Study of ϱ0 production in γd, γp and γn reactions at 7.5 GeV using linearly polarized photon beam

Nuclear Physics B69 (1974) 445--453. North-Holland Publishing Company

S T U D Y O F pO P R O D U C T I O N I N 7d, ~,p AND 3,n R E A C T I O N S AT 7.5 GeV U S I N G L I N E A R L Y P O L A R I Z E D P H O T O N BEAM G. ALEXANDER, J. GANDSMAN, A. LEVY, D. LISSAUER and L.M. ROSENSTEIN Department of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, Israel

Received 2 October 1973 Abstract: The reaction 7d--->dnn, 7p---rpnn and 7n--+nnn were studied in the SLAC 82" deuterium filled bubble chamber, exposed to a linearly polarized photon beam of 7.5 GeV. All three reactions are dominated by pO production. The differential cross section has a slope of ,~6.5 GeV-2 for nucleon reactions and a slope of ,~27 GeV- 2 for coherent deuteron reactions. The behaviour of the density matrix elements shows that p production conserves s-channel e.m.s, helicity and is dominated by natural panty exchange.

1. Introduction Photoproduction of vector mesons on protons has been studied extensively in both bubble chamber and counter experiments [1-7]. The SBT collaboration [2] has investigated the production mechanism and decay characteristics of the vector mesons using a polarized photon beam at 2.8, 4.7 and 9.3 GeV. These experiments have found that the pO cross section is approximately constant above 2 GeV, indicating that the diffractive part of the reaction is already dominant at these energies. By investigating the decay angular distributions and density matrix elements they found that at low m o m e n t u m transfer the t-channel amplitude is completely dominated by natural parity exchange and that the pO conserves the c.m.s, helicity in the s-channel. Photoproduction on neutrons and deuterons [8, 9] has also been studied, with unpolarized photon beams, at energies up to 4.5 GeV. The coherent vector meson reactions are of special interest since they are produced through pure ! = 0 exchange in the t-channel. Vector mesons produced off neutrons can be used in conjunction with their complementary 710 reactions to investigate the effects of isoscalar-isovector interference. The production of p mesons by a linearly polarized photon beam further enables us to study in detail the production mechanism. In particular we are able to measure the nine independent density matrix elements of the p-meson, and thus separate the orthogonal contributions from natural ( P = ( - 1 ) ~) and unnatural ( P = - ( - 1 ) J) parity exchange in the t-channel.

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G. Alexander et aL, pO production in yd, )'13and yn reactions

In this experiment we studied pO production in the following reactions: YP---'7r+ re- P,

(1)

~n--* 7r+ n - n ,

(2)

yd --, 7r+ 7r- d.

(3)

In sect. 2 we present the experimental details. General features of the data are presented in sect. 3. In sect. 4 we discuss the density matrix elements and production mechanism of the p-meson. Our conclusions are given in sect. 5.

2. Experimental details This analysis is based on 170 000 pictures taken in the 82" SLAC deuterium filled bubble chamber, which was exposed to a nearly monochromatic, linearly polarized, photon beam of 7.5 GeV [10]. The beam m o m e n t u m spread was determined from the measurement of 5000 e÷e - pairs and was found to be A p / p ~ 4 % [10]. The film was scanned twice for all hadronic interactions and disagreements between scans were resolved on the scanning table. All events were measured on conventional Vangard measuring machines and geometric reconstructions and kinematical fits were made using programs T V G P and SQUAW. For reactions with an unseen positive track, that is even prong topologies, the invisible track was treated in the kinematical fit as a measured track with zero momentum. The error assignment was APx = APy = A P z x 0.75 = 30 Mev/c in the case of a proton and A P x = APy = APz x 0.75 = 40 MeV/c for a deuteron. The difference in the errors reflects the fact that a proton is invisible at a m o m e n t u m less than 80 MeV/c, while a deuteron is invisible up to 120 MeV/c. Because of the steep m o m e n t u m transfer distribution which characterizes coherent reactions we expect to find the coherent events of reaction (3) in both two and three prong topologies. In the latter case, in order to identify the coherent events, we require such three prong events to pass the corresponding 4c kinematical fit of reaction 3. However, these events will also pass the corresponding lc fit for proton and neutron break-up. Consequently in order to be accepted as a coherent reaction, we require that, for the lc fit, the invariant mass of the proton and neutron must be less than 1884 MeV and that the cosine of the angle between them in the laboratory be greater than 0.95. In the case of 2 prong topologies the corresponding lc fit is not as meaningfull but we can still require the proton-neutron invariant mass to be less than 1884 MeV. Note that it is possible to fit those events only because the spectator proton is treated as a measured track (of 0 MeV momentum) and thus there remains only one missing particle. The separation between reactions 1 and 2 is made according to the nucleon momenta, that is, if the outgoing proton m o m e n t u m is greater than that of the neutron, the reaction is assumed to be on a proton. In order to reduce the number of double scattered events

G. Alexander et al., pO production in ),d, 7P and 7n reactions

447

we required the spectator momentum to be less than 300 MeV/c. The spectator momentum distribution thus obtained is in agreement with the theoretical H~Uthen distribution.

3. General features of the data We have determined the cross sections for reactions (1), (2), and (3) by normalizing our data to the total pair production cross section at 7.5 GeV and correcting for measurement errors and scanning efficiency. The resulting cross sections are 14.3+ 1.5, 13.8+ 1.5 and 9.8-t-1 for reactions 1, 2 and 3 respectively [12]. In fig. 1 we show a compilation of the cross sections for these reactions. It is interesting to note that the yp cross section is approximately constant in our energy range, consistent with the assumption that the total cross section is dominated by pomeron exchange. The yn-~ nnn cross section is nearly equal to that for yp ~ pTtn, both at 4.3 GeV and 7.5 GeV. Finally, the ~,d~ dnrr cross section is roughly constant, as expected for a purely diffractive channel. [

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S~r (GeV) F i g . 1. C r o s s s e c t i o n s f o r t h e r e a c t i o n s ?p---->pzt + z~- , yn---->nn+n - a n d 7d---->dn+ zt - versus b e a m e n e r g y .

In fig. 2a, b we show the invariant mass plots of M(P, n +) and M(n, zc-) for reactions 1 and 2, respectively. Both distributions exhibit a small peak in the A + +, A- region. The corresponding cross section for A production in both reactions is less than 0.5/Lb. Fig. 2c is a plot of the invariant mass M(d, n±) for reaction 3 and shows a small enhan-

G. Alexander et al., pO production in 7d, 7P and ~n reactions

448

cement at M(d, z0"~2100 MeV corresponding to d* production. Unfortunately, we do not have enough data to further investigate this d*, which has been analyzed in detail in other reactions [13].

I0

5 0

Inn ,

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> t.iJ (.9

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0

~. I

2

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.(N,rt-)

5

0

N

rn

2.

4.

3

5

6.

u(o, rl) Fig. 2. Invariant mass plot o f (a) M ( p , n +) (b) M ( n , lr-) (c) M ( d , n+).

In fig. 3a, b, c we show the rr+r~- invariant mass M(n+zr -) for all the reactions and clearly all are dominated by pO production. Because of our limited statistics we are not 45

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z

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15

w

0 2

6

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14

2

6

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M (rr+,rt -)

Fig. 3. Invariant mass plot o f M(rr +, zt-) for reactions (a)),d---,dn+zt -, (b) yp----~pn+n- , (c) 7n--* n~+~ - . Curves are results o f best fits as explained in sect. 3.

G. Alexander et al., pO production in 7d, 7P and 7n reactions

449

able to study the t dependence of the p-mass distribution and we have fitted the nn mass to a Breit-Wigner distribution with an energy dependent width (Jackson's Breit-Wigner) multiplied by a mass skewing factor (Mp/M,=)" derived from a diffractive dissociation model by Ross and Stodolsky [14]. The results of the fits for each reaction are given in table 1, including the range of acceptable values for n. In all the cases the amount of non-p background is very small and is estimated to be less than 5% of the total cross section. Table 1

Mp (Mev) Fp (Mev) n A (/zb GeV-~) B(GeV -2)

dpO

ppO

npO

757 4-10 165 4-20 1.5
777 4-12 195 4-25 0.5
772 4-9 135 4-20 2
In fig. 4a, b, c we show the momentum transfer distribution dtr/dt for the three reactions. The four-momentum transfer t is defined between the incoming photon and the outgoing n+zc- system. In addition we have restricted the n+n - mass to the p region 0.4 < M(zc + n - ) < 1 GeV. The da/dt distributions were each fitted to an exponential function Ae -bt and the best fit values for A and B are given in table 1. We note that the slopes for single nucleon

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OI

.I

.z

.3

hl(GeV t)

.4

.5

.I

.2

3

.4

,5

.6

Itl (GeV z)

Fig. 4. Momentum transfer distribution for the reaction (a) 7d--+dp (b) 7p---~pp(c) ~ra = np.

450

G. Alexander et aL, pO production in 7d, ~PPand yn reactions

reactions are the same, within the statistical errors, while the slope for the deuteron reaction is approximately equal to that for the nucleon multiplied by the deuteron form factor:

d•(•d•pd)

= 4H(t) da

(vN-+ pN).

(4)

This latter formula can be obtained from the treatment of the elastic break-up reactions within the frame of the so called "closure approximation" [15], with the additional assumption of equal amplitudes on protons and neutrons. Using the experimentally observed cross section da(yd--,pd)/dt,,~exp(-27.5t) and da(yN--+pN)/dt~exp ( - g 6 . 5 t ) , one finds for the form factor H(t)=exp(-21 t) in fair agreement with the expected behaviour of H(t). In particular, relation (4) predicts a ratio of four in the forward direction where H(t = 0 ) = 1 and experimentally we find 3.8+0.2.

4. pO production mechanism The decay angular distribution of the p was studied within the formalism developed by Schilling et al. [17] to study the production mechanism of vector mesons by polarized photons. We present our results in the helicity system which is defined as follows: the z axis is taken in the direction opposite to that of the outgoing proton in the pO center of mass; the y axis is defined as normal to the production plane; the decay angles 0 and ~bare the polar and azimuthal angles of the zr+ direction if the p rest system. We define also the additional angle • as the angle between the electric vector of the photon and the production plane, in the total center of mass system: cos ¢ = ~-(~xp),

sin • = p. g, where ~ is a unit vector in the incoming photon direction. The decay angular distribution W(cos 0, ~b, 4) of the vector meson produced by a linearly polarized photon can be expressed in terms of the nine independent spin density matrix parameters p~: 3 W(cos 0,4b,4~) - ~

[Wo(cOsO,~b)-Pvcos2~Wl(cosO,~)-Prsin2~W2(cosO,cb)l,

where 3 Wo(cOs 0, ~b) = .-7- [½(1-p°oo)+½(3p°0-1) cos 2 0 - x / 2 Re p°o sin 20 cos q~ 47r --pO_ I sin20 COS 2~[,

G. Alexander et al., pO production in 7d, 7P and 7n reactions

451

3 W'(cos 0,(k) = ~ IPll sin20+p~o c o s 2 0 - x / 2 Re Plo sin 20 cos 4) - P ] - I sin20 cos 24)1, W2(cos 0, 4)) = ~3 ix/: Im P~o sin 20 sin qS+Im p~_ ~ sin 2 0 sin 24)1. Pv is the degree of linear polarization of the photon, calculated to be 82% at our energy [18]. Note that in the case of an unpolarized beam (Pr = 0) and only the first term in eq. (2) remains. We can further simplify this relation by introducing the angle ~k = - t k and assuming the p to be transverse and linearly polarized in the helicity system, then we get: PI-1 = ½;

I m p ~ _ l = -½,

and all other p~ = 0. Thus W(cos 0, ~k) = sin 2 0 cos 2 ~b.

(2)

In fig. 5a, b, c we show the cos 0 and ~b distributions for reactions 1-3. The curves are proportional to sin20 and 1 + P~ cos 2q; and are the expected distributions for a polarized p. In table 2 we give the nine independent density matrix elements P~'kcalculated for the different reactions. We note that within errors all the reactions exhibit the same density matrix elements, in particular P l - t = - I m p 2 - 1 =0.5 and all the other p~ = 0 consistent with s-channel helicity conservation.

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360

COS e .

Fig. 5. Decay angular distributions of 0, ~, for the reactions (a) 7d-->dp (b) 7p-->pp (c) 7n = np.

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G. Alexander et aL, pO production in yd, ~p and ?n reactions

Table 2 Density matrix p~=

dpO

po°o /)°_ 1 Re p°o Po~0 P~I P~-x Re pzXo Im P~-I Im P~o

0.01 -0.1 0.01 -0.07 -0.1 0.47 0.01 -0.42 0.03 0.95

Pet

4-0.03 4-0.04 4-0.02 4-0.05 4-0.05 4-0.05 4-0.03 4-0.05 4-0.03 4-0.07

ppO

npO

0.08 -0.04 0.01 -0.15 -0.15 0.4

0.1 -0.09 -0.02 0.05 -0.02 0.55 0.04 -0.59 0.03 0.8

4-0.04 4-0.05 4-0.03 4-0.06 4-0.07 4-0.07 0.04 4-0.05 - 0 . 6 5 4-0.1 0.07 4-0.04 0.8 4-0.08

4-0.03 4-0.03 4-0.03 4-0.06 :t:0.05 4-0.1 -4-0.04 4-0.12 4-0.03 4-0.1

The relative contributions a n, a u from natural and unnatural parity exchange in the t-channel can be obtained from the matrix density elements by defining [19]: 0-n~ 0-u 0 -n -{_ 0 -u

where P, =

2p -l-p o.

(4)

The calculated values of P, are consistent with one for all relations (1-3), showing that p is produced predominantly by natural parity exchange. At sufficiently high energy the following relations can be derived: p~U

0 i 1 = ½P~k--+(-1) P-~,k,

Tr p " + T r pU = 1. Combining these equations and using the data of table 2 we obtain that p~ are all consistent with zero showing again that natural parity exchange dominates at our energy. Finally we calculate the asymmetry parameter Z defined as: 1

1

Z = all--~l = P ~ I + P l - 1 0 0 ' all-I- tri Pll --P1-1

(5)

where o'11and a . are the cross sections for the pions from symmetric p decay (0 = ½n, ~b = ½n) to emerge in the plane of the photon polarization and perpendicular to it. As the helieity flip terms, Polo, p~ 1, Poo, o P ot - 1, are close to zero Z is nearly equal to P~.

G. Alexander et al., pO production in ~,d, ~p and ~n reactions

453

5. Conclusions

We have studied the reactions y p ~ p n + n -, y n = n n + n - and ~,d~drr+n -. All are dominated by pO production with A + +, A- and d* production being smaller than 0.5 #b. The pO cross sections are nearly energy independent, their differential cross section having slopes of ~ 6.5 GeV-2 for the nucleon reactions and --~27 GeV-2 for the deuteron reaction, as expected from a diffractive process. Finally, the production amplitude of the pO is predominantly s-channel helicity conserving while the p itself is produced mainly by natural parity exchange. The cooperation of SLAC in the performance of this experiment is gratefully acknowledged. In particular we are indebted to J. Ballam and G.B. Chadwick. Our thanks are also due to R. Watt and the SLAC bubble chamber operation crew and the SLAC Research Areas Division personnel. Finally we would like to acknowledge the valuable help of our technical and scanning staff at Tel-Aviv.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [111 [12] [13] [14] [15] [16] [17] [18] [19]

J. Ballam et al., Phys. Rev. 5D (1972) 15. J. Ballam et al., Phys. Rev. D7 (1973) 3150. M. Davier et al., Phys. Rev. D1 (1970) 790. H. Alvensleben et al., Phys. Rev. Letters 23 (1969) 1058. R. Anderson et al., Phys. Rev. D1 (1970) 27. C. Berger et al., Phys. Letters 38B (1972) 659. K.C. Moffeit, UCRL-19890 (Ph.D. thesis, unpublished). Y. Eisenberg et al., Nucl. Phys. B42 (1972) 349. A.G. Hilpert et al., Nuel. Phys. B21 (1970) 93. G. Alexander et al., Phys. Rev. D8 (1973) 712. T.M. Knasel, DESY report DESY 70/3, 1970 (unpubhshed). G.A. Alexander et al., TAUP-374-72. L Bar Nir et al., Nucl. Phys. B54 (1973) 17; D. Evrard et al., Nucl. Phys. BI4 (1969) 699. M. Ross and L. Stodolsky, Phys. Rev. 149 (1966) 1172. V. Franco and R.J. Glauber, Phys. Rev. 142 (1966) 1195. D. Lissauer, UCRL-20644 (Ph.D. thesis, unpublished). K. Schilling et al., Nucl. Phys. B15 (1970) 392; BI8 332 (E) (1970). J.J. Murray and P. Klein, SLAC report TN-67-19 (1967, unpublished). G. Cohen-Tannou DJI et al., Nuovo Cimento 55A (1968) 412.