P. Nason, 3rd Topical Seminar on Heavy Flavours, San Miniato 17-21 June ... S. Frixione, M. L. Mangano, P. Nason and G. Ridolfi, preprint CERN-TH.6921/93,.
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gu; 9 9 EDS Heavy Flavour Production in Perturbative QCD
Paolo N asonl
CERN TH-Division, CH—1211 Geneva 23, Switzerland Stefano Frixione
Dip. di Fisica, Universita di Genova, and INFN, Sezione di Genova, Genoa, Italy
Michelangelo L. Mangano INFN, Scuola Normale Superiore and Dipartimento di Fisica, Pisa, Italy Giovanni Ridolfiz
CERN TH-Division, CH-1211 Geneva 23, Switzerland
Abstract
We review the status of heavy flavour production in QCD. In particular we discuss recent results on the doubly—diH`erential cross section for the photopro
duction of heavy flavours. Comparison of experimental results with theoretical
calculation is discussed both for b production at hadron colliders and for c pro duction in fixed-target hadroproduction and photoproduction. The possibility of using photoproduction of heavy flavours in order to determine the gluon density in the proton is also discussed.
Talk given at the Advance Study Conference on Heavy Flavours, Pavia, 3-7 Sept. 1993, Italy.
CERN-TH.7134/94 January 1994 On leave of absence from INFN, Sezione di Milano, Milan, Italy. On leave of absence from INFN, Sezione di Genova, Genoa, Italy. OCR Output
Although the first next-to-leading-order calculations of heavy flavour production
were performed more than five years agolll, progress in this field is constantly being made. The work of ref. [2] has confirmed the results of ref. A calculation of the next-to-leading cross section to the photoproduction of heavy quarks has been given in ref. [3], and has recently been confirmed by ref. The computation of the radiative corrections to the electroproduction of heavy quarks, via an off-shell photon,
was presented in ref. A method that accounts for the correlation of heavy quarks
at next—to—leading order was developed in ref. [6] for heavy quark hadroproduction. An application of this calculation to fixed—target production of heavy quarks is given in ref. The method was recently extended to the photoproduction of heavy quarks in ref.
The phenomenology of heavy quark production at next—to-leading order has re
ceived contributions by many authors (besides the works quoted so far, see also refs. The main features of the phenomenological results are the following. For top hadroproduction, it was found that radiative corrections are generally well under
control. This allows us to make predictions for top cross sections with a relatively small error. For bottom the situation is much worse. Radiative corrections are large,
and various estimates of corrections of even higher order (as given for example by the renormalization and factorization scale dependence) lead to theoretical uncertainties of the order of a factor of 2 to 3. These uncertainties, when combined with other
physical uncertainties, such as the error in the knowledge of AQCD and of the struc ture functions, result in a rather poor theoretical prediction. For charm, theoretical uncertainties are even higher. Figure 1 gives an instructive picture of the uncertainties
in charm and bottom cross section at fixed—target experiments. Observe the consider
able improvement that takes place when going from charm to bottom. Observe also the strong mass dependence of the charm result. Needless to say, similar uncertainties
plague the pN cross sections, as shown in fig. 2. New-generation fixed-target experiments have accumulated very large statistics
of charm events. For a (possibly incomplete) list of recently published results, see refs.[10] and [11]. For recent reviews of the current experimental situation and future perspectives, see refs. [12], [13]. For an older review see [14]. Results on bottom production at fixed target are given in refs. [15-18]. For a recent result of E672, see [19]. As one can see, experimental results on total cross sections for charm and bottom OCR Output
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production at fixed target are in reasonable agreement with theoretical expectations. We remind the reader that many puzzling ISR results in pp collisions at 62 GeV
remain difficult to explain (see the review [14]), in particular the large Ab production
rates reported in ref. [18]. The status of b production at hadron colliders has been quite puzzling for some
time. Owing to recent progress, however, the situation has considerably clarified. Let me briefly review the history of the theoretical predictions and experimental results on the b spectrum at hadron colliders. Early calculations agreed quite well with UA1
measurementslml. In fig. 3 the comparison between UA1 data and the theoretical calculation is displayed. As first pointed out in ref. [1], the perturbative computation of the b cross section at hadron colliders reaches a difficult kinematical regime when going from the SppS energies to the Tevatron. This is due to the appearance of large
logarithms of S/mz (where S is the c.m. energy squared, and m is the mass ofthe heavy quark being produced) in the perturbative expansion. In other words, at very
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set, which is clearly disfavourcd by experimental results on jet production in photon lm photon collisionsand photon—ha.dron co]]jsions[38].
In conclusion, the starting of HERA opens up new possibilities in QCD studies using heavy quark production. The more moderate size of the radiative effects in
heavy quark photoproduction than in hadroproduction offers a considerable advan tage. Observe that there is no reason why fixed-target photoproduction experiments
could not attempt a similar measurement. Because of the limited energy the 2: range
will be more restricted, but nevertheless the measurement would be a valuable QCD test.
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Figure 8: Contribution of the hadronic component of the photon, compared with the pure photon component, for two extreme choices of the photon structure functions. OCR Output
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