LI~.TT~.RE AL NUOVO CI~ENTO YOL. 15, N. 15 10 Aprile 1976

Characteristic High-Energy Neutrino Reaction in the Coloured-Quark Model.

M. KA~UYA

.5aboratory o] .Physics. 8hiz~oIca Women's University - Shiz~oka 422

S. 0GAWA and T. YANAGIDA

Department o] Physics, Hiroshima University - Hiroshima 730

(rieevuto il 12 Febbraio 1976)

A first event of the AS/AQ = - 1 process, yap--> ~-A~+~+~+~ -, has recently been reported by CAZZOT.I e t a / . (1), which suggests a real production of a new kind o~ par- ticle. I t has already been pointed out (~), on the basis of the Glashow-Iliopoulos- Maiani (a) (GIM) model, that the apparent AS/AQ = - - 1 process is induced if the charmed particle is produced and subsequently decays into ordinary hadrons by weak nonleptonic interactions.

In this note we show that the apparent violation of the AS/AQ = 1 (or 0) rule arises also in the coloured-quark model, by using the Han-Nambu model (a) as an example. And we propose some characteristic high-energy neutrino processes which may be induced in the coloured-quark model but cannot be induced in the GIM model. We take the hadronic charged current as follows:

(1) J~= (~, ~)~+ (~, ~)~+ (~, ~)~,

and n representation of S U s and S U~, respectively. In our where (m, _n) stands for the _m_ _ �9 r discussions, the (8, 8) components play an essential role in the apparent violation of the AS/AQ = 1 (or 0) rule. (A AS/AQ = - - 1 process does not occur if there are no (8, 8)

(1) E . G . CAZZOLI, A. l~. CNOPS, P. L. CONNOLLY, R. I . LOUTTIT, M. J. RURTAGH, R. B. PALMER, N. P. SAMIOS, T. T. TSO an4 H. H. WILLIAMS; Phys. RoY. Lctt., 34, 1125 (1975). (g) T. HAYASKI, ~ . KOBAYAS~, Z~r NAK&GAWA and H. Nrl 'ro: Prog. Theor. Phys., 46, 1944 (1971); M. KOBAYASHI, 1~[. NAKAGAWA and H. NITRO: Prog. Theor. Phys., 47, 982 (1972). (a) S . L . GLASHOW, J. ILIOPOULOS and L. MAIANI: Phys. Roy. D, 2, 1285 (1970). The corresponding weak current including the fourth quantum number in the original Sakata model was first discussed by Y. KATAYA~IA, K. YJ.ATU~tOTO, S. TA~CAKA and E. YA~IADA: Prog. Theor. Phys., 28, 675 (1962); Z. MAKI, 1~. NAKAGAWA and S. SAKATA: Prog. Theor. Phys., 28, 870 (1962). And also see B. J. BJORKElV and S. L. GLASHOW: Phys. Left., 11, 255 (1964). (~) M . Y . HAN and Y. NAMBU: Phys. Roy., 139, B 1906 (1965); for other coloured-quark models, s e e

N. CABIBBO, L. MAIANI and G. PREP2LRATA: Phys. Lett., 25 B, 132 (1967); S. Horn: Prog. Theor. Phys., 36, 131 (1966); Y. MXyAMOTO: Prog. Theor. Phys., Suppl., E x t r a Number, 187 (1965); T. TATI: Prog. Theor. Phys., 35, 126, 973 (1966).

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CItARACT:ERISTIC IIIGH-~NEI~GY N~UTRINO R]~ACTION ETC. 561

componen t s ) . Moreover , some au tho r s (5) have a l r eady p o i n t e d out t h a t t he A I = �89 rule can be de r ived if we in t roduce t h e (g, 8) componen t s .

F i r s t we cons ider t he case of t he coloured s t a t e i nduced by the neu t r ino (ant ineu- t r ine) and decay ing t h r o u g h the semi- lep ton ic in te rac t ions . The concerned process is

v ~ --> ~- + coloured par t ic le + X I

> ~+vtt + X ' ,

whe re X and X ' are o rd ina ry hadrons . The hadron ic p a r t of t he r e l evan t in te rac t ions m a y be w r i t t e n as (e)

(2) j ~ Q j t = (1, 1)~, + (8, 1)~, + (10, 1)~, + (10*, 1)~, + (17, 1)~,.

F r o m th i s r ep resen ta t ion , we ob ta in the rule (~) for t he processes v~(~v)JY'-+~-9+X as fol lows:

A S = - - 2 , - - 1 , 0, 1, 2 ,

(3) A? 0 .

F o r the processes va2C-->9-9-X (~3V-+Iz+~+X) rule (s) as

(4) AS~A? = o, �89 1 ,

we can der ive the select ion

even be low the th re sho ld of t he co loured-par t ic le pa i r p roduc t ion . The recen t r epo r t (9) of t he ra t io a ( v v ~ ? - ~ - ~ - X ) / a ( v ~ f ~ - ~ - ~ + X ) _ 0,1 impl ies t he suppress ion of J(a , 6 :E i7) c o m p o n e n t s w i t h a = 1 + i2, 1 - - i 2 , 4 + i5 a n d 4 - - / 5 , where J(a , b) is t he a - t h and b- th c o m p o n e n t of t he (8, 8 ) - representa t ion . (The X-matrices of SU~ are def ined co r respond ing ly to those of S U~.)

N e x t we discuss the case of t he coloured par t ic le decaying t h r o u g h non lep ton ie in te rac t ions . The r e l evan t i n t e r ac t ion for t he process v v ~ - ~ l z - + h a d r o n s ( ~ f ' - ~ + +

(5) 1:~. L. KINGSLEY: Phys. Left., 40 B, 387 (1972); K. FUJII, 1VL KATUY&, S. OKUBO and S. TAMURA: Prog. Theor. Phys., 49, 975 (1973); M. KATUYA, K. FUJII and S. TAMURA: Prog. Theor. Phys., 50, 1675 (1973). (6) Note that eq. (2) does not mean the nouleptonic interaction but means the effective matrix element in the ease of the coloured particle induced and decaying through semi-leptonic interaction. Since only the Jr | J-type interactions induce the event, but not the Jr | J-type, the (10, 1) and (1O*, 1) repre- sentations do not always vanish. (D For example, a coloured state is induced by

v~ + S ( I ' = �89 I; = - � 8 9 r ' = 1; i" = r " = o ) - . ~ - + s ( v = r , = 0; i~ = �89 z; = �89 r - = 1),

and decays as

s ( I ' = r ' = o ; i ' = �89 i ; =�89 r ' = l ) - + z ( i ' = � 8 9 i~=�89 r ' = - 1; r = r ' = o )W,~ .

We will observe these processes apparently as the AS = 2 process vlzn--~[z-~+VlL~ ~ (a) We have a characteristic process v-~p --Nz+lz+vtt~ - through

~t t+S(I '= �89 I~ =�89 Y ' = I ; I ' = r "= O)-+W +S( I '= Y'=O; I ' = � 8 9 I = - � 8 9 Y ' = I ) ,

S( I '= Y '= O; I" = �89 I: = -- �89 Y"= 1) -~S(I '= �89 I~' = -- �89 F ' = -- 1; I ' = Y" = O)~+vp .

(') B. BARISti: The VI Hawaii Topical Conference on Particle Physics, Hawaii, August 1975; C. RUBBIA. ~ The VII International Symposium on Lepion and Photon Interactions at High Energies, Stanford, August 1975.

5~2 M. KATUYA, S. 0GAWA and T. YANAGIDA

-~ hadrons) is

(5) 3", | (J~J~'+ ~ J~J ) =

----- (8, 1)~ ~- (10, 1)~,-~ (10", 1)~ ~- (27, 1)~-~ (3__55, 1)~-~ (35*, 1)~-[- (64, 1)~.

The selection rule is obtained as follows:

(6) A S / A Q = - - 2 , - - 1 , O, 1, 2, 3 .

For example, a typical AS/AQ = 3 process is 9~p-~ ~+r:+~-, for which the responsible interact ions are (lo)

J~(6 ~- i7, 1 ~- i2) | [J~(6 - - i7, 4 ~- i5) jr+ (4 + i5, 6 ~- i7) -~ h . e . ] .

This process cannot be induced in the GIM scheme. We conclude by emphasizing tha t the proposed high-energy neutrino reactions,

for example, v~n.+t~-~+~0(~), ~p.~t~+~+Z-(s) and ~p~t~+r :+~-(1~ could be in- duced in the eoloured-quark model but not in the GIi-~ model.

$ $ $

We thank Profs. M. YON]~ZXWA and Y. KoID~ for their careful discussions and useful comments.

(10) Note that the A~ = 2 nonleptonic interaction cannot be rejected at present in the case of the eoloured-partiele decays into ordinary hadrons.