SLAC-PUB-2105 April 1978 (T/E)

EVIDENCE FOR r BEING A SPIN + LEPTON*

Yung Su Tsai Stanford Linear Accelerator Center

Stanford University, Stanford, California 94305

ABSTRACT

Evidence for r being a spin % lepton and not anything else is

discussed.

(Submitted to Physical Review Letters)

*Work supported by the Department of Energy.

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In this note, we discuss the evidence for 'c being a spin 5 lepton

and not anything else. By lepton we mean a fermion which does not interact

strongly, hence except for a small correction due to higher order electro-

magnetic interactions, it has a constant form factor and no anomalous

magnetic moment (g=2). That 'c is consistent with being a heavy lepton has

been shown by Per1 et al.' at SLAC and by groups2 working with the DASP and

PLUTO detectors at DORIS (DESY). I would like to show that the recent

results from DELCO3 and DASP4 , especially those from DELCO, can be used to

show that r is indeed a heavy lepton and cannot be anything else. The

argument goes as follows:

i) r cannot be a baryon. If T were a baryon its decay products would

contain one nucleon. The missing neutral in the decay 'c + ev + neutral has a 5 mass upper limit of .25 GeV. Hence "neutral" cannot contain a nucleon

and thus r cannot be a baryon. (We assume baryon number conservation.)

ii) 'I cannot be a boson. A boson and its antiparticle have the

same parity. Since the virtual photon has quantum number Jp= l-, the

orbital angular momentum of the boson- antiboson pair cannot be in the s

state. Experimental results of both the DELCO3 and DASP4 groups clearly show

the s-wave threshold behavior of r events. Two bosons can be produced

in the s state only if they have opposite parity; for example,

O-+1+, O++l-, l-+l+etc. Only one of the two particles produced can be

stable against strong and electromagnetic interactions. (For example

in the production of Di-D* only D is stable.) This means that if T events

were due to the production of two bosons with opposite parity, their decay

would always be accompanied by y's or B 0’ s. Experimentally this seems

to have been ruled out by the DELCO results. 3

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iii) T cannot be a point-like particle with spin equal to or greater

than $ . The s-dependence of the cross section for high-spin particle

production is at least two powers of s more divergent than that for spin

% particles when the energy is far above the threshold. The energy

dependence of the T production cross section excludes such a steep energy

dependence. (See Fig. 1 and Fig. 2).

In Fig. 1, the experimental result3 of the DELCO Group for

e++e- * e+ one charged prong (# e) + no detected photons is plotted.

The quantity plotted is the ratio R which is the cross section of interest

divided by the muon-pair production cross section. The solid line is

0.11 x Rr(spin $), where Rr(spin II) is the ratio of the spin & heavy lepton

cross section to the muon cross section:

Rr(spin %> = or/uu = 8 q (1)

The factor 0.11 comes from a theoretical estimate of the branching ratios6

(see Table 1):

2 x(BP + Br + BR + +) X Be (2)

= 2x(0.16 + 0.098 + 0.006 + 0.23/3) x 0.164 = 0.11

The factor 1 3 in front of BP comes from the fact that the probability of

missing the IT' in the decay p- + R- + ITO is i for the detector used. We

observe that the theoretical curve has the right shape and magnitude. The

correct shape implies that r is a spin 4 particle with unit form factor

and no anomalous magnetic moment,whereas the correct magnitude implies

that the assumptions made in the calculation of branching ratios are

right. The decay branching ratios given in Table I are the updated

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version of a similar table published in my 1971 paper. A detailed con-

sideration of decay modes is not crucial to the main point we want to

make in this paper.

In Fig. 2 four curves are plotted, each representing the production

cross section (divided by the muon cross section) of a point-like particle

of a particular spin. The curve labeled s=% represents R for the pro-

duction of spin $ particles with no anomalous magnetic moment (Eq. (1)).

The curve labeled s=l, K=O represents R for a spin 1 particle with no

anomalous quadrupole moment and gyromagnetic ratio equal to one. 7 This

corresponds to K=O, A=0 in the notation of Reference 7. Rr(spin 1, K=O)

= B3(0.75 + y2). This choice of K and X gives the least divergent

asymptotic behavior. Any other choice of K and A values will yield an

asymptotic s dependence equal to that of the next case. The curve labeled

s=l, ~=l represents R for a spin 1 particle with no anomalous quadrupole

moment and a gyromagnetic ratio equal to two. Yang-Mills particles have

this property. This corresponds to ~=l and A=0 in the notation of Ref. 7.

Rr(spin 1, ~=l) = f33 (0.75 + 5v2 + y4). This has a p wave threshold

behavior and asymptotic behavior =s2. The curve labeled s = +, A=l,

B=C=D=O represents R for a spin $ particle with the least divergent

asymptotic behavior. A spin 3 particle can have four multipoles, thus

we need four arbitrary numbers to describe its electromagnetic interactions.

Let us write the vertex function as

where A, B, C, D are four constants related to the four multipoles. U a 3 and v B are the vector-spinors of Rarita and Schwinger' representing spin - 2

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particle and antiparticle respectively. The general expression for

the cross section is rather long. However the results of the calculation

show that the choice B=C=D=O yields the least divergent result when s is

large. Letting A-l, which corresponds to unit charge, we obtain

RT(spin 2 3 = W9)(15r-2 + 30B2 + 40y2B4 + 16y4B6) ,

where I3 and Y are velocity and E/M of r.

Since a spin $ particle is a fermion it has an s wave threshold behavior.

The asymptotic behavior is the same as in the spin 1 case. This is to

be expected because a spin 3 particle can be regarded as a direct product

of spin 4 and spin 1 states, hence its asymptotic behavior must be at

least as divergent as that of spin 1 state. This argument can be general-

ized to higher spins. From Fig. 1 and Fig. 2 we conclude that r events

cannot be due to the decay of high spin (s > -i) point-like fermions.

Thus we conclude by elimination that T must be a spin 4 particle with no

baryonic number and hence it must be a heavy lepton.

The facts mentioned above are sufficient to establish that 'c is

indeed a heavy lepton. There is also much additional evidence in support

of T being a heavy lepton.

4 Both the DASP4 and DELCO3 groups have shown that T is produced

below the threshold of D. Hence T events could not have been due to the

decay of charmed particles. Notice that points i.) and ii) listed above

can also be used to rule out the possibility that 'c events are due to

the decay of charmed particles. There is also the observation made by

G. Feldman" who investigated Ko's accompanying ue events and found that

the ue events could not all have been due to the decay of D particles.

b) The spectra of e(or u) in the eu events, l-4 e (or u) + 1 prong

events3'4'11 and uAl events 12 are all the same, implying that they have

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the same origin, and furthermore they are consistent with the decay

f- + v + e- + Ge using V-A theory and zero neutrino mass. The hadronic T

decay modes observed are, except for the controversy over the pionic mode,

consistent with theoretical calculations. I believe the pionic mode will

eventually come out correctly.

Now that r is well established as a heavy lepton, what else can we

learn about it? In 1971 the author, and about at the same time Thacker

and Sakurai, 13 made a systematic study of the properties of heavy leptons

under some simple assumptions. Amazingly none of these simple assumptions

have been shown to be incorrect by the experiments so far. Let me list

the assumptions made in my paper and then discuss the alternative assump-

tions and the experimental consequences.

1. T has its own lepton number and its own neutrino, and they are

distinct from their counterparts for muons and electrons. If (T-,vr)

had the same leptonic number as (e-,v,) then 'c- would decay into e- via

't- + e--Fy predominantly. This is ruled out experimentally. Similarly

(r-,vr) cannot have the same leptonic number as (u-'vu). If (T-,v~) had

the same quantum number as (e +,;,) th en in the decay r- + vr + e- + Ge

two neutrinos would be identical and the ratio 14 of e to u would be

r(~- -t vT+e- + Ce)/r(~- -t vT+p7Gp) Q 2. This has also been ruled out

experimentally.

2. vr is massless and left-handed (3r is right-handed). Experi-

mental results seem to agree with this assumption, l-4 but more work is needed.

3. The decay of T is mediated by the same kind of W boson which

mediates all other known weak interactions, and no additional vector

bosons or scalar particles need to be introduced. If this were not true,

the decay modes calculated would not come out correctly. .

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4. In the interaction between W and hadrons, CVC holds and no second

class current is allowed. The consequences of these assumptions can be

checked experimentally:

a) 'c- + vr + 6- (970 MeV) not allowed

b) 'I- + vr + B- (1235 MeV) not allowed

c) T-+v T + 2n pions is related to e + + e- + 2n pions (see Table

I and Eq. (3.14) of Ref. 6, and also Gilman and Miller15)

5. Approximate SU3 x SU3 symmetry. It would be interesting to see

whether Weinberg's sum rules and Das-Mathur-Okubo sum rules are valid

when the upper limit of integration (m) is replaced by the mass of the

heavy lepton (see Eqs. 3.19, 3.20, 3.25, 3.26, 3.27 of Ref. 6).

In the opening sentence of my 1971 paper6 I said, "Since muons exist

in nature for no apparent reason, it is possible that other heavy leptons

may also exist in nature. If one discovers heavy leptons, one may be able

to understand why muons exist and obtain some clue as to why the ratio of

the muon mass to the electron mass is roughly m /me=: 210." Now that Per1 IJ

and coworkers have discovered r, and its mass is known to be 1.777 GeV,

we still do not understand why these leptons should exist and we do not yet

understand why they have such a mass spectrum. Worse, we do not know even

how to construct an empirical formula to predict what the mass of the next

heavy lepton should be. However, we observe that the u mass is rather

close to the pion mass, and the 'c mass is very close to the D mass, so

perhaps the next lepton mass will be very close to the top quark mass. Let

us assume that the upsilon states found by Lederman 16 et al are bound

states of the bottom quark pair and that the top and bottom quark masses

are not very far apart. In this case the next heavy lepton would be in

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the 5 to 15 GeV mass range, which is within the energy range of PETRA

and PEP machines. In Table I we give the branching ratios of these

heavy leptons, if they exist, in order to facilitate the discovery of

them. They are calculated according to the recipe given in Ref. 6 except

that the continuum part is estimated using the data of e+ + e- -f hadrons

whenever the data is available; otherwise we used the quark-parton model

with small corrections due to asymptotic freedom. Notice that if leptons

heavier than T exist, they will decay into T as well as charmed states.

I thank Jasper Kirkby for discussion of the DELCO results. I also thank

Al Odian, John Jaros, Bill Kirk, Mike Barnett, Fred Gilman and Y. J. Ng

for kindly reading the manuscript and making valuable comments.

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REFERENCES

1. M. L. Per1 et al., Phys. Rev. Lett. 35, 1489 (1975).

2. S. Yamada in Proceedings of the 1977 International Symposium on Lepton

and Photon Interactions at High Energies (Hamburg, 1977); G. Rnies,

ibid.; M. L. Perl, ibid.; H. F. W. Sadrozinski, ibid.

3. L. J. Nodulman, (SLAC PUB-2104 (1978) to be published).

4. R. Brandelik et al., Phys. Lett. z, 109 (1978).

5. DASP Collaboration (Ref. 4) gives the upper limits on the tau neutrino

mass m < 0.74 GeV for V-A and m < 0.54 GeV for V+A. m < 0.25 GeV VT VT VT

was given by DELCO Group (Jasper Kirkby SLAC Seminar and private

communication).

6. This is the updated version of branching ratios given in Table II of

Y. S. Tsai, Phys. Rev. g, 2821 (1971). The major change comes from

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

the estimate of the continuum. The details of the construction of

this Table will be published elsewhere.

Equations (34) and (35) in Y. S. Tsai, Phys. Rev. 12D, 3533 (1975).

D. R. Yennie et al., Rev. Mod. Phys. 2, 144 (1957).

W. Rarita and J. Schwinger, Phys. Rev. 60, 61 (1941).

M. L. Per1 et al., Phys. Lett. 63B, 466 (1976).

G. J. Feldman et al., Phys. Rev. Lett. 38, 117 (1977).

J. A. Jaros et al., (SLAC PUB-2084 (1978) to be published);

G. Alexander et al., Phys. Lett. 73B, 99 (1978).

H. B. Thacker and J. J. Sakurai, Phys. Lett. 36B, 103 (1971).

J. D. Bjorken and C. H. Llewellyn Smith, Phys. Rev. E, 887 (1973).

F. J. Gilman and D. H. Miller, XX-PUB-2046 (1978) to be published.

W. R. Innes et al., Phys. Rev. Lett. 2, 1240 (1977).

TABLE I

Branching Ratios (in W) of Heavy Lepton (Sequential)

\ ML (GeV) Decay Mode

1.8 4.0 6.0 8.0 10.0 12.0

"L V L

"L

"L

"L

"L

"L

"L

vL

+ ve + e-

+ yJ + lJ-

+ VT + T-

+ IT-

+ K- 0.62 0.11 0.05 0.03 0.01 0.01

+ P- 23.01 3.85 1.77 0.89 0.52 0.36

+ K*- 1.57 0.28 0.13 0.07 0.04 0.02

+ A; 9.34 1.98 0.91 0.46 0.27 0.19

+ Q- 0.41 0.13 0.06 0.03 0.02 0.01

+ ud > 1.1 GeV 21.27 37.81 41.08 37 .Ol 33.54 33.13

+ & > 1.1 GeV

+ &s > 2. GeV

+ cd > 2 GeV

+ Eb > 12 GeV

16.41 12.41 12.8

15.97

0

12.34 12.7

2.41 6.17

9.80 1.51 0.69 0.35 0.20 0.14

1.54

0

0

0

2.78 3.00 2.70 2.44 2.44

22.93 33.6 33.23 31.40 31.66

1.67 2.45 2.42 2.29 2.31

0 0 0 0 0

11.45

11.45

7.57

10.52 10.43

10.52 10.43

7.99 8.63

Total Rate in 10 10 -1 set 395 2.83 x lo4 2.09 x lo5 9.78 x lo5 3.28 x lo6 8.18 x

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FIGURE CAPTIONS

1. Experimental values for the cross section/o P for e++e- + e+l charged

prong (fe) + no detected photon from DELCO versus theoretical estimate

(solid line) assuming r to be a spin % particle. Notice the threshold

s wave behavior and the energy dependence of the cross section at high

energies.

2. Energy dependence of Rr = ar/oV assuming T to be spin %; spin 1,

K=O ; spin 1, ~=l and spin 2 2, A=l, B=C=D==O. Notice that the scale of

the ordinate is linear from 0 to 1, but it is logarithmic above 1.0.

n -. (0 . d

B 10

0 x

Re+

I p

rong

(#e)

+noY

ET

2 -CD

l 0

100

R 7

I 08 l

04 l

3-78

I I I I I I I I I I I I I -J -

. . . . . . . s = 1 ) K = 1 -

s= S/2, A=l, B=O, C=O, D =0 : -- s=l/2 _ -a- s= I, K = 0

3.6 4.0 50 ;GeV)

6.0

Fig. 2