Table Of ContentBicocca-FT-03-1
January 2003
hep-ph/0301003
HEAVY FLAVOUR PRODUCTION ∗
P. Nason
INFN, Sez. di Milano, Milan, Italy
February 1, 2008
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0 Abstract
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I discuss few recent developmentsin HeavyFlavour Production phenomenology.
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1 Introduction
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1 The phenomenologyofHeavyflavourproductionattractsconsiderabletheoreticalandexperimental
v interest.
3 The theoretical frameworkfor the description of heavy flavourproduction is the QCD improved
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parton model. Besides the well-established NLO corrections to the inclusive production of heavy
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quark in hadron-hadron[1, 2, 3, 4], hadron-photon[5, 6, 7], and photon-photon collisions[8], much
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0 theoretical work has been done in the resummation of contributions enhanced in certain regions of
3 phase space: the Sudakov region, the large transverse momentum region and the small-x region.
0 The theoretical effort involved is justified by the large variety of applications that heavy quark
/
h production physics has, in top, bottom and charm production. Besides the need of modeling these
p processes, heavy quark production is an important benchmark for testing QCD and parton model
- ideas, due to the relative complexity of the production process, the large range of masses avail-
p
able,andtheexistenceofdifferentproductionenvironments,likee+e− annihilation,hadron-hadron,
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h photon-hadron and photon-photon collisions. Although the order of magnitude of the total cross
: sections, and the shape of differential distribution is reasonably predicted, in some areas large dis-
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i crepancy are present, especially for b production.
X
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a 2 Total cross section for top and bottom
Top production[9, 10] has been a most remarkable success of the theoretical model. The measured
cross section has been found in good agreement with theoretical calculations, as shown in fig. 1.
Resummationofsoftgluoneffects[11]reducesthetheoreticaluncertaintyinthecrosssection,pushing
it toward the high side of the theoretical band. It remains, however, inside the theoretical band of
the fixed order calculation, thus showing consistency with the estimated error.
Recently,theHERA-Bexperimenthasprovidedanewmeasurementoftheb¯btotalcrosssection[12].
Their result is in good agreement with previous findings[13, 14]. More details on this measurement
have been givenin Saxon’s talk[15]. Here I will only make some remarkson the theoretical aspects.
This experiment is sensitive to the moderate transverse momentum region, where the bulk of the
total cross section is concentrated. Since the production is (in a certain sense) close to threshold,
resummation of Sudakov effects is important also in this case, and brings about a considerable re-
duction of the theoretical uncertainty[11]. The HERA-b result is compatible with the central value
prediction, with the b pole mass around 4.75 GeV. Higher precision may constrain further the b
quark mass.
∗Invited reviewtalkattheFirstInternational WorkshoponFrontierScience, “Charm,BeautyandCP”,October
6-11,2002,INFNLaboratory,Frascati,Italy.
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Figure 1: Results on top cross sections at the Tevatron.
3 Differential distributions
The Tevatron has had a longstanding disagreement with QCD in the b transverse momentum spec-
trum. A recent publication of the B+ differential cross section by CDF[16] has quantified the
disagreement as a factor of 2.9±0.2±0.4 in the ratio of the measured cross section over the the-
oretical prediction. This discrepancy has been present since a long time, and it has been observed
both in CDF and D0. Some authors[17] have arguedthat the discrepancy could be interpreted as a
signal for Supersimmetry.
Because of the large theoretical uncertainties, this discrepancy has been often downplayed. In
fact, several effects may conspire to raise the b cross section to an appropriate value: small-x
effects[1, 18, 19], threshold effects[11] and resummation of large logp . It is not however clear
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whether these effect can be added up without overcounting. Furthermore, they are all higher order
effects,andthusshouldnotpushthecrosssectiontoofaroutofthetheoreticalband,whichincludes
estimates of unknown higher order effects.
Recently,asmall-xformalism[20,21,22,23]hasbeenimplementedinaMonteCarloprogram[24]
(the CASCADE Monte Carlo), and it has been claimed that this programs correctly predicts the
b spectrum at the Tevatron[25]. Although encouraging, this result should be regarded with a word
of caution. The formalism involved only accounts for leading small x effects, and does not correct
for the lack of leading terms, that are known to be important for heavy flavour production at the
Tevatron regime. Experience with other contexts where resummation techniques have been applied
has taught us that it is not difficult to overestimate the importance of resummation effects, and
much study is needed to reliably assess their importance[26].
It has been observed since some time that an improper understanding of fragmentation effects
may be one of the causes of the Tevatron discrepancy. This possibility stems from the fact that b
quark cross sections are in reasonable agreement with the Tevatron measurements of the B meson
spectrum, while the cross section obtained by applying a standard fragmentation function of the
Peterson form[27] with ǫ = 0.006 to the quark cross section yields too soft a spectrum. It was
suggested[28] to study b quark jets rather than B meson’s distributions. In fact, the jet momentum
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should be less sensitive to fragmentation effects than the hadron momentum. A D0 study [29] has
demonstrated that by considering b jets instead of B hadrons the agreement between theory and
data improves considerably.
It was recently shown[30] that an accurate assessment of fragmentation effects brings about a
reductionofthediscrepancyfromthefactorof2.9quotedbyCDFtoafactorof1.7. Thisremarkable
reduction is essentially due to recent progress in fragmentation function measurements by LEP
experimentsandtheSLD[31,32,33,34](thecurrentstatusoffragmentationmeasurementshasbeen
reviewed in Boccali’s talk[35]), and by a particular method for extracting the relevant information
aboutnon-perturbativefragmentationeffectsfromthee+e− data. HereIwillnotenterinthedetails
of the method, that have been described in[30]. I will instead try to give an overall illustration of
the main features of the method. First of all, strictly speaking, the description of fragmentation
effects in terms of a fragmentation function (i.e., a probability distribution for an initial quark to
hadronizeintoahadronwithagivenfractionofitsmomentum)isonlyvalidatverylargetransverse
momenta. One could then extract the fragmentation function from LEP data, and use it in high
p B production at the Tevatron. Unfortunately, the regime of large transverse momenta is not
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quite reachedattheTevatron. Forexample,thedifferentialcrosssectiondσ/dp2dy attheTevatron,
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for p = 10,y = 0, computed at the NLO level including mass effects is 12.1nb/GeV2, while in
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the massless approximation (i.e., neglecting terms suppressed as powers of m/p ) is 1.78nb/GeV2.
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At p = 20 we have 0.372nb/GeV2 for the full massive, and 0.220nb/GeV2 for the massless limit,
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which starts to approach the asymptotic value. As a rule of thumb, the massless approximation
starts to approach the massive one around p ≈ 5m1. It does therefore make no sense to use any
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massless approach for p < 5m. In earlier work on heavy quark production at large transverse
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momentum[37],this factwentunnoticed,since largehigherorderterms(i.e. beyondthe NLO level)
in the fragmentation function approach accidentally compensated for the lack of mass terms, thus
giving the impression that the massless approach is good down to p ≈2m.
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Inordertoperformacalculationthatisreliableinboththelowandthehightransversemomen-
tum regime, we have thus to merge the massive NLO calculation with the fragmentation function
approach. The merging point must therefore be around pt ≈ 5m. A summary of the theoretical
tools that have lead to the matched (so called FONLL) approachare summarised as follows:
1 Single inclusive particle production in hadronic collisions[38]. Single hadron production are
described in term of NLO single parton cross section convoluted with a NLL fragmentation
function;
2 Heavy quark Fragmentation Function[39]; a method for the computation of the heavy quark
fragmentationfunction at all orders in perturbation theory is developed, and applied at NLL.
Several applications in e+e− physics have appeared [40, 41, 42, 43].
3 Single inclusive heavy quark production at large pT[37]; item 1 and 2 are combined to give a
NLL resummation of transverse momentum logarithms in heavy quark production;
4 FONLL calculation of single inclusive heavy quark production; item 3 is merged without
overcounting with standard NLO calculations. This procedure has been implemented both in
hadroproduction[44] and in photoproduction[45, 46].
A summary of comparison of the FONLL calculation with data is given in fig. 2. More details
on the CDF measurement have been given in Saxon’s talk. The comparison with D0 data (still
preliminary) shows very good agreement, compared to the discrepancy of a factor of order 3 found
in the D0 publication.
1Thiselementaryfacthasbeenknownformorethanfiveyears,although,surprisinglyenough,someauthorsprefer
toignoreitevennow[36].
3
Figure 2: Comparison of CDF[16] and D0[47] data with the FONLL calculation[30].
4 Conclusions
The theory ofheavy flavourproductionseems to givea goodqualitative descriptionof the available
data. In the case of top production, the comparison between theory and experiment is satisfactory
also at a quantitative level.
Recent progresshas taken place in the field of b hadroproduction. The HERA-b experiment has
providedacrosssectionforbproductionatrelativelylowCMenergy. Someprogressinunderstand-
ingtheroleoffragmentationhasconsiderablyreducedthelongstandingproblemofthebmomentum
spectrum at the Tevatron.
Major problems do remain in the (perhaps less developed) areas of bottom production in γγ
and γp collisions. Discussion of these problems were reported in Saxon’s and Achard’s talk in this
conference[15, 48]. In both contexts, while charmproduction seems to be reasonablywell described
by QCD, there is an excess of bottom production, which seems to be far out of the theoretical
uncertainty band. These problems have been around for sometimes now. On the positive side,
the recent Zeus measurements presented in[15] seem to show a smaller discrepancy than previously
found.
References
[1] P. Nason, S. Dawson and R. K. Ellis, Nucl. Phys. B303 (1988) 607.
[2] P. Nason, S. Dawson and R. K. Ellis, Nucl. Phys. B327 (1989) 49–92.
[3] W. Beenakker, W. L. van Neerven, R. Meng, G. A. Schuler and J. Smith, Nucl. Phys. B351
(1991) 507–560.
[4] M. L. Mangano, P. Nason and G. Ridolfi, Nucl. Phys. B373 (1992) 295–345.
[5] R. K. Ellis and P. Nason, Nucl. Phys. B312 (1989) 551.
[6] J. Smith and W. L. van Neerven, Nucl. Phys. B374 (1992) 36–82.
[7] S. Frixione, M. L. Mangano, P. Nason and G. Ridolfi, Nucl. Phys. B412 (1994) 225–259,
[hep-ph/9306337].
4
[8] M. Drees, M. Kramer, J. Zunft and P. M. Zerwas, Phys. Lett. B306 (1993) 371–378.
[9] CDF Collaboration, T. Affolder et. al., Phys. Rev. D64 (2001) 032002,[hep-ex/0101036].
[10] D0 Collaboration,V. M. Abazov et. al., [hep-ex/0205019].
[11] R. Bonciani, S. Catani, M. L. Mangano and P. Nason, Nucl. Phys. B529 (1998) 424–450,
[hep-ph/9801375].
[12] HERA-B Collaboration,I. Abt et. al., [hep-ex/0205106].
[13] D. M. Jansen et. al., Phys. Rev. Lett. 74 (1995) 3118–3121.
[14] E771 Collaboration,T. Alexopoulos et. al., Phys. Rev. Lett. 82 (1999) 41–44.
[15] D. H. Saxon, this proceedings.
[16] CDF Collaboration, D. Acosta et. al., Phys. Rev. D65 (2002) 052005,[hep-ph/0111359].
[17] E. L. Berger et. al., Phys. Rev. Lett. 86 (2001) 4231–4234,[hep-ph/0012001].
[18] S. Catani, M. Ciafaloni and F. Hautmann, Nucl. Phys. B366 (1991) 135–188.
[19] J. C. Collins and R. K. Ellis, Nucl. Phys. B360 (1991) 3–30.
[20] M. Ciafaloni, Nucl. Phys. B296 (1988) 49.
[21] S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B234 (1990) 339.
[22] S. Catani, F. Fiorani and G. Marchesini, Nucl. Phys. B336 (1990) 18.
[23] G. Marchesini, Nucl. Phys. B445 (1995) 49–80, [hep-ph/9412327].
[24] H. Jung, Comput. Phys. Commun. 143 (2002) 100–111,[hep-ph/0109102].
[25] H. Jung, Phys. Rev. D65 (2002) 034015,[hep-ph/0110034].
[26] S. Catani, M. L. Mangano, P. Nason and L. Trentadue, Nucl. Phys. B478 (1996) 273–310,
[hep-ph/9604351].
[27] C. Peterson, D. Schlatter, I. Schmitt and P. M. Zerwas,Phys. Rev. D27 (1983) 105.
[28] S. Frixione and M. L. Mangano, Nucl. Phys. B483 (1997) 321–338,[hep-ph/9605270].
[29] D0 Collaboration,B.Abbott et. al., Phys. Rev. Lett.85 (2000)5068–5073,[hep-ex/0008021].
[30] M. Cacciari and P. Nason, Phys. Rev. Lett. 89 (2002) 122003 [hep-ph/0204025].
[31] ALEPH Collaboration, A. Heister et. al., Phys. Lett. B512 (2001) 30–48,[hep-ex/0106051].
[32] SLD Collaboration, K. Abe et. al., [hep-ex/0202031].
[33] OPAL Collaboration, G. Abbiendi et. al., [hep-ex/0210031].
[34] DELPHI Coll., ICHEP 2002 Abstract 583.
[35] T. Boccali, this conference proceedings.
[36] B. A. Kniehl, [hep-ph/0211008].
[37] M. Cacciari and M. Greco, Nucl. Phys. B421 (1994) 530–544,[hep-ph/9311260].
5
[38] F. Aversa, M. Greco, P. Chiappetta and J. P. Guillet, Phys. Rev. Lett. 65 (1990) 401–403.
[39] B. Mele and P. Nason, Nucl. Phys. B361 (1991) 626–644.
[40] G. Colangelo and P. Nason, Phys. Lett. B285 (1992) 167–171.
[41] M. Cacciari, M. Greco, S. Rolli and A. Tanzini, Phys. Rev. D55 (1997) 2736–2740,
[hep-ph/9608213].
[42] M. Cacciari and M. Greco, Phys. Rev. D55 (1997) 7134–7143,[hep-ph/9702389].
[43] P. Nason and C. Oleari, Nucl. Phys. B565 (2000) 245–266,[hep-ph/9903541].
[44] M. Cacciari, M. Greco and P. Nason, JHEP 05 (1998) 007, [hep-ph/9803400].
[45] M. Cacciari, S. Frixione and P. Nason, JHEP 03 (2001) 006, [hep-ph/0102134].
[46] S. Frixione and P. Nason, JHEP 03 (2002) 053, [hep-ph/0201281].
[47] D0 Collaboration,B.Abbott et. al., Phys. Rev. Lett.84 (2000)5478–5483,[hep-ex/9907029].
[48] P. Achard, this conference proceedings.
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