IL NUOV0 CIMENI~0 VOL. X X X I X , N. 4 16 0 t tob re 1965

SUe , S UeW and the Meson Photoproduction.

R. JENGO and R. 0DORlCO

Istituto di Fisica dell'Universit~ - Bologna

(ricevuto il 4 Agosto 1965)

I . - In this paper some predictions oi SUe and SUeW on the photoproduct ion processes on nucleons are discussed.

I t is well known tha t S U e may give predictions on the processes in which spin- couplings are absent. In the photomeson product ion this happens for the electric dipole transit ions, which proceed via S-wave. If we look at the processes at thresh- old this is the only te rm which appears. In this case the ampli tudes are real, as i t follows generalizing the argument used by F~RMI (1) for the p i ca photoproduc- t ion (s~e below). Making the usual assumptions on the S U s t ransformat ion proper- ties of the electric dipole ampli tude one is left in general with four independent am- plitudes. In the SU a case the independent ampli tudes are seven (3).

SUsW is a group different from SUe: in analogy to SU e i t embeds SUs×SU 2, but SU~ is the group with generators roa~, y0av, a~ (3). I t connects ampli tudes corresponding to unidimensional processes such as for instance forward and back- ward reactions.

I t is clear tha t the amplitudes at threshold are also characterized by a single direction and are therefore suitable to the S U~W analysis.

As to the experimental si tuation of photomeson production at threshold the da ta are good for the production of charged picas, somewhat poor for tha t of neutral picas, and very poor for other cases with the exception of K+A production.

In 2. and 3. we proceed to derive the relations for the SUe and SUeW case respectively. In 4. we discuss the experimental da ta and the way to extract from them the ampli tudes of interest. In 5. and 6. comparisons between ampli tudes are made and discussed for the two cases respectively.

(1) E. FEP~[I: Suppl . Nuovo Cimenlo, 2, 54 (1955). (2) L. HOLLOWA¥ and A. FUJII: Nuovo Cimento, 28, 1517 (1963). (3) See lec tures g iven by M. J. L~K~N a t the Seminar on Theoretical Phys ics at Trieste (May-

J u n e 1965).

SU6, S U 6 W AND TItle: MESON PIfOTOPRODUCTION 1179

2. - In strict analogy with B~G et. al . (~) we assume tha t the electric dipole • mplitudes for photomeson production processes transform under S Us as

(i) 1

Then the more general ampli tude is

(ii) aB~e: B ~efl ~ "' '~' 1.~ ~,,,o~ ~ ' ~Ar~' ~ 1~oo~7 ~,rZ ~,~

where B~o,/, B "ey and M~ are respectively the barion, ant ibar ion and meson tensors (a). A t threshold the ampli tudes are real: this follows from the argument used by

Fermi (~) (for instance) for pion photoproduction, replacing I -spin symmetry with tho SU6 one.

Indeed these ampli tudes are complex numbers the phases of which are the' meson- nucleon scattering o~es, which at threshold are zero.

We report in Table I the photoproduct ion ampli tudes for piocesses which may be o~ par t icular interest in terms of a, b, c and d which appear in (ii), taking into account the sum over polarizations (see also 4.).

TABLE I.

Final s ta te a b

nn- - - ( 5 V2)/54 (5 V~)/27

p=- (5 V~)/27

d

- - ~ / 2 / 1 0 8

- -5 / (27 ~ 2 ) - -1 / (54 ~/2,)

pnO 7/54 7/54 1/54

nn ° 1/27 1/27 1/27

AK + - ~/~/9 - ( 3 V~)/lO8

ZOK ~

Z - K +

Z+KO

1/27 - - 11/lO8

2/(27 ~/2) 2/(27 ~/2)

1/(27 v~) (2 ~/~)/27

1/(6 V~)

~/3/18

- - 1/54

- - 1 / ( 2 7 x / 2 )

1/(27 ~/~)

1/(6 V~) 1/(6 V~) P~

~N'*++n - - - ( 2 ~/2)/(9 ~¢J3) ~/2/(9 ~/3) ~/2/(9 ~/3)

~v*0n÷ - V~727 (2 ~/~)/27 (2 V~)/27

(~) M. A. B. B~(~, B. W. LEg and A. PMS: Phys. Rev. Left., 13, 514 (1964).

1180 R. JENGO and R. ODORICO

The ampl i tudes o cont r ibu te on ly to processes of pho top roduc t ion of f~ ° and w°8 wi th nonzero hel ie i ty : we have here v e r y poor exper imenta l da t a and we cannot make compar ison wi th p ther processes where this ampl i tudes do no t appear .

F r o m the Table we ob ta in the re la t ions:

V~ (A) K ' A -- 2 ~ 2 (

(B) K+X ° 1

-- (-- 67~r+n + 63~z-p - - 45 V2 hop), 20

1 (C) K+X - = - - ( 41~+n - - 49z-p + 35 ~/~nOp),

4O

1 (D) K°Z + = - ( - - 9Jz+n + 9 z - p - - 7 ~/,~n0p),

4

9

V~ (F) ~-JV *++ = - -

20 ( - - 21z~+n + 2 9 ~ - p - 15 V'2n°p) ,

1

20 ( - - 41~+n ~- 49n-p - - 35 V-2~°p) ,

We emphasize here t h a t different ly f rom other predict ions of un i t a ry s y m m e t r y these relat ions involve real ampli tudes, because we are at threshold. There remains an ambigu i ty of sign. W i t h S Ua one is left for pho toproduc t ion on nucleons wi th seven independen t ampl i tudes (2), instead of three.

3. - The w a y one proceeds in order to get SU6W predict ions is v e r y similar to the preeeeding SU6 case. One has only to replace in (;i) t he zero-hel ic i ty componen t of vec to r mesons wi th the pseudoscalar mesons and vi=eversa (3).

We repor t in Table I I only the results f rom which we can ob ta in useful relations. A first re la t ion which follows f rom the tab le is

7 (A) V ~ o p = ~ ( ~ p - - ~+n).

This re la t ion makes i t impossible to solve a, b, d in t e rms of nn+, pr:-, pn 0 and therefore in order to ob ta in o ther re la t ions we m a y no t proceed as in t he SU e case. Bu t happ i ly as one can see f rom the Table we have a set of immedia te re la t ions:

' (B) K°X+::r°P:n°n:~P:'~n-- 3 3 V ' 2 : 3 : V 2 " "

4. - I n order to tes t S/}6 and S UeW predict ions we t ake re la t iv is t ic ampli tudes, according to MESHKOV et al. (5). These are obta ined mul t ip ly ing the differential

(5) S. MESIIKOV, G. A. SNOW a n d G, YODII: Phys. Rev. Left., 12, 87 (1965).

SU6, S U 6 W AND THE MESON PHOTO:PRODUCTION 1181

T A B L E II.

I Final state a b d

,1,:+ - ( 5 ~/~)/54 J - 1 / ( 6 ~/~)

p=- 10/(27 V'2)

- - ( 5 ~ / 2 ) / 2 7

5/(27 V~)

p=O 7/54 --7/54

1/(6 ~/~)

afro 1/27 - - 1/27

E+K ° 1/(27 ~/2) - 1/(27 . ~ )

p~ 1/(6 ~/~) -1/(6 ~/3) i 0

m] - - 1/(9 \/.3) 1/(9 x 3 ) i I 0

cross-sections in the c.m. system by E*e(p~,/po,t) (where E* is the total energy, Pin and Pout are the initial and final relative momentum) and taking the square root. We recall that near threshold the pure S-wave term in the eorss-section depends lilxearly on Po,,t, whereas all other terms coutain higher powers of this quantity.

Let us now look into the experimental situation. Experimentally at threshold ~+n = (4.2 ± 0.1) and ~-p -- (4.8 ~: 0.2) (6). All

data are in units of 10 3 (~b.MeV/sr). As to T:Op one may extract the electric dipole amplitude E~ from the knowledge

of A, B and C in the angular distribution of ](0) - -A g- B cos 0 + C cos z 0, which are reported by GOLDANSKY et al. (7).

This may be done by using the relations (s)

A + C E ~ + K 2, B = - - 2 E a K ,

and ckoosiag the solution for E,z which is linear in Po,~t. We may conclude ~0p= 0.25 ± 0.1. However we observe that the conclusions

that may be drawn are not critical with respect to this datum. We are interested only in its smallness.

The relative signs of =+n, =-p and =0p are fixed by the I-spin relation

1

z V

taking into account the absolute values given above of these amplitudes and

(s) W. 1 ). SWANSON, D. C. (~ATES, T. L. /JENKINS and lR. W. KENNEY: Phys. Rev., 137, B 1188 (1965).

(7) V, I . GOLDANSKV, IL B. G o v o a K o v a n4 R, G. V,tSSILKOV: NutS. Phys., 12, 32 (1959). (s) K. ~[. ~VATSON, J . C . KECK, A. V. TOLLESTRUP and H. L. ~VALKER: Phys. Rev., 101,

1159 (1956).

1182 R. JENGO and R. 0DORXCO

taking n°n negligible at threshold, as indicated in ref. (7) and by some simple theoretical arguments.

I t follows that one must take them positive in the relations of Sect. 2 and 3.

5 . - We now discuss the relations of Sect 2, relative to SU e. 0nly the relation (A) may be checked experimentally with some reliability.

We have for the 1.h.s. (9) 0.83 ± 0.03 and for the r.h.s. 3.5 ± 0.4. There is a discrep- ancy. However, we observe that there is a relevant difference in the threshold for K and ~ photoproduction.

For the relation (B) the modulus of the r.h.s, is < 1, which is consistent with the data available for the K+Z ° (~o). From these, however, it is impossible to extract in a confident manner the S-wave term.

For the other relations the available data near threshold are few and uncertain (n).

6. - As to SUsW, we get for the relation (A), Sect. 3, substi tuting the experimental values above discussed

0.25.± 0.1 = 0.5 ± 0.3.

The relations (B) cannot be tested to date. We outline tha t the ratio pn~/n:z°= ~, thanks to the equality of the masses of

the corresponding particles, may be a good test of SUeW symmetry. We note that in this case the same relation holds also for forward and backward reactions at arbitrary energy. The amplitudes will be now complex in general, which does not obtrude here, since only ratios between them appear.

Up to date there exist only some indications on the relative magnitude of =0p and r~n in backward direction derived from photoproduction on deuterium (12). The data are not in disagreement with the above ratio.

7. - In conclusion the only SUe relation which may be compared with the experimental data is not satisfied. As to SUaW we may only say that there is not disagreement with the present data, which are somewhat uncertain. There are, however, many relations, both in SU e and SU~W, that could be checked as soon as the growing information on photomeson production shall accumulate.

We thank Prof. D. AMATI for helpful discussions.

(0) R . L. ANDERSON, :E. GA.BETHULEE, D. JONES, B. D. McDANIEL a n d A. J . SADOFF: Phys. heY. Left., 9, 131 (1962).

(10) ANDERSON et al. ref . (e); B. D. MCDANIEL, A. SILVERM.AN, R . R . WILSON a n d G. CORTEL- LESSA: Phys. Rev., 1 t5 , 1039 (1959).

(~) F o r t h e process Tp -~ '~p see B. DEIASOURT, J . LEFRENCOIS, 5. P . PEREZ Y JORBA a n d J . K . W'ALXER: PHYS. Le~t., 7, 215 (1963). F o r t he process ~,n---~K+~ - see R . L. ANDERSON, F . TURKOT a n d W. M. WOODWARD : Phys. l~e'o., 123, 1003 (1961 ). F o r t h e process yp--~:K°Z + see A. D. MCINTURFF a n d C. E. ROOS: Phys. Rev. Left., 13, 246 (1964). F o r t h e processes V p - - ~ - 2 ~ *++, .~+~V *° see H . R . CROUCH, R . HARGRAVES, B. ~ENDAT.I, R . :E. LANOU, A. M. SHAPIRO, iVY. WIGDOFF, G. F . FISHER, A. :E. BREMER, M. E. LAU, ]~. E. RONAT, 2 . STRAUCH, J . C. STREET, J . J . SZYI~ANSKI, J . D. TEAL, t J. BASTION, Y. :EISENBERG, B. T. ]~ELD, V. K . FISHER, I . A. PLESS, A. ROGERS, C. ROGERS, L. ROSENSON, T. L. W'ATTS, 1:. K . YAMAMOTO, L. GUERRIERO a n d G. A. SALANDIN: Phys. Rev. Lett., 13, 640 (1964).

(is) Be e fo r a r e v i e w E. H . BELI, A.~IY; Progr. NucL Ph~,.s., 8, 270 (1960).