An analytic expression for the neutrino charged current structure function F sub 2 (x, Q sup 2) in deep inelastic scattering, consistent with quantum chromodynamics, is proposed. The calculated results are in good agreement with experiment

Aleem, F.

Saleem, M.

English

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168 HE 5.3-23
QCD ANALYSIS OF NEUTRINO CHARGED CURRENT STRUCTURE FUNCTION F2
IN DEEP INELASTIC SCATTERING
Mohammad Saleem
Centre for High Energy Physics
University of the Punjab
Lahore-20, Pakistan
and
The Institute for Basic Research
96 Prescott Street, Cambridge
Massachusetts 02138
U.S.A.
AND
Fazal-e-Aleem
Centre for High Energy Physics
University of the Punjab
Lahore-20, Pakistan.
ABSTRACT
An analytic expression for the neutrino
charged current structure function F2(x,Q2)
in deep inelastic scattering, consis£ent
with quantum chromodynamics, is proposed.
The calculated results are in good agree-
ment with experiment.
I. Introduction. Recently, the CCFRR group[l] has measured
the neutrino charged current structure functions. The data
were obtained using the Fermilab narrow band beam and the
Laboratory E neutrino detector[2-4]. The structure function
F2(x,Q2) extracted from the neutrino and antineutrino event
samples is plotted versus Q2 in Fig.1.
A number of attempts have been made to fit the data for
lepton-nucleon deep inelastic scattering by using QCD. The
analyses are based on fitting of Altarelli-Parisi (A-P) equ-
ations. For a fixed Q2_ 2
-QQ, the structure function F2 is assu-
med to b9 of a particular form, so as to give x dependence
consistent with experimental data at QS. The A-P equations
are then solved numerically to yield r_sults which are con-
sistent with experiment. The arbitrariness of Q2 is, however,
restricted to sufficiently large values of Q2 fSr which per-
turbative calculations can be trusted. In th_s paper, an ana-
lytic expression for F2(x,Q=), Consistent with QCD, is propo-
sed.
2. Calculations and Discussion. According to QCD, the sing-
let structure function F2(x,Q2 ) and its momenta are related
to each other[5] by the equation
_d n
llxn-2o F2S(x'Q2)dx = _2AS[in(Q2/A2)]sn s (I)
The function F2(x,Q2 ) can not be expressed•as a product of
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169 HE 5.3-23
two functions, one depending upon x only and the other depend-
ing upon Q2 alone, because then the function of Q2 alone as
evaluated by using left hand side of equation(1) would be inde-
pendent of n. This is not valid because right hand side of
equation(1) depends upon n. To incorporate this n dependence,
we assume that
-dE
F2(x,Q2) = A(1-x)e
where a = [In(Q2/A2)] 0"747
For large value of Q2, this expression when substituted in
equation(1) gives results which are consistent with QCD.
A very good agreement with experimental data for Q2>5
(GeV/c) 2 is obtained by using A=2, A=0.5GeV/c.
I Fig.1 shows experimental
- _ data as well as theoretical pre-
I_ : x_45 l dictions for Fp(x,Q 2) plotted
- - • ] against Q2 at _ixed values of x.i ×=_ The agreement is quite satisfac-
I ;- • - • tory and confirms our assumptioni ×=.15 about the form of F2(x,Q2).
1 t _X'.25
F2 3. Conclusion. Quantum chromo-
_ dynamics is now believed to bei _X_'3s • the promising theory of strong
I "L-_-J_L._X o_S I interactions. The perturbativecalculations of cross sections
i_ ...... x-s5 _ for deep inelastic scattering
based on QCD are confirmed
1 experimentally. However, nume-
i ""_4"-_ x''65 rical integration has to be
.'T'L'i_"L-L'IX'a5 I performed to obtain various• 01 . .., .... L , ;....._., ',, .... ,
• _0 i00 i_0 results. We have proposed a
_GeV/_)2 simple analytic expression for
Fig. 1 The str_cture func- the structure function F2(x,Q2).
tion F2 extracted from the This expression yields results
CCFRR data versus Q2 for which are consistent with experi-
fixed values of x. The solid mart.
curves represent the predic-
tions of the model described 4. Acknowledgement. The finan-
in the text. cial assistance from the Pakistan
Science Foundation under contract
No.P-PU/Phys(11/2) is gratefully
acknowledged.
170 HE 5.3-23
References
1. R.E.Blair et al., Preprint UR-831, C00-3065-339(1983).
2. P.Rapidis et al., Proceedings of the Summer Institute on
Particle Physics, ed. A.Mosher, p.641, SLAC, Standford,
California (1982)..
3. R.Blair, Total Cross Section and -Distribution Measure-
ments for Muon-Type Neutrinos and Antineutrinos in Iron,
Ph.D. Thesis(1982), California Institute of Technology,
Pasadena, California.
4. J.Lee, Measurements of u N Charged Current Cross Sections
from Eu=25 GeV to Eu=360_GeV, Ph.D. Thesis(1980), Cali-
fornia Institute of Technology, Pasadena, California.
5. A.J.Buras, Rev.Mod. Phys.5__2, (1980)199.


QCD analysis of neutrino charged current structure function F2 in deep inelastic scattering

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