'. ,,- ' ; ( 4 ,,,":', ~ ~.~-' ·~~.f':h: ,~: ,).: ~ ... !~,. .; ~ ,~~ ~~ " ,.: .. ~ : ,'. -',- ,',,:\ ... ~\.~,:',.J I ,~. ,.~ . ~; • ~i. " .~-4> ... ~ ) .. _ . .',:" _: :.:. I' l _ "oj", _, ;;~ .:': • .;. .... 1..., '. t ~' "-.; . , , ...... :.,~'. ~:r;' ,,~, • : , ,> ... r •• _,.i :':(: ~ oj: '~" ' ' . ..1 .,.~.: ,~~.: ~ .;;.' -~r~~tD)tjq-'~4il"'-·A-;e,:ti~W~~)#it&1E@~4~tSSrlt!. 4 .... ~~..t;,;? .'''l1Gl''c.'.p.~·~_· __ '''''''''im:-~ ~Nr ' ii&:r .. @e· \¢;Z~~~_DO'!i..Wf" ~

1t4ii .,... • ~

-.- .. ---- --------~-.~ 1 ~-... ------------------.---------------- .------ ---i.ff~;d~- -i~~~

.:..~- -i'l i - '0.'-/ k l L) I CfJd~ OaUaw

PDI07011 PRVDA,OIJUL9DYKIOI,9 U;Jm6.f6(t no. of

Weak effects in 2:0 decay

Stephen Wolfram California Institute of Technology, Pasadena. California 91125

(Received 2 November 1978)

It is pointed out that weak interactions should admix a small parity-violating E I component into the M I electromagnetic decay 'J.°-+Ay.

PACS numbers: 13.40.Hq, 13.30.Eg

The decay ,,£0 _ A y is dominantly an M1 electro- I magnetic transition. Strangeness-conserving weak interactions should, however, admix a small E1 component into the decay, leading to (0' p) '" 0 for the A and y even from an unpolarized "£0. The

. most general amplitude for ,,£0 - Ay is (u"vYs is not second-class l )

"

uAu"v(l+<5ys)uc(Pc -PA)V€':' (1 )

The average helicity of the A or y produced in the decay of an unpolarized ,,£0 is then2

(A ./!,)_NL-NR ~ U l' - 2'

NL +NR 1 + <5 (2)

If the ,,£0 is polarized, then the angular distribu­tion of the outgoing y with respect to the initial ,,£0 spin direction is

dW _cc dU

The parameter <5 is a measure of the strength of the nonleptonic strangeness-conserving part of the weak-interaction Hamiltonian. Wand Z exchanges between free quarks in the ,,£0 and A

give ~

(3 )

IThis coupling to the photon can arise from ')1,,')1 5 cou­plings between the quarks, and therefore does not cor­respond to a second-class effect, which should be (essentially) absent in a gauge theory.

2R. E. Behrends, Phys. TIev. Ill , 1691 (1958). 3M. A. Shifman, A. I. Vainshtein, and V. I. Zakh::trov,

f·

(4)

Quantum-chromodynamics effects do not appear to modify this result significantly,3 although dia­grams conSisting of weak vertex corrections to gluon exchange could be important. If the weak amplitude is taken to be equal to that in "£+ -py (multiplied by cotee ), then one finds

(5)

A measurement of these small t.S = 0 weak-inter­action effects should help to clarify the structure of the nonleptonic weak Hamiltonian.

Several authors4 have suggested measurements of parity violation resulting from interference between the processes

,,£o_AY.e+._ and ,,£o-AZ~e+e-'

This effect should be entirely swamped (except perhaps for very small A momenta) by the E1 ad­mixture into the photon-mediated decay ,,£0 - Ay.,+,­

discussed here.

This work was supported in part by the U. S. Department of Energy under Contract No. EY76-

- C-03-0068, and by a Feynman fellowship.

ITEP Report No. ITEP-113, 1976 (unpublished), 4H. S. Mani and H. S. Sharatchandra, Phys. TIev. D 10,

2849 (1974); J. Schecter and M. Singer , Nuovo Cimento 26A, 117 (1975); E. S. Abers and M. Sharif, Phys. Hev. D 16, 2237 (1977); M. A. Perez, ibid 19,400 (1979).

I i i I I:

h

,

I I