VOLUME 14,NUMBER25 P H Y S I C A L R E V I E W L E T T E R S 21 JUNE 1965

lished). L. Durand, III, and Y. T. Chiu, to be pub­lished.

14If this problem is ignored, and the nucleon-ex-change contributions are included, the oo decay dis­tribution is improved, but the production angular dis­tribution acquires a large peak at backward angles which is apparently not observed.

15The decay u)-* n + + u ~~ was assumed to proceed through the conversion of the a; into a p through an effective interaction gpuFup^Fuv^ > followed by the decay of the p. In a more sophisticated theory than that used here, g could be complex (see, for ex­ample, the p-cj mixing theory of Bernstein and Fein-berg, reference 1). This would result in a shift in the mass at which the p-aj interference term in the mass spectrum passes through zero, and some change

In November 1964 we repor ted evidence for the exis tence of a pion-nucleon resonance at a m a s s of -1425 MeV/c 2 . 1 We have now c o m ­pleted a full analys is of the events in which this resonance s e e m s to occur and have evidence for the ass ignment of some per t inent quantum n u m b e r s .

Cocconi et al .2 at CERN were the f i r s t to r e ­por t any indications of a nN r esonance in this energy reg ion . Their momentum spec t r a , done for the reac t ion

p+p-N+N*

yN + nir (1)

at nine values of incident proton momentum, showed a peak whose position var ied with the incident momentum from 1.4 GeV/c at P o = 3.60 GeV/c to 1.51 GeV for P 0 ^ 6 . 2 3 GeV/c , as well a s two other peaks , one at 1.24 GeV/c and one at 1.69 GeV/c, which remained constant with varying incident e n e r g i e s . They in te rpre ted the peak at 1.24 GeV/c a s the N33* i sobar and the one at 1.69 GeV/c a s the appearance of the N15* resonance» But they in te rpre ted the shift­ing peak a s an indication of a poss ible nucleon isobar at 1.4 GeV/c which gradual ly became submerged by the iV13*(1512) with inc reased incident energy and momentum.

At the s a m e t ime , B a r e y r e et a l . 3 at Saclay

in the magnitude of the effects. These points can only be examined on the basis of a detailed theory of the decayc

16We have omitted the small contributions of the e° meson [T - 0+, J**-- U+ KIT resonance near 700 MeV; see L. Durand, III, and Y. T. Chiu, Phys* Rev, Let­ters 14, 329, 680(E) (1965), for a discussion of the indirect evidence for this particle. Some direct evi­dence has accumulated recently (private communica­tions from J0 Halpern and W. Selove)]. Although the e° affects the di-pion decay distribution markedly, it has a negligible effect on the di-pion mass spectrum in the oo mass region. The angular distributions of the 7r 7r~" pairs from the decay of the p° and u are similar, and the overall distribution is affected rather little by the p°-u; interference.

studied u-N total c r o s s sect ions at 300 MeV

^ ^7rlab ^ 7 ^ M e V anc* f o u n c i a n indication of a nN r e sonance in the T= \ s ta te in the total c r o s s - s e c t i o n cu rves at -1400 MeV and in the i n v a r i a n t - m a s s spec t rum of the final s ta te

77 " " + / > - * 77+ + 77~~ +p +7T"~. (2 )

The Saclay group found their bump in the e l a s ­tic c r o s s sect ion at 7^ = 430 MeV, i .e . , M^ -1400 MeV; then, making the assumption that the res idua l c r o s s sect ion in that region of kinetic energy was dominated by a single p a r ­tial wave, observed that the T = | inelast ic c r o s s sect ion reached i ts maximum value in that r e ­gion in an angular momentum s ta te J-\. In addition, they noted a shoulder in the m a s s spec t rum (2) dis t inct from the bump at M^ = 1512 MeV but of b a r e s t a t i s t i ca l s ignif icance.

Up to this t ime this was the only d i rec t ex ­pe r imen ta l evidence for a r e sonance in the ATTT sys t em at a m a s s approximating 1.4 GeV. But by far the most convincing work was the ex­haust ive phase-shif t analys is of the p ion-nucle­on sys t em between Tn = 0 and 700 MeV by Roper 4

at the L i v e r m o r e Radiation Labora tory of the Universi ty of California at Berke ley . Roper and Wright repor ted 5 that the Pu phase shift was found to pass through 90° at a value of Tn

= 556 MeV and of MnN = 1485 MeV. It should be noted that this is dis t inct from the D13 phase

QUANTUM NUMBER ASSIGNMENTS FOR THE iV*(1425) RESONANCE

Stuart Lee Adelman

Cavendish Laboratory, University of Cambridge, Cambridge, England (Received 2 March 1965; revised manuscript received 12 April 1965)

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VOLUME 14,NUMBER25 P H Y S I C A L R E V I E W L E T T E R S 21 JUNE 1965

shift which was also observed to pass through 90° but at a value of T^ = 676 MeV and MnN

= 1559 MeV. If one is inclined to interpret the D13 wave as representing the iV13*(1512), then this is an indication that a new isobar distinct from the 1238 and 1512 exists in this region and is a direct indication that its spin ought to be J= | . Following the report of the experi­ment done at Cambridge,6 Donnachie et al.7

in London obtained a set of pion-nucleon phase shifts that indicate that the Pu wave passes through 90° at Tn = 490 MeV, M^ = 1440 MeV, then peaks at 100° at Tn = 600 MeV and decends again.

Later still, Moorhouse8 reported phase-shift studies of the same type that indicate a Plx

wave possibly going through 90° at 475 MeV, Mm = 1435 MeV, and finally Roper9 has told us that his latest results indicate a phase shift of 90° in Pu at Tn ~ 500 MeV.

It is interesting to observe that Roper and Donnachie also agree on a Dl3 phase shift at 1559 MeV, while Moorhouse puts this at 1520 MeV, an indication that the D13 may indeed be the AT13*(1512) and that the Pu is clearly dis­tinct from this.

Further experimental evidence for the exis­tence of a resonance in this mode has recent­ly become available,10'11 and two possibilities have been indicated for its placement in the SU(6) scheme.12 '13

The angular distributions of the decay prod­ucts of what are assumed to be ]V*(1425) events have been plotted by considering the analog of the Feynman diagram, Fig. 1. Entering the rest frame of particle d, Fig. 2, the decay an­gles 0 and cp are defined by Jackson14 where p is the momentum of the nucleon decay prod­uct of d, n is the normal to the production plane,

<* b c d

FIG. 1. Assumed Feynman diagram for the produc­tion reaction: a +b-*c +rf=/C""+AT — K~~+N*.

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II

"P

r©-v!

^ 1 n

x ^ ^

FIG. 2. Defining coordinates for 0, <p, andw.

and p^ is the momentum of particle b in this frame.

We now observe that <p is in fact the angle defined in the the test proposed by Treiman and Yang15 which states that in the case of the exchange of a single particle with spin angular momentum = 0, the distribution in <p ought to be isotropic since a spinless particle cannot carry information from the production plane to the decay plane in a peripheral interaction. Now, turning to the diagram in Fig. 1, it is clear that if the iV*(1425) has spin J= | and if it decays as a free particle, then the decay angular distributions, W($)d cosd and W(cp), will be isotropic. If, on the other hand, J= | , then it has been shown14'18 that the two distr i­butions are given by

W(e)=asm28 + (l-a)($ + cos2e) (3)

and

W(cp)=(lTi+ccos2(p), (4)

under the assumption of the production mech­anism indicated in Fig. 1.

Jackson and Gottfried have shown that the constant a in Eq. (3) is equivalent to the spin-space density matrix element p33, and the con­stant c in Eq. (4) contains the element Reps 1?

both of which have been predicted16"18 to be nonzero in the case of an AT* with J= | .

Figure 3 shows the distribution in 0 of all the events whose TT-nucleon invariant mass fell between the values 1375 and 1475 MeV/c2. The cross-hatched areas indicate those events where

VOLUME 14, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 21 JUNE 1965

£ 2 0

JACKSON ANGLE DISTRIBUTION N*(I425)

SUM 0 ^ % ANDTT°P

cos U

FIG. 3. Distribution of events in 0. The cross-hatched areas show those events whose invariant mass lay in the channels 1375-1400 MeV/c2 and 1450-1475 MeV/c2.

the invariant m a s s of the ir-N sys t em fell in the channels 1375-1400 MeV/c 2 and 1450-1475 MeV/c 2 . Fit t ing both dis t r ibut ions in F ig . 3 by leas t s q u a r e s to Eq. (3) produced the follow­ing:

p__ = 0 .23±0.05 , 33 na r row

pQ Q ._ - 0 . 3 3 ±0 .06 . 33 wide

F igure 4 shows the dis t r ibut ion in <p of the s a m e sample of even ts . The c ro s s -ha t ched a r e a has the same significance a s in F ig . 3 . A l e a s t - s q u a r e s fit of the dis t r ibut ions in <p

3 0

I IS

TREIMAN-YANG ANGLE N (1425)

SuMOFTT+n ANDTT°p

Ln_r 2TT

FIG. 4. Distribution in (p. The clear and cross-hatched areas have the same significance here as in Fig. 3.

to Eq. (4) gave the r e s u l t s

R e p c i = - 0 . 1 4 ± 0 . 0 5 , 3 , - 1 na r row

R e P o , ^ = - 0 . 5 3 1 ±0 .1 5 . 3 , - 1 wide

Once again it is in teres t ing to note that as the width surrounding the Bre i t -Wigner peak at 1425 MeV/c 2 is dec rea sed , a be t te r fit to i so t -ropy is obtained.

Angular d is t r ibut ions (3) and (4) can be t r a n s ­formed into a dis t r ibut ion with r e s p e c t to the normal n, and this d is t r ibut ion for a J= f s y s ­tem has been shown19 to be

- 7 ^ 3 , - 1 ' + ^ (5a)

The p-pf t r ans format ions a r e given by

i (P33 , + P-3 , -3 / ) = i ( i - 2 p 3 3 - 2 v T R e p 3 ^ 1 ) , (5b)

i ( P i i , + P - i , - i , ) = 4(i + 2p33 + 273"Rep3 j„1), (5c)

^ R e ( p 3 ) _ / + p _ 3 / ) = - \ + p 3 3 - ^ = R e p 3 ) . 1 , (5d)

1 2 ^ I m ( p 8 > _ 1 ' - p _ 3 > 1 ' ) = - ^ - R e p 3 1 , (5e)

and the Stodolsky-Sakurai model for J- | r e ­qui res that only p n ' and p _ 1 _ / be nonzero .

Fitt ing a dis t r ibut ion of al l N*(1425) events

once again produced isotropy, and the fitted coefficients agreed well with those calculated from (5a)-(5e) s ta r t ing with the fitted values of (5a) and (5c). The values obtained for co ­efficients (5b)-(5e) were as follows:

for (5b), | ( p 3 3, + P - 3 , - 3 / ) = 0 .225±0.03;

(5c), | ( p 1 1 ' + p _ 1 ) _ 1 ' ) = 0 . 2 7 0 ± 0 . 0 1 ;

(5d), ^ R e ( p 3 > _ 1 ' + p _ 3 ) 1 ' ) = - 0 . 0 7 5 ± 0 . 0 5 ;

(5e), ^ I m ( p 8 > _ 1 ' - p _ 3 y l/ ) = -0 .0058± 0.0026.

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VOLUME 14, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 21 JUNE 1965

Here it is apparent that p ' coefficients other than p n ' and p_-x _ / a r e nonvanishing, and this is inconsistent with an ass ignment of J= f u s ­ing the p resen t model .

Finally, if it is a s sumed that J= \ for the AT*(1425), then knowing that the reac t ion r e p ­resented by Fig. 1 must proceed by vec to r -meson exchange (if it p roceeds by o n e - p a r t i ­cle exchange at all) and knowing that Jp of the nucleon is | + , it is possible to make a par i ty ass ignment for the N*(1425) of JP = +1 only for the case 1 = 1. If / = 0 in fact, a par i ty P = - 1 would be r equ i red .

Phase-shi f t evidence mentioned above lends weight to the assumption of 7 = 1, but no expe r ­imental conclusion can be drawn from the data available h e r e .

It is felt that the evidence of the na r row width dis t r ibut ions in 9 and <p, while not unambiguous, i s , within the l imi t s of the s ta t i s t i c s of this ex ­per iment and of the model employed, c o n s i s ­tent with an ass ignment of J= \ to this resonant peak.19 Phase-shi f t r e su l t s a lso support such a conclusion.

The value of the m a s s ass ignment made for the new peak was obtained by taking the mean value of the events whose invar iant m a s s fell in the channels 1400 ^MnN ^1450 MeV/c 2 and calculating

TJN

N -1 S M.(N*). (6)

The e r r o r on this value was obtained from

6M = o/N, (7)

where 6M = e r r o r on m a s s , cr = width e s t ima te , N = total number of events . The width es t imate a was obtained by fitting the peak dis t r ibut ion to the Bre i t -Wigner equation

/ / \ N r/2 77 (w-M 0 ) 2 + ( f / 2 ) 2 (8)

T = resonance full width, N = total number of events , A/0 = 1425 MeV (es t imate for f i r s t i t e r a ­tion). The values obtained were

M(AT*(1425)) = 1425.3± 14 MeV,

T - 5 8 MeV.

The r e s u l t s from the exper iment desc r ibed in this a r t i c l e s e e m to offer the following c lea r indicat ions: (1) the p re sence of a pion-nucleon resonance at -1425 MeV; (2) a production mech­anism, which, because of a K"p initial s ta te , must be vec tor meson exchange; (3) the a b ­sence of the resonant peak in the K~~ +p — 7r~ +p+K° final s t a te , pointing to oo r a t h e r than p exchange and thus an ass ignment of T - \ to the resonance ; (4) angular d is t r ibut ions con­s is tent with the ass ignment of Jp = \+.

The author wishes to acknowledge the aid, advice, and c r i t i c i s m of P ro fesso r O. R. F r i s c h , D r . J . G. Rushbrooke, and D r . K. F . Riley of the Cavendish Labora tory , and the m e m b e r s of the Nuclear Group, Cavendish Labora tory , for their aid in the ana lys i s .

1s. 2G.

L. Adelman, Phys. Rev. Letters L3, 555 (1964). Cocconi et al., Phys. Letters £, 134 (1964).

3P. Bareyre et aL, Phys. Letters 8_, 137 (1964). 4L. D. Roper, Phys. Rev. Letters 12!, 340 (1964). 5L. D. Roper and R. M. Wright, University of Cali­

fornia Radiation Laboratory Report No. UCRL-7846, 1964 (unpublished).

6S. L. Adelman, thesis, University of Cambridge, 1964 (unpublished).

7P. Auvil, A. Donnachie, A. T. Lea, and C. Lovelace, Phys. Letters 12., 76 (1964).

8R. G. Moorehouse, private communication; R. H. Dalitz and R. G. Moorehouse, Phys. Letters _14, 159 (1965).

9L. D. Roper, private communication (1965). 10A. Wetherell, Bull. Am. Phys. Soc. 1_0, 485 (1965). UN. Schmitz et al., unpublished. 12M. Miller, Phys. Rev. Letters 14, 416 (1965). 13R. W. Griffith, Phys. Rev. (to be published). 14J. D. Jackson, CERN Report No. TH-416 (to be pub­

lished). 15S. B. Treiman and C.N. Yang, Phys. Rev. Letters

8., 140 (1962). 16J. D. Jackson and H. Pilkuhn, Nuovo Cimento 3*3,

906 (1964). 17M. Ferro-Luzzi et al., CERN Report No. TC 64-30

(to be published). 18L. Stodolsky and J. Sakurai, Phys. Rev. Letters LI,

90 (1964). 19J. D. Jackson, Proceedings of the Topical Confer­

ence on Correlations of Particles Emitted in Nuclear Reactions, Gatlinburg, Tennessee, 1964, Rev. Mod. Phys. (to be published); J. D. Jackson, private com­munication.

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