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Determination of parton sea from μ pair production data
Volume 73B, number 1
PHYSICS LETTERS
30 January 1978
DETERMINATION OF PARTON SEA FROM/~ PAIR PRODUCTION DATA* V. BARGER
PhysicsDepartment, Universityof Wisconsin,Madison, I4'153706, USA and R.J.N. PHILLIPS
Rutherford Laboratory, Chilton, Didcot, Oxon, England Received 21 October 1977
We describe a determination of the parton sea from pN ~ g+~-X via the Drell-Yan formula, making a minimum of theoretical assumptions. The method requires deep inelastic eN, gN structure functions to be extrapolated to suitable values of x, Q2. We determine the non-strange sea component fi(x, Q2) + d-(x, Q2) between x = 0.2 and 0.5 with Q2 =x2s, and s = 750 GeV2 .
There has been great interest in comparing massive lepton pair production data [1 4 ] with the D r e l l - Y a n formula, based on the parton model [ 5 - 1 4 ] . Usually these comparisons start with a particular parton parametrization, previously adjusted to fit deep inelastic lepton scattering, and simply examine its predictions. In the present letter we suggest that this procedure should be inverted; the massive-pair production and deep inelastic scattering data can be combined directly, with a minimum o f theoretical assumptions or prejudices, to determine the nonstrange p a t t o n sea components in the nucleon if(x, Q2) + d(x, Q2) at particular values o f x and Q2. We illustrate this approach with presently available data in the range x = 0 . 2 - 0 . 5 , with Q2 = 750x 2 in GeV 2. The D r e l l - Y a n formula for AB ~ / a + / a - X inclusive pair production is
do 8na2x+x dydm 9m 3
~ k
e2 A X B X qk( +)q~-( -)'
(1)
* Work supported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and in part by the Energy Research and Development Administration under contract EY-76-C-02-0881, COO-881-4.
where y and m are the rapidity and invariant mass o f the pair. The sum runs over all flavors o f quarks and antiquarks (three colors assumed), q~(x) is the fractional m o m e n t u m distribution of flavor k in particle A, x_+ = exp(-+y) m / ~ , and s = (PA +PB) 2 is the c.m. energy squared. This formula ignores transverse pair effects of order p2/m2, which is at most a few percent for the range m > 6 GeV considered here; it also ignores Fermi motion in the target nucleus. The quark distributions in eq. (1) can be written in terms o f valence distributions u - ~, d - d and sea distributions ~ = d = ~, g = s = f s ~, E = c =fe~, where the f a c t o r s f s a n d f c describe the probable suppression o f strange and charmed sea components. Furthermore, we can express the valence distributions in terms o f electromagnetic structure functions vW~p , vB~2nminus sea contributions. Eq. (1) then gives a relation between sea terms (at x+ and x ) and measurable quantities do/dydm, vW~p, v~2n. At y = 0 this relation is particularly simple: for a proton beam on a nuclear target (with Z protons, N neutrons, N + Z = A ) the cross section per nucleon has the form
91
Volume 73B, number 1 0.5
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30 January 1978
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Fig. ]. Typical examples of the extrapolation of electromagnetic structure functions vW2,at fixed x, to the required values of Q2. do ( y = 0 ) = 8 7 r o t 2 x ~ { _ ~ dydm 9m 3
vW2ep+Nvw~n
-z}[10 - ( f s - 1)2 - 4 ( f c - 1)21x~} ' t
(2)
where ~(x) and vW2(x) are both evaluated at x = m/~. Hence ~(x) can be determined. In the range x = 0 . 2 - 0 . 5 covered by the best high-energy data [4], the ~vW2 92
terms in eq. (2) dominate over the ~2 terms, so the solution for ~ is rather insensitive to the strangeness and charm suppression factors fs and re- In the follow. hag we take fs = 1, fc = 0. Thus, so far we have ignored scalebreaking and assumed that ~ and vW2 depend on x alone. However, scalebreaking is an established fact in deep inelastic eN and oN scattering, and corresponding corrections
to the Drell-Yan formalism may be expected. In the quark-parton language, the parton distributions become functions of the invariant mass of the current Q2 as well as x. In ref. [ 11 ] it is argued that the parton distributions and pW 2 in eqs. (1), (2) should be those corresponding to spacelike Q2 = m 2 (see also refs. [ 1 5 - 1 8 ] ) ; in the following we accept this ansatz. We can therefore use eq. (2) and input experimental values of da/dydm and vW2(x, Q2), extrapolated where necessary to Q2 = m 2 : the output is the nonstrange sea distribution ~(x, Q2) at the corresponding values o f x = m/vrs- and Q2 = m 2. To illustrate this approach to determining ~ we have taken the latest pair-production data from ref. [4], in the range 6 < m < 13 GeV, with 400 GeV protons on Cu and Pt targets; i.e., s = 750 GeV 2, Z/A = 0.46 and 0.40. For present purposes we set Z/A = 0.42. For simplicity and to eliminate the "I"(9.5) resonance effects, we represent these data by the empirical continuum fit do/dydm(y = 0) = 1.26 e x p ( - 0 . 9 5 3 m ) nb/GeV/nucleon quoted by the experimenters [4]. The error on this formula has been estimated at each m from the experimental event distribution. Electromagnetic structure functions ul# 2 from refs. [19,20] have been extrapolated at fixed x to the required value of Q2 = m 2 = x,s, assuming a simple power dependence [21] on Q2; the coefficient and power are fitted independently at each x-value, and some typical results are shown in fig. 1. Hence values ofx~(x, Q~) have been extracted, using eq. (2): the results at a representative range of values are given in table 1. Systematic errors resulting from the extrapolation o f uW2 cannot easily be estimated. If initially we neglect the Q2.dependence of ~, we may try to compare our results with the popular scaling parameterization x~ = a(1 - x) b, where a and b Table 1 Non-strange sea values x~ determined from eq. (2), using pair production data at s = 750 GeV 2 . x
Q2 (GeV 2)
0.25 0.27
47 54
0.30 0.33 0.40 0.42
68 82 120 131
30 January 1978
PHYSICS LETTERS
Volume 73B, number 1
x~(x, Q2) 0.018 0.017
± 0.001 ± 0.002
0.011 ± 0.001 0.0073 ± 0.0009 0.0030 +-0.0007 0.0023 -+0.0007
are adjustable parameters. Various models use different powers b; ref. [22] fits deep inelastic scattering data with x~ = 0.15(1 - x ) 9, while ref. [6] takes x~ = 0.2(1 - x) 7, where the power b = 7 comes from quark counting arguments. Recently it has been argued that the leading power should be b = 5 instead [23]. It is interesting therefore to plot x~ versus (1 - x ) on log-log scales, to test the simple power parameterization above. Fig. 2 shows our raw results from table 1 plotted in this way, compared with the parameterization mentioned from refs. [6,22]. Neglecting Q2. dependencej the results in table 1 suggest a sea x~(x) = 0.19(1 - x) 8. There is independent evidence on the sea near x = 0. Recent measurements [20] give uW~p = 0.36 -+ 0.05 at x = 0.005 and Q2 = 2 GeV 2, and hence x~(x -~ 0, Q2 = 2) = 0.27 +- 0.04 (neglecting charm [24] because Q2 ~ rn~ ). If we ignore Q2-dependence, this value and our present results would be consistent with a Qz (GeV)Z 17s Iso ~25 Ioo 75
50
25
x~ (x)=0.20(I-x) 7
O'102 (x)=~ I()"~ ~xg(xl=O.15(I-x)
0.5
016
017
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0'.8
019
1,0
(t-x) Fig. 2. L o g - l o g plot of x~ versus 1 - x. The x > 0.2 points shown are our results from table 1, simply neglecting possible Q2-dependence. The straight lines are the parameterizations x~ = 0.15(1 - x) 9 from ref. [22] and x~ = 0.20(1 - x) 7 from ref. [6], and the fit x~ = 0.19(1 - x) s to the results of table 1. The point at x = 0.005 is determined directly from recent vlC~P data [20] at Q2 = 2 GeV 2.
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Volume 73B, number 1
PHYSICS LETTERS
straight line in fig. 2, given by x~(x) = 0.26(1 - x) 9. The Q2-dependence of ~ is probably not negligible, however, judging from the observed nonscaling of structure functions and the explicit Q2-dependence predicted by models based on asymptotically free gauge theories [ 2 5 - 2 9 ] . To illustrate such effects, we have taken the Q2.dependence of the sea from the calculations of Hinchliffe and Llewellyn Smith [ 11 ], and used it to renormalize our results from table 1 to a common value Q2 = 2 GeV 2 : see fig. 3. The effect is to make the distribution rather flatter, compatible with x~ = 0.19(1 - x ) 6. As another example we have taken the prescription o f Perkins et al. [21 ]
x~(x, Q2) = f(x)(Q2)0.25 - x ,
(3)
used to empirically describe the Q2-dependence of vW2; the Q~-dependence o f eq. (3) is similar to the asymptotic freedom parametrization of ref. [26], for the Q 2 range of interest here. This leads to the result x~(x, Q2 = 2) = 0.08(1 - x) 5 , also shown in fig. 3.
I
0.5
X
0.4 0.3 0.2 0.1 0 i
i
i
i
sx((x,2)=~ O.1?9(t_x)6
10-I tM ii
~ o ~o-2 x
EXTRAPOLATING TO Q~'=2
to-~,
I0 -4
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0.5
FOLLOWING REF. It FOLLOWING REF. 21,26
These results together with the small x sea determination, imply that the shape ofx~ may be flatter for x > 0.2 than at small x. Clearly the Q2 dependence of is crucially important in interpreting results of DrellYan analyses. It can be probed directly by making measurements at different energies s. In conclusion, we emphasize the following points. (i) Our approach uses the minimum of theoretical assumptions, but some assumptions are inevitable, in particular the Drell-Yan formula itself and the appropriate Q2 for vW2 and ~. (ii) If the prescription of evaluating v14/2 and ~ at the appropriate Q2 in the Drell-Yan formula is valid, then the slope ofx~ at fixed Q2 may be flatter than previously supposed, such as x~ ~ (1 - x) 6 or x~ ~ (1 - x ) 5 at Q 2 _ 2, approaching the prediction o f ref. [23] (iii) The dcr/dydm data ofref. [4] were taken on Cu and Pt targets and corrected to cross sections per nucleon by assuming a linear A-dependence. If in fact the dependence deviates [30] toward A 1 - e at the smaller m-values, the results for ~ should be increased correspondingly at small x. The present experimental limit o n A dependence [4] is e = 0.05 + 0.15 for m ~ > 5.5 GeV. (iv) There are rather few ways to study parton sea components directly. If NN ~ ~kX proceeds by c~ fusion, it probes the charm sea [10]. Antineutrino dimuons, assuming they are produced via charm, offer a measure [31 ] of the strange quark sea in the small x region where it is substantial. Antineutrino single muon distributions probe the nonstrange sea in the y ~ 1 limit [32]. The Drell-Yan approach - if valid offers an exceptionally good way to measure the nonstrange sea ~ (x, Q 2 ) + if(x, Q 2 ) at relatively large xvalues, and perhaps ultimately to establish the leading ( 1 - x)-dependence. Measurements at different energies s can help to determine the O2.dependence. We thank G. Weller for help with the computations and A.J. Buras for correspondence.
I
I
I
I
o.6
o.z
0.8
0.9
t.o
(l-x)
Fig. 3. Log-log plot of x~ versus 1 - x. The points shown are our results from table 1, corrected to Q2 = 2 GeV2 according to reL [11] or refs. [21,26]. The straight lines are approximate fits to these points, x~ = 0.19(1 - x) 6 and x~ = 0.08(1 - x) s . The point at x = 0.005 is determined directly from recent vl¢~up data [20] at Q2 = 2 GeV2. 94,
30 January 1978
Postscript. Revised experimental results [33] change the continuum distribution to do/dydm(y = 0) = 2.60 e x p ( - 0 . 9 8 m ) nb/GeV/nucleon. With this change our results for x~ in table 1 are multiplied by 2.06 exp(-0.90x) and the linear fits in figs. 2 and 3 are multiplied by 2.0(1 - x ) 0"65 , approximately.
Volume 73B, number 1
PHYSICS LETTERS
References [1] J. Christenson et al., Phys. Rev. D8 (1973) 2016. [2] M. Binkley et al., Phys. Rev. Lett. 37 (1976) 571,574. [3] K.J. Anderson et al., Phys. Rev. Lett. 37 (1976) 799; J.G. Branson et al., Phys. Rev. Lett. 38 (1977) 1334; D. Antreasyan et al., Phys. Rev. Lett. 39 (1977) 906. [4] D.C. Horn et al., Phys. Rev. Lett. 37 (1976) 1374; S.W. Herb et al., Phys. Rev. Lett. 39 (1977) 252; W.R. Innes et al., Phys. Rev. Lett. 39 (1977) 1240. [5] S.D. Drell and T.M. Yan, Phys. Rev. Lett. 25 (1970) 316. [6] G. Chu and J.F. Gunion, Phys. Rev. D10 (1974) 3672. [7] G.R. Farrar, Nucl. Phys. B77 (1974) 429. [8] J. Finjord and F. Ravndal, Phys. Lett. 62B (1976) 438. [9] J. Okada et al., Nuovo Cimento Lett. 16 (1976) 555. [10] A. Donnachie and P.V. Landshoff, Nucl. Phys. Bl12 (1976) 233. [1 I] I. Hinchliffe and C.H. Llewellyn Smith, Phys. Lett. 66B (1976) 281; Nucl. Phys. B128 (1977) 93. [12] L.M. Lederman and B.G. Pope, Phys. Lett. 66B (1976) 486. [13] C. Quigg, Rev. Mod. Phys. 49 (1977) 297. [14] R.F. Peierls et al., BNL-22628 (1977). [15] J.C. Polkinghorne, Nucl. Phys. B116 (1976) 347. [16] J.B. Kogut, Phys. Lett. 65B (1976) 377.
30 January 1978
[17] [18] [19] [20]
D.E. Soper, Phys. Rev. Lett. 38 (1977) 461. H.D. Politzer, Nucl. Phys. B129 (1977) 301. E.M. Riordan et al., SLAC-PUB-1634 (1975). H.L. Anderson et al., Phys. Rev. Lett. 37 (1976) 4; 38 (1977) 1450; N. Booth, T. Quirk and L.C. Myrianthopoulos, private communication. [21] D.H. Perkins et al., Phys. Lett. 67B (1977) 347. [22] V. Barger and R.J.N. Phillips, Nucl. Phys. B73 (1974) 269. [23] F.E. Close and D. Sivers, ANL-HEP-PR-77-49 (1977). [24] F.E. Close and D.M. Scott, Phys. Lett. 69B (1977) 173. [25] G. Parisi and R. Petronzio, Phys. Lett. 62B (1976) 331; G. Altarelli et al., Phys. Lett. 63B (1976) 183. [26] M. Gluck and E. Reya, Phys. Rev. D14 (1976) 3034; Mainz preprints MZ-TH-76-10, MZ-TH-77-3. [27] R.M. Barnett et al., Phys. Rev. Lett. 37 (1976) 1313. [28] A. De Rtljula et al., Ann. Phys. 103 (1977) 315. [29] A.J. Buras, Nucl. Phys. B125 (1977) 125; A.J. Buras and K.J.F. Gaemers, CERN-TH-2322 (1977). [30] G.R. Farrar, Phys. Lett. 56B (1975) 185. [31] V. Barger et al., Phys. Rev. D13 (1976) 2511. [32] J. Steinberger, Lectures at Carg~se Summer Institute (1977). [33] D.M. Kaplan et al., Stony Brook-Fermilab-Columbia preprint (December 1977).
95
PHYSICS LETTERS
30 January 1978
DETERMINATION OF PARTON SEA FROM/~ PAIR PRODUCTION DATA* V. BARGER
PhysicsDepartment, Universityof Wisconsin,Madison, I4'153706, USA and R.J.N. PHILLIPS
Rutherford Laboratory, Chilton, Didcot, Oxon, England Received 21 October 1977
We describe a determination of the parton sea from pN ~ g+~-X via the Drell-Yan formula, making a minimum of theoretical assumptions. The method requires deep inelastic eN, gN structure functions to be extrapolated to suitable values of x, Q2. We determine the non-strange sea component fi(x, Q2) + d-(x, Q2) between x = 0.2 and 0.5 with Q2 =x2s, and s = 750 GeV2 .
There has been great interest in comparing massive lepton pair production data [1 4 ] with the D r e l l - Y a n formula, based on the parton model [ 5 - 1 4 ] . Usually these comparisons start with a particular parton parametrization, previously adjusted to fit deep inelastic lepton scattering, and simply examine its predictions. In the present letter we suggest that this procedure should be inverted; the massive-pair production and deep inelastic scattering data can be combined directly, with a minimum o f theoretical assumptions or prejudices, to determine the nonstrange p a t t o n sea components in the nucleon if(x, Q2) + d(x, Q2) at particular values o f x and Q2. We illustrate this approach with presently available data in the range x = 0 . 2 - 0 . 5 , with Q2 = 750x 2 in GeV 2. The D r e l l - Y a n formula for AB ~ / a + / a - X inclusive pair production is
do 8na2x+x dydm 9m 3
~ k
e2 A X B X qk( +)q~-( -)'
(1)
* Work supported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and in part by the Energy Research and Development Administration under contract EY-76-C-02-0881, COO-881-4.
where y and m are the rapidity and invariant mass o f the pair. The sum runs over all flavors o f quarks and antiquarks (three colors assumed), q~(x) is the fractional m o m e n t u m distribution of flavor k in particle A, x_+ = exp(-+y) m / ~ , and s = (PA +PB) 2 is the c.m. energy squared. This formula ignores transverse pair effects of order p2/m2, which is at most a few percent for the range m > 6 GeV considered here; it also ignores Fermi motion in the target nucleus. The quark distributions in eq. (1) can be written in terms o f valence distributions u - ~, d - d and sea distributions ~ = d = ~, g = s = f s ~, E = c =fe~, where the f a c t o r s f s a n d f c describe the probable suppression o f strange and charmed sea components. Furthermore, we can express the valence distributions in terms o f electromagnetic structure functions vW~p , vB~2nminus sea contributions. Eq. (1) then gives a relation between sea terms (at x+ and x ) and measurable quantities do/dydm, vW~p, v~2n. At y = 0 this relation is particularly simple: for a proton beam on a nuclear target (with Z protons, N neutrons, N + Z = A ) the cross section per nucleon has the form
91
Volume 73B, number 1 0.5
PHYSICS LETTERS .
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30 January 1978
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Fig. ]. Typical examples of the extrapolation of electromagnetic structure functions vW2,at fixed x, to the required values of Q2. do ( y = 0 ) = 8 7 r o t 2 x ~ { _ ~ dydm 9m 3
vW2ep+Nvw~n
-z}[10 - ( f s - 1)2 - 4 ( f c - 1)21x~} ' t
(2)
where ~(x) and vW2(x) are both evaluated at x = m/~. Hence ~(x) can be determined. In the range x = 0 . 2 - 0 . 5 covered by the best high-energy data [4], the ~vW2 92
terms in eq. (2) dominate over the ~2 terms, so the solution for ~ is rather insensitive to the strangeness and charm suppression factors fs and re- In the follow. hag we take fs = 1, fc = 0. Thus, so far we have ignored scalebreaking and assumed that ~ and vW2 depend on x alone. However, scalebreaking is an established fact in deep inelastic eN and oN scattering, and corresponding corrections
to the Drell-Yan formalism may be expected. In the quark-parton language, the parton distributions become functions of the invariant mass of the current Q2 as well as x. In ref. [ 11 ] it is argued that the parton distributions and pW 2 in eqs. (1), (2) should be those corresponding to spacelike Q2 = m 2 (see also refs. [ 1 5 - 1 8 ] ) ; in the following we accept this ansatz. We can therefore use eq. (2) and input experimental values of da/dydm and vW2(x, Q2), extrapolated where necessary to Q2 = m 2 : the output is the nonstrange sea distribution ~(x, Q2) at the corresponding values o f x = m/vrs- and Q2 = m 2. To illustrate this approach to determining ~ we have taken the latest pair-production data from ref. [4], in the range 6 < m < 13 GeV, with 400 GeV protons on Cu and Pt targets; i.e., s = 750 GeV 2, Z/A = 0.46 and 0.40. For present purposes we set Z/A = 0.42. For simplicity and to eliminate the "I"(9.5) resonance effects, we represent these data by the empirical continuum fit do/dydm(y = 0) = 1.26 e x p ( - 0 . 9 5 3 m ) nb/GeV/nucleon quoted by the experimenters [4]. The error on this formula has been estimated at each m from the experimental event distribution. Electromagnetic structure functions ul# 2 from refs. [19,20] have been extrapolated at fixed x to the required value of Q2 = m 2 = x,s, assuming a simple power dependence [21] on Q2; the coefficient and power are fitted independently at each x-value, and some typical results are shown in fig. 1. Hence values ofx~(x, Q~) have been extracted, using eq. (2): the results at a representative range of values are given in table 1. Systematic errors resulting from the extrapolation o f uW2 cannot easily be estimated. If initially we neglect the Q2.dependence of ~, we may try to compare our results with the popular scaling parameterization x~ = a(1 - x) b, where a and b Table 1 Non-strange sea values x~ determined from eq. (2), using pair production data at s = 750 GeV 2 . x
Q2 (GeV 2)
0.25 0.27
47 54
0.30 0.33 0.40 0.42
68 82 120 131
30 January 1978
PHYSICS LETTERS
Volume 73B, number 1
x~(x, Q2) 0.018 0.017
± 0.001 ± 0.002
0.011 ± 0.001 0.0073 ± 0.0009 0.0030 +-0.0007 0.0023 -+0.0007
are adjustable parameters. Various models use different powers b; ref. [22] fits deep inelastic scattering data with x~ = 0.15(1 - x ) 9, while ref. [6] takes x~ = 0.2(1 - x) 7, where the power b = 7 comes from quark counting arguments. Recently it has been argued that the leading power should be b = 5 instead [23]. It is interesting therefore to plot x~ versus (1 - x ) on log-log scales, to test the simple power parameterization above. Fig. 2 shows our raw results from table 1 plotted in this way, compared with the parameterization mentioned from refs. [6,22]. Neglecting Q2. dependencej the results in table 1 suggest a sea x~(x) = 0.19(1 - x) 8. There is independent evidence on the sea near x = 0. Recent measurements [20] give uW~p = 0.36 -+ 0.05 at x = 0.005 and Q2 = 2 GeV 2, and hence x~(x -~ 0, Q2 = 2) = 0.27 +- 0.04 (neglecting charm [24] because Q2 ~ rn~ ). If we ignore Q2-dependence, this value and our present results would be consistent with a Qz (GeV)Z 17s Iso ~25 Ioo 75
50
25
x~ (x)=0.20(I-x) 7
O'102 (x)=~ I()"~ ~xg(xl=O.15(I-x)
0.5
016
017
s
0'.8
019
1,0
(t-x) Fig. 2. L o g - l o g plot of x~ versus 1 - x. The x > 0.2 points shown are our results from table 1, simply neglecting possible Q2-dependence. The straight lines are the parameterizations x~ = 0.15(1 - x) 9 from ref. [22] and x~ = 0.20(1 - x) 7 from ref. [6], and the fit x~ = 0.19(1 - x) s to the results of table 1. The point at x = 0.005 is determined directly from recent vlC~P data [20] at Q2 = 2 GeV 2.
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straight line in fig. 2, given by x~(x) = 0.26(1 - x) 9. The Q2-dependence of ~ is probably not negligible, however, judging from the observed nonscaling of structure functions and the explicit Q2-dependence predicted by models based on asymptotically free gauge theories [ 2 5 - 2 9 ] . To illustrate such effects, we have taken the Q2.dependence of the sea from the calculations of Hinchliffe and Llewellyn Smith [ 11 ], and used it to renormalize our results from table 1 to a common value Q2 = 2 GeV 2 : see fig. 3. The effect is to make the distribution rather flatter, compatible with x~ = 0.19(1 - x ) 6. As another example we have taken the prescription o f Perkins et al. [21 ]
x~(x, Q2) = f(x)(Q2)0.25 - x ,
(3)
used to empirically describe the Q2-dependence of vW2; the Q~-dependence o f eq. (3) is similar to the asymptotic freedom parametrization of ref. [26], for the Q 2 range of interest here. This leads to the result x~(x, Q2 = 2) = 0.08(1 - x) 5 , also shown in fig. 3.
I
0.5
X
0.4 0.3 0.2 0.1 0 i
i
i
i
sx((x,2)=~ O.1?9(t_x)6
10-I tM ii
~ o ~o-2 x
EXTRAPOLATING TO Q~'=2
to-~,
I0 -4
F
0.5
FOLLOWING REF. It FOLLOWING REF. 21,26
These results together with the small x sea determination, imply that the shape ofx~ may be flatter for x > 0.2 than at small x. Clearly the Q2 dependence of is crucially important in interpreting results of DrellYan analyses. It can be probed directly by making measurements at different energies s. In conclusion, we emphasize the following points. (i) Our approach uses the minimum of theoretical assumptions, but some assumptions are inevitable, in particular the Drell-Yan formula itself and the appropriate Q2 for vW2 and ~. (ii) If the prescription of evaluating v14/2 and ~ at the appropriate Q2 in the Drell-Yan formula is valid, then the slope ofx~ at fixed Q2 may be flatter than previously supposed, such as x~ ~ (1 - x) 6 or x~ ~ (1 - x ) 5 at Q 2 _ 2, approaching the prediction o f ref. [23] (iii) The dcr/dydm data ofref. [4] were taken on Cu and Pt targets and corrected to cross sections per nucleon by assuming a linear A-dependence. If in fact the dependence deviates [30] toward A 1 - e at the smaller m-values, the results for ~ should be increased correspondingly at small x. The present experimental limit o n A dependence [4] is e = 0.05 + 0.15 for m ~ > 5.5 GeV. (iv) There are rather few ways to study parton sea components directly. If NN ~ ~kX proceeds by c~ fusion, it probes the charm sea [10]. Antineutrino dimuons, assuming they are produced via charm, offer a measure [31 ] of the strange quark sea in the small x region where it is substantial. Antineutrino single muon distributions probe the nonstrange sea in the y ~ 1 limit [32]. The Drell-Yan approach - if valid offers an exceptionally good way to measure the nonstrange sea ~ (x, Q 2 ) + if(x, Q 2 ) at relatively large xvalues, and perhaps ultimately to establish the leading ( 1 - x)-dependence. Measurements at different energies s can help to determine the O2.dependence. We thank G. Weller for help with the computations and A.J. Buras for correspondence.
I
I
I
I
o.6
o.z
0.8
0.9
t.o
(l-x)
Fig. 3. Log-log plot of x~ versus 1 - x. The points shown are our results from table 1, corrected to Q2 = 2 GeV2 according to reL [11] or refs. [21,26]. The straight lines are approximate fits to these points, x~ = 0.19(1 - x) 6 and x~ = 0.08(1 - x) s . The point at x = 0.005 is determined directly from recent vl¢~up data [20] at Q2 = 2 GeV2. 94,
30 January 1978
Postscript. Revised experimental results [33] change the continuum distribution to do/dydm(y = 0) = 2.60 e x p ( - 0 . 9 8 m ) nb/GeV/nucleon. With this change our results for x~ in table 1 are multiplied by 2.06 exp(-0.90x) and the linear fits in figs. 2 and 3 are multiplied by 2.0(1 - x ) 0"65 , approximately.
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References [1] J. Christenson et al., Phys. Rev. D8 (1973) 2016. [2] M. Binkley et al., Phys. Rev. Lett. 37 (1976) 571,574. [3] K.J. Anderson et al., Phys. Rev. Lett. 37 (1976) 799; J.G. Branson et al., Phys. Rev. Lett. 38 (1977) 1334; D. Antreasyan et al., Phys. Rev. Lett. 39 (1977) 906. [4] D.C. Horn et al., Phys. Rev. Lett. 37 (1976) 1374; S.W. Herb et al., Phys. Rev. Lett. 39 (1977) 252; W.R. Innes et al., Phys. Rev. Lett. 39 (1977) 1240. [5] S.D. Drell and T.M. Yan, Phys. Rev. Lett. 25 (1970) 316. [6] G. Chu and J.F. Gunion, Phys. Rev. D10 (1974) 3672. [7] G.R. Farrar, Nucl. Phys. B77 (1974) 429. [8] J. Finjord and F. Ravndal, Phys. Lett. 62B (1976) 438. [9] J. Okada et al., Nuovo Cimento Lett. 16 (1976) 555. [10] A. Donnachie and P.V. Landshoff, Nucl. Phys. Bl12 (1976) 233. [1 I] I. Hinchliffe and C.H. Llewellyn Smith, Phys. Lett. 66B (1976) 281; Nucl. Phys. B128 (1977) 93. [12] L.M. Lederman and B.G. Pope, Phys. Lett. 66B (1976) 486. [13] C. Quigg, Rev. Mod. Phys. 49 (1977) 297. [14] R.F. Peierls et al., BNL-22628 (1977). [15] J.C. Polkinghorne, Nucl. Phys. B116 (1976) 347. [16] J.B. Kogut, Phys. Lett. 65B (1976) 377.
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