LETTERE AL NUOVO CIMENTO VOL. 19, N. 15 13 Agosto 1977

On the Size of the Coulomb-Nuclear Interference Polarization in Hadronic Reactions at High Energy and Large Momentum Transfer.

C. BOURRELY and J . SOFFER

Centre de P h y s i q u e Thdorique, C N ~ S - Marse i l l e

(r icevuto il 2 Maggio 1977)

The effect of the Coulomb-nuclear in te r fe rence is known to be i m p o r t a n t in differen- t ia l cross-sections and polar izat ions (1) a t low m o m e n t u m t ransfer (It[ ~<5.10 -3 (GeV) 2) in elast ic hadron ie reac t ions ; th is effect becomes negligible in the dif ferent ia l cross-sections as the t ransfer increases. In the case of polar iza t ion expe r imen t s when the measured polar iza t ion is smalll t he Coulomb-nuclear in ter ference polar iza t ion cannot be neglec ted even at large m o m e n t u m transfer . The purpose of t h i s note is to draw a t t en t ion to these fea tures as t he measu remen t of elast ic polar iza t ion =J~ and JWJ~ at h igh energies is being per formed . Several expe r imen t s are under way (2.4) at C E R N and F N A L and p re l im ina ry resul ts (~) f rom one F N A L expe r imen t are shown in fig. 1.

Fo r ~~ e las t ic sca t ter ing the one-photon cont r ibut ions to t he nonflip ampl i tude q+ and to t he single flip ampl i tude ~5 are g iven in t he l imi t of h igh energies by

q$ . . . . [Fl(t)]~, 2 Itl

2e 2 %/~ ~t - - 1

~ -- Fl(t)/V~(t), ~ / ~ 2M

where Fl ( t ) and E2(t ) are re la ted to t h e usua l electr ic and magne t i c form factors in the fol lowing w a y :

GE(t ) - - ( t / 4 M 2) G~(t) ~ ( t ) =

1 - - t / 4 M ~

G:~(t) - - GE(t ) F d t ) =

( t * - - ] ) ( 1 - - t / 4 z u ~ ) '

t~ is the t o t a l magne t ic m o m e n t of t he nucleon.

(*) P o s t a l a d d r e s s : C e n t r e de P h y s i q u e Th~or ique , C N R S , 31, c h e m i n J o s e p h Aigu ie r , F-13274 Marse i l l e C E D E X 2 ( F r a n c e ) . (1) t . P . VANZHA, L. I . LAPIDUS a n d A. V. TARASOV: Soy. Journ. Nuc l . P h y s . , 16, 565 (1973); ]]. Z. KOPELIOVICtt &Rd L. I . LAPIDUS: SOY. Journ . :u Phys . , 19, 114 (1974). (2) CEI~N-PADOVA-TRIESTE-VIENNA COLLABORATION: Exper iment ~,VA006 at SPS. (3) O. CHAMBERLAIN et al.: Exper imen t 961 ol F N A L . (4) G . W . ABSHIRE el al.: Exper iment 313 at F N A L ~. (s) R . V. KLINE: A I P Con]erence Proceedings, e d i t e d b y l~I. L. 1VIARSRAK, Vol. 35 (1976), p. 152"

569

5 7 0 C. BOURRELY and J . SOFFER

0.08

P

0.04

--0.04

- -0.08

0.16

P

0.12

0.08

0.04

--0.04

--0.08

--0.12

--0.16

~ l

b)

~--

! I I I ! 0.4 0.8 1.2

- t [(Gev/~)~ Fig. 1. - P r e l i m i n a r y w~p, pp po la r iza t ion d a t a f r o m ref. Q). 100 GeV/c; �9 w-; ~ w+,

The polarization parameter P for JN'-J~' elastic scattering may be written in terms of helicity amplitudes

dff P ~ - / - = - - I m {(~o~ + ~o, + ~ . - ~ o , ) C } �9

Now if we assume that the nuclear interaction contributes only to r (no hadronie spin effects) the polarization arising from the interference between the Coulomb ampli- tude ~ and the hadronie amplitude ~ reads

4 VKe~( (# - - 1 ) /2M)Ex( t )P2( t ) Im ~(t) P~.t = ~F~l(dah/dt)

ON THE SIZE OF THE COULOMB-NUCLEAR INTERFERENCE POLARIZATION ETC. 571

The Coulomb and the interference contributions to the differential cross-section have been neglected because we are interested in a t-range outside the Coulomb region (Itl ~> 0.01 (GeV)'~). We have also neglected the relative phase between the electromag- netic and the nuclear amplitudes. If we define ~(t)= Rer r one can write

/V Pi.t = -• 4 v '~e 2 #-- - - 1 dah 2 M E~(t)l~',(t) [1 + e~(t)]ltl--~/-,

the plus or minus sign is the sign of h n ~( t ) . Now

where (Pi,t)~a~ gives an upper (or lower) bound for Pi,t corresponding to ~(t)= 0. Unfortunately ~(t) is not known experimentally but in the t-range where it is supposed to be small (for It I < 0.5 (GeV)~), (P i~t )~ provides a good estimate of the expected po- larization effect. Assuming that Im ~ ( t ) is always positive (*), we have calculated (Pi~t)~ in the case of p p ~ pp, using experimental data (7) for dab~dr at Plab= 100 and 280 GeV/c and the known proton form factor; the results are shown in fig. 2.

0.15

P

0.10

0.05

I l I I I

o ~ ~ ~ ~ o o ~~176 6~ elo ~o ~e �9 i o ~

I J t - -

0.5 1.0 1.5 210 2.5 lel [(Gev)2~

Fig. 2. - (Pia~)max for pp e las t ic s c a t t e r i n g a t 100 (e) a nd 280 (o) GeV/c.

The errors in the polarization (Pl,~)m~ come from experimental errors in dah/dt. The effect reaches 11% in the dip region for Pith= 280 GeV/c but we expect ~o(t) to be nonnegligible at this t-value. In the case of np-> np, for the neutron polarization, the effect is opposite in sign and approximately half in size because # = - - 1 . 9 1 and GE(t )~O for the neutron.

(*) A r ecen t ana lys i s (e) us ing dispers ion re la t ions suppor t s th is a s sumpt ion . (~} P. KROLL: Forts. der Phys. , 24, 565 (1976). (~) C. ~V. AKERLOF, R. KOTTHAUS, R. L, LOVELESS, I). I . MEYER, I . A~IBATS, W. T. MEYER, C. E. W. ~VARD, D. P. EARTLY, R. A. LUND, S. M. ]:)RUSS, D. D. YOVANOVITCH a n d D. R. RUST: Phys. Rev. Left., 35, 1406 (1975); N. KWAK, E. LOHRMAI~,N, E. NAGY, 1~. REGLER, W. SCH~IIDT-PARZEFALL, K. R. ~CHUBERT, K . ~VINTER, A. BAN'DT, H. DIEOI~', G. FLL+GGE, F. NIEBERGALL, P. •. SCHUMACHER, J . J . AUBERT, C. BROLL, G+ COIGNET, $. FAVIER, IJ. MASSONNET, 1YL VIVARGENT, VY ~. BARTL, I~. EICHINGER, CtL GOTTFRIED a n d G. NEUHOFER: Phys. Left., 58 B, 233 (1975).

$72 C. BOURRELY and a. SOFFER

The sign of Im ~_(t) for large t is not yet established. Figure 2 would look different if we had not assumed that Im q0~_(t) is always positive and in particular, as predicted by several models (s), if Im 9~_(t) vanishes and changes sign at the dip position, (Pln*)m~ would also vanish and become negative for Itl ~1.5 (GeV) 2. A careful analysis of the polarization data at high energies would help to answer this question of sign provided the nuclear polarization is very small.

In the case of rc-p scattering the analogous expression for Pint reads

- - 2 / ' ~ - 1 / ] / dab (pl~t)m~/~v/~+#2(t) P'*= -- 4 v/=e - ~ - F2(t)Fn(t)l r[1 + q2(t)]ltl ~ - ~

where FT:(t ) is the pion form factor. The results of the calculation of (Pi,0maa in this case are shown in fig. 3. The effect for ~+p would be mirror symmetric, provided the differential cross-sections are the same.

0.05

"p

--0.05

I I t I [

I ] I / ] 0.5 1.0 1.5 2 0 2.5

Itl I(Gev)~

Fig . 3. - (Pint)max fo r ~ - p e l a s t i c s c a t t e r i n g a t 10O a n d 200 GeV/c .

In conclusion we would like to stress that, when one compares these results with prel iminary experimental results on T:• pp at PILb----- 100 GeV/c from FNAL (3) which indicate total-polarization effects of the order of 1% or 2 %, (see fig. l), one has to take into account Coulomb-nuclear interference effects in the interpretation of the data.

We thank Prof. L. I. LAPII)US for some valuable comments, and Dr. A. MARTIN for fruitful discussions.

(a) W . 2r Yuovo Cimento, 2 5 A , 117 (1975); G. L . I~ANE a n d A. SEIDL: Rev. 21Iod. Phys., 48, 309 (1976); C. BOURRELY, A. ]V[ARTI/~, J . SOFFER a n d D. WRAY: J. Phys. G, 3, 295 (1977).