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An experiment to measure the electric form factor of the proton
Volume
29B,
number 9
AN
PHYSICS
EXPERIMENT
TO MEASURE OF THE
LETTERS
4 August 1969
THE ELECTRIC PR.OTON
FORM
FACTOR
N. BOMBEY $ Daresbury
Nuclear Physics
Laboratory, Daredmy, Nr. Warrington, a& University of Sussex, UK Received
where GE(k2) and Go are the electric and magnetic form factors of the proton, k2 is the square of the momentum transfer and r = = k2/4i@. E, E’ and $ are the initial and final electron energies and the electron scattering angle, all measured in the laboratory. In eq. (1) the electron mass is neglected. GM,(O)/GE(O) = 2.79 so for large values of k2, say r ,> *, we see from eq. (1) that the magnetic terms are much larger than the electric. Thus, which is measured in the in practice, it is existing experimen(? s at large momentum transfer for it is assumed in the analysis of these experiments that G (k2)/‘GE (k2) = 2.79. There is, however, no real theoretical basis for this scaling law and a recent experiment [l] has indicated a deviation from it for large momentum transfer. An independent measurement of GE would therefore be very interesting. In a previous paper [2] it is shown that this could be accomplished using polarized muon beams scattered elastically off a polarized proton target (or alternatively by measuring the recoil proton polarization in place of a polarized target). If unpolarized electron beams could be used it would be easier to do the experiment; now, however, we would need both a polarized target and a measurement of the recoil proton polarization
[31-
That a measurement of this sort is possible in principle is well known [4]. It is, however, important to emphasize that good polarized targets suitable for use even with electron beams 588
UK
16 June 1969
An experiment is proposed to determine GE. It requires initial and final proton states in elastic e-p scattering.
The Rosenbluth formula describing the elastic scattering of electrons by protons is (1)
Lancashire,
the measurement
of the spin correlation
between
have recently been developed [5] and so, these experiments are now feasible. Zn addition, we show here that a simple configuration exists in which the recoil proton polarization is directly proportional to GE. The relevant formulae follow immediately from the analysis of ref. 2. In the proton Breit frame, the four-momenta of the initial and final electrons 11 and 12 are I1 =gk(cot$~,
0, 1, i cosech+B)
12 = $k(cot$@,
0, -1, i cosec &C/B)
(2)
1 where k = (k2)” and @B is the electron scattering angle in the Breit frame. So the elements of the symmetric tensor Lpv which describes the electron contribution to the scattering assuming exchange of one virtual photon (for unpolarized electrons) are k2LClv = Q,,$
+ $,llp
This gives (x,y,Z, elements 2Lll
= cosec’$@B,
+ $k2 6n,, .
(3)
are 1,2,3) for the non-zero 2L22 = 1, 2L44 = -cot2+@B,
2L14 = 2L41 = i cOt&B cosec$tl/B .
(4)
The proton current in its Breit frame is given by Jj = x2*f p Xl,
(5)
where f1 =ikGMuy,
f 2 = -ikGp,px,
f 3 = 0: f 4 = IMAGE.
Thus the proton polarization must be arranged to pick out (14) or (24) components in order to measure GE GM. As L24 = 0, this implies that $ Daresbury Nuclear Physics Laboratory and University of Sussex.
PHYSICS
Volume 29B, number 9
we need a (14) contribution and so an X-Z corre-
lation is required. The practical configuration is therefore the target proton polarized in the z-direction (the direction of the recoil proton in the laboratory) and the polarization of the recoil proton must then be measured in the x-direction, i.e. perpendicular to its direction of motion and in the scattering plane. The polarization P for this is given by p =
Tr{fV+%fp(1+ %))+,, = Tr{f *+f ‘1 Lgv 27i GE GMcot iJ/B cosec $#B
=
rG$(2+cot
2+*)+G
cot+B
(6)
where
LETTERS
4 August 1969
we find E =B,
P = 55%
+ The form factors Fl@),
cot2 $B
= cot2 @/( 1 + 7) .
(7)
(12)
assuming the scaling law. Even in less favourable situations the order of magnitude of P is given by GE/GM N 30% unless GE(k3) decreases much more rapidly than GM(k2). This is measureable even for quite small polarization of the target proton. It was noted in ref. 2 that as GE = F1 - rF3 * it is quite likely that GE becomes negative for large values of 7. If the results of Berger et al. [l] are extrapolated to large values of 7, GE passes through zero at some value of T between 3 and 6. The experiment proposed here determines the sign of GE and will, in principle, resolve this problem. F2(k2) are defined hy
Jp = $2~~ ql Fl- (ik,,/2M)$2 ‘J&l
p-2.
In terms of the virtual photon polarization [2] E cot2@B
= 2c/(1 -E)
(6)
the Bosenbluth formula is
(9) and
(10)
P= For electron energies E of 5 GeV and T = 1 l+~
cosec2 B*B =l_~
=
(E/M-& (I+ 7)
8
(11)
References 1. Chr.Berger, E. Gersing, G.Knop, B. Langenbeck, K. Rith and F. Schumacher, Phvs. Letters 28B (1968) . . 276. 2. N. Dombey, Rev. Mod. Phys.41 (1969) 236. The use of polarized muon beams in this way was first pointed out by M. Gourdin, Nuovo Cimento 47A (1967) 195. 3. This was suggested by P. K. Kabir. 4. It follows for example from the general analysis of J. H. Scofield, Phys. Rev. 141 (1966) 1352. 5. S. Mango, 0. Runolfsson and M. Borghini, A butanol polarized proton target, CERN report, January, 1969 (to be published); L. van Rossum, private communication (communicated by A. Kemp).
589
29B,
number 9
AN
PHYSICS
EXPERIMENT
TO MEASURE OF THE
LETTERS
4 August 1969
THE ELECTRIC PR.OTON
FORM
FACTOR
N. BOMBEY $ Daresbury
Nuclear Physics
Laboratory, Daredmy, Nr. Warrington, a& University of Sussex, UK Received
where GE(k2) and Go are the electric and magnetic form factors of the proton, k2 is the square of the momentum transfer and r = = k2/4i@. E, E’ and $ are the initial and final electron energies and the electron scattering angle, all measured in the laboratory. In eq. (1) the electron mass is neglected. GM,(O)/GE(O) = 2.79 so for large values of k2, say r ,> *, we see from eq. (1) that the magnetic terms are much larger than the electric. Thus, which is measured in the in practice, it is existing experimen(? s at large momentum transfer for it is assumed in the analysis of these experiments that G (k2)/‘GE (k2) = 2.79. There is, however, no real theoretical basis for this scaling law and a recent experiment [l] has indicated a deviation from it for large momentum transfer. An independent measurement of GE would therefore be very interesting. In a previous paper [2] it is shown that this could be accomplished using polarized muon beams scattered elastically off a polarized proton target (or alternatively by measuring the recoil proton polarization in place of a polarized target). If unpolarized electron beams could be used it would be easier to do the experiment; now, however, we would need both a polarized target and a measurement of the recoil proton polarization
[31-
That a measurement of this sort is possible in principle is well known [4]. It is, however, important to emphasize that good polarized targets suitable for use even with electron beams 588
UK
16 June 1969
An experiment is proposed to determine GE. It requires initial and final proton states in elastic e-p scattering.
The Rosenbluth formula describing the elastic scattering of electrons by protons is (1)
Lancashire,
the measurement
of the spin correlation
between
have recently been developed [5] and so, these experiments are now feasible. Zn addition, we show here that a simple configuration exists in which the recoil proton polarization is directly proportional to GE. The relevant formulae follow immediately from the analysis of ref. 2. In the proton Breit frame, the four-momenta of the initial and final electrons 11 and 12 are I1 =gk(cot$~,
0, 1, i cosech+B)
12 = $k(cot$@,
0, -1, i cosec &C/B)
(2)
1 where k = (k2)” and @B is the electron scattering angle in the Breit frame. So the elements of the symmetric tensor Lpv which describes the electron contribution to the scattering assuming exchange of one virtual photon (for unpolarized electrons) are k2LClv = Q,,$
+ $,llp
This gives (x,y,Z, elements 2Lll
= cosec’$@B,
+ $k2 6n,, .
(3)
are 1,2,3) for the non-zero 2L22 = 1, 2L44 = -cot2+@B,
2L14 = 2L41 = i cOt&B cosec$tl/B .
(4)
The proton current in its Breit frame is given by Jj = x2*f p Xl,
(5)
where f1 =ikGMuy,
f 2 = -ikGp,px,
f 3 = 0: f 4 = IMAGE.
Thus the proton polarization must be arranged to pick out (14) or (24) components in order to measure GE GM. As L24 = 0, this implies that $ Daresbury Nuclear Physics Laboratory and University of Sussex.
PHYSICS
Volume 29B, number 9
we need a (14) contribution and so an X-Z corre-
lation is required. The practical configuration is therefore the target proton polarized in the z-direction (the direction of the recoil proton in the laboratory) and the polarization of the recoil proton must then be measured in the x-direction, i.e. perpendicular to its direction of motion and in the scattering plane. The polarization P for this is given by p =
Tr{fV+%fp(1+ %))+,, = Tr{f *+f ‘1 Lgv 27i GE GMcot iJ/B cosec $#B
=
rG$(2+cot
2+*)+G
cot+B
(6)
where
LETTERS
4 August 1969
we find E =B,
P = 55%
+ The form factors Fl@),
cot2 $B
= cot2 @/( 1 + 7) .
(7)
(12)
assuming the scaling law. Even in less favourable situations the order of magnitude of P is given by GE/GM N 30% unless GE(k3) decreases much more rapidly than GM(k2). This is measureable even for quite small polarization of the target proton. It was noted in ref. 2 that as GE = F1 - rF3 * it is quite likely that GE becomes negative for large values of 7. If the results of Berger et al. [l] are extrapolated to large values of 7, GE passes through zero at some value of T between 3 and 6. The experiment proposed here determines the sign of GE and will, in principle, resolve this problem. F2(k2) are defined hy
Jp = $2~~ ql Fl- (ik,,/2M)$2 ‘J&l
p-2.
In terms of the virtual photon polarization [2] E cot2@B
= 2c/(1 -E)
(6)
the Bosenbluth formula is
(9) and
(10)
P= For electron energies E of 5 GeV and T = 1 l+~
cosec2 B*B =l_~
=
(E/M-& (I+ 7)
8
(11)
References 1. Chr.Berger, E. Gersing, G.Knop, B. Langenbeck, K. Rith and F. Schumacher, Phvs. Letters 28B (1968) . . 276. 2. N. Dombey, Rev. Mod. Phys.41 (1969) 236. The use of polarized muon beams in this way was first pointed out by M. Gourdin, Nuovo Cimento 47A (1967) 195. 3. This was suggested by P. K. Kabir. 4. It follows for example from the general analysis of J. H. Scofield, Phys. Rev. 141 (1966) 1352. 5. S. Mango, 0. Runolfsson and M. Borghini, A butanol polarized proton target, CERN report, January, 1969 (to be published); L. van Rossum, private communication (communicated by A. Kemp).
589