4 1 .73 1 .45 3 0 . 9 - - 13 .2 1 .23 - - 0 . 0 3 0 .41

8 . 2 6 4 1 .50 1 .25 3 1 . 5 - - 13 .2 1 .24 - 0 .01 0 . 4 2

30

u~

~2o co

l0

--i-

0 0.5 1.0 (,o 0.65GeV/c)/(p~o., 0.65GeV/c)

cO

~ 2 0

IIL

io ,X

0.5 1.0 (p--0.65 GeV/c)/(p~a• GeV/c)

Fig. 1. Fig. 2.

Fig. 1. - M o m e n t u m d i s t r i b u t i o n of a l l t h c even t s vs. (p-- 0.65 GeV/c)/(ioma x - 0.65 GeV/c). The dot- dashed and dashed l i ne s correspond, r e spec t ive ly , to 3-body decay and 2-body decay. The sol id l i ne is for the t o t a l c o n t r i b u t i o n .

Fig. 2. - S imi l a r to fig. 1. Here t he a n g u l a r d i s t r i b u t i o n of t he two-body decay is a s s u m e d to be 1 +cos Ocoll)'.

3 2 S. IWAO and ~ . SHAKO

nalysis of the SU4 mass formula of BORCHARDT et al. (6), by assuming that the Z(3530) (7) is a member of the 1 + multiplet. Experimentally, the momentum distribution of all the events (2) is very close to the three-body decays, if a single fit is performed. Under these circumstances it would be desirable to separate the relative contribution of two- and three-body decays from the experimental distribution, forgetting the real source of the anomaly.

Making use of experimental data and of the single-mode analysis plotted in the same work (2), we finally find the following two possibilities:

1) 76 and 24% mixture of 3-body decay ( V - - A , rag= 1.8 GeV)and 2-bodyde- cay (isotropic angular distribution), respectively, with reduced chi-square 2 Zr = 0.87 and

2) 81 and 19% mixture of 3-body decay ( V - - A , mu= 1.8 GeV) and 2-body de- cay (experimental angle distribution (1 § cos0oon)2), respectively, with Z~=2 0.83.

These results are better than a single fit, but not appreciably. For the sake of com- pleteness, we give our results in fig. 1 and 2.

As a consequence of our analysis we feel that it is too early to conclude that the ob- served anomaly is due ~o heavy leptons.

The numerical calculations have been performed with the electronic computer of FACOM 230-35 at Kanazawa University.

One of the authors (M.S.) thanks Profs. E. HIRAI and T. KOBORI for their kind support.

(*) S. BORCHAEDT, V. S. MATKUIr a~4 S. OKUBO: Phys . Rev. Le t t . , 34, 38 (1975); Phys . Rev. 1), 11, 2572 (1975). (~) G. S. ABRAMS, t . ~r BOXrARSKI, 1~. BREIDENBACH, F. ]:~ULOS, W. CHINOWSKY, G. J . FELDMAN, C. E. FRIEDBERG, G. GOLDHABER, G. HANSON, D. L. HARTILL, B. JEAN-MARIE, J . A. KADYK, 1~. ~:~. LARSEN, ~A_. M. LITKE, D. LUKE, B. A. LULU, V. LUTH, H. L. LYNCII, C. (2. 1VIOREHOUSE, J . M. PATERSON, ~ . F. SCItWITTERS, ~V. TANENBAUM, G. t I . TRILLING, F. VANNUCCI, J . S. WHITAKER, F. C. WINKELMANN an4 J. E. WISS : Radiative decays of the ~(3684) to new high Mass states, SLAC-PUB-1659 (September 1975).

(~ by Sooiet~t Italiana di Fisica

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Direttore responsabile: CARLO CASTAGNOLI

Stampato in Bologna dalla Tlpogratta Compositori coi tipi della Tipografla Monograf

Questo fascicolo ~ stato licenziato dai torchi i l 16-IV-1976