Heavy quark production has been extensively studied at a number of fixed target experiments at centre of mass energies of about 10 - 40 GeV. At this energy the cross-section for beauty quarks is low so most studies concentrated on the charm quark.
If one considers the photoproduction d a ta for the total charm production cross- sections at fixed target experiments compared to pQCD calculations, qualitative agreement but quantitative deviations can be clearly seen (see Figure 3.1). These results from collisions clearly show a broad agreement with QCD predictions, but no consistent value of charm mass or renorm alisation scale can be interpreted from the comparison. Looking at a d a ta set from one experiment in isolation, one can see th a t the E687 d ata is consistent with a charm mass of 1.2 GeV and inconsistent with a value of 1.8 GeV whilst the E691 d ata is inconsistent with
r r i c = 1.2 GeV, but consistent with tU c = 1.8 GeV. To constrain the physical param eters, the (sometimes large) discrepancies between experiments need to be resolved. g b 1 - 1 7S o lid : m g = 1 .5 GeV N c c r o s s s e c t i o n D o tte d : m <,=1.8 GeV D a s h e d : m ^ = l . 2 GeV □, X, o : NA14. E 6 8 7 . E691 d a t a 1 - 2 0 .0 5 0.1 0 .5 E^ (TeV)
Figure 3.1: Total pair cross-section for c production in j N collisions from the
N A I4 [30], E687 [31] and E691 [32] collaborations compared to QCD predictions.
The bands represent (for a given charm mass) the variation due to the choice
of the renormalisation scale, where the limits shown here are, plr = mc/2 and
//A = (from /g P //
Single inclusive distributions have also been measured at fixed target experiments and compared to QCD predictions. The effect of non-perturbative phenomena
Chapter 3 3.1 Heavy Quark Production at Fixed Target Experiments
coupled to the pQCD predictions have also been studied by, for example, introducing an intrinsic transverse momentum for the incoming partons (the so- called kick” ) and introducing a hadronisation for the charm quark. Figure 3.2 shows the inclusive distribution of charmed hadrons in ' y N collisions from the E687 (Left) and E691 (Right) collaborations. On comparison of the d a ta with theoretical predictions, it can be seen th a t some non-perurbative component is needed to describe the data, although it is reasonably insensitive to the value of the “/ct kick” chosen. The convolution of the pQCD prediction with a fragm entation function is however necessary.
yN c o llis io n s , < E ^ > = 2 2 0 GeV X: E 6 8 7 d a t a _ L S o lid : p u r e QCD D a s h e d : f r a g m . + <1Ct> = 0 .5 GeV® T b _ T D o tte d : f r a g m . + < k ® > = l GeV® T D o t - d a s h e d : f r a g m . + < k® >= 2 GeV® T . . . . I . . . . I . . . . I . . . . I . . . . I . 1 yN c o llis io n s , < £ .,> = 145 GeV X: E691 d a t a 1-3 So lid : p u r e QCD D a s h e d : f ra g m . + < k® > = 0 .5 GeV® D o tte d : f ra g m . + <k®> = l GeV® D o t - d a s h e d : f ra g m , + < k |> = 2 GeV® . . ■ 1 ■ ■ ■ , i , ■ ■ . 1 . . . ■ I 2 4 P? (GeV®) 10 2 4 PT (GeV®)
Figure 3.2: Distribution in for charmed hadrons from the E687 [31] (left) and E691 [32] (right) collaborations compared to NLO pQCD (me = 1.5 GeV) and NLO pQCD with non-perturbative effects (from [29]).
Correlations between charmed quarks have also been studied in photoproduction data; namely Açi, the angle between the momenta projections of the pair onto the transverse plane, and the transverse momentum of the pair Pt{QQ)- These values are again thought to be sensitive to non-perturbative effects such as the “/cr kick” . Photoproduction d a ta has been compared to NLO QCD calculations with an added “/cr kick” [29]. Both distributions indicate a sensitivity to “/ct kick” but the value which gives the best description of the d ata is dependent on experiment and distribution.
Erom these results it can be seen th a t the d ata from fixed target experiments yields more questions than it answers being hindered by the lim ited kinematic range and differences between experiments. No serious kinematic constraints on the charm quark can be placed and no serious measurement of the beauty quark was made, due to lack of statistics.
Heavy Quark Production C hapter 3
3.2
H e a v y Q uark P r o d u c tio n a t H E R A
There are two theoretical advantages to th e stu d y of heavy ra th e r th a n light quarks in photoproduction. As m entioned a t th e beginning of th e chapter, the large mass {nig ^ A q c d ) ensures th a t pertu rb ativ e calculations are m ore reliable although corrections oc (A qcd/?^?)” m ight be non-negligible for th e charm quark. W ith accurate values of nig and Aqcd? reliable to ta l cross-sections could be predicted. Secondly, the stu d y of heavy quarks also reduces th e num ber of contributing partonic processes such th a t the boson-gluon fusion (Figure 2.5b) process;
79 -> QQ,
is the only direct photon process at LO. To LO this process is directly sensitive to the gluon content of th e proton. T he question of th e relative contribution of LO resolved processes is less clear. Heavy quark “excitation” processes;
Qg -> Qp,
(the charge conjugate being im plied), where th e heavy quark comes from the photon, may contribute. The size of th e contribution relative to the gluon-gluon fusion process;
99 —^ QQ:
is a question th a t studies a t HERA hope to answer. It is addressed in this thesis. Coupled to the unexplored kinem atic region in photoproduction available a t HERA, the study of heavy quarks promises to yield interesting results.
At LO, heavy quark production, like light quark production, is considered as the sum of direct (pointlike) and resolved (hadronic) components. Therefore, the general photoproduction description given by E quations (2.21 - 2.23), also describes photoproduction for heavy quarks. However, we m ust rem em ber th a t approxim ations such as )$> m g are not necessarily valid and the mass m ust be included. We should also consider th a t th e pseudorapidity is a massless approxim ation of th e rapidity, y, which is given by,
C hapter 3 3.2 Heavy Quark Production at HERA
The subsequent treatm en t of w hat constitutes direct and resolved and in which proportions is where differences in theoretical models occur. For exam ple, th e “excitation” process, stated in the previous paragraph, can be considered, a t sufficiently high transverse m om enta, as a LO resolved process or alternatively a NLO direct process.