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Volume 104B, number 3 PHYSICS LETTERS 27 August 1981

APPLICATION OF THE BOHR RESONANCE CRITERION

TO NON-STRANGE DI-BARYON AMPLITUDES

A.S. RINAT Department of Nuclear Physics, We&mann Institute of Science, Rehovot, Israel

and

J. ARVIEUX Laboratoire National Saturne, F-91190 Gif-sur- Yvette, France and Institut des Sciences Nucl&ires, F-38026 Grenoble, France

Received 6 May 1981 Revised manuscript received 1 June 1981

Using information on ~rd --, zrd, pp ~ pp and pp ~- nd we apply the Bohr criterion to several A = 2 partial wave amplitudes. The negative outcome for jTr = 3- makes the existence of a b ro ad 3F 3 di-nucleon r e sonance B 2 hardly consistent with the information presently available. We ascribe alleged evidence for B 2 to s-dependence of intermediate NA states. An additional B 2 test is suggested.

The observation of structures in total pp cross sections with beam and target in several states of polari- zation [1] has reopened the question whether these signal exotic A = 2 resonances [2]. Additional evidence has been claimed from irregular energy dependence of expansion coefficients for pp correlation cross sections [3], of proton polarizatio n in 3' + d -+ p + n [4] and in the excitation functions for 3' + d ~ p + p + 7r [5]. New experiments allegedly provide more evidence from reactions involving also A / > 3 nuclei [6].

One clearly needs a decisive test discriminating between genuine resonances and resonance-like behaviour. We first emphasize that when a resonance is spread out over several channels, observables them- selves in any given one, no longer provide definite sig- nals. In that case Argand plots for extracted partial wave ampl i tudes f / may well be the most expedient tool, but large inelasticities preclude a clean test per- formed on a single channel: Information is needed on at least one additional channel.

Below we shall apply the Bohr criterion which veri- fies that a resonance decays independently of its for- mation (factorization of residue of amplitude). In case

(i) one can separate a resonance p a r t f res from a smooth background,

(ii) there are no overlapping resonances with iden- tical quantum numbers, one can use the Bohr test, which in terms o fpa~ = (P~I '~) I /2 /F ( I ' J F are relative widths) requires

9 /,~1/2,~1/2 = 1 (1) a3twc~a w33

For application to A = 2 one needs the following largely available material (c~, 3 = PP, n+d):

pp -~ pp: Three analyses for Tp ~ 7 5 0 - 8 0 0 MeV agree on real parts of phases and to a somewhat lesser degree on inelasticities [ 7 - 9 ] .

rrd --> 7rd: For the present purpose we recently un- dertook a phase-shift analysis of accurate elastic and total cross-section data [10].

pp ~ 7rd: A semi-phenomenological partial-wave analysis has been reported [11,12] but the resulting amplitudes strongly depend on doubtful underlying theoretical models. Instead we shall use the recently

calculated amplitudes fpJ ;~rd [13] which fit the angu-

lar distribution within about 30%. From elastic pp data, three I = 1 resonances have

182 0 0 3 1 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland Publishing Company

Volume 104B. number 3 PHYSICS LETTERS 27 August 1981

been claimed to exist with quantum numbers lD,, 3F, and lG4 [14]. For Jn = 4+ the structure is suggested at an energy sR ‘I2 - 2.46 GeV, which is beyond

the range of our nd + nd and nd * NN analyses and no reliable estimates for p,_+ can be given.

Data for (S$ - 6,&/2i; (Y, fl= pp, nd; J” = 2+, 3- (“,S” denotes the S-matrix) are represented in figs. 1, 2. One notices that all Argand plots show parts of nearly circular sections. With no unique prescription to separate f=fb t fres, we use as definition for fres the amplitude which traverses a pure Breit-Wigner circle as close as possible to the above sections (McVoy [14]). Consequentlyf - fres will be a smooth background.

In table 1 we assemble our results. For nd + nd and pp -+ pp, cited uncertainties in p are due to experiment and to circle fitting. For nd + pp taken from theory only-the last exists. We added a factor (1 .3)1/2 in the last column as if the -30% underestimate of the rrd + pp cross section were due to an overall scale factor.

Whereas an exotic .P = 2+, A = 2 resonance is a definite possibility, for .P = 3- the ratio (1) is a factor -3 too small. Clearly a sharpening of our conclusion necessitates better determined nd phaseshifts, re- quiring, in turn, deuteron vector- and tensor-polariza-

J=,L+2+,1 I

I

0.5

t

9 0.4

!=

z 0.3

0.2 1

0. I

t

a

0.2

!

L I I I I I I I

- 0.3 -0.2 -0.1 0 0. I 0.2 0.3-

Re k,fzj

tion data *l. In addition, one eventually needs pp

* nd amplitudes extracted from experimental data

P61. Assuming now that future data will not substan-

tially change our conclusion, one needs an interpreta- tion of pseudo-resonance behaviour, which is by no means new. Back in 1958 Mandelstam showed that the peak of the angle-integrated pp + rrd cross section as function of energy may be explained by the open- ing of the NA channel [ 171. Numerous calculations on observables of the A = 2 system have since shown that the excitation above produces resonance-like be-

haviour [13,18-241. Finally, we mention a second test based on unitar-

ity for fres. With rPP/r < 1, the decay into nNN and rrd must provide the missing strength. Since most of the total flux is channeled into nNN, this is presum- ably also the case with the resonant part of it. One could thus measure inclusive differential cross sections

*r Recent vector analyzing power data exhibit an oscillating

pattern at 25 6 MeV [ 15 ] in disagreement with Fadde’ev-

type calculations. Changes in the small amplitude fl’, L

= 2+, 3 account for the data and do not alter the conclu- sions reached above.

Fig. I. (a), @I, (~1. Argand plots for (SLyp - s,p)/2i; Jn = 2+ and a, P = NN,nd. (the drawn line for nd,nd represents a theoretical prediction.)

183


Q3

0.2

0.1

I

d "~, L-n -= 5 - 2 ' 217 254. ,,'~ I ~ / ~ 217 __

,'+--v--~\ r ) - f ~ /

'

, / I g

(3 I ,6 ~ , < I J I I I

-0,10 0 O.lO Re k. n- f'n"d

7T J ; LTr, L N = 3;2,3

3F 3

2.22 228 2.26 2.22 22~.~_~, 2,8 i~,~

2.20 2.16

2.18

b 2~A2 2.t4 ~

2?~xo~..w~, ' o 0.05 oJ,o '/ - - -o.,-'"- s.,,.u/_ 1/2 1/2 Re n.~N#NN Re kTr fTrd,NN kN

0.2

J o.I E

Fig. 2. (a), (b), (c). Same as fig. 1 forJ lr = 3-.

n+d ~ p + X (X = p). A partial-wave ampli tude analy- p+p sis should show large relative strengths p a, NN;r(J ~r) and for genuine resonances one should find fulfilled

2 = 1 (2) Pc~ • ~fl=~d,

NN, rrNN

In summary, using the available informat ion on nNN ampli tudes, the Bohr test speaks against a broad 3 - d ibaryon resonance at s 1 /2 ~ 2.26 GeV. For most o f the observed effects on experimental data or Argand

plots we return to the explanat ion of Mandelstam [17] which has now been checked on a detailed model to a n y order and for al l measurable 2-body amplitudes. In all, low LNL x intermediate states provide an ortho- dox explanat ion of resonance-like behaviour. The same behaviour is predicted for other partial waves, no tab ly j r = 2 + and for which the test (1) does no t rule out a genuine resonance. This common description and addi- t ional theoretical support like, for instance, a descrip- t ion of all Argand loops by low(est)-order per turbat ion

Table 1 Relative radii o~O = (I'aP#)l/2/P. Last column gives result of Bohr test (with extreme errors). Not yet available experimental val- ues of Pnd,pp may have larger uncertainties (see text).

j n ppp,pp Pnd,rrd c) P~rd,pp d) Pnd,pp

(PTrd#rdPpp,pp) 1/2

2 + Ava) 0.14 + 0.01

0.4 -+ 0.i 0.19 -+ 0.03 H b) 0.095 + 0.005

37 AV a) 0.20 +- 0.02 0.15 ± 0.03 0.06 + 0.009 H b) ~0.2

+0.31 0.80 -0.22

+0.37 0.97 -0.25

+0.12 0.35 -0.09

a) Ref. [8]. b) Ref. [7]. c) Ref. [10]. d) Ref. [13].

184


t h e o r y s t rongly h in t s against 100 MeV (or m o r e ) wide

d i b a r y o n resonances a r o u n d the NA mass.

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