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On the angular distribution of the brookhaven 1962 neutrino experiment
Volume 5, number 3
PHYSICS
r e s u l t 4) (~ = 5 + 2), however, did not a g r e e with theoretical calculations 7, 8) which predicted a negative sign for k. Results of r e c e n t B-~ c i r c u l a r polarization c o r relation m e a s u r e m e n t s on the allowed B3-~3 c a s cade (see fig. 1) were not compatible with the 0spin a s s i g n m e n t to the p r 1 4 4 ground state; a spin of I o = 1- was suggested 1). This a s s i g n m e n t seemed to be supported by the r e s u l t s of B-~ d i r e c tional c o r r e l a t i o n m e a s u r e m e n t s 3 ) o n ' t h e B2-~l cascade which did not a g r e e with the predictions for a unique B-transition f r o m a 0- spin state. Eman and Tadic 2) r e c e n t l y published an analysis of all p r 1 4 4 B-decay data and showed that the Io = 1a s s i g n m e n t is not inconsistent with the experimental data. In o r d e r to test the new spin assignment of Io = 1-, we m e a s u r e d the e n e r g y dependence of the B-~ directional c o r r e l a t i o n of the (?) - B2 -" (2+) - ~1 -" (0+) cascade. The m e c h a n i c a l apparatus and the methods of m e a s u r e m e n t s have been described before 9). The multichannel B-~' coincidence s p e c t r o m e t e r used, however, was different. T r a n s i s t o r i s e d DDL a m p l i f i e r s were used in the slow channels to allow higher single counting r a t e s and to improve the r e solving time. The r e s u l t s of the m e a s u r e m e n t s of the B-~' anisotropy f a c t o r A2(W) in the B-~' d i r e c tional c o r r e l a t i o n function
LETTERS
1July1963
7 XlP2 A2(W) - 5 q2 + klp2 (F2(2202))2 ; p and q are the electron and anti-neutrino momenta r e s p e c t i v e l y , in units moc2. The Coulomb c o r r e c tion f a c t o r kl(Z, W) was taken f r o m Kotani and R o s s 10). The t h e o r e t i c a l A2(W) curve is c o r r e c t e d f or the finite solid angle of the B- and ~ - d e t e c t o r s and for the effects of b a c k s c a t t e r i n g in the B-scintillation detector. The experimental data a g r e e v e r y well with the theoretical predictions for a unique B-transition f r o m a nuclear state with Io = 0-. Thus the p r e s e n t data give strong support to the p r e v i o u s ly accepted 0- a s s i g n m e n t to the p r 1 4 4 ground state. F u r t h e r r e f i n e m e n t s of the experiment and the analysis a r e in p r o g r e s s . In p a r t i c u l a r , the v e r y unlikely possibility of explaining the experimental directional c o r r e l a t i o n on the b a s i s of a (1-) - B " (2 +) - ~ -~ (0) cascade, a s s u m i n g a v e r y special choice of the 4B-matrix elements that contribute to a 1- -. 2+ B-transition will be further investigated.
References 1) V.M. Lobashov and V.A. Nazarenko, J. Exptl. Theoret. Phys. (USSR) 41 (1961) 1433. 2) B. Eman and D. Tadic, Physics Letters 4 (1963) 13. 3) R. L. Grah~m, J.S.Geiger and T.A.Eastwood, Can. J. Phys. 36 (1958) 1084. 4) F.T.Porter and P.P.Day, Phys. Rev. 114 (1959) 1286. 5) C.P.Bhalla and M.E ~ose, Phys. Rev. 120 (1960) 1415. 6) D.Tadic, Nuclear Phys. 18 (1960) 13. 7) T. Ahrens and E. Feenberg, Phys. Rev. 86 (1952) 64. 8) D. L. Pursey, Phil. Mag. 42 (1951) 1193. 9) R.M. Steffen, Phys. Rev. 123 (1961) 1787. 10) T.Kotani and M.Ross, Phys. Rev. 113 (1959) 622.
W(0) = 1 + A2(W) e 2 ( c o s 0) a r e shown in fig. 1. The data a r e c o r r e c t e d for B - B r e m s s t r a h l u n g coincidences and f o r ~,-~, coincidences. The solid curve r e p r e s e n t s the B-',¢ dir e c t i o n a l c o r r e l a t i o n f a c t o r A2(W) expected for a unique B-transition in a (0-) - B2 "~ (2 +) - ~ -" (0 +) cascade * * * * *
THE
ON T H E A N G U L A R D I S T R I B U T I O N OF BROOKHAVEN 1962 NEUTRINO EXPERIMENT J. L•VSETH
CERN, Geneva Received 13 June 1963
The angular distribution for the BNL e x p e r i ment 1) has been given by Gaillard 2). It is shown in fig. 1 and contains the 34 events with "long" single t r a c k s corresponding to muons with a visible momentum l a r g e r than 300 MeV/c. The e x p e r i mental distribution is thought to have no p a r t i c - l ~ v ang~,l~r bias, except.that it contains - 5 c o s m i c r a y events, m o s t l y at high angles 3).
The purpose of this note is to p r e s e n t a calculation which shows that this experimental angular distribution, within the r a t h e r large experimental uncertainties f r o m bad s t a t i s t i c s and uncertainties about the neutrino s p e c t r u m , is compatible with the c u r r e n t l y accepted ideas of weak interactions 4). The interaction for the p r o c e s s 199
Volume5, number 3
PHYSICS
v+n--p+/-
(1)
is a s s u m e d to be of the f o r m G H = ~ i (K' [Fl~'c~ - --~ F2~c~q fl
LETTERS
1 J u l y 1963
q2 B(q 2 ) = ~ - ~ ( F I + . F 2 ) C(q2 ) =
+ )`FAVa? 5 - i 6 FpqcxlK) i (k' I?a(l+),s)lk)
(2)
1 (F 2 + ) ` 2 F 2 4M2 +~
XFA q2
(9)
,
, 2 F~)
(I0) '
s - u --- - (k+K) 2 + ( k ' - K ) 2 = - 2 k ( K + K ' ) .
(n)
where K , K ' and k, k' a r e the initial, final 4 - m o m e n t a The c r o s s section for the r e a c t i o n and M and m the m a s s e s for nucleons and leptons P + p -" n + l+ (12) respectively. G is the v e c t o r coupling constant and the p a r a m e t e r s u, )` and b give the relative strength is obtained by changing the sign of B in (7) *. of the other couplings. The f o r m f a c t o r s F i are S o m e words about form factors. A s s u m i n g C V C functions of and e-, universality, then q2 = (k-k')2
F 1 = F 2 = F e = (1 + 1.25 q 2 / M 2 ) - 2 ,
and n o r m a l i s e d so that F(0) = 1 .
(3)
A s nuclear model w e will use the ideal F e r m i gas. For simplicity w e will consider only the case N = Z and neglect effects of an effective nucleon mass.
In the initial state all levels will be filled up to the F e r m i momentum P F . F o r r o = 1.12 fm one has 5) P F = 267 M e V / c . For a scattering
(4)
event to take place,
the exclusion
principle r e q u i r e s that the 3 - m o m e n t u m of the final nucleon, P ' , satisfies P' > P F
•
(5)
To p e r m i t c o m p a r i s o n with the experimental d i s t r i bution, we r e q u i r e that the final lepton momentum p' satisfies p ' > 300 MeV/c .
(6)
By neglecting the lepton m a s s except in the pseudos c a l a r t e r m and a s s u m i n g the f o r m f a c t o r s to be r e a l , the differential c r o s s section can be obtained as
d~ G2M 4 3 f'd3p dr3 = 81r~ 4~PF3
× e ' 2 [ A ( q 2) + (s-u) B(q2) + (s-u)2 C(q2)]
(7)
e E(-)(k.K)
The p r i m e (on the integral) indicates that the conditions in eqs. (5) and (6) m u s t be fulfilled, e and e' a r e initial and final lepton e n e r g y , E initial nucleon e n e r g y (= J ( p 2 + M2)). The e x p r e s s i o n in the square b r a c k e t s r e p r e s e n t s the invariant p a r t , where q2 q2 A(q2) = q2 {(1 + ~--~) (- F 2 + )`2 F 2 _ ~__~)
q2
+~-2 200
m
q2 b2F }, is)
(F1 + " F 2 ) 2 - M ) ` b F A F p + - 4 - ~
(13)
this being an e m p i r i c a l r e p r e s e n t a t i o n of the nucleon i s o v e c t o r e l e c t r o m a g n e t i c f o r m f a c t o r s 6). About F A and F p little is known. F o r simplicity we will a s s u m e that they a r e of the s a m e f o r m ,
F A = (1 + q 2 / M 2 ) - 2
,
(14)
F p = (1 + q 2 / M 2 p ) - 2 .
(1.5)
If the interaction is mediated by a v e c t o r boson of m a s s M W , then this can be accounted f o r by u s ing modified f o r m f a c t o r s F ' given by 8)
F i, = Fi(1 + q 2 / M 2 ) - I
,
i = 1,2,A ,
Fp' = F p + ~2)'m FA(1 + q 2 / M ~ ) - I
.
(16) (17)
F o r the coupling p a r a m e t e r s we will take the usual values
GM 2 = 10 -5 ,
)` = 1.25 , (18)
.=3.71
,
b= 8),=10.
The differential c r o s s section (17) has been c a l culated by a M o n t e - C a r l o method and a v e r a g e d o v e r the appropriate neutrino spectrum for the BNL exp e r i m e n t 1 )). The calculated c u r v e s axe shown together with the experimental points in fig. 1. As is seen, the curve with all f o r m f a c t o r s = F e (eq. (13)) and M W = oo is v e r y n e a r l y the same as the one with F A = 1 and M W = 0.6 GeV. A m o r e detailed study shows that it will be difficult to disentangle the influence of the axial f o r m f a c t o r and the v e c t o r boson, if direct evidence is not obtained for the latter. Lapidus 9) has suggested that the predominance * T h a t the c o v a r i a n t m a t r i x e l e m e n t is a q u a d r a t i c in (s-u) depends s o l e l y on the c u r r e n t - c u r r e n t f o r m of the i n t e r a c t i o n , a s s h o w n by M a r t i n and G o u r d i n 7). T h a t only the s i g n of the l i n e a r t e r m is changed for the a n t i n e u t r i n o r e a c t i o n d e p e n d s , a c c o r d i n g to Bell 8), only on PCT, u n i t a r i t y , and the n e g l e c t of n e u t r o n - p r o t o n mass difference.
Volume 5, number 3
PHYSICS
LETTERS
1 July 1963
--~/IO-39cmz/STERAD
d~/10-3~ cm2/STERAD
FA= I MW=.8 GcV I 2 PURE PS b= I ~ l O
I
l
5
15
25
35
45
55
65 ~
e
5
Fig. 1. Data from the 1962 BNL experiment compared with theoretical curves. Unless otherwise indicated, form factors are taken equal to the electromagnetic form factor with M W = ~. of m u o n s in t h i s e x p e r i m e n t m i g h t be due to a s t r o n g p s e u d o s c a l a r coupling. To t e s t t h i s h y p o t h e s i s we show a c u r v e l a b e l l e d " p u r e P S " which c o r r e s p o n d s to F p = F e , b = 1 0 J 1 0 , F 1 = F 2 = F A = 0. O b v i o u s l y it d o e s not a g r e e with the e x p e r i m e n t a l d i s t r i b u t i o n . One could m a k e the shape b e t t e r by r e d u c i n g M p in (15), but the v a l u e of b t h e n r e q u i r e d to m a k e the t o t a l c r o s s s e c t i o n of r i g h t o r d e r would be e v e n m o r e difficult to a c c e p t . A s u p p r e s s i o n of the p s e u d o s c a l a r c o n t r i b u t i o n by p u t t i n g b = 0 would on the c o n t r a r y i m p r o v e the a g r e e m e n t with the e x p e r i m e n t a l d i s t r i b u t i o n . E f f e c t i v e l y the s a m e s u p p r e s s i o n can a l s o be o b t a i n e d b y m a k i n g the n a t u r a l a s s u m p t i o n that the o n e - p i o n pole d o m i n a t e s in the p s e u d o s c a l a r i n t e r a c t i o n . I n s t e a d of (15) one then h a s Fp = Fp1 =
(1 + q 2 / m 2 ) - 1
(1 + m/~/m~2) .
(19)
T h i s f a l l s off m u c h m o r e r a p i d l y than F e with q 2. C a l c u l a t i o n shows that the p s e u d o s c a l a r c o n t r i b u t i o n (b = 10) i s t h e n quite n e g l i g i b l e f o r t h i s e x periment. * For the purpose of fig. 1 the number of neutrinos has been assumed equal to the number of antineutrinos. For fig. 2 the ratio between neutrinos and antineutrinos has been taken to be 1 : 1 for the pion and 3 : 1 for the kaon part, since K+ is known to be more abundantly produced than K-.
15
25
35
45
55
65
w, e
Fig. 2. Calculated cross section for ~ and K neutrinos compared with experimental results.
In fig. 2 we show the c a l c u l a t e d d i s t r i b u t i o n s f r o m ~ and K n e u t r i n o s s e p a r a t e l y *. The f a c t that t h e r e a r e s l i g h t l y m o r e e v e n t s in the f o r w a r d d i r e c t i o n than c a l c u l a t e d , s u g g e s t s that the i n t e n s i t y of K n e u t r i n o s m a y have b e e n u n d e r e s t i m a t e d . An u p w a r d r e v i s i o n would s t r e n g t h e n the e v i d e n c e
against "neutrino flip" I). The a u t h o r i s i n d e b t e d to D r s . J. S. Bell and J. M. G a i l l a r d f o r m a n y d i s c u s s i o n s and h e l p f u l criticism. References
1) G.Danby et al., Phys. Rev. Letters 9 (1962} 36. 2) J. M. Galliard, CERN NP Internal Report 63-1, unpublished. 3) J. M. GaHlard, pr~¢ate communication. 4) Neutrino reactions have been treated by: Y. Yamaguehi, CERN 61-2 and Progr. Tbeoret. Phys. 23 {1960) 1117. N. Cabibbo and R. Gatto, Nuovo Cimento 15 {1960) 304. T.D. Lee and C.N.Yang, Phys,Rev. Letters 4 {1960} 307. 5} J . S . B e l l and E.J.Squtres, Adv. Phys. 10 (1961} 211. 6) R.Hofstadter, Revs. Modern Phys. 28 {1956) 214; 30 0958) 482. 7) M. Gourdin and A. Martin, Nuovo Cimento, in press. 8) J.S.BeI1, Lectures at CERN, unpublished. 9) L. Lapidus, J. Exptl. Theoret. Phys. (USSR), in press.
201
PHYSICS
r e s u l t 4) (~ = 5 + 2), however, did not a g r e e with theoretical calculations 7, 8) which predicted a negative sign for k. Results of r e c e n t B-~ c i r c u l a r polarization c o r relation m e a s u r e m e n t s on the allowed B3-~3 c a s cade (see fig. 1) were not compatible with the 0spin a s s i g n m e n t to the p r 1 4 4 ground state; a spin of I o = 1- was suggested 1). This a s s i g n m e n t seemed to be supported by the r e s u l t s of B-~ d i r e c tional c o r r e l a t i o n m e a s u r e m e n t s 3 ) o n ' t h e B2-~l cascade which did not a g r e e with the predictions for a unique B-transition f r o m a 0- spin state. Eman and Tadic 2) r e c e n t l y published an analysis of all p r 1 4 4 B-decay data and showed that the Io = 1a s s i g n m e n t is not inconsistent with the experimental data. In o r d e r to test the new spin assignment of Io = 1-, we m e a s u r e d the e n e r g y dependence of the B-~ directional c o r r e l a t i o n of the (?) - B2 -" (2+) - ~1 -" (0+) cascade. The m e c h a n i c a l apparatus and the methods of m e a s u r e m e n t s have been described before 9). The multichannel B-~' coincidence s p e c t r o m e t e r used, however, was different. T r a n s i s t o r i s e d DDL a m p l i f i e r s were used in the slow channels to allow higher single counting r a t e s and to improve the r e solving time. The r e s u l t s of the m e a s u r e m e n t s of the B-~' anisotropy f a c t o r A2(W) in the B-~' d i r e c tional c o r r e l a t i o n function
LETTERS
1July1963
7 XlP2 A2(W) - 5 q2 + klp2 (F2(2202))2 ; p and q are the electron and anti-neutrino momenta r e s p e c t i v e l y , in units moc2. The Coulomb c o r r e c tion f a c t o r kl(Z, W) was taken f r o m Kotani and R o s s 10). The t h e o r e t i c a l A2(W) curve is c o r r e c t e d f or the finite solid angle of the B- and ~ - d e t e c t o r s and for the effects of b a c k s c a t t e r i n g in the B-scintillation detector. The experimental data a g r e e v e r y well with the theoretical predictions for a unique B-transition f r o m a nuclear state with Io = 0-. Thus the p r e s e n t data give strong support to the p r e v i o u s ly accepted 0- a s s i g n m e n t to the p r 1 4 4 ground state. F u r t h e r r e f i n e m e n t s of the experiment and the analysis a r e in p r o g r e s s . In p a r t i c u l a r , the v e r y unlikely possibility of explaining the experimental directional c o r r e l a t i o n on the b a s i s of a (1-) - B " (2 +) - ~ -~ (0) cascade, a s s u m i n g a v e r y special choice of the 4B-matrix elements that contribute to a 1- -. 2+ B-transition will be further investigated.
References 1) V.M. Lobashov and V.A. Nazarenko, J. Exptl. Theoret. Phys. (USSR) 41 (1961) 1433. 2) B. Eman and D. Tadic, Physics Letters 4 (1963) 13. 3) R. L. Grah~m, J.S.Geiger and T.A.Eastwood, Can. J. Phys. 36 (1958) 1084. 4) F.T.Porter and P.P.Day, Phys. Rev. 114 (1959) 1286. 5) C.P.Bhalla and M.E ~ose, Phys. Rev. 120 (1960) 1415. 6) D.Tadic, Nuclear Phys. 18 (1960) 13. 7) T. Ahrens and E. Feenberg, Phys. Rev. 86 (1952) 64. 8) D. L. Pursey, Phil. Mag. 42 (1951) 1193. 9) R.M. Steffen, Phys. Rev. 123 (1961) 1787. 10) T.Kotani and M.Ross, Phys. Rev. 113 (1959) 622.
W(0) = 1 + A2(W) e 2 ( c o s 0) a r e shown in fig. 1. The data a r e c o r r e c t e d for B - B r e m s s t r a h l u n g coincidences and f o r ~,-~, coincidences. The solid curve r e p r e s e n t s the B-',¢ dir e c t i o n a l c o r r e l a t i o n f a c t o r A2(W) expected for a unique B-transition in a (0-) - B2 "~ (2 +) - ~ -" (0 +) cascade * * * * *
THE
ON T H E A N G U L A R D I S T R I B U T I O N OF BROOKHAVEN 1962 NEUTRINO EXPERIMENT J. L•VSETH
CERN, Geneva Received 13 June 1963
The angular distribution for the BNL e x p e r i ment 1) has been given by Gaillard 2). It is shown in fig. 1 and contains the 34 events with "long" single t r a c k s corresponding to muons with a visible momentum l a r g e r than 300 MeV/c. The e x p e r i mental distribution is thought to have no p a r t i c - l ~ v ang~,l~r bias, except.that it contains - 5 c o s m i c r a y events, m o s t l y at high angles 3).
The purpose of this note is to p r e s e n t a calculation which shows that this experimental angular distribution, within the r a t h e r large experimental uncertainties f r o m bad s t a t i s t i c s and uncertainties about the neutrino s p e c t r u m , is compatible with the c u r r e n t l y accepted ideas of weak interactions 4). The interaction for the p r o c e s s 199
Volume5, number 3
PHYSICS
v+n--p+/-
(1)
is a s s u m e d to be of the f o r m G H = ~ i (K' [Fl~'c~ - --~ F2~c~q fl
LETTERS
1 J u l y 1963
q2 B(q 2 ) = ~ - ~ ( F I + . F 2 ) C(q2 ) =
+ )`FAVa? 5 - i 6 FpqcxlK) i (k' I?a(l+),s)lk)
(2)
1 (F 2 + ) ` 2 F 2 4M2 +~
XFA q2
(9)
,
, 2 F~)
(I0) '
s - u --- - (k+K) 2 + ( k ' - K ) 2 = - 2 k ( K + K ' ) .
(n)
where K , K ' and k, k' a r e the initial, final 4 - m o m e n t a The c r o s s section for the r e a c t i o n and M and m the m a s s e s for nucleons and leptons P + p -" n + l+ (12) respectively. G is the v e c t o r coupling constant and the p a r a m e t e r s u, )` and b give the relative strength is obtained by changing the sign of B in (7) *. of the other couplings. The f o r m f a c t o r s F i are S o m e words about form factors. A s s u m i n g C V C functions of and e-, universality, then q2 = (k-k')2
F 1 = F 2 = F e = (1 + 1.25 q 2 / M 2 ) - 2 ,
and n o r m a l i s e d so that F(0) = 1 .
(3)
A s nuclear model w e will use the ideal F e r m i gas. For simplicity w e will consider only the case N = Z and neglect effects of an effective nucleon mass.
In the initial state all levels will be filled up to the F e r m i momentum P F . F o r r o = 1.12 fm one has 5) P F = 267 M e V / c . For a scattering
(4)
event to take place,
the exclusion
principle r e q u i r e s that the 3 - m o m e n t u m of the final nucleon, P ' , satisfies P' > P F
•
(5)
To p e r m i t c o m p a r i s o n with the experimental d i s t r i bution, we r e q u i r e that the final lepton momentum p' satisfies p ' > 300 MeV/c .
(6)
By neglecting the lepton m a s s except in the pseudos c a l a r t e r m and a s s u m i n g the f o r m f a c t o r s to be r e a l , the differential c r o s s section can be obtained as
d~ G2M 4 3 f'd3p dr3 = 81r~ 4~PF3
× e ' 2 [ A ( q 2) + (s-u) B(q2) + (s-u)2 C(q2)]
(7)
e E(-)(k.K)
The p r i m e (on the integral) indicates that the conditions in eqs. (5) and (6) m u s t be fulfilled, e and e' a r e initial and final lepton e n e r g y , E initial nucleon e n e r g y (= J ( p 2 + M2)). The e x p r e s s i o n in the square b r a c k e t s r e p r e s e n t s the invariant p a r t , where q2 q2 A(q2) = q2 {(1 + ~--~) (- F 2 + )`2 F 2 _ ~__~)
q2
+~-2 200
m
q2 b2F }, is)
(F1 + " F 2 ) 2 - M ) ` b F A F p + - 4 - ~
(13)
this being an e m p i r i c a l r e p r e s e n t a t i o n of the nucleon i s o v e c t o r e l e c t r o m a g n e t i c f o r m f a c t o r s 6). About F A and F p little is known. F o r simplicity we will a s s u m e that they a r e of the s a m e f o r m ,
F A = (1 + q 2 / M 2 ) - 2
,
(14)
F p = (1 + q 2 / M 2 p ) - 2 .
(1.5)
If the interaction is mediated by a v e c t o r boson of m a s s M W , then this can be accounted f o r by u s ing modified f o r m f a c t o r s F ' given by 8)
F i, = Fi(1 + q 2 / M 2 ) - I
,
i = 1,2,A ,
Fp' = F p + ~2)'m FA(1 + q 2 / M ~ ) - I
.
(16) (17)
F o r the coupling p a r a m e t e r s we will take the usual values
GM 2 = 10 -5 ,
)` = 1.25 , (18)
.=3.71
,
b= 8),=10.
The differential c r o s s section (17) has been c a l culated by a M o n t e - C a r l o method and a v e r a g e d o v e r the appropriate neutrino spectrum for the BNL exp e r i m e n t 1 )). The calculated c u r v e s axe shown together with the experimental points in fig. 1. As is seen, the curve with all f o r m f a c t o r s = F e (eq. (13)) and M W = oo is v e r y n e a r l y the same as the one with F A = 1 and M W = 0.6 GeV. A m o r e detailed study shows that it will be difficult to disentangle the influence of the axial f o r m f a c t o r and the v e c t o r boson, if direct evidence is not obtained for the latter. Lapidus 9) has suggested that the predominance * T h a t the c o v a r i a n t m a t r i x e l e m e n t is a q u a d r a t i c in (s-u) depends s o l e l y on the c u r r e n t - c u r r e n t f o r m of the i n t e r a c t i o n , a s s h o w n by M a r t i n and G o u r d i n 7). T h a t only the s i g n of the l i n e a r t e r m is changed for the a n t i n e u t r i n o r e a c t i o n d e p e n d s , a c c o r d i n g to Bell 8), only on PCT, u n i t a r i t y , and the n e g l e c t of n e u t r o n - p r o t o n mass difference.
Volume 5, number 3
PHYSICS
LETTERS
1 July 1963
--~/IO-39cmz/STERAD
d~/10-3~ cm2/STERAD
FA= I MW=.8 GcV I 2 PURE PS b= I ~ l O
I
l
5
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35
45
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65 ~
e
5
Fig. 1. Data from the 1962 BNL experiment compared with theoretical curves. Unless otherwise indicated, form factors are taken equal to the electromagnetic form factor with M W = ~. of m u o n s in t h i s e x p e r i m e n t m i g h t be due to a s t r o n g p s e u d o s c a l a r coupling. To t e s t t h i s h y p o t h e s i s we show a c u r v e l a b e l l e d " p u r e P S " which c o r r e s p o n d s to F p = F e , b = 1 0 J 1 0 , F 1 = F 2 = F A = 0. O b v i o u s l y it d o e s not a g r e e with the e x p e r i m e n t a l d i s t r i b u t i o n . One could m a k e the shape b e t t e r by r e d u c i n g M p in (15), but the v a l u e of b t h e n r e q u i r e d to m a k e the t o t a l c r o s s s e c t i o n of r i g h t o r d e r would be e v e n m o r e difficult to a c c e p t . A s u p p r e s s i o n of the p s e u d o s c a l a r c o n t r i b u t i o n by p u t t i n g b = 0 would on the c o n t r a r y i m p r o v e the a g r e e m e n t with the e x p e r i m e n t a l d i s t r i b u t i o n . E f f e c t i v e l y the s a m e s u p p r e s s i o n can a l s o be o b t a i n e d b y m a k i n g the n a t u r a l a s s u m p t i o n that the o n e - p i o n pole d o m i n a t e s in the p s e u d o s c a l a r i n t e r a c t i o n . I n s t e a d of (15) one then h a s Fp = Fp1 =
(1 + q 2 / m 2 ) - 1
(1 + m/~/m~2) .
(19)
T h i s f a l l s off m u c h m o r e r a p i d l y than F e with q 2. C a l c u l a t i o n shows that the p s e u d o s c a l a r c o n t r i b u t i o n (b = 10) i s t h e n quite n e g l i g i b l e f o r t h i s e x periment. * For the purpose of fig. 1 the number of neutrinos has been assumed equal to the number of antineutrinos. For fig. 2 the ratio between neutrinos and antineutrinos has been taken to be 1 : 1 for the pion and 3 : 1 for the kaon part, since K+ is known to be more abundantly produced than K-.
15
25
35
45
55
65
w, e
Fig. 2. Calculated cross section for ~ and K neutrinos compared with experimental results.
In fig. 2 we show the c a l c u l a t e d d i s t r i b u t i o n s f r o m ~ and K n e u t r i n o s s e p a r a t e l y *. The f a c t that t h e r e a r e s l i g h t l y m o r e e v e n t s in the f o r w a r d d i r e c t i o n than c a l c u l a t e d , s u g g e s t s that the i n t e n s i t y of K n e u t r i n o s m a y have b e e n u n d e r e s t i m a t e d . An u p w a r d r e v i s i o n would s t r e n g t h e n the e v i d e n c e
against "neutrino flip" I). The a u t h o r i s i n d e b t e d to D r s . J. S. Bell and J. M. G a i l l a r d f o r m a n y d i s c u s s i o n s and h e l p f u l criticism. References
1) G.Danby et al., Phys. Rev. Letters 9 (1962} 36. 2) J. M. Galliard, CERN NP Internal Report 63-1, unpublished. 3) J. M. GaHlard, pr~¢ate communication. 4) Neutrino reactions have been treated by: Y. Yamaguehi, CERN 61-2 and Progr. Tbeoret. Phys. 23 {1960) 1117. N. Cabibbo and R. Gatto, Nuovo Cimento 15 {1960) 304. T.D. Lee and C.N.Yang, Phys,Rev. Letters 4 {1960} 307. 5} J . S . B e l l and E.J.Squtres, Adv. Phys. 10 (1961} 211. 6) R.Hofstadter, Revs. Modern Phys. 28 {1956) 214; 30 0958) 482. 7) M. Gourdin and A. Martin, Nuovo Cimento, in press. 8) J.S.BeI1, Lectures at CERN, unpublished. 9) L. Lapidus, J. Exptl. Theoret. Phys. (USSR), in press.
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