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Testing spin properties of constituents from massive lepton pair production
Volume 85B, number 4
PHYSICS LETTERS
27 August 1979
TESTING SPIN PROPERTIES OF CONSTITUENTS FROM MASSIVE LEPTON PAIR PRODUCTION
J. SOFFER 1 and P. TAXIL 2 Centre de Physique Th~orique, CNRS, Marseille, F-13288 Marseille Cddex, France Received 30 March 1979
We propose to use massivelepton pair production by polarized protons to study the spin properties of the constituents. We have established restrictive bounds on the up-down asymmetry and we have calculated the proton spin-muon spin asymmetry. Both should be tested experimentally.
Many large-p± experiments at high energy are usually interpreted in a parton picture in which hadrons are assumed to be made of constituents. These constituents (valence quarks, antiquarks and gluons) which share the momentum of a fast proton can produce particles at large p± after a single large-angle 2 ~ 2 scattering [1 ]. The hadronic constituents are not spinless objects and one needs to know in the case of a fully polarized proton, how its spin is distributed among them, how well the constituents remember the spin state of the proton. This important question has been partially answered for the valence quarks from recent experiments with polarized electron beams at SLAC which allow one to study spin dependence in deep inelastic scattering [2]. These results show that the asymmetry A "rp is positive, in agreement with the naive parton model [3], but for large x values it grows above 5•9, the SU(6) limit. Although this has to be confirmed by more accurate measurements, there is a tendency for the longitudinally polarized quarks to remember the parent proton's helicity at large x [4] which leads to an asymmetry A~P of 100% for x = 1. Of course, since gluons do not interact directly with leptons and photons, we learn nothing from deep inelastic scattering about their spin distributions within the polarized proton. On the contrary, production of massive lepton pairs in ha&on1 ~esent address: Theory Division, CERN, Geneva, Switzerland. 2 Allocataire D.G.R.S.T. 404
ic collisions has already been recognized as a useful tool to study the structure of the hadrons and more specifically, the role of antiquarks and gluons in the framework of QCD [5]. The purpose of this paper is to argue that lepton pair production by polarized protons may provide further tests of QCD and give us new insight in the spin properties of hadronic constituents. Let us first consider the reaction pp~ ~ #~X where t denotes the transversality of one proton (beam or target). The simplest measurable quantity to test the spin dependence of this reaction is the u p - d o w n asymmetry A which is expressed in the helicity frame as [6] A - Im(+l-) ( + l +)
'
(1)
where (+ I - ) is the discontinuity of the Mueller flip amplitude and (+ I +) is simply the unpolarized cross section. It is important to note that A vanishes unless, first, (+1 - ) has a non-zero imaginary part and, secondly, the lepton pair has a non-zero transverse momentum p±. Concerrling the first point, perturbative QCD predicts for the hard asymmetry an effect of order (as(M2)/:r)(mq/M) where mq is the mass of the quarks and M is that of the lepton pair. This gives of course for A a small contribution [7,8] .1. Concerning the second point, we know that the observed transverse ~=1Anyway, one should be careful about "strong" arguments to rule out a phase difference and remember a similar situation for ~N charge exchange in the old glorious time of Regge pole theory!
Volume 85B, number 4 IAI
I
0.8
".,,~. ~
PHYSICS LETTERS i
ppl_p,~X (or 90"S SD Bounds ' M=S.SGeV ..... 400 GeV/c M =75 GeV--•-~....~ M=5.5GeV--.-" . - . ~ ~ WDBounds tVl=7.5GeV~
0.6 0.4 0.2
.... ~::.:~;~.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
I
1
2
I
I
3
/-,
Px (GeV/c)
Fig. 1. Results of numerical evaluation of the strong and weak dilution bounds (see text) on the modulus of the up-down asymmetry Ial at Plab = 400 GeV/c for two values of the mass M of the lepton pair. momentum of the lepton pair [9] is larger than previously expected but the p± distributions, i.e. (+1 +), are correctly described in QCD provided one includes the important contribution of hard gluon scattering [10,11]. Of course we are not able to give an exact evaluation of A but, by allowing the polarization of the hard scattering to be maximal through a nonperturbative mechanism, we can use positivity constraints to derive bounds on A by the same method which was used in ref. [12]. There are two cases of interest. First, only the valence quarks remember the spin of the proton but not the antiquarks or the gluons. In this situation, it means that since the gluons are known to be important at large p±, if they do not carry the spin information, even a quark polarization of 100% will be strongly diluted (SD) inside polarized protons and indeed we obtain the SD bounds shown in fig. 1. Secondly, the antiquarks and the gluons are also 100% polarized and the bounds obtained in this case show that the spin properties of the constituents are weakly diluted (WD) (see fig. 1, WD bounds). For numerical estimates we have used the cross section of ref. [11 ] which agrees well with the data [9] and details of our calculation will be given in a separate paper. The bounds show very little energy dependence between 400 GeV[c and 800 GeV/c and they become less restrictive when the mass M of the lepton pair increases from 5.5 GeV to 7.5 GeV for p± less than 3 GeV/c (see fig. 1). The measurement of A at large p± is therefore a direct way to confirm the role of the gluons in massive lepton pair production and to learn about their spin distributions provided they are polarized by a nonperturbative mechanism. The transverse polarization of the A, P(A), in pp ~ AX has already measured up to
27 August 1979
p± ~. 2 GeV/c at FNAL and ISR energies [13]. P(A)is about - 2 5 % and this large value could also be related to gluon spin properties [14]. Next, consider massive lepton pair production at p± = 0, where the classical Drell-Yan annihilation model including bremsstrahlung corrections can be applied [15]. Suppose one initial proton is longitudinally polarized, if one is able to measure the helicity of one outgoing lepton one can determine the following asymmetry: ]gDY doC~p - ff/TX) - do('~p do(~p -~'/~X) + do(pp
...
4--B
ta/zX),
(2)
uuX)
where ~ label the helicity of the proton and the muon. In terms of the quark and antiquark distributions this quantity reads ,2 ]~DY = ~'iei2 (Aqi(xl)qi(x2) - qi(x2)Aqi(xl))
Xie? {qi(xl)~i(x2) + qi(xz)~i(Xl)}
(3)
x 1 -x 2 X - x 1 +x 2 , where &/(x) = q+(x) - q - ( x ) is the difference of the quark distributions in a proton with helicity parallel and opposite to the proton helicity. The same def'mition holds for z~(x). Here x I refers to a quark (antiquark) from the polarized proton and x 2 refers to an antiquark (quark) from the other proton. The kinematic factor (x 1 - x2)/(x 1 + x2) comes from helicity conservation at the photon coupling in qCt -~ #/7 and says that ~DY vanishes when x F = x 1 - x 2, the Feynman x of the lepton pair, is zero (i.e. at 90 ° in the c.m.). From the behaviour of the distribution functions it is easy to see that for x F > 0 (i.e. x 1 > x 2 ) ~DY reflects the spin properties of the quarks and for x F < 0 (i.e. x I < x2) it reflects the spin properties of the antiquarks. We have calculated ~DY by using Aq (x) from refs. [3] and [4]. It has been argued that perturbative QCD provides a mechanism for the polarization of antiquarks [16] and this is what we have assumed for A~(x). The numerical results at 200 GeV/c are shown in figs. 2a,b by the solid lines. The dashed lines represent the asymmetry in the case where the antiquarks ,2 Although scaling violations require some Q2-dependence for the distribution functions, we neglect them for a rough estimate of ~DY. 405
Volume 85B, number 4
PHYSICS LETTERS I
I
I
(a)
P P--F/.1. X 2 0 0 GeV/c
27 August 1979 I
p ~-p.# x
(hi
2 0 0 GeV/c
M'= 50 GeV'
M' = 50 GeV'
KUTI - WEISSKOPF DISTRIBUTIONS
CARLITZ - KAUR DISTRIBUTIONS
0.5
,{
/jk /z z
I/IL
// /z s zz////
I -0.5
0
1
I
05
-05
XF
I 0
0,5
XF
Fig. 2. Theoretical evaluations of the proton spin-muon spin asymmetry ~DY (see text) for the/a~ pair of massM ~ 7 GeV at Plab = 200 GeV/c. (a) Quark distributions from ref. [31, (b) quark distributions from ref. [4]. are n o t polarized (i.e. A~ = 0). Polarization of the antiquarks gives a sizeable ~DY in the backward direction which is not very sensitive to the choice of the quark distributions. This choice affects only the values of ~DY for x F > 0 as expected. We have found that for the same lepton pair mass ~DY for x F < 0 decreases when the energy increases and this remains to be checked by future experiments. As a final remark, we strongly believe that polarization measurements in massive lepton pair production is an interesting field which may yield new insight into the dynamics of hadronic constituents. We are indebted to C. Bourrely for valuable discussions on the subject of this paper. We thank Ed. Berger for an interesting correspondence and M. Jacob for some helpful remarks.
References [1 ] R.D. Field, Plenary report on Dynamics of high energy reactions at the XIXth Intern. Conf. on High energy physics (Tokyo, 1978).
406
[2] M.J. Alguard et al., Phys. Rev. Lett. 41 (1978) 70. [3] J. Kuti and V.F. Weisskopf, Phys. Rev. D4 (1971) 3418, [4] R. Caflitz and J. Kaur, Phys. Rev. Lett. 38 (1977) 673, 1102; J. Kaur, Nucl. Phys. B128 (1977) 219. [5] For a recent review, see: E.L. Berger, invited paper at the Intern. Conf. at Vanderbilt University (March 1978), preprint ANL-HEP-PR-78-12. [6] R.J.N. PhilliPs, G.A. Ringland and R.P. Worden, Phys. Lett. 40B (1972) 239. [7] G.L. Kane, J. Pumplin and W. Repko, Phys. Rev. Lett. 41 (1978) 1689. [8] D. Sivers, Talk at the 3rd Intern. Symp. on High energy physics with polarized beams and targets (Argonne, October 1978), preprint ANL-HEP-CP-78-50. [9] D.M. Kaplan et al., Phys. Rev. Lett. 40 (1978) 435. [10] G. Altarelli, G. Parisi and R. Petronzio, Phys. Lett. 76B (1978) 356. [11 ] R. Petronzio, Proc. XIllth Rencontre de Moriond (March 1978), ed. Tran Than Van, p. 129. [12] C. Bourrely and J. Softer, Phys. Lett. 71B (1977) 330. [13] G. Bunce et al., Phys. Rev. Lett. 36 (1976) 1113; K. HeUer et al., Phys. Rev. Lett. 41 (1978) 607; S. Erhan et al., Phys. Lett. 82B (1979) 301. [14] G.L. Kane and Y.P. Yao, Nucl. Phys. B137 (1978) 313. [15] C.T. Sachrajda, Phys. Lett. 73B (1978) 185. [16] F. Close and D. Sivers, Phys. Rev. Lett. 39 (1977) 1116.
PHYSICS LETTERS
27 August 1979
TESTING SPIN PROPERTIES OF CONSTITUENTS FROM MASSIVE LEPTON PAIR PRODUCTION
J. SOFFER 1 and P. TAXIL 2 Centre de Physique Th~orique, CNRS, Marseille, F-13288 Marseille Cddex, France Received 30 March 1979
We propose to use massivelepton pair production by polarized protons to study the spin properties of the constituents. We have established restrictive bounds on the up-down asymmetry and we have calculated the proton spin-muon spin asymmetry. Both should be tested experimentally.
Many large-p± experiments at high energy are usually interpreted in a parton picture in which hadrons are assumed to be made of constituents. These constituents (valence quarks, antiquarks and gluons) which share the momentum of a fast proton can produce particles at large p± after a single large-angle 2 ~ 2 scattering [1 ]. The hadronic constituents are not spinless objects and one needs to know in the case of a fully polarized proton, how its spin is distributed among them, how well the constituents remember the spin state of the proton. This important question has been partially answered for the valence quarks from recent experiments with polarized electron beams at SLAC which allow one to study spin dependence in deep inelastic scattering [2]. These results show that the asymmetry A "rp is positive, in agreement with the naive parton model [3], but for large x values it grows above 5•9, the SU(6) limit. Although this has to be confirmed by more accurate measurements, there is a tendency for the longitudinally polarized quarks to remember the parent proton's helicity at large x [4] which leads to an asymmetry A~P of 100% for x = 1. Of course, since gluons do not interact directly with leptons and photons, we learn nothing from deep inelastic scattering about their spin distributions within the polarized proton. On the contrary, production of massive lepton pairs in ha&on1 ~esent address: Theory Division, CERN, Geneva, Switzerland. 2 Allocataire D.G.R.S.T. 404
ic collisions has already been recognized as a useful tool to study the structure of the hadrons and more specifically, the role of antiquarks and gluons in the framework of QCD [5]. The purpose of this paper is to argue that lepton pair production by polarized protons may provide further tests of QCD and give us new insight in the spin properties of hadronic constituents. Let us first consider the reaction pp~ ~ #~X where t denotes the transversality of one proton (beam or target). The simplest measurable quantity to test the spin dependence of this reaction is the u p - d o w n asymmetry A which is expressed in the helicity frame as [6] A - Im(+l-) ( + l +)
'
(1)
where (+ I - ) is the discontinuity of the Mueller flip amplitude and (+ I +) is simply the unpolarized cross section. It is important to note that A vanishes unless, first, (+1 - ) has a non-zero imaginary part and, secondly, the lepton pair has a non-zero transverse momentum p±. Concerrling the first point, perturbative QCD predicts for the hard asymmetry an effect of order (as(M2)/:r)(mq/M) where mq is the mass of the quarks and M is that of the lepton pair. This gives of course for A a small contribution [7,8] .1. Concerning the second point, we know that the observed transverse ~=1Anyway, one should be careful about "strong" arguments to rule out a phase difference and remember a similar situation for ~N charge exchange in the old glorious time of Regge pole theory!
Volume 85B, number 4 IAI
I
0.8
".,,~. ~
PHYSICS LETTERS i
ppl_p,~X (or 90"S SD Bounds ' M=S.SGeV ..... 400 GeV/c M =75 GeV--•-~....~ M=5.5GeV--.-" . - . ~ ~ WDBounds tVl=7.5GeV~
0.6 0.4 0.2
.... ~::.:~;~.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
I
1
2
I
I
3
/-,
Px (GeV/c)
Fig. 1. Results of numerical evaluation of the strong and weak dilution bounds (see text) on the modulus of the up-down asymmetry Ial at Plab = 400 GeV/c for two values of the mass M of the lepton pair. momentum of the lepton pair [9] is larger than previously expected but the p± distributions, i.e. (+1 +), are correctly described in QCD provided one includes the important contribution of hard gluon scattering [10,11]. Of course we are not able to give an exact evaluation of A but, by allowing the polarization of the hard scattering to be maximal through a nonperturbative mechanism, we can use positivity constraints to derive bounds on A by the same method which was used in ref. [12]. There are two cases of interest. First, only the valence quarks remember the spin of the proton but not the antiquarks or the gluons. In this situation, it means that since the gluons are known to be important at large p±, if they do not carry the spin information, even a quark polarization of 100% will be strongly diluted (SD) inside polarized protons and indeed we obtain the SD bounds shown in fig. 1. Secondly, the antiquarks and the gluons are also 100% polarized and the bounds obtained in this case show that the spin properties of the constituents are weakly diluted (WD) (see fig. 1, WD bounds). For numerical estimates we have used the cross section of ref. [11 ] which agrees well with the data [9] and details of our calculation will be given in a separate paper. The bounds show very little energy dependence between 400 GeV[c and 800 GeV/c and they become less restrictive when the mass M of the lepton pair increases from 5.5 GeV to 7.5 GeV for p± less than 3 GeV/c (see fig. 1). The measurement of A at large p± is therefore a direct way to confirm the role of the gluons in massive lepton pair production and to learn about their spin distributions provided they are polarized by a nonperturbative mechanism. The transverse polarization of the A, P(A), in pp ~ AX has already measured up to
27 August 1979
p± ~. 2 GeV/c at FNAL and ISR energies [13]. P(A)is about - 2 5 % and this large value could also be related to gluon spin properties [14]. Next, consider massive lepton pair production at p± = 0, where the classical Drell-Yan annihilation model including bremsstrahlung corrections can be applied [15]. Suppose one initial proton is longitudinally polarized, if one is able to measure the helicity of one outgoing lepton one can determine the following asymmetry: ]gDY doC~p - ff/TX) - do('~p do(~p -~'/~X) + do(pp
...
4--B
ta/zX),
(2)
uuX)
where ~ label the helicity of the proton and the muon. In terms of the quark and antiquark distributions this quantity reads ,2 ]~DY = ~'iei2 (Aqi(xl)qi(x2) - qi(x2)Aqi(xl))
Xie? {qi(xl)~i(x2) + qi(xz)~i(Xl)}
(3)
x 1 -x 2 X - x 1 +x 2 , where &/(x) = q+(x) - q - ( x ) is the difference of the quark distributions in a proton with helicity parallel and opposite to the proton helicity. The same def'mition holds for z~(x). Here x I refers to a quark (antiquark) from the polarized proton and x 2 refers to an antiquark (quark) from the other proton. The kinematic factor (x 1 - x2)/(x 1 + x2) comes from helicity conservation at the photon coupling in qCt -~ #/7 and says that ~DY vanishes when x F = x 1 - x 2, the Feynman x of the lepton pair, is zero (i.e. at 90 ° in the c.m.). From the behaviour of the distribution functions it is easy to see that for x F > 0 (i.e. x 1 > x 2 ) ~DY reflects the spin properties of the quarks and for x F < 0 (i.e. x I < x2) it reflects the spin properties of the antiquarks. We have calculated ~DY by using Aq (x) from refs. [3] and [4]. It has been argued that perturbative QCD provides a mechanism for the polarization of antiquarks [16] and this is what we have assumed for A~(x). The numerical results at 200 GeV/c are shown in figs. 2a,b by the solid lines. The dashed lines represent the asymmetry in the case where the antiquarks ,2 Although scaling violations require some Q2-dependence for the distribution functions, we neglect them for a rough estimate of ~DY. 405
Volume 85B, number 4
PHYSICS LETTERS I
I
I
(a)
P P--F/.1. X 2 0 0 GeV/c
27 August 1979 I
p ~-p.# x
(hi
2 0 0 GeV/c
M'= 50 GeV'
M' = 50 GeV'
KUTI - WEISSKOPF DISTRIBUTIONS
CARLITZ - KAUR DISTRIBUTIONS
0.5
,{
/jk /z z
I/IL
// /z s zz////
I -0.5
0
1
I
05
-05
XF
I 0
0,5
XF
Fig. 2. Theoretical evaluations of the proton spin-muon spin asymmetry ~DY (see text) for the/a~ pair of massM ~ 7 GeV at Plab = 200 GeV/c. (a) Quark distributions from ref. [31, (b) quark distributions from ref. [4]. are n o t polarized (i.e. A~ = 0). Polarization of the antiquarks gives a sizeable ~DY in the backward direction which is not very sensitive to the choice of the quark distributions. This choice affects only the values of ~DY for x F > 0 as expected. We have found that for the same lepton pair mass ~DY for x F < 0 decreases when the energy increases and this remains to be checked by future experiments. As a final remark, we strongly believe that polarization measurements in massive lepton pair production is an interesting field which may yield new insight into the dynamics of hadronic constituents. We are indebted to C. Bourrely for valuable discussions on the subject of this paper. We thank Ed. Berger for an interesting correspondence and M. Jacob for some helpful remarks.
References [1 ] R.D. Field, Plenary report on Dynamics of high energy reactions at the XIXth Intern. Conf. on High energy physics (Tokyo, 1978).
406
[2] M.J. Alguard et al., Phys. Rev. Lett. 41 (1978) 70. [3] J. Kuti and V.F. Weisskopf, Phys. Rev. D4 (1971) 3418, [4] R. Caflitz and J. Kaur, Phys. Rev. Lett. 38 (1977) 673, 1102; J. Kaur, Nucl. Phys. B128 (1977) 219. [5] For a recent review, see: E.L. Berger, invited paper at the Intern. Conf. at Vanderbilt University (March 1978), preprint ANL-HEP-PR-78-12. [6] R.J.N. PhilliPs, G.A. Ringland and R.P. Worden, Phys. Lett. 40B (1972) 239. [7] G.L. Kane, J. Pumplin and W. Repko, Phys. Rev. Lett. 41 (1978) 1689. [8] D. Sivers, Talk at the 3rd Intern. Symp. on High energy physics with polarized beams and targets (Argonne, October 1978), preprint ANL-HEP-CP-78-50. [9] D.M. Kaplan et al., Phys. Rev. Lett. 40 (1978) 435. [10] G. Altarelli, G. Parisi and R. Petronzio, Phys. Lett. 76B (1978) 356. [11 ] R. Petronzio, Proc. XIllth Rencontre de Moriond (March 1978), ed. Tran Than Van, p. 129. [12] C. Bourrely and J. Softer, Phys. Lett. 71B (1977) 330. [13] G. Bunce et al., Phys. Rev. Lett. 36 (1976) 1113; K. HeUer et al., Phys. Rev. Lett. 41 (1978) 607; S. Erhan et al., Phys. Lett. 82B (1979) 301. [14] G.L. Kane and Y.P. Yao, Nucl. Phys. B137 (1978) 313. [15] C.T. Sachrajda, Phys. Lett. 73B (1978) 185. [16] F. Close and D. Sivers, Phys. Rev. Lett. 39 (1977) 1116.