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the production of lepton pairs in hadron collisions @xmath3 proceeds through an intermediate virtual photon and its subsequent leptonic decay .
traditionally , interest in this drell - yan process has concentrated on lepton pairs with large mass @xmath0 which allows for the application of perturbative qcd and the extraction of the antiquark density in the proton @xcite .
prompt photon production @xmath4 can be calculated in perturbative qcd if the transverse momentum @xmath1 of the photon is sufficiently large .
this process then provides essential information on the gluon density in the proton at large @xmath5 @xcite .
unfortunately , it suffers from considerable fragmentation , isolation , and intrinsic transverse momentum uncertainties .
alternatively , the gluon density can be constrained from the production of jets with large transverse momentum at hadron colliders @xcite , which however suffers from ambiguous information coming from different experiments and colliders .    in this paper
we demonstrate that , like prompt photon production , lepton pair production is dominated by quark - gluon scattering in the region @xmath2 .
this leads to sensitivity to the gluon density in kinematical regimes that are accessible both at collider and fixed target experiments while eliminating the theoretical and experimental uncertainties .    in sec .
[ sec:2 ] , we briefly discuss the relationship between virtual and real photon production in hadron collisions in next - to - leading order qcd . in sec .
[ sec:3 ] we present our numerical results , and sec .  [ sec:4 ] contains a summary .
in leading order ( lo ) qcd , two partonic subprocesses contribute to the production of virtual and real photons with non - zero transverse momentum : @xmath6 and @xmath7 .
the cross section for lepton pair production is related to the cross section for virtual photon production through the leptonic branching ratio of the virtual photon @xmath8 .
the virtual photon cross section reduces to the real photon cross section in the limit @xmath9 .
the next - to - leading order ( nlo ) qcd corrections arise from virtual one - loop diagrams interfering with the lo diagrams and from real emission diagrams . at this order
processes with incident gluon pairs @xmath10 , quark pairs @xmath11 , and non - factorizable quark - antiquark @xmath12 processes contribute also .
singular contributions are regulated in @xmath13 dimensions and removed through @xmath14 renormalization , factorization , or cancellation between virtual and real contributions .
an important difference between virtual and real photon production arises when a quark emits a collinear photon .
whereas the collinear emission of a real photon leads to a @xmath15 singularity that has to be factorized into a fragmentation function , the collinear emission of a virtual photon gives a finite logarithmic contribution since it is regulated naturally by the photon virtuality @xmath0 . in the limit @xmath9 the nlo virtual photon cross section reduces to the real photon cross section if this logarithm is replaced by a @xmath15 pole .
a more detailed discussion can be found in @xcite .
the situation is completely analogous to hard photoproduction where the photon participates in the scattering in the initial state instead of the final state . for real photons ,
one encounters an initial - state singularity that is factorized into a photon structure function . for virtual photons ,
this singularity is replaced by a logarithmic dependence on the photon virtuality @xmath0 @xcite .
in this section we present numerical results for the production of lepton pairs in @xmath16 collisions at the tevatron with center - of mass energy @xmath17 and 2.0 tev and in @xmath18 collisions at fixed target experiments with @xmath19 gev .
we analyze the invariant cross section @xmath20 averaged over the rapidity interval -1.0 @xmath21 1.0 at the tevatron and averaged over the scaled longitudinal momentum interval 0.1 @xmath22 0.3 at fixed target experiments .
we integrate the cross section over various intervals of @xmath0 and plot it as a function of the transverse momentum @xmath1 .
our predictions are based on a nlo qcd calculation @xcite and are evaluated in the @xmath14 renormalization scheme .
the renormalization and factorization scales are set to @xmath23 .
if not stated otherwise , we use the cteq4 m parton distributions @xcite and the corresponding value of @xmath24 in the two - loop expression of @xmath25 with four flavors ( five if @xmath26 ) . the drell - yan factor @xmath8 for the decay of the virtual photon into a lepton pair
is included in all numerical results .    in fig .
[ fig:1 ] we display the nlo qcd cross section for lepton pair    ( 7.6,10.5 )    production at the tevatron at @xmath17 tev as a function of @xmath1 for four regions of @xmath0 .
the regions of @xmath0 have been chosen carefully to avoid resonances , _
i.e.  _ between the @xmath27 and the @xmath28 resonances , between the @xmath28 and the @xmath29 resonances , above the @xmath29 s , and a high mass region .
the cross section falls both with the mass of the lepton pair @xmath0 and , more steeply , with its transverse momentum @xmath1 .
unfortunately , no data are available yet from the cdf and d0 experiments .
however , data exist for prompt photon production out to @xmath30 gev ,
where the cross section is about @xmath31 pb / gev@xmath32 . it should therefore be possible to analyze run i data for lepton pair production up to at least @xmath33 gev where one can probe the parton densities in the proton up to @xmath34 .
the ua1 collaboration measured the transverse momentum distribution of lepton pairs at @xmath35 gev up to @xmath36 @xcite , and their data agree well with our theoretical results @xcite .
the fractional contributions from the @xmath37 and @xmath38 subprocesses up through nlo are shown in fig .
[ fig:2 ] .
it is evident from fig .
[ fig:2 ]    ( 7.6,10.5 )    that the @xmath37 subprocess is the most important subprocess as long as @xmath39 .
the dominance of the @xmath37 subprocess diminishes somewhat with @xmath0 , dropping from over 80 % for the lowest values of @xmath0 to about 70 % at its maximum for @xmath40 30 gev .
in addition , for very large @xmath1 , the significant luminosity associated with the valence dominated @xmath41 density in @xmath16 reactions begins to raise the fraction of the cross section attributed to the @xmath38 subprocesses .
data obtained by the fermilab e772 collaboration @xcite from an 800 gev proton beam incident on a deuterium target are shown in fig .
[ fig:3 ] along with theoretical calculations .
( 7.6,10.5 )    for our analysis we have chosen a lepton pair mass region between the @xmath28 and @xmath29 resonances .
the solid line shows the purely perturbative nlo expectation .
the transition to low @xmath1 can be described by the soft - gluon resummation formalism and is shown in the dashed curve in fig .
[ fig:3 ] @xcite .
the resummed result can be expanded in a power series in @xmath25 asymptotically around @xmath42 .
its nlo component ( dotted curve ) can then be matched to the perturbative result ( dot - dashed curve ) @xcite . from fig .
[ fig:3 ] it becomes clear that resummation is not needed and fixed order perturbation theory can be trusted when @xmath2 .
unfortunately , the data from e772 do not extend into this region .
however , the cross section should be measurable in forthcoming experiments down to @xmath31 pb / gev@xmath32 , _
i.e. _ out to at least @xmath43 gev or @xmath44 where the gluon density is poorly constrained now .    in fig .
[ fig:4 ] we demonstrate that in fixed target experiments also the    ( 7.6,10.5 )    lepton pair cross section is dominated by quark - gluon scattering at the level of 80 % once @xmath45 . the results in fig .
[ fig:4 ] also prove that subprocesses other than those initiated by the @xmath38 and @xmath46 initial channels are of negligible import .
we will now turn to a previously unpublished study of the sensitivity of collider and fixed target experiments to the gluon density in the proton .
the full uncertainty in the gluon density is not known . here
we estimate this uncertainty from the variation of different recent parametrizations .
we choose the latest global fit by the cteq collaboration ( 5 m ) as our point of reference @xcite and compare it to their preceding analysis ( 4 m @xcite ) and to a fit with a higher gluon density ( 5hj ) intended to describe the cdf ( and d0 ) jet data at large transverse momentum .
we also compare to global fits by mrst @xcite , who provide three different sets with a central , higher , and lower gluon density , and to grv98 @xcite . for this study
we update the tevatron center - of - mass energy to run ii conditions ( @xmath47 tev ) which increases the invariant cross section for the production of lepton pairs with mass 5 gev @xmath48 6 gev by 5 % at low @xmath49 gev and 20 % at high @xmath50 gev .    in fig .
[ fig:5 ] we plot the cross section for lepton pairs between the    ( 7.6,10.5 )    @xmath28 and @xmath29 resonances at run ii of the tevatron which should be measurable up to at least @xmath33 gev ( @xmath51 ) . for the cteq parametrizations
we find that the cross section increases from 4 m to 5 m by 2.5 % ( @xmath52 gev ) to 5 % ( @xmath53 gev ) and from 5 m to 5hj by 1 % in the whole @xmath1-range .
the largest differences to cteq5 m are obtained with grv98 at low @xmath1 ( minus 10 % ) and with mrst(g@xmath54 ) at large @xmath1 ( minus 7% ) .    a similar analysis for conditions as in fermilab s e772 experiment is shown in fig .
[ fig:6 ] .
( 7.6,10.5 )    in fixed target experiments one probes substantially larger regions of @xmath55 than in collider experiments .
therefore one expects a much larger sensitivity to the gluon distribution in the proton .
indeed we find that cteq5hj increases the cross section by 7 % ( 26 % ) w.r.t .
cteq5 m at @xmath56 gev ( @xmath57 gev ) and even by 134 % at @xmath53 gev . for mrst(g@xmath58 )
the cteq5 m cross section drops by 17 % , 40 % , and 59 % at these three values of @xmath1 .
in summary , we have demonstrated that the production of drell - yan pairs with low mass and large transverse momentum is dominated by gluon initiated subprocesses . in contrast to prompt photon production , uncertainties coming from fragmentation , isolation , and intrinsic transverse momentum are absent .
the hadroproduction of low mass lepton pairs is therefore an advantageous source of information on the gluon density in the proton at large @xmath5 in collider experiments and even more in fixed target experiments .
massive lepton pair production data could provide new insights into the parametrization and size of the gluon density .
it is a pleasure to thank l.e .
gordon for his collaboration .
mcgaughey _ et al . _
[ e772 collaboration ] , phys . rev . *
d50 * ( 1994 ) 3038 .
the normalization of the published data seems incorrect .
we have multiplied the published cross sections by a factor 3.7 , consistent with information provided to us by j.  moss ( private communication ) .
the hadroproduction of lepton pairs with mass @xmath0 and transverse momentum @xmath1 can be described in perturbative qcd by the same partonic subprocesses as prompt photon production . 
 we demonstrate that , like prompt photon production , lepton pair production is dominated by quark - gluon scattering in the region @xmath2 . 
 this leads to sensitivity to the gluon density in kinematical regimes that are accessible both at collider and fixed target experiments while eliminating the theoretical and experimental uncertainties present in prompt photon production .    
 anl - hep - cp-99 - 72