Possibility of large CP and T violation in weak interactions

Volume 12, mam~r 2

POSSIBILITY

PHYSICS

OF

LARGE

CP AND

LETTERS

T VIOLATION

IS September 1964

IN W E A K

INTERACTIONS

N. CABIBBO C'ER.'¢, Genet a, Su tlzerland Received I~ August 1964 A r e c e n t e x p e r i m e n t 1) has Identified the =*t" decay ot the long lived component of a n e u t r a l K b e a m , with a branching r a t i o o v e r o t h e r clm.rged d e c a y m o d e s of ( 2 x 0 . 4 ) , I0 "3. T h i s r e s u l t g i v e s evidence for ('P v i o l a t i o n in weak i n t e r a c t i o n s * (and also of time reversal violation, assuming the validity of the CPTtheorem). It is aJ. open question to decide w h e t h e r the s m a l l e x p e r i m e n tal branching r a t i o i m p l i e s ( o r Is consistent w i t h ) a tonsil o r a large violation of C P s y ~ m e t r y Given our ignorance in th~ dynamics of non-leptonic weak interactions, we feel that this problem cannot find a satisfactory theoretical solution o*, but that f u r t h e r e x p e r t m e n t a t l o n is n e e d e d , e s p e c i a l l y In the b e t t e r u n d e r s t o o d field of leptonte d e c a y s , On g e n e r a l g r o u n d s l a r g e violation of C P Is m o r e palatable than a s m a l l one. In thl~ p a p e r we d i s c t m s the p o s s i b i l i t y of a l a r g e vtolati+m of C/" ~ y m m e t r y within the l i a r s of the V-A t h e o r y of weak i n t e r a c t i o n s 3), a s c o m p l e t e d by a s s u m p t i o n s of definite SU3 4) behavtour of weak c u r r e n t s 4 , 5 ) and of the n o n - l e p tonic Lagrangtan 6 - 8 ) . The s c h e m e obtained In t h i s way is not in d i s a g r e e m e n t with p r e s e n t l y available data., including the p r e c i s e m e a s u r e m e n t s on the d e c a y el the f r e e neutron 9) ***. The s c h e m e g i v e s a l s o precise. Ind i c a t t o n t of e x p e r i m e n t s w h e r e r e l a t i v e l y l a r g e T violation ef+ects could be f o u n d In the following we will a s s u m e s t r i c t validity of the CPT t h e o r e m . The t w o - c o m p o n e n t nature o( the n e u t r i n o p'ats strong l i m i t s on the violation of C P by lepton c u r r e n t s ; we s h a h a s s u m e that they axe stillgiven by

l;~ : (/~'rX ( 1 . 7 5 ) v ~ ) , (dyX (1 +),5)Vc)

s o that C P violation should be r e s t r i c t e d to the weak c u r r e n t s of s t r o n g l y m t e r a c t i n g p a r t i c l e s • Our b a s i c a s s u m p : l o n s will be that: w e a k c u r r e n t s are members of a single octet of Hermitian curr e n t s , JX i

j~i =jj*

L ~ =diemjxldx

m .

L~NL ~ a L 3 + b L 8 + e L 6 •

(2)

(3)

(4)

II t h e j x i have definite C P behavlour *~ , i . e . , C'PJ~i(cp)'I

= ~(i)d~i

f o r ;~ = 1 , 2 , 3 (5) (for ;~ = 4, a m i n u s sign)

w h e r e r/= +1 f o r i = 2 : 3 , 5 , 6 , 8 , and ~ = -1 f o r i = 1,4, 7, the o c t e t L z a l s o t r a n s f o r m s in the s a m e way, and Z~NL c o n s e r v e s CP. T h e r e f o r e , under our a s s u m p t i o n s , a C P v i o l a tion in n o n - l o p t o n i e d e c a y s r e q u i r e s the c u r r e n t s ,Ix! to have ratxed C P behavlour. Let us divide Jx z into a " r e g u l a r " p a r t d x i , R and an i r r e g u l a r p a r t d x i, 1 (each of them a m i x t u r e of axial and vector)

Istet~e.

t e s t s of ('P. l~ciudlng the m e a s u r e m e n t = of e l e c t r i c ~ , p o l e m o m e n t = , a r e not c o n c l u s i v e a g a t a s t a l a r g e C P v i o l a t i o n in w e a k i n t e r a c t i o n s .

8)

Z'NL can be any combination of L3, LS, L6, L7, but since a L 7 co.mponent can bo e l i m i n a t e d by a t r a n s f o r m a t i o n e t a Y (redefinition of the r e l a t i v e p h a s e s of p a r t i c l e s with d i f f e r e n t h y p e r c h a r g e ) , we put h e r e

"* For example we do not u~derstal~ why certain weak decays llke L- - n + '~" are nearly parity con~ervlag. Other

(i=1,2 ....

J~° being equal t o J A + f o r ;~ = 1 , 2 , 3 , and to - J x + for ;~ = 4. We a l s o a s s u m e that: t h e non-.'e.plonic L a g r a n g i a n 2?NL i~ m e m b e r o f an o c t e t L+

• other more exotic I,q~rpretatlotut are poalble: Bcrtu;teila, l~e ~ Clbtbbo 2) have COl~ll~lered the the pOellbility of Ioug rlmge force= different from the ele~tromsgnetlc and gravltatlotml otto= and d i s cussed the vltpcrtmental Implication= of their e x -

• **

(1)

f

CP violating effects could be Introduced into the lepton current (preserving tbe two-componeut hypo= thesis), by means of dorlvatlve .couplings of the form [(p~t _pkv) (1 +-.5)v or r(P~I *PX") (1 + ¥5):. where l = e o r t~. A good l i m i t vn the latter kind of current can be obtained from the experimental value of the '*",+- e + + v / - ÷ ~ ~ * * "J ratio. 1" The definition of charge conjugation In the frame of SU3 Is discussed In ref. 6. The definition of CP follows along similar lines.

Volume 12. m,m.~r 2

PHYSICS LETTERS

which e x c l u d e s a l a r g e CP violation In weak in~ctlons, so that s o m e of the e x p e r i m e n t s ind i c a t e d above should be s e r i o u s l y c o n s i d e r e d .

Re/~e~'es l! J.H.Cbrimtm~o~, J.W.CronL~, V.L. Fitch taxi R. Turlay, Phys. Rmv. lJetters 13 (1964) 138. 2} J.lqmrm~m. T.D.Lee m~d H.Cab/bbo, toLo p~b-

Imbed. R. i~.Yeymnam avd Id.Gell-Ma~m, Phys. Rev. 109 (Is58} I~3; R.E.Mar~hak and E.C.G.Sudarsh~m. Proc. PaduaV ~ t o e f',o~, on mNon~ and r~oe~tly discovered

ASYMPTOTIC PROCESSES

15 September 1964

particles (Socfe~ Rallmm di Fisica. Padua-Venlce,

19SS).

4) M.Gell°Mnnn, California fnstltute of Technology Report CTSL-20, 1~61 (unpublished); Y.Ne'eman, Nucl. Phys. 20 (1961) 222. 5) N. Cabfbbo, Phys. Rev LettBrs ~0 (1964) 531. 6) N. Cabfbbo, Phys. Reg. Letters 12 (1964) 62. " ~ ~. W. Lee, Phys. Rev. Letters 12 0964) 83. 8) M.Gell-Mann, Phys. Rev. Letters 12 (1964) 155. 9) M.T. Burgy, V.E.Krohn, T.B.Novey, G.R.R .1go a~l V.L.Telegdi, Phys. Rev. Letters 1 (1958) 324. 10) S.Wetnlmrg, Phys. Rev. 112 (1958) 1375. 11) J.J.sekurat, Phys. Rev. 109 (1958) 980.

RELATIONS BETWEEN AMPLITUDES OF THE WITH A VARIABLE NUMBER OF PARTICLES

A. A. L O G U N O V ,

NGUYEN

V A N HIEU and L T. T O D O R O V

JoiMt Ixstitule for Nuclear Research, Laboratory o f Theoretical Physics Reculvod 15 AuguSt 1964

The a s y m p t o t i c r e l a t i o n s between the a m p l i t u d e s of the b i n a r y c r o s s e d p r o c e s s e s ( s c a t t e r i n g ~nd phutopr~lucticm) h a w been obtained tn r ~ s . I-3. On the b e s t s of t h e s e r e l a t i o n s t h e r e have been found the a s y m p t o t i c e q u a l i t i e s (g th.~ "qfferential c r o 6 s s e c t i o n s and p o l a r i z a t i o n s . In t h i s p a p e r we e s t a b l i s h the a~ymptotlc r e l a t i o n s b(.tween the a m p i / t u d e s of the p r o c e s s e s with a v a r i a b l e n u m b e r qd l ~ r t i c l e s . Further on we edmll be a b l e , with U~e aid of t h e s e r e l a t i o n s , to get the a s y m p t o t i c e q u a l i t i e s ~ the d U f e r e n t t a l c r o s s sections for these p r o c e s s e s . F o r the s a k e v¢ s i m p l i c i t y we will be c o n c e r n e d with the pion production p r o c , , ~ s ~ s in pl.,n-nucleon co ilistrms • • N'"

a',

s"*

N' ,

~.N'-. ~ ' * ~ " + N ,

(I)

a+e--c+a÷b.

,

crossed photoproduction processes was given in ref. 3. W e denote by p and p' the 4-momenta of nucleons in the initial and final states, and by q, q' and q" the pion 4-momenta, respectively, p+q=p'÷q'+q', p2 =p,2 = M 2,

q2=q,2=q.2

=m2.

where M and m are the nucleon and pion masses. The klnem;ttics of the proce,Js involving Live particles Is characterized by five invariant variables. Following refs. 4 and 5 we chose as independent variables the In~artants t = (p-p')2 ,

t" =(q-q')2

,

W2 = ( q , + q . ) 2 .

(n)

where r , s ' o r r" denote cme of the p l o n s , and N o r N' s t a n d s f o r p or n. The r e a s o n i n g given b e tow, if slightly modified k i n e m a t i c a l l y , may be applied to any o t h e r processes of the f o r m a÷b--c+d+e

called c r o s s e d . A s i m i l a r definition of the

(I') (rl')

P r o c e s s e s (I) and (If) o r (I') and (II') w i l l be

q ~+p)'

4 cosh~./~z-¼/

Such a cholce is convenlent because, by fixing the vaxtables t -< 0, t" ~ 0, W 2 >~ 4 m 2 cosh2~,~, we can m a k e the energy va.,.'lable~o tend to infinitely, remaining in the physical region. The f i r s t t h r e e variable:~ h a w an obvious p h y s ical m e a n i n g , the v a r i a b l e .o i s connected with the total e n e r g y of the p r o c e s s L,~ the c m s by the following e x p r e s s i o n

139