Volume 31B, number 7 PHYS ICS LETTERS 30 March 1970
THE ~-p~ un CROSS SECT ION IN A SMALL TRANSFER RANGE AT
J. HLADKY, A. M. BALDIN, M. N. KHACHATURYAN, M. S. KHVASTUNOV Joint Institute for Nuclear Research, Dubna, USSR
L. N. SHTARKOV P. N. Lebedev Institute of Physics, Moscow, USSR
Received 12 February 1970
The reaction ~--+p-*??+ n, 77 ~ 27 has been studied in a 0 --< It I "-< 0.24 (GeV/ct 2 range at 4.0 GeV/c using spark chambers and Cerenkov total absorption gammaspectrometers . The coefficients a = 4.3 0.8 (GeV/c) -2 and b = 190 18 pb/(GeV/c) 2 from the equation d(~/dt = b exp (at) were estimated.
A programme of exper iments on the observa- t ion of the e lec t romagnet ic decays of meson res - onances is be ing per fo rmed us ing the J INR pro - ton -synchroton in Dubna. As a par t of th i s p ro - g ramme, the 7--* 27 decay was observed .
In th i s paper the resu l t s f rom the react ion
n- +p-~n+ ~1, z?~27 (i)
at a T--meson momentum of 4 GeV/c 1.5% in the range of the transfer momentum 0 --< Itl --< 0.24 (GeV/c)2 are discussed. The pre- liminary data have been presented at the Lund Conference [i]. This paper has three improve- ments in comparison with the preliminary one: i) the statistics was increased by about 50~c; 2) the number of Monte-Carlo events in the de- tection probability calculations was also in- creased by a factor of five. The precise knowl- edge of this parameter is of great importance. For this reason the data from the Monte-Carlo programme were tested by the other used in JINR for many years . Making these tests, good agreement has been obtained. Finally, 3) the interval for the dcr/dt histogram was di- minished, in order to have the possibility of studying better the differential cross section plot structure.
The reaction (i) is very interesting from the point of view of the simple Regge-pole model, especially in the range of I t r ~ 0 because it in- volves only the A2-trajectory.
In practice, the only experimental data for the reaction (I) treated in all theoretical papers are given in ref.3, when the reaction (1) was investigated in wide ranges of 7T--meson ener-
gies and squared momentum t rans fers . The fo rward peak in the d i f fe rent ia l c ross sect ion d~/dt and i ts f la t ten ing between I tl = 0.2 and 0(GeV/c ) 2 was observed at a l l momenta .
Our exper imenta l a r rangement us ing spark chambers and erenkov tota l absorpt ion gamma- spect rometers has been descr ibed e l sewhere . Measur ing the opening ang le of the 77~ 27 decay and the energy of each gamma, we get the accu- racy Gt in I t l : t = + 0.015 (GeV/c ) 2 at Itl ~ 0(GeV/c ) 2 and zkt = 0.030 (GeV/c ) 2 at Itj ~ 0 .24(GeV/c ) 2.
Th is a l lowed us to invest igate the react ion (1) at l ti ~ 0 with bet ter accuracy &t than in ref .3.
A f te r a tw ice scann ing procedure , about 9000 p ic tures conta in ing only convers ion of the neu- t ra l par t i c le in each channe l were found. A par t , of about 4200 two-gamma events , was measured wi th a ha l f -automet ica l dev ice , and the tape was hand led by a computer . The geometr i ca l recon- s t ruc t ion programme determines the point of the t rack in tersect ion and f i ts the angu lar para - meters of the t racks . For fu r ther ana lys i s only two-gamma decays hav ing the in tersect ion point wi th in the e f fec t ive ta rget vo lume were se lected . Only events wi th P(X 2) >I 1% were taken. The k inemat ic se lec t ion of the two-gamma events was made by the react ion -channe l ident i f i ca t ion programme. Thus , about 1500 events were de- te rmined to ful f i l the react ion (1).
There are two sources of the background in our spect rum: (a) T -+p ~ n+ n+ T ~ n+27 and (b) ~-+p ~ n+0- n+n7~n+27. The back- ground is fo rmed when two- or one-gamma f rom four - o r th ree-gamma decays are not conver ted
Vo lume 31B, number 7 PHYS ICS LETTERS 30 March 1970
Tab le 1 D i f fe rent ia l c ross sect ion fo r react ion (1).
Number of Iti [(GeV/c} 2] d(~ [dt] ~tb [(GeV/c)2] intervals
1 0.01 82 i 18 2 0 .03 158 =~ 19 3 0 .05 155 i 18 4 0.07 143 i 20 5 0 .09 144 17 6 0 .11 108 15 7 0 .13 112 i 17 8 0.15 106 i 17 9 0 .17 94 18
i0 0 .19 76 18 i i 0 .21 69 :~ 19 12 0.23 74 _~ 19
in a spark chamber conver ter or have escaped. The main source of the background is the f i rs t kind.
This background was subtracted by us ing the exper imenta l th ree-gamma events , detected in the same runs, as fol lows: each three-gamma event was spl it into the two-gamma events handled in the same way as natura l two-gamma events. Mult ip ly ing the i r spect ra by the (1-K)/K convers ion factor (here K is the probabi l i ty of one-gamma convers ion in the spark chamber assembly) , the background of about 25% has been obtained and subtracted. The background, (a) and (b), when some of the gammas have escaped, was est imated to be about 5% using the Monte- Car lo calculat ions.
Each event was weighted by its inverse de- tect ion probabi l i ty ca lcu lated by the Monte -Car lo method. The d i f ferent ia l c ross -sect ion (after background subtract ion) for react ion (1) as a function of the squared momentum t rans fer (-t) is given in table 1. The quoted er rors a re only due to stat is t ics . These resu l t s a re a lso plotted in fig. 1. For compar i son , the data f rom ref. 3 at momentum 3.72 GeV/c a re a lso presented. As
is seen, there is no wide f lattening in the forward peak. For the hypothesis of f lattening in the range 0 ~< it r --< 0.24 (GeV/c) 2 the value of 2=28 by 9 degrees of f reedom was obtained. It cor re - sponds to P(X 2) less than 10 -3.
In the f i rs t in terva l , up to I tl = 0.02 (GeV/c) 2, the d i f ferent ia l c ross -sect ion decreases with I ti ~ 0. The va lue d(~/dt in the f i r s t in terva l was sys temat ica l ly lower in al l the runs of our exper iment indicat ing the change of s lope for smal l va lues of i t i . In the range 0.02 ~< It i ~< --< 0.24 (GeV/c) 2 (e.g. when the f i r s t point is ex- cluded) the data were approx imated by
d(~/dt = b exp (at) (2)
The fol lowing resu l ts have been obtained by the best fit p rocedure : ~ = 4.3 0.8 (GeV/c) -2 b = 190 18 ttb/(Ge~/c) 2 by 2 = 2.1 (9 de- g rees of f reedom).
The s lope a is in good agreement with the s lope f rom ref.3 obtained in the greater range of t: 0.2 --< iti < 0.7 (GeV/c) 2.
The measurements of react ion (1) in the range of smal l It I va lues a re very important for the parametr i za t ion of the res idue function in the Regge-po le model. A ser ies of ana lyses [5 - 7] us ing both exper imenta l and theoret i ca l data f rom ~ N and KN in teract ions , in the Regge- pole model parametr i za t ion has been per fo rmed dur ing recent years . The data in the high energy reg ion were completed by the data in the low energy reg ion on the bas is of the f inite energy sum ru les . It is poss ib le to ana lyse the data for the react ion (1), where only the A2-meson contr ibutes , on the bas is of a one-po le exchange formula:
dcr/dt = F(t) E 2(~(t)-2 (3)
The function F(t) is s t rongly dependent un the model used. It contains the hel ic i ty fl ip and non- fl ip ampl i tudes and ghost -k i l l ing factors . The
"/C , h 0.1
~ GUISAN ET AL
' 0'. 2 ' O' 3 ' ' ' ~- - '~ ' 04 05 06
-TRANSFER ,'/C'JM. .(GEV/c)~
F ig . 1. The d i f fe rent ia l c ross sect ion fo r the react ion 7r -+p ~n+ ~, 17~2~. The squares are f rom the present paper , The circles are from ref.  at 3.72 GeV/c.
Volume 31B, number 7 PHYS ICS LETTERS 30 March 1970
main uncer ta in ty of F(t) is the exponent ia l fac - to rs in the ampl i tudes of the type exp (ct). It is imposs ib le to exp lore the aA 2 - t ra jec tory without the i r determinat ion . Unfor tunate ly , t i l l now, there are no exper imenta l data in the range of smal l it] 7r-meson energ ies E with suf f ic ient accuracy for such ana lyses .
References 1. J. Hladk] et al. Lund Con~renee, Lund, 1969.
2. V. E. Komolova, G. I. Kopylov. Preprint JINR P-2027, Dubna. 1965.
3. O. Guisan et al. Phys. Letters 18 (1965) 200. 4. M. N. Khaehgturyan et al. Phys. Letters 24B (1967)
349. 5. G.V. Dass. C. Michael and R. J. N. Phillips.
Nucl. Phys. B9 (1969) 549. 6. R. J .N. Phillips and W. Rarita. Phys. Rev. Letters
15 (1965) 807. 7. K.A. Ter-Mart irosian. Preprint ITEF (1968). 8. A. A. Logunov, L. D. Soloviev and A. N. Tavkhelidze.
Phys. Letters 24B (1967) 181.