SLAC-PUB-177 July 1976 m INELASTIC ELECTRON DEUTERON SCATTERING IN THE THRESHOLD 4 REGION AT HIGH MOMENTUM TRANSFER* W. P. Schiitz, R. G. Arnold, B. T. Chertok, E. B. Dally, ** A; Grigorian, tt C. L. Jordan,% andr. Zdarkof-j- _ American Universitys Washington, D. C. 216 F. Martin Stanford Linear Accelerator Center Stanford University, Stanford, California 9435 B. A Mecking Physikalisches Institut Universit%t Bonn, Bonn, West Germany ABSTRACT At squared momentum transfers.8~ q2 5 6. (GeV/c)2, we measured nine spectra of inelastic electron deuteron scattering cross sections in the threshold region between and 2.3% in Ap/p below the elastic peak and deduced the deuteron inelastic structure -function vw2. We found vw2(wt) approaching a universal scaling curve and a close relation between vw2 and the deuteron elastic structure function A(q2). (Submitted to Phys. Rev. Letters.) *Work supported in part by the Energy Research and Development Administration. **On leave from Naval Postgraduate School, Monterey, California 9394. T fpresent address: High Energy Physics Laboratory, Stanford University, Stanford, California 9435. $Present address: LeCroy Research Systems Corp., 1 First Street, Los Altos, California 9422. $ Research supported by the National Science Foundation under Grant No. MPS 75-7325.
-2- In this letter, we report preliminary results of inelastic electron deuteron scattering in the threshold region at high momentum transfer q. The data were 4 taken from a SLAC experiment whose main purpose was to measure the elastic scattering cross sections and the deuteron structure function A(q2) at nine values of q2 in the region.8 1 q2 5 6. (GeV/c). The experimental conditions were such that we measured not only the elastic events, but also inelastic events from deuteron breakup and pion production between ~ &/pe L-2.3%, where p, is the scattered electron momentum at the center of the elastic peak. The nine inelastic electron spectra span an unusual dynamic region of large q2 and small energy transfer v = Ei-Ef, the difference between initial and final electron energy. This region has not been explored before. both q2 and v are large compared with Mi, Bjorken scaling is expected when the square of the nucleon mass, as in deep inelastic electron scattering. The data presented here are on a scale where q2 is expected to resolve the nucleons into fermion quaric currents while v is typical of excitation energies where nucleon-nucleon final state interaction effects may be significant. The deuteron, then, is an ideal system to study the approach to scaling and the interplay between nuclear and particle physics. We used the 2 GeV/c spectrometer of SLAC End Station A to detect scat- tered electrons at a fixed Be = 8 from liquid deuterium, liquid hydrogen (for system calibration) and from a dummy target to determine the empty target back- ground. To filter the elastic events out of the inelastic and background events, we used the 8 GeV/c spectrometer in coincidence with the 2 GeVjc spectrometer to detect the recoil deuterons with elastic kinematics. The 2 GeV/c spectrometer with 5% momentum acceptance was set to cover the region in 4 between -. 3 ( 4/pe L+. 2. Events from the electron arm were logged when a coincidence signal in three scintillator trigger counters and
-3- a large pulse height in a lead glass and lead lucite shower counter was regis- tered. Thus, simultaneous with the double arm elastic events, we recorded - single arm events from inelastic processes in the threshold region. Five planes of multiwire proportional chambers recorded the particle trajectory at the spectrometer exit. The angle and momentum of the-particles leaving the target were reconstructed using the well-known optical properties of the spectrometer. A typical electron spectrum is shown in Fig. 1 displaying the total spectrum and the elastic and empty target background events. Subtracting the background and elastic events from the total spectrum gives us the inelastic events we want to investigate here. The finite resolution, mainly caused by the initial electron beam momentum spread, is roughly.5% of p, and given by the width of the elastic peak. Figure 2 shows the kinematic region of our nine spectra on a q2-v-plane. The dotted line indicates the experimental limit at 2.3% of p, below the center of tie elastic peak. The pion threshold is always inside, the center of the quasielastic peak always outside the spectra. For radiative unfolding, we used a method suggested by Crannell using the radiative correction formulas given by Tsai. 3 This gave an enhancement to the spectra of typically a factor 1.8 with very little energy dependency. The solid angle A!J was determined in a Monte Carlo simulation. Experimental corrections were applied for dead time losses (5 to 1%) and for wire chamber track inefficiencies (1%). Our results for the inelastic cross sections d2g/dndef versus Ef are presented in Fig. 3. The error bars on the data points represent the statistical errors only. The systematical errors, mainly from uncertainties in Aa and
-4- the corrections, are estimated to +2/o. The spectra rise almost exponentially with dgcreasing Ef, with a sharp rise from zero at the threshold. The influence of the resolution on the shape of the spectra at threshold was studied by folding the resolution into faked lttrue! spectra. This study indicated _ that the true spectra apparently rise from zero with nonzero slope. Thus, the threshold enhancement cannot be explained as a resolution effect. It is pos- sible that it is caused by final state interactions between the outgoing proton and neutron which have small relative momentum. as In one photon exchange approximation, d2 om dszdef = 7 the cross section can be written 1 2 e - tan 2. - where u M is the Mott cross section and WI and W2 are the deuteron inelastic structure functions, depending on the Lorentz invariants q2 and v. Formulas connecting WI and W2 are given, e. g., in Ref. 4. Assuming R=.18, 5 we find for our case which means that we are practically only sensitive to uw2. For q2, v --m, it is observed that vw2 becomes a function of the scaling variable w only, with w = l+ W2/q2 and W2 = M2+ 2Mv - q2, the square of the missing mass. Figure 4 shows a comparison of our data with data from Refs. 5 and 7 on a vw2 vs. w plot. At q2 below 2 (GeV/c)2, we are not yet in the scaling region, but at q2l 2 (GeV/c)2, our spectra merge with increasing q2 into a universal vw,(w ) curve. We find empirically that the spectra with q2z 2 (GeV/c)2 can be described by the relation vw2 - (w -. 5)n, with n= 6 &.5.
-5 - We find a close relation between the elastic A(q2) and W2 at constant W2, A(q2) is observed to approach the power-law behavior Fd= 4 - (q2)-5 (see Ref. T) as predicted by Brodsky and Farrar s dimensional-scaling quark model. 8 Using the form (1) with Fp= (l+q2/. 71)-2 and m2=. 47/2 GeV2 (see Ref. 9) the onset of scaling was observed to be already below q2 =.8 (GeV/c)2. For W (Ref. 6) close to Md, we find empirically that our data follow the relation w2 - Fg12) * p W2) (2) with Fd given by Eq. (1) and a function p only depending on W2 (see Fig. 5).. - A connection between F and vw2 near threshold has been given by Drell- Yanl and WestII for the case of the proton: 2 VW2 -x - (l-x) P ) F N (1,q2)(pf1)/2, x=&-l. If we extend this prediction to the deuteron, we postulate p=9, since F -( l/q2)5. From our data, we could not get a reasonable fit within 4 < p < 11. So, we do - - not have any evidence that this connection works for the deuteron. However, we seem to be at too small q2, v-values to observe scaling in x. If G(q2) is the excitation form factor of a resonance at M=MR, is its contribution to vw2 in the narrow resonance approximation. This has been shown by Bloom and Gilman. 12 Our data indicate that this relation works in
I -6 - our case % M Md), i.e., vw2 -q2.f2d*p(w2), similar to Eq. (2). Thus, our measurements indicate that VW 2 at threshold behaves like a resonance with G(qT- Fd(q2). This leads, in the language of the quark model, to the conclu- sion that, like in the elastic case, all six quarks participate inelastic scattering process. in the threshold - We thank Dr. S. Brodsky for many helpful suggestions and discussions.
-7- REFERENCES 1. R. Arnold et al., -- Phys. Rev. Letters 35 776 (1975). - 2. L Crannell, Nucl. Instr. Meth. 2, 28 (1969). 3. P. Tsai, Stanford Linear Accelerator Center preprint SLAC-PUB-848 (1971). - 4. 5. 6. S. Stein et al --- Phys. Rev. D 12, 1884 (1975). J. S. Poucher et al., -- Phys. Rev. Letters 32 118 (1974). - For comparison with Refs. 5 and 7, we calculated W2 with MN =. 938 GeV. Our data are then in the range -2.12 5 W2 <.76 GeV2. For comparison of vw2 with Fd, we definedw2withmd= 1.876 GeV (3.52~W~55.2 GeV2). 7. 8. 9. E. M. Riordan, thesis, MIT Report No. COO-369-176. S. Brodsky and G. Farrar, Phys. Rev. D 2, 139 (1975). S. Brodsky and B. Chertok, to be published.. - 1. S. D. Drell and T. M. Yan, Phys. Rev. Letters 24, 181 (197). 11. G. B. West, Phys. Rev. Letters 24, 126 (197). 12. E. D. Bloom and F. J. Gilman, Phys. Rev. Letters 25, 114 (197).
-8-1. Electron -ci events at q2 = 1 (GeV/g2. 2. Kinematic region of this experiment. FIGURE CAl?TIONS 3. Inelastic cross sections versus final electron energy. 4. Our data compared with results from Refs. 5 ( =6, 1 ; W > 2 GeV; q2 > 1 (GeV/c)2) and 7 (= 18, 26, 34 ; W 2 2 GeV; q2 2 4 (GeV/c)2). 5. Inelastic structure function W2 divided by the elastic structure function A at constant missing mass. F = A l/2 d. The lines are eyeball fits.
6 = 8, q $as+ic = I (GeW * total pelas+ic = 7.36 GeV/c Oooo OO background OOOO X XxXxXxX X xxxxxx xx xxx xx X,. elastic * Lxx. x;xq@g +w++++ t++ (t)+++++ P Ap ( /> elastic Fig. 1
7-r -Thmchqjd 2 I I. - I /+y Experimental limit 5 25.5 1. I.5 2. v =E-Ef (GeV) 2892D2 Fig. 2 -
c -I IO z # c,-..... 1-l E l a.@.*. q2=8. (GeV/d2 f - -)+ Ee ; 6.519 GeV I lo-2 I I I 6.3 6.25 6.2 6.15 IO-- 1-2 m lo-4..@-. lo-3 h.a..o.. l - q 2 = 2... E;L 1.47 1-41 I I I I I I 9.9 9.8 9.i lo-3 r I I I I I.*@@ m.@.o@..ji- 9 2 = 2.5 - Ey= I I.671 -z I I I I I -I Il. 1.9 1.8 I 2 Iv- 7.5 7. 6.95 6.9 bw %Z - lo-2 i= I I I I 3 4..O.....*.. l * 9 2 = 1.5 lo-3. E;L 8.981 l6-2% tl I I I I 1 8.6 8.5 8.4 I I I I I.O@ /. l *.@ 4,: = 1.75 - Ei= 9.718 z I I I I 9.2 9.1 E; (GeV) 1-5 a- I I I I I 12. II.9 Il.8 lo-5 lo+ 13.8 13.7 13.6 13.5 16.8 16.7 16.6-16.5 16.4 Fig. 3
IO t c, IO-- E- lo-2 E Io-3 E =.8 (GeV/c)* t IO -4 = lo+ lo+ f f A Poucher et al. I Riordan et al. @ This Experiment 2 3 QJ = I + wvq2 4 2962C2 Fig. 4.e r_ -..- _.,,.
Fd = Fp2(,3-/4,j l+q*/+n*)- Fp = (I+q*/O.71)-*.rn * =.47/2 GeV* - \uev.2.15.1,o.o 5 I 1-l I I 2 3 4 5 6 7 9* (W/d2 Fig. 5