8 - p - A , E X C H A N G E D E G E N E R A C Y A N D T H E A D L E R S U M R U L E 4221

School of Physics at Varenna (Academic, New York, 1968).

I0J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969).

"J. D. Bjorken and S. F. Tuan, Comments Nucl. Part. Phys. 5, 71 (1972).

or the neutrino reactions, the current-algebra constant in the Adler sum rule is 2. Similarly for (7).

i 3 ~ n this scheme, $ decouples from the pA2 system. I4p. G. 0. Freund, Phys. Rev. Lett. 20, 235 (1968);

H. Harari, ibid. 20, 1395 (1968). 1 5 ~ . D. Bloom and F. J. Gilman, Phys. Rev. Lett. 25,

1140 (1970); Phys. Rev. D 4, 2901 (1971). I6s. D. Drell, in Proceedings of the Amsterdam Inter-

national Conference on Elementary Par t ic les , 1971, edited by A. G. Tenner and M. Veltman (North-Holland, Amsterdam, 1972).

I ~ H . D. I. Abarbanel, M. L. Goldberger, and S. B. Treiman, Phys. Rev. Lett. 22, 500 (1969). In this

paper, the structure functions in the Bjorken scaling limit are discussed in terms of the Regge asymptotic functions.

I81t has been argued that, for large w (u' =w as q2--), the nonscaling photon-dissociation contribution to v W2 in the electroproduction may be important. However, such contributions are canceled in the differences vW2(-), Y(w$*-win) , a n d v ( ~ g * - ~ ~ ~ ) . See H. T. Nieh, Phys. Rev. D 7, 3401 (1973).

he he elastic Born term for w2(-) is p:(q2)l2 +q2pT(q2)/ %Ul2, whereas that for WrP - W i n is Ff(q2)F~(q2) + q 2 P ; ( q 2 ) / 2 ~ l [ F D ~ ~ ) / Z M I .

"1t i s interesting to compare this ratio (5.34) with that (1.45) from (12) based on SU(6) symmetry [ ( f,&) =31. The discrepancy may be attributed to the failure of the VDM in the scaling region.

2 1 ~ . H. Llewellyn Smith, SLAC Report No. SLAC-PUB- 817, 1970 (unpublished).

PHYSICAL R E V I E W D VOLUME 8 , NUMBER 11 1 D E C E M B E R 1 9 7 3

Consistency of New Meson-Nucleon Elastic Scattering Data with a Previously Conjectured Universal Curve*

Stephen Blahat and Uday B. Sukhatmex Physics Department, University of Washington, Seattle, Washington 98195

(Received 13 August 1973)

We show that important new large-t r-p data atpl = 13.8 and 22.6 GeV/c are in good agree- ment with a universal curve suggested last year.

Recently a detailed experimental study' of e las t i c pion-proton scat ter ing was made at l a r g e energ ies ( p , = 13.8 and 22.6 GeV/c) over a substantial par t of the forward scat ter ing region [ I t 1s 5 ( G ~ V / C ) ~ ] in o r d e r "to determine if the shapes and magni- tudes of the c r o s s sect ions are approaching limit- ing values as the momentum increases." ' In this note we will show that these new data are in close agreement with a n apparently universal curve for meson-nucleon scat ter ing which was found last year in a study2 of the high-energy ( p , 2 5 GeV/c) elast ic data then available. At that t ime i t was shown that existing forward and backward data fell on a s imple curve if c r o s s sections normalized t o unity at t = 0,

were plotted v e r s u s the dimensionless variable

where b(s) is the slope of the forward peak [ I tl 2 0.5 ( G ~ V / C ) ~ ] appropriate to the react ion and en- ergy. The angular regions which fell on the uni- v e r s a l curve were defined by 1 t ( s 3 (GeV/c)' in the forward region and 1 u 1s 1 ( G ~ V / C ) ~ i n the back- ward region. The quadratic charac te r of the vari- able r re f lec t s the backward peak onto the forward peak. The universal charac te r of the curve was expected to become even more evident at higher energies . If th i s curve i s valid, a la rge body of existing data h a s been reduced to a determinat ion of two quantities of obvious geometr ical (optical) significance, b and a, (which f ixes du/dtl,,, v ia the optical theorem, assuming the r e a l par t of the forward amplitude is small).

The r e c e n t high-energy forward-region data of Cornillon et al.' give s t rong additional support to

4222 S T E P H E N B L A H A A N D U D A Y P . S U K H A T M E

the universality of the curve. Figure 1 shows a plot of their r -p data at p, = 13.8 and 22.6 GeV/c in the mznner described above compared with the conjectured curve of Fig. 1 in Ref. 2. The agree- ment for values of ( t 1 s 3 (GeV/c)' over six de- cades i s striking. The points not on the curve a t large T are beyond the boundary of the curve's validity a t t r 3 (GeV/c)'.

In order to plot the data in Fig. 1 we used3 o, = 26 mb at p, = 13.8 GeV/c and o, = 25 mb at p, = 22.6 GeV/c. In both cases the slope parameter was kken to be 7.5 (GeV/c)", consistent with the data.

The disappearance of the dip at t=-0.8 (GeV/c)' and the appearance of a marked change in slope are in good agreement with the piecewise exponen- tial character of the universal curve which has a break a t T = 5.

In addition Cornillon et al. noted that the data be- tween 1 <- t < 3 (GeV/c)' cannot be simply fitted with a Regge parametrization. The conjectured curve of Ref. 2 provides a simple parametrization of meson-nucleon data and is apparently applicable where naive Regge theory i s not. The authors feel that the data a re displaying a geometrical charac- ter which (considering that the regularity is only observed in the forward and backward regions) may be understood within the framework of an optical model.

FIG. 1. A plot of new n-p data taken from Ref. 1. The solid line i s a reproduction of the previously conjectured universal curve shown in Fig. 1 of Ref. 2.

*Work supported in par t by the U. S. Atomic Energy Commission.

?Address after September, 1973: Physics Department, Cornell University, Ithaca, New York 14850.

$Address after September, 1973: Physics Department, University of Michigan, Ann Arbor, Michigan 48104. 'P. Corniflon, G. Grindhammer, J. H. Klems, P. 0.

Mazur, J. Orear, J. Peoples, R. Rubinstein, and W. Faiss ler , Phys. Rev. Lett. 30, 403 (1973). Other

data in good agreement with our curve at 13.8 GeV/c a r e given in R. Rubinstein, P . Cornillon, G. Grind- hammer, J. Klems, P. Mazur, J. Orear, J. Peoples, and W. Faiss ler , Phys. Rev. Lett. 30, 1010 (1973).

's. Blaha, W. J. Pardee, and U. P. Sukhatme, Phys. Lett. e, 435 (1972).

'E. Bracci, J. P. Droulez, E. Flaminio, J. D. Hansen, and D. R. 0. Morrison, CERN Report No. CERN/HERA 72-1, 1972 (unpublished).