Using a subset of the current Run II data, the CDF and \D0 have performed
several measurements on heavy flavor production. In this paper, we present a
new measurement of prompt charm meson production by CDF. We also report the
latest CDF II measurements of inclusive $J/\Psi$ production and $b$-production
without requirement of minimum transverse momentum on $J/\Psi$ and $b$-quark.
They are the first measurements of the total inclusive $J/\Psi$ and $b$ quark
cross section in the central rapidity region at a hadron collider. The results
of $J/\Psi$ cross section as a function of rapidity, and $b$-jet production
cross section measured by \D0 are also reviewed.Comment: Invited talk the 9th International Conference on B-Physics at Hadron
  Machines - BEAUTY 2003, Carnegie Mellon University, Pittsburgh, October
  14-18, 2003. Proceedings to be published by AI

Chen, Chunhui

English

arXiv

Chunhui Chen

Crossref

Heavy Flavor Production at the Tevatron

Using a subset of the current Run II data, the CDF and D0 have performed several measurements on heavy flavor production. In this paper, we present a new measurement of prompt charm meson production by CDF. We also report the latest CDF II measurements of inclusive J/{Psi} production and b-production without requirement of minimum transverse momentum on J/{Psi} and b-quark. They are the first measurements of the total inclusive J/{Psi} and b quark cross section in the central rapidity region at a hadron collider. The results of J/{Psi} cross section as a function of rapidity, and b-jet production cross section measured by D0 are also reviewed

UNT (University of North Texas) Digital Library

Fermilab FERMILAB-Conf-04/024-E  February 2004Heavy Flavor Production at the TevatronChunhui Chen(Representing the CDF and DØ Collaboration)Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.Abstract. Using a subset of the current Run II data, the CDF and DØ have performed several measurements on heavy flavorproduction. In this paper, we present a new measurement of prompt charm meson production by CDF. We also report the latestCDF II measurements of inclusiveJ/Ψ production andb-production without requirement of minimum transverse momentumon J/Ψ and b-quark. They are the first measurements of the total inclusiveJ/Ψ and b quark cross section in the centralrapidity region at a hadron collider. The results ofJ/Ψ cross section as a function of rapidity, andb-jet production crosssection measured by DØ are also reviewed.INTRODUCTIONMeasurements of the production cross section of heavyflavor quarks (c andb quarks) in thepp̄ collisions pro-vide us an opportunity to test the prediction based onthe Quantum Chromodynamics (QCD). No only is QCDone of the four fundamental forces of the nature, but alsomany searches of new physics beyond Standard Modelrequire a good understanding of the QCD background.The Bottom quark production cross section has beenmeasured by both the CDF and DØ experiments [1,2] at the Fermilab Tevatron inpp̄ collision at√s =1.8TeV, and found to be about three times larger thanthe next-to-leading order (NLO) QCD calculation [3,4]. Since then, several theoretical explanation has beenproposed to solve the disagreement, such as the largecontributions from the NNLO QCD processes, possiblecontribution from “new physics” [5] etc. Recently, amore accurate description ofb quark fragmentation hasreduced the discrepancy to a factor 1.7 [6]. Nevertheless,further experimental measurements on the heavy flavorproduction are essential to shed light on the remainingclouds of this long standing issue.Since the end of Run I (1996), the Tevatron had un-derdone major upgrade. The center of mass energy in thepp̄ collision was increased from√s= 1.8TeV to√s=1.96TeV. The large luminosity enhancement dramati-cally increases the discovery reach and moves the exper-imental program into a regime of precision hadron col-lider physics. At the same time, both CDF [7] and D0 [8]experimental collaborations significantly upgraded theirdetectors to enrich the physics capabilities, especially forthe heavy flavor physics program. The Tevatron Run IIdata taking period started in April 2002, so far the ac-celerator has delivered about 300pb−1 integrated lumi-nosities, both experiments collected more than 200pb−1physics quality data. In this paper, we will give a briefsummary of the latest results on heavy flavor productionfrom Tevatron Run II.PROMPT CHARM MESONPRODUCTION CROSS SECTIONIn order to help understanding the discrepancy betweenmeasured Run I Bottom quark cross section measure-ment and theoretical calculation, one can repeat previ-ous measurement with better control of experimental un-certainties. An alternative approach is to examine theproduction rate of another heavy quark. Charm mesonproduction cross sections have not been measured inpp̄collisions and may help to solve this disagreement. ForCDF II upgrade, one of the crucial improvement with re-spect to the CDF I is the implementation of a Silicon Ver-tex Trigger (SVT) [9], which allows us to trigger on dis-placed tracks decayed from long-lived charm and bottomhadrons. With this trigger, large amount of fully recon-structed charm meson has been collected, opening a newwindow for heavy flavor production studies at hadroncollider.Using just 5.8±0.3pb−1 data, CDF performs a mea-surement of prompt charm meson production crosssection [10]. The charm mesons are reconstructed inthe following decay modes:D0 → K−π+, D∗+ → D0π+with D0 → K−π+, D+ → K−π+π+, D+s → φπ+ withφ → K+K−, and their charge conjugate, as shown inFig. 1. We separate charm directly produced inpp̄ in-teraction (prompt charm) from charm decayed fromB]2)  [GeV/c+π-m(K1.8 1.85 1.92Entries per 2 MeV/c0100020003000+π-K→0D (a)]2)  [GeV/c+π-)-m(K+π+π-m(K0.14 0.15 0.162Entries per 0.3 MeV/c0200400600800 ,+π0D→+D*+π-K→0D(b)]2)  [GeV/c+π+π-m(K1.7 1.8 1.9 22Entries per 2 MeV/c010002000+π+π-K→+D (c)]2)  [GeV/c+π-K+m(K1.8 1.9 2 2.12Entries per 5 MeV/c0100200300+πφ→s+D+πφ→+D(d)FIGURE 1. Charm signals summed over allpT bins: (a)invariant mass distribution ofD0 → K−π+ candidates; (b)mass difference distribution ofD∗+ → D0π+ candidates; (c)invariant mass distribution ofD+ → K−π+π+ candidates; (d)invariant mass distribution ofD+ → φπ+ and D+s → φπ+candidates.mesons (secondary charm) using the impact parameter ofthe charm candidate with respect to the primary interac-tion point. Prompt charm meson points to the beamlineand its impact parameter is zero. The secondary charmmeson candidate does not necessarily point back to theprimary vertex, it has a rather wide impact parameterdistribution. The shape of the impact parameter distri-bution of secondary charm is obtained from a MonteCarlo simulation. The detector impact parameter resolu-tion is modeled from a sample ofK0S → π+π− decaysthat satisfy the same trigger requirement. The promptcharm fraction is measured as a function of charm me-son pT . Average over allpT bins, (86.6± 0.4)% of theD0 mesons,(88.1±1.1)% of D∗+, (89.1±0.4)% of D+,and(77.3±3.8)% of D+s are promptly produced (statis-tical uncertainties only).The measured prompt charm meson integrated crosssection are found to beσ(D0, pT ≥ 5.5GeV/c, |y| ≤1) = 13.3±0.2±1.5µb,σ(D∗+, pT ≥ 6.0GeV/c, |y| ≤1) = 5.2± 0.1± 0.8µb, σ(D+, pT ≥ 6.0GeV/c, |y| ≤1)= 4.3±0.1±0.7µbandσ(D+s , pT ≥ 8.0GeV/c, |y| ≤1) = 0.75± 0.05± 0.22µb, where the first uncertaintyis statistical and the second systematic. The measureddifferential cross sections are compared to two recentcalculations [11, 12], as shown in Fig. 2 and Fig. 3.They are higher than the theoretical predictions by about100% at lowpT and 50% at highpT . However, they arecompatible within uncertainties. The same models also  [GeV/c]Tp5 10 15 20  [nb/GeV/c]T/dpσd102103104  [nb/GeV/c]T/dpσd0D  [GeV/c]Tp5 10 15 20  [nb/GeV/c]T/dpσd102103  [nb/GeV/c]T/dpσd+D*  [GeV/c]Tp5 10 15 20  [nb/GeV/c]T/dpσd102103  [nb/GeV/c]T/dpσd+D  [GeV/c]Tp5 10 15 20  [nb/GeV/c]T/dpσd10102103  [nb/GeV/c]T/dpσd+sDFIGURE 2. The measured differential cross section mea-surements for|y| ≤ 1, shown by the points. The inner barsrepresent the statistical uncertainties; the outer bars are thequadratic sums of the statistical and systematic uncertainties.The solid curves are the theoretical predictions from Cacciariand Nason [11], with the uncertainties indicated by the shadedbands. The dashed curve shown with theD∗+ cross sectionis the theoretical prediction from Kniehl [12]; the dotted linesindicate the uncertainty. No prediction is available yet forD+sproduction.underestimateB meson production at√s = 1.8TeV bysimilar factors [2, 6, 13].INCLUSIVE J/Ψ PRODUCTION CROSSSECTIONThe CDF II detector has improved the dimuon triggersystem with a lower threshold of 1.5GeV/c. This allowsus to trigger theJ/Ψ→ µ−µ+ event with transverse mo-mentum all the way down topT(J/Ψ) = 0GeV/c. Usingabout 39.7pb−1 data, CDF reconstructed 299800± 800J/Ψ candidates (statistical uncertainty only), as shownin Fig. 4. A new measurement of the total inclusiveJ/Ψcross section in the central rapidity region|y| ≤ 0.6 hasbeen carried out. This is the first measurement of the to-tal inclusiveJ/Ψ cross section in the central rapidity re-gion at a hadron collider. The differential cross section isshown in Fig. 5, and the integrated cross section is mea-sured to be:σ(pp̄→ J/ΨX, |y(J/Ψ| ≤ 0.6)×Br(J/Ψ → µµ)= 240±1(stat)+35−28(syst)nb,(1)  [GeV/c]Tp5 10 15 20Data/Theory00.511.522.5Data/Theory0D  [GeV/c]Tp5 10 15 20Data/Theory00.511.522.5Data/Theory+D*  [GeV/c]Tp5 10 15 20Data/Theory00.511.522.5Data/Theory+DFIGURE 3. Ratio of the measured cross sections to the the-oretical calculation from Cacciari and Nason. The inner errorbar represents the statistical uncertainty, the outer error bar thequadratic sum of the statistical and systematic uncertainty. Thehatched band represents the uncertainty from varying the renor-malization and factorization scale.Taking advantage of the large azimuth coverage of itsmuon system, the DØ measured the differential crosssection of the inclusiveJ/Ψ as a function of the rapidityusing 4.74pb−1. The distribution is shown in Fig. 6.BOTTOM QUARK PRODUCTIONCROSS SECTIONThe Run I centralb-quark production cross section mea-sured by CDF and DØ has a minimum transverse mo-mentum cut on theb-hadrons due to the trigger require-ments. Since those measurements only explore a smallfraction (∼ 10%) of theb-hadronpT spectrum, it is notclear from the data whether the excess over the theory isdue to an overall discrepancy of thebb̄production rate, orit is caused by a shift in the spectrum toward higherpT .An inclusive measurement of bottom quark productionover all transverse momentum can certainly help resolvethis ambiguity.Notice that large fraction ofb-hadronHb decays toJ/Ψ final states, whereHb denotes both hadron and anti-hadron. CDF performed an analysis to extract the in-clusive b-hadron cross section from the measured in-clusive J/Ψ production cross section. Due to the longlive lifetime of theb-hadrons, the vertex of theJ/Ψ de-cayed from ab-hadron (secondaryJ/Ψ) is usually hun-dreds microns away from the primary vertex, while forCDF Run II Preliminary2.70 2.90 3.10 3.30 3.50M(µµ) GeV/c2010000200003000040000Events/5 MeV/c2299,800 ± 800 EventsLuminosity = 39.7 pb-1Width = 24 MeV/c2FIGURE 4. The invariant mass distribution of triggeredJ/Ψevents reconstructed in the 39.7pb−1 of CDF II data.CDF Run II Preliminary0 4 8 12 16pT(J/ψ) GeV/c10-11101102dσ/dp T(|y|<0.6) . Br(J/ψ→µµ) nb/(GeV/c)Data with stat. uncertaintiesSystematic uncertaintiesFIGURE 5. The differential cross section for inclusiveJ/Ψas a function ofpT with |y| ≤ 0.6.the promptJ/Ψ’s, which are directly produced or de-cayed from higher charmonium states, their vertex areat the proton-antiproton interaction point. As the result,we can statistically separate these two components byexamining the projectedJ/Ψ decay distance along its RapidityψJ/0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Cross Section, nb110102 Cross Section per unit of rapidityψJ/Dzero Run2 PRELIMINARY)>5GeV/cψ pT(J/)>8GeV/cψ pT(J/FIGURE 6. The differential cross section forJ/Ψ as a func-tion of |y|.transverse momentum. The measuredb-fraction is thenapplied to the previously measured inclusiveJ/Ψ crosssection to obtain the differential production cross sectionof Hb → J/ΨX as a function ofpT(J/Ψ). However, theabove algorithm to extractb-fraction does not work forJ/Ψ candidate with low transverse momentum, becauseab-hadron with lowpT does not travel far away from theprimary vertex in the transverse plane. Therefore a mini-mumpT(J/Ψ)≥1.25GeV/c requirement is imposed fortheb-hadron cross section measurement as a function ofpT(J/Ψ) in order to have a reliable determination ofb-fraction. The measured differential cross section result isshown in Fig. 7.Luckily, the b-hadron decayed at rest can still trans-fer a few (∼ 1.7) GeV/c transverse momentum to itsJ/Ψ daughter because of the largeb-hadron mass. Theknowledge of the secondaryJ/Ψ production with trans-verse momenta less than 2.0GeV/c allows us to probethe b-hadrons with low transverse momenta down tozero. Therefore using the measuredb-hadron differen-tial cross section with 1.25≤ pT(J/Ψ) ≤ 17.0GeV/c,we are able to extract theb-hadron differential cross sec-tion as a function ofpT(Hb) down topT(Hb) = 0GeV/c.To do so, we perform a convolution that is based on theMonte Carlo template of theb-hadron transverse mo-mentum distribution. The unfolding procedure is thenrepeated using the measuredb-hadron production spec-trum as the input spectrum for the next iteration, untilthe χ2 comparison between the input and output spec-trum calculated after each iteration becomes stable. Themeasuredb-hadron cross section as a function ofpT(Hb)is plotted in Fig. 8. The totalb-hadron cross section isfound to beσ(pp̄→ HbX, |y(Hb)| ≤ 0.6)×Br(Hb → J/ΨX)×Br(J/Ψ → µµ) = 24.5±0.5(stat)+4.7−3.9(syst)nb,(2)CDF Run II Preliminary0 4 8 12 16pT(J/ψ) GeV/c10-210-11101dσ/dp T(J/ψ) . Br(J/ψ→µµ) nb/(GeV/c)(Includes correlated uncertainties)From bData with statistical uncertaintiesSystematic uncertaintiesFIGURE 7. b-hadron differential cross section as a functionof pT(J/Ψ).CDF Run II Preliminary0 5 10 15 20 25pT(Hb) GeV/c10-210-11101dσ/dp T(Hb) . Br(Hb→J/ψ X) . Br(J/ψ→µµ) nb/(GeV/c)(Includes correlated uncertainties)Data with statistical uncertaintiesSystematic uncertaintiesFIGURE 8. b-hadron differential cross section as a functionof pT(Hb) with |y| ≤ 0.6.The total singleb-quark cross section is obtained by di-vided this measurement by two, the branching fractions,and the rapidity correction factors obtained from MC. We (GeV)jetTE20 30 40 50 60 70 80 90 100 (nb/GeV)jetTdEσd10-310-210-1 DataR<0.3δPythia, CTEQ4M, DØ Run 2 PreliminaryFIGURE 9. Measured Run IIb-jet cross section compared totheoretical prediction.find:σ(pp̄→ b̄X, |y(b)| ≤ 0.6)= 18.0±0.4(stat)±3.8(syst)µb,(3)andσ(pp̄→ b̄X, |y(b)| ≤ 1)= 29.4±0.6(stat)±6.2(syst)µb.(4)B-JET PRODUCTION CROSS SECTIONUsing 3.4pb−1 of data, ab-jet production cross sectionanalysis has been performed by DØ . The candidate eventis selected by associating a muon track with a jet, whichis defined withR=√∆η2 + ∆φ2 cone algorithm. Noticethe fact that the muon decayed fromb quark has a highertransverse momentum with respect to the net momentumvector of combined muon and jet, the correspondingdistribution is then used to fit the b-jet fraction. Thesignal template is modeled from ab → µ Monte Carlosimulation, and the background template is extractedfrom 1.5 million QCD events. After correcting the muonand jet reconstruction efficiency, and the calorimeter jetenergy resolution, theb-jet cross section is obtained. Thepreliminary result is shown in Fig. 9 compared to thetheoretical prediction. This measurement is consistentwith the previous Run I measurement [14].CONCLUSIONThe understanding of the heavy flavor production is cur-rently one of the most important challenges faced byQCD. In this paper, we present the most recent mea-surements from CDF and DØ experiments. Given largeamount of data that have already been collected, rapidimprovement of Tevatron performance, and further un-derstanding of the detector, we expect that much moreprecise measurements on the heavy flavor productionwill be available in the near future. At the same time,several other analyses have also been carried out to ex-plore other aspects of heavy flavor production mecha-nism, such as thebb̄ correlation andcc̄ correlation duringthe production. In the next a few years, a combination ofbetter experimental data and improved theory should ad-vance our knowledges of the heavy quarks production.ACKNOWLEDGMENTSWe thank the CDF and DØ collaboration for their helpswhile preparing this paper. We also thank the conferenceorganizers for a wonderful meeting.REFERENCES1. Abbott, B., et al.,Phys. Lett., B487, 264–272 (2000).2. Acosta, D., et al.,Phys. Rev., D65, 052005 (2002).3. Nason, P., Dawson, S., and Ellis, R. K.,Nucl. Phys.,B327, 49–92 (1989).4. Albajar, C., et al.,Phys. Lett., B186, 237 (1987).5. Berger, E. L., et al.,Phys. Rev. Lett., 86, 4231–4234(2001).6. Cacciari, M., and Nason, P.,Phys. Rev. Lett., 89, 122003(2002).7. Blair, R., et al. (1996), FERMILAB-PUB-96-390-E.8. Abachi, S. (1996), FERMILAB-PUB-96-357-E.9. Ashmanskas, W., et al.,Nucl. Instrum. Meth., A447,218–222 (2000).10. Acosta, D., et al.,Phys. Rev. Lett., 91, 241804 (2003).11. Cacciari, M., and Nason, P.,JHEP, 09, 006 (2003).12. Kniehl., B. (Private communication), Their calculationemploys the method described in B.A. Kniehl, G. Kramer,B. Potter, Nucl. Phys.B597, 337-369 (2001).13. Binnewies, J., Kniehl, B. A., and Kramer, G.,Phys. Rev.,D58, 034016 (1998).14. Abbott, B., et al.,Phys. Rev. Lett., 85, 5068–5073 (2000).

Heavy flavor production at the Tevatron

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Heavy Flavor Production at the Tevatron
Chunhui Chen
(Representing the CDF and DØ Collaboration)
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.
Abstract. Using a subset of the current Run II data, the CDF and DØ have performed several measurements on heavy flavor
production. In this paper, we present a new measurement of prompt charm meson production by CDF. We also report the latest
CDF II measurements of inclusiveJ/Ψ production andb-production without requirement of minimum transverse momentum
on J/Ψ and b-quark. They are the first measurements of the total inclusive J/Ψ and b quark cross section in the central
rapidity region at a hadron collider. The results ofJ/Ψ cross section as a function of rapidity, andb-jet production cross
section measured by DØ are also reviewed.
INTRODUCTION
Measurements of the production cross section of heavy
flavor quarks (c andb quarks) in thepp̄ collisions pro-
vide us an opportunity to test the prediction based on
the Quantum Chromodynamics (QCD). No only is QCD
one of the four fundamental forces of the nature, but also
many searches of new physics beyond Standard Model
require a good understanding of the QCD background.
The Bottom quark production cross section has been
measured by both the CDF and DØ experiments [1,
2] at the Fermilab Tevatron inpp̄ collision at
√
s =
1.8TeV, and found to be about three times larger than
the next-to-leading order (NLO) QCD calculation [3,
4]. Since then, several theoretical explanation has been
proposed to solve the disagreement, such as the large
contributions from the NNLO QCD processes, possible
contribution from “new physics” [5] etc. Recently, a
more accurate description ofb quark fragmentation has
reduced the discrepancy to a factor 1.7 [6]. Nevertheless,
further experimental measurements on the heavy flavor
production are essential to shed light on the remaining
clouds of this long standing issue.
Since the end of Run I (1996), the Tevatron had un-
derdone major upgrade. The center of mass energy in the
pp̄ collision was increased from
√
s = 1.8TeV to
√
s =
1.96TeV. The large luminosity enhancement dramati-
cally increases the discovery reach and moves the exper-
imental program into a regime of precision hadron col-
lider physics. At the same time, both CDF [7] and D0 [8]
experimental collaborations significantly upgraded their
detectors to enrich the physics capabilities, especially for
the heavy flavor physics program. The Tevatron Run II
data taking period started in April 2002, so far the ac-
celerator has delivered about 300pb−1 integrated lumi-
nosities, both experiments collected more than 200pb−1
physics quality data. In this paper, we will give a brief
summary of the latest results on heavy flavor production
from Tevatron Run II.
PROMPT CHARM MESON
PRODUCTION CROSS SECTION
In order to help understanding the discrepancy between
measured Run I Bottom quark cross section measure-
ment and theoretical calculation, one can repeat previ-
ous measurement with better control of experimental un-
certainties. An alternative approach is to examine the
production rate of another heavy quark. Charm meson
production cross sections have not been measured inpp̄
collisions and may help to solve this disagreement. For
CDF II upgrade, one of the crucial improvement with re-
spect to the CDF I is the implementation of a Silicon Ver-
tex Trigger (SVT) [9], which allows us to trigger on dis-
placed tracks decayed from long-lived charm and bottom
hadrons. With this trigger, large amount of fully recon-
structed charm meson has been collected, opening a new
window for heavy flavor production studies at hadron
collider.
Using just 5.8±0.3pb−1 data, CDF performs a mea-
surement of prompt charm meson production cross
section [10]. The charm mesons are reconstructed in
the following decay modes:D0 → K−π+, D∗+ → D0π+
with D0 → K−π+, D+ → K−π+π+, D+s → φπ+ with
φ → K+K−, and their charge conjugate, as shown in
Fig. 1. We separate charm directly produced inpp̄ in-
teraction (prompt charm) from charm decayed fromB
]2)  [GeV/c+π-m(K
1.8 1.85 1.9
2
E
n
tr
ie
s 
p
er
 2
 M
eV
/c
0
1000
2000
3000
+π-K→0D (a)
]2)  [GeV/c+π-)-m(K+π+π-m(K
0.14 0.15 0.16
2
E
n
tr
ie
s 
p
er
 0
.3
 M
eV
/c
0
200
400
600
800 ,+π
0D→+D*
+π-K→0D
(b)
]2)  [GeV/c+π+π-m(K
1.7 1.8 1.9 2
2
E
n
tr
ie
s 
p
er
 2
 M
eV
/c
0
1000
2000
+π+π-K→+D (c)
]2)  [GeV/c+π-K+m(K
1.8 1.9 2 2.1
2
E
n
tr
ie
s 
p
er
 5
 M
eV
/c
0
100
200
300
+πφ→s+D
+πφ→+D
(d)
FIGURE 1. Charm signals summed over allpT bins: (a)
invariant mass distribution ofD0 → K−π+ candidates; (b)
mass difference distribution ofD∗+ → D0π+ candidates; (c)
invariant mass distribution ofD+ → K−π+π+ candidates; (d)
invariant mass distribution ofD+ → φπ+ and D+s → φπ+
candidates.
mesons (secondary charm) using the impact parameter of
the charm candidate with respect to the primary interac-
tion point. Prompt charm meson points to the beamline
and its impact parameter is zero. The secondary charm
meson candidate does not necessarily point back to the
primary vertex, it has a rather wide impact parameter
distribution. The shape of the impact parameter distri-
bution of secondary charm is obtained from a Monte
Carlo simulation. The detector impact parameter resolu-
tion is modeled from a sample ofK0S → π+π− decays
that satisfy the same trigger requirement. The prompt
charm fraction is measured as a function of charm me-
son pT . Average over allpT bins, (86.6± 0.4)% of the
D0 mesons,(88.1±1.1)% of D∗+, (89.1±0.4)% of D+,
and(77.3±3.8)% of D+s are promptly produced (statis-
tical uncertainties only).
The measured prompt charm meson integrated cross
section are found to beσ(D0, pT ≥ 5.5GeV/c, |y| ≤
1) = 13.3±0.2±1.5µb,σ(D∗+, pT ≥ 6.0GeV/c, |y| ≤
1) = 5.2± 0.1± 0.8µb, σ(D+, pT ≥ 6.0GeV/c, |y| ≤
1)= 4.3±0.1±0.7µbandσ(D+s , pT ≥ 8.0GeV/c, |y| ≤
1) = 0.75± 0.05± 0.22µb, where the first uncertainty
is statistical and the second systematic. The measured
differential cross sections are compared to two recent
calculations [11, 12], as shown in Fig. 2 and Fig. 3.
They are higher than the theoretical predictions by about
100% at lowpT and 50% at highpT . However, they are
compatible within uncertainties. The same models also
  [GeV/c]Tp
5 10 15 20
  [
nb
/G
eV
/c
]
T
/d
p
σd
10
2
10
3
10
4
  [
nb
/G
eV
/c
]
T
/d
p
σd
0D
  [GeV/c]Tp
5 10 15 20
  [
nb
/G
eV
/c
]
T
/d
p
σd
10
2
10
3
  [
nb
/G
eV
/c
]
T
/d
p
σd
+
D*
  [GeV/c]Tp
5 10 15 20
  [
nb
/G
eV
/c
]
T
/d
p
σd
10
2
10
3
  [
nb
/G
eV
/c
]
T
/d
p
σd
+D
  [GeV/c]Tp
5 10 15 20
  [
nb
/G
eV
/c
]
T
/d
p
σd
10
10
2
10
3
  [
nb
/G
eV
/c
]
T
/d
p
σd
+
sD
FIGURE 2. The measured differential cross section mea-
surements for|y| ≤ 1, shown by the points. The inner bars
represent the statistical uncertainties; the outer bars are the
quadratic sums of the statistical and systematic uncertainties.
The solid curves are the theoretical predictions from Cacciari
and Nason [11], with the uncertainties indicated by the shaded
bands. The dashed curve shown with theD∗+ cross section
is the theoretical prediction from Kniehl [12]; the dotted lines
indicate the uncertainty. No prediction is available yet for D+s
production.
underestimateB meson production at
√
s = 1.8TeV by
similar factors [2, 6, 13].
INCLUSIVE J/Ψ PRODUCTION CROSS
SECTION
The CDF II detector has improved the dimuon trigger
system with a lower threshold of 1.5GeV/c. This allows
us to trigger theJ/Ψ→ µ−µ+ event with transverse mo-
mentum all the way down topT (J/Ψ) = 0GeV/c. Using
about 39.7pb−1 data, CDF reconstructed 299800± 800
J/Ψ candidates (statistical uncertainty only), as shown
in Fig. 4. A new measurement of the total inclusiveJ/Ψ
cross section in the central rapidity region|y| ≤ 0.6 has
been carried out. This is the first measurement of the to-
tal inclusiveJ/Ψ cross section in the central rapidity re-
gion at a hadron collider. The differential cross section is
shown in Fig. 5, and the integrated cross section is mea-
sured to be:
σ(pp̄ → J/ΨX , |y(J/Ψ| ≤ 0.6)×Br(J/Ψ→ µµ)
= 240±1(stat)+35−28(syst)nb,
(1)
  [GeV/c]Tp
5 10 15 20
D
at
a/
T
h
eo
ry
0
0.5
1
1.5
2
2.5
D
at
a/
T
h
eo
ry
0D
  [GeV/c]Tp
5 10 15 20
D
at
a/
T
h
eo
ry
0
0.5
1
1.5
2
2.5
D
at
a/
T
h
eo
ry
+D*
  [GeV/c]Tp
5 10 15 20
D
at
a/
T
h
eo
ry
0
0.5
1
1.5
2
2.5
D
at
a/
T
h
eo
ry
+D
FIGURE 3. Ratio of the measured cross sections to the the-
oretical calculation from Cacciari and Nason. The inner error
bar represents the statistical uncertainty, the outer errobar the
quadratic sum of the statistical and systematic uncertainty. The
hatched band represents the uncertainty from varying the renor-
malization and factorization scale.
Taking advantage of the large azimuth coverage of its
muon system, the DØ measured the differential cross
section of the inclusiveJ/Ψ as a function of the rapidity
using 4.74pb−1. The distribution is shown in Fig. 6.
BOTTOM QUARK PRODUCTION
CROSS SECTION
The Run I centralb-quark production cross section mea-
sured by CDF and DØ has a minimum transverse mo-
mentum cut on theb-hadrons due to the trigger require-
ments. Since those measurements only explore a small
fraction (∼ 10%) of theb-hadronpT spectrum, it is not
clear from the data whether the excess over the theory is
due to an overall discrepancy of thebb̄ production rate, or
it is caused by a shift in the spectrum toward higherpT .
An inclusive measurement of bottom quark production
over all transverse momentum can certainly help resolve
this ambiguity.
Notice that large fraction ofb-hadronHb decays to
J/Ψ final states, whereHb denotes both hadron and anti-
hadron. CDF performed an analysis to extract the in-
clusive b-hadron cross section from the measured in-
clusive J/Ψ production cross section. Due to the long
live lifetime of theb-hadrons, the vertex of theJ/Ψ de-
cayed from ab-hadron (secondaryJ/Ψ) is usually hun-
dreds microns away from the primary vertex, while for
CDF Run II Preliminary
2.70 2.90 3.10 3.30 3.50
M(µµ) GeV/c2
0
10000
20000
30000
40000
E
ve
nt
s/
5 
M
eV
/c
2
299,800 ± 800 Events
Luminosity = 39.7 pb-1
Width = 24 MeV/c2
FIGURE 4. The invariant mass distribution of triggeredJ/Ψ
events reconstructed in the 39.7pb−1 of CDF II data.
CDF Run II Preliminary
0 4 8 12 16
pT(J/ψ) GeV/c
10-1
1
101
102
dσ
/d
p T
(|y
|<
0.
6)
 . 
B
r(
J/
ψ
→
µµ
) 
nb
/(
G
eV
/c
)
Data with stat. uncertainties
Systematic uncertainties
FIGURE 5. The differential cross section for inclusiveJ/Ψ
as a function ofpT with |y| ≤ 0.6.
the promptJ/Ψ’s, which are directly produced or de-
cayed from higher charmonium states, their vertex are
at the proton-antiproton interaction point. As the result,
we can statistically separate these two components by
examining the projectedJ/Ψ decay distance along its
 RapidityψJ/
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
C
ro
ss
 S
ec
ti
o
n
, n
b
1
10
10
2
 Cross Section per unit of rapidityψJ/
Dzero Run2 PRELIMINARY
)>5GeV/cψ pT(J/
)>8GeV/cψ pT(J/
FIGURE 6. The differential cross section forJ/Ψ as a func-
tion of |y|.
CDF Run II Preliminary
0 4 8 12 16
pT(J/ψ) GeV/c
10-2
10-1
1
101
dσ
/d
p T
(J
/ψ
) 
. B
r(
J/
ψ
→
µµ
) 
nb
/(
G
eV
/c
)
(Includes correlated uncertainties)
From b
Data with statistical uncertainties
Systematic uncertainties
FIGURE 7. b-hadron differential cross section as a function
of pT (J/Ψ).
transverse momentum. The measuredb-fraction is then
applied to the previously measured inclusiveJ/Ψ cross
section to obtain the differential production cross section
of Hb → J/ΨX as a function ofpT (J/Ψ). However, the
above algorithm to extractb-fraction does not work for
J/Ψ candidate with low transverse momentum, because
ab-hadron with lowpT does not travel far away from the
primary vertex in the transverse plane. Therefore a mini-
mumpT (J/Ψ)≥1.25GeV/c requirement is imposed for
theb-hadron cross section measurement as a function of
pT (J/Ψ) in order to have a reliable determination ofb-
fraction. The measured differential cross section result i
shown in Fig. 7.
CDF Run II Preliminary
0 5 10 15 20 25
pT(Hb) GeV/c
10-2
10-1
1
101
dσ
/d
p T
(H
b)
 . 
B
r(
H
b→
J/
ψ
 X
) 
. B
r(
J/
ψ
→
µµ
) 
nb
/(
G
eV
/c
)
(Includes correlated uncertainties)
Data with statistical uncertainties
Systematic uncertainties
FIGURE 8. b-hadron differential cross section as a function
of pT (Hb) with |y| ≤ 0.6.
Luckily, the b-hadron decayed at rest can still trans-
fer a few (∼ 1.7) GeV/c transverse momentum to its
J/Ψ daughter because of the largeb-hadron mass. The
knowledge of the secondaryJ/Ψ production with trans-
verse momenta less than 2.0GeV/c allows us to probe
the b-hadrons with low transverse momenta down to
zero. Therefore using the measuredb-hadron differen-
tial cross section with 1.25≤ pT (J/Ψ) ≤ 17.0GeV/c,
we are able to extract theb-hadron differential cross sec-
tion as a function ofpT (Hb) down topT (Hb) = 0GeV/c.
To do so, we perform a convolution that is based on the
Monte Carlo template of theb-hadron transverse mo-
mentum distribution. The unfolding procedure is then
repeated using the measuredb-hadron production spec-
trum as the input spectrum for the next iteration, until
the χ2 comparison between the input and output spec-
trum calculated after each iteration becomes stable. The
measuredb-hadron cross section as a function ofpT (Hb)
is plotted in Fig. 8. The totalb-hadron cross section is
found to be
σ(pp̄ → HbX , |y(Hb)| ≤ 0.6)×Br(Hb → J/ΨX)
×Br(J/Ψ→ µµ) = 24.5±0.5(stat)+4.7−3.9(syst)nb,
(2)
The total singleb-quark cross section is obtained by di-
vided this measurement by two, the branching fractions,
and the rapidity correction factors obtained from MC. We
 (GeV)jetTE
20 30 40 50 60 70 80 90 100
 (
n
b
/G
eV
)
je
t
T
d
Eσd
10
-3
10
-2
10
-1 Data
R<0.3δPythia, CTEQ4M, 
DØ Run 2 Preliminary
FIGURE 9. Measured Run IIb-jet cross section compared
to theoretical prediction.
find:
σ(pp̄ → b̄X , |y(b)| ≤ 0.6)
= 18.0±0.4(stat)±3.8(syst)µb,
(3)
and
σ(pp̄ → b̄X , |y(b)| ≤ 1)
= 29.4±0.6(stat)±6.2(syst)µb.
(4)
B-JET PRODUCTION CROSS SECTION
Using 3.4pb−1 of data, ab-jet production cross section
analysis has been performed by DØ . The candidate event
is selected by associating a muon track with a jet, which
is defined withR =
√
∆η 2+∆φ2 cone algorithm. Notice
the fact that the muon decayed fromb quark has a higher
transverse momentum with respect to the net momentum
vector of combined muon and jet, the corresponding
distribution is then used to fit the b-jet fraction. The
signal template is modeled from ab → µ Monte Carlo
simulation, and the background template is extracted
from 1.5 million QCD events. After correcting the muon
and jet reconstruction efficiency, and the calorimeter jet
energy resolution, theb-jet cross section is obtained. The
preliminary result is shown in Fig. 9 compared to the
theoretical prediction. This measurement is consistent
with the previous Run I measurement [14].
CONCLUSION
The understanding of the heavy flavor production is cur-
rently one of the most important challenges faced by
QCD. In this paper, we present the most recent mea-
surements from CDF and DØ experiments. Given large
amount of data that have already been collected, rapid
improvement of Tevatron performance, and further un-
derstanding of the detector, we expect that much more
precise measurements on the heavy flavor production
will be available in the near future. At the same time,
several other analyses have also been carried out to ex-
plore other aspects of heavy flavor production mecha-
nism, such as thebb̄ correlation andcc̄ correlation during
the production. In the next a few years, a combination of
better experimental data and improved theory should ad-
vance our knowledges of the heavy quarks production.
ACKNOWLEDGMENTS
We thank the CDF and DØ collaboration for their helps
while preparing this paper. We also thank the conference
organizers for a wonderful meeting.
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Heavy Flavor Production at the Tevatron

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