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heavy quarks are believed to be mostly created from initial gluon fusion in hadronic collisions . since they are massive , heavy flavor hadrons are proposed to be ideal probes to study the early stage dynamics in heavy - ion collisions .
measurements of heavy quark production in p+p interactions at collider energies serve as important tests for perturbative quantum chromo dynamics ( pqcd ) , while measurements in d+au collisions serve to calibrate the effects of the cold nuclear medium .
both observations create a very important baseline for understanding the hot - dense matter created in au+au collisions .
since the initial formation of open and closed charm are both sensitive to initial gluon densities , open charm production serves as an appropriate normalization for @xmath1 production .    in @xmath2 gev d+au collisions at rhic , measurements at forward rapidity ( deuteron direction ) probe the shadowing region with momentum fractions in au near @xmath3 while the anti - shadowing region is probed in backward rapidity ( gold going direction ) with momentum fractions in au near @xmath4 .
recent models of gluon shadowing  @xcite , color glass condensate  @xcite and recombination  @xcite are implemented to understand the hadron and open charm production at forward rapidity .
all of these three models predict suppression in the small @xmath5 region .
it is very important to have precise measurements of open heavy flavor and hadron production to disentangle these different models .
the phenix experiment  @xcite has measured open charm production through observation of semi - leptonic decays at forward and backward rapidity with the phenix muon spectrometer .
the phenix muon arms cover both forward and backward directions in the rapidity range of @xmath6 , which covers both shadowing and anti - shadowing regions .    the decay of heavy flavor is prompt , and produces a track with an origin at the collision vertex .
another source of prompt muon - like tracks is hadrons that punch through the shielding in front of the muon spectrometer .
the acceptance of the spectrometer for these prompt tracks is relatively independent of the vertex location @xmath7 .
another background source is the weak decay of those same hadrons before reaching the shielding 
these non - prompt muon tracks have an origin separated from the collision vertex , and the acceptance for these tracks is strongly @xmath7-dependent .
a pythia simulation shows around 75@xmath8 of prompt muons with @xmath9 0.9 gev/@xmath10 come from open charm decay in d+au collisions , while 11@xmath8 come from open bottom decay .
prompt muons are produced close to the collision vertex .
we can separate heavy flavor decays and light hadron decays experimentally by studying the shape of the vertex distribution .
the normalized event vertex distribution of reconstructed muons is given by    @xmath11    where @xmath7 is the event vertex and @xmath12 cm for north and south arms , respectively .
@xmath13 and @xmath14 are determined from event vertex distribution .
the distribution of detected muons from light hadron decay is collision vertex dependent due to the acceptance of the muon spectrometers , and this is described by the @xmath15 parameter .
the prompt muon and the hadron punch through tracks will contribute to the vertex independent part and this is described by the @xmath16 .
the data were used to subtract the hadron punch through .
the phenix muon spectrometer includes a `` muon identifier '' consisting of thick iron sheets with detectors in the gaps between the sheets .
muons are more likely to penetrate into the deeper gaps than are hadrons . by analyzing the hadrons stopped at gap 2 and 3
, one can estimate the hadron contribution at gap4 using an attenuation model  @xcite . with this statistical method
, we can measure the yield of muon from heavy flavor decays with the phenix muon arms .
-3.3 cm    -1 cm
the invariant differential cross section for prompt muon production at forward rapidity @xmath17 has been measured by the phenix experiment over the transverse momentum range @xmath18 gev/@xmath10 in @xmath19 = 200 gev p+p collisions at the relativistic heavy ion collider .
the resulting muon spectrum from heavy flavor decays is compared to pythia and a next - to - leading order perturbative qcd calculation showing in figure 1 .
phenix muon arm data ( at forward and backward rapidity ) is compatible with the phenix charm measurement at y = 0  @xcite , and it exceeds predictions from pythia and fonll .
the nuclear modification factor of d+au collisions is defined as the particle yield per nucleon - nucleon collision relative to the yield in p+p collisions .
the nuclear modification factors with muons from light hadron decay and from heavy flavor decay are shown in figure 2 and figure 3 .    -1.9
cm    -1.6 cm    muons from both light hadron decay and prompt single muon production show suppression at forward rapidity and enhancement in the backward direction .
fonll and pythia 6.205 under - predict the prompt @xmath20 yield at forward rapidity in p+p collisions at 200 gev/@xmath10 . we observe a significant cold nuclear medium effect in forward and backward rapidity in d+au collisions at 200 gev/@xmath10 . for both muons from open heavy flavor
decays and light hadron decays , a suppression in forward rapidity is observed .
it is consistent with cgc and power correction model  @xcite .
the mechanism of the observed enhancement at backward rapidity needs more theoretical investigation .
anti - shadowing and recombination could lead to such enhancement .
we need a more precise d+au measurement to understand the cold nuclear medium effects as a baseline for understanding the hot dense matter produced in au+au collisions .
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heavy flavor production in hadronic collisions is dominated by gluonic processes and so is a sensitive probe of the gluon structure function in the nucleon and its modification in nuclei . 
 a study of heavy flavor production in p+p and d+au collisions in various kinematic regions presents an opportunity to probe cold nuclear medium effects ; parton shadowing , color glass condensate , initial state energy loss , and coherent multiple scattering in final state interactions . 
 the phenix muon arms cover both forward and backward directions in the rapidity range of @xmath0 . 
 we investigate single muon production from open heavy flavor and light mesons decay in p+p and d+au collisions at forward and backward rapidity .