I discuss heavy flavor production at hadronic facilities. I present total
cross sections and differential distributions for top quark, bottom quark, and
charm quark production at the Tevatron and LHC colliders, and at fixed-target
experiments such as HERA-B. The calculations include complete next-to-leading
order corrections as well as higher-order soft-gluon corrections which are
important near kinematical threshold.Comment: 6 pages, 7 figures; invited talk at PANIC 2008, Eilat, Israel,
  November 9-14, 200

Aybat

Kidonakis

Martin

Nadolsky

Nikolaos Kidonakis

English

arXiv

Crossref

I discuss heavy flavor production at hadronic facilities. I present total cross sections and differential distributions for top quark, bottom quark, and charm quark production at the rrevatron and LHC colliders, and at fixed-target experiments such as HERA-B. The calculations include complete next-to-leading order corrections as well as higher-order soft-gluon corrections which are important near kinematical threshold

Kidonakis, Nikolaos

DigitalCommons@Kennesaw State University

Kennesaw State UniversityDigitalCommons@Kennesaw State UniversityFaculty Publications8-15-2009Heavy-Flavor Production at AcceleratorsNikolaos KidonakisKennesaw State University, nkidonak@kennesaw.eduFollow this and additional works at: https://digitalcommons.kennesaw.edu/facpubsPart of the Elementary Particles and Fields and String Theory Commons, and the NuclearCommonsThis Article is brought to you for free and open access by DigitalCommons@Kennesaw State University. It has been accepted for inclusion in FacultyPublications by an authorized administrator of DigitalCommons@Kennesaw State University. For more information, please contactdigitalcommons@kennesaw.edu.Recommended CitationKidonakis N. 2009. Heavy-flavor production at accelerators. Nuclear Physics a 827(1-4):448C-53C.arXiv:0901.2155v1  [hep-ph]  15 Jan 2009 Heavy-Flavor Production at AcceleratorsNikolaos Kidonakis1Kennesaw State University, Kennesaw, GA 30144, USAAbstractI discuss heavy flavor production at hadronic facilities. I present total cross sections and differ-ential distributions for top quark, bottom quark, and charm quark production at the Tevatronand LHC colliders, and at fixed-target experiments such as HERA-B. The calculations includecomplete next-to-leading order corrections as well as higher-order soft-gluon corrections whichare important near kinematical threshold.Key words: top quark, bottom quark, charm quark, soft gluonsPACS: 12.38.Bx, 12.38.Cy, 14.65.Ha, 14.65.Fy, 14.65.Dw1. IntroductionQCD corrections are typically large for heavy quark production. The current state-of-the-art theoretical calculations of cross sections include higher-order corrections beyondnext-to-leading order (NLO). Soft-gluon corrections of the form [lnk(s4/m2)/s4]+, withs4 the kinematical distance from threshold, are dominant near threshold and can beresummed. At next-to-leading-logarithm (NLL) accuracy this requires one-loop calcu-lations in the eikonal approximation; at next-to-next-to-leading-logarithm (NNLL) itrequires two-loop calculations. Approximate next-to-next-to-leading order (NNLO) crosssections can be derived from the expansion of the resummed cross section.In the next section I present some recent calculations for top quark pair production atthe Tevatron and the LHC. This is followed by a section on single top quark production,and a section on bottom and charm quark production at fixed-target facilities, includingHERA-B. In the last section I discuss recent work on two-loop calculations in the eikonalEmail address: nkidonak@kennesaw.edu (Nikolaos Kidonakis).URL: http://science.kennesaw.edu/∼nkidonak/ (Nikolaos Kidonakis).1 This work was supported by the National Science Foundation under Grant No. PHY 0555372.Preprint submitted to Elsevier 20 January 2014165 170 175 180m (GeV)5678910σ (pb)NLO  µ=mNLO  µ=m/2, 2mNNLO  approx µ=mNNLO  approx µ=m/2, 2mp p -> t t   at  Tevatron      S1/2=1.96 TeV     MRST2006 pdf 165 170 175 180m (GeV)5678910σ (pb)NLO  µ=mNLO  µ=m/2, 2mNNLO approx µ=mNNLO approx µ=m/2, 2mp p -> t t   at  Tevatron      S1/2=1.96 TeV     CTEQ6.6 pdf Fig. 1. The NLO and approximate NNLO tt¯ cross sections in pp collisions at the Tevatron using theMRST 2006 NNLO (left) and CTEQ6.6M (right) pdf.approximation that are relevant for increasing the accuracy of resummation for heavyquark production.2. Top quark pair productionThe dominant process for top quark production in hadron colliders is pair productionvia the processes, at leading order, qq¯ → tt¯ and gg → tt¯. There is very good agreementof theory, including soft-gluon corrections [1], with Tevatron data [2,3]. The same isexpected to hold with future LHC data.Figure 1 shows the cross section from an approximate NNLO calculation [1] for Teva-tron energy, using two different parton distribution function (pdf) sets, MRST 2006NNLO [4] and CTEQ6.6M [5].For reference, below is the cross section for a top mass of 172 GeV,σpp¯→tt¯(1.96TeV,mt = 172GeV,MRST) = 7.80± 0.31+0.03−0.27+0.23−0.19 pb = 7.80+0.39−0.45 pb ,σpp¯→tt¯(1.96TeV,mt = 172GeV,CTEQ) = 7.39± 0.30−0.03−0.20+0.48−0.37 pb = 7.39+0.57−0.52 pb .The first uncertainty indicated is a kinematics uncertainty arising from the choice ofusing single-particle-inclusive (1PI) or pair-invariant mass (PIM) kinematics; the seconduncertainty is from scale variation over a rangem/2 ≤ µ ≤ 2m, and the third uncertaintyis from the pdf and varies quite a bit between the MRST and CTEQ sets used. The totaluncertainty indicated comes from the addition in quadrature of the three individualuncertainties. It is interesting to note that at present the experimental and theoreticaluncertainties are of similar size. It is also clear from Figure 1 that the scale dependenceis greatly decreased at NNLO.Figure 2 shows the corresponding results [1] for LHC energy. The cross sections anduncertainties for mt = 172 GeV areσpp→tt¯(14TeV,mt = 172GeV,MRST) = 968± 4+79−50+12−13 pb = 968+80−52 pb ,σpp→tt¯(14TeV,mt = 172GeV,CTEQ) = 919± 4+70−45+29−31 pb = 919+76−55 pb .2165 170 175 180m (GeV)600800100012001400σ (pb)NLO  µ=mNLO  µ=m/2, 2mNNLO  approx µ=mNNLO  approx µ=m/2, 2mp p -> t t   at  LHC     S1/2=14 TeV     MRST2006 pdf 165 170 175 180m (GeV)600800100012001400σ (pb)NLO  µ=mNLO  µ=m/2, 2mNNLO approx  µ=mNNLO approx  µ=m/2, 2mp p -> t t   at  LHC     S1/2=14 TeV     CTEQ6.6 pdf Fig. 2. The NLO and approximate NNLO tt¯ cross sections in pp collisions at the LHC using the MRST2006 NNLO (left) and the CTEQ6.6M (right) pdf.0 50 100 150 200 250 300pT (GeV)00.010.020.030.040.050.06dσ /dp T (pb/GeV)NLO  µ=mNLO  µ=m/2, 2mNNLO approx µ=mTop pT distribution at Tevatron  S1/2=1.96 TeV  m=175 GeV  0 100 200 300 400 500pT (GeV)0123456dσ /dp T (pb/GeV)NLO  µ=mNLO  µ=m/2, 2mNNLO approx µ=mTop pT distribution at LHC   S1/2=14 TeV   m=175 GeV  Fig. 3. The NLO and approximate NNLO top quark pT distributions at the Tevatron (left) and the LHC(right).Figure 3 shows the top quark transverse momentum, pT , distribution at the Tevatronand the LHC for a top quark mass of 175 GeV [6].3. Single top quark productionThere is now evidence for single top production at the Tevatron [7] with a cross sectionconsistent with theory [8]. The partonic processes at leading order are the t channel, qb→q′t and q¯b→ q¯′t; the s channel: qq¯′ → b¯t; and associated tW production, bg → tW−. Inthe results below we include soft-gluon corrections at NNLO and NNNLO [8,9,10] anduse the MRST 2004 NNLO pdf [11].We begin with results for the Tevatron [8,10]. For the t channel we findσt−channeltop (1.96TeV,mt = 172GeV) = 1.14+0.02−0.01 ± 0.06 pb = 1.14± 0.06 pb ,where the first uncertainty is from scale variation over m/2 ≤ µ ≤ 2m and the secondis from the pdf, and we add the two in quadrature for the total uncertainty. The crosssection for single antitop production is identical.For the s channel we find3160 165 170 175 180mt (GeV)0.911.11.21.31.4σ  (pb)LONLO approxNNLO approxNNNLO approxSingle top at  Tevatron   t-channel    S1/2=1.96 TeV       µ=mt160 165 170 175 180mt (GeV)00.10.20.30.40.50.60.70.80.91σ  (pb)LONLO approxNNLO approxNNNLO approxSingle top at  Tevatron   s-channel    S1/2=1.96 TeV       µ=mtFig. 4. The single top quark cross sections at the Tevatron in the t channel (left) and s channel (right).160 165 170 175 180mt (GeV)02468101214σ  (pb)LONLO approxNNLO approxNNNLO approxSingle top at the LHC   s-channel    S1/2=14 TeV       µ=mt160 165 170 175 180mt (GeV)20304050607080σ  (pb)LONLO approxNNLO approxNNNLO approxbg --> tW-  at  the  LHC     S1/2=14 TeV       µ=mtFig. 5. The single top quark cross sections at the LHC in the s channel (left) and tW channel (right).σs−channeltop (1.96TeV,mt = 172GeV) = 0.53± 0.02± 0.01 pb = 0.53± 0.02 pb .Again, the cross section for single antitop production is identical.In Figure 4 we plot the cross sections for the t and s channels at various orders versusthe top quark mass, with the scale set at µ = mt.The cross section for single top production at the Tevatron via the tW channel issmaller: σtW (1.96TeV,mt = 172GeV) = 0.14± 0.02± 0.02 pb = 0.14± 0.03 pb, with anidentical result for t¯W production.We continue with single top production at the LHC [9,10]. We note that here in the tand s channels the results are different for the single top and single antitop cross sections.In the t channel the threshold approximation is not good at the LHC energy, and thuswe do not include soft-gluon corrections. The exact NLO cross section for single top isσt−channeltop (14TeV,mt = 172GeV) = 149± 5± 3 pb = 149± 6 pb, while for single antitopit is σt−channelantitop (14TeV,mt = 172GeV) = 91± 3± 2 pb = 91± 4 pb.In the s channel the cross section, including soft-gluon corrections through NNNLO,for single top production isσs−channeltop (14TeV,mt = 172GeV) = 7.7+0.6−0.5 ± 0.1 pb = 7.7+0.6−0.5 pb ,while for single antitop production it is4Fig. 6. (Left) The bb¯ cross section in pp collisions. Shown are NLO (solid) and NNLO-NNLL (dot-dashed)results for mb = 4.75 GeV, and NNLO-NNNLL+ζ results for mb = 4.5, 4.75, 5 GeV (other curves) withµ = mb/2 (a), µ = mb (b) and µ = 2mb (c). (Right) The cc¯ cross section in pp collisions. Shown are NLO(solid), NNLO-NNLL (dashed) and NNLO-NNNLL+ζ (dot-dashed) results for mc = 1.2 GeV (a,b), 1.5GeV (c,d) and 1.8 GeV (e,f), with µ = mc (a,c,e) and µ = 2mc (b,d,f).σs−channelantitop (14TeV,mt = 172GeV) = 4.3± 0.1± 0.1 pb = 4.3± 0.2 pb .In the tW channel the cross section, including soft corrections through NNNLO, isσtW (14TeV,mt = 172GeV) = 43± 5± 1 pb = 43± 5 pb ,with an identical result for t¯W production.In Figure 5 we plot results for the s channel and tW production at the LHC.4. Bottom and charm quark pair productionWe now turn to bottom pair and charm pair production at fixed-target facilities. InFigure 6 we show results for the theoretical cross section [12] in pp collisions versus√Susing the MRST 2002 NNLO pdf [13], and compare with some experimental data. Forboth bb¯ and cc¯ production there are large theoretical and experimental uncertainties.For the HERA-B experiment the theoretical cross section is [12]σpp→bb¯(41.6GeV,mb = 4.75GeV) = 28± 9+15−10 nb ,where the first uncertainty is due to scale variation and the second is due to uncertaintyin the bottom quark mass, 4.5 ≤ mb ≤ 5 GeV. This is in agreement with HERA-B data[14].5. Two-loop soft-gluon resummation for heavy quarksFurther progress in the soft-gluon resummation program at NNLL requires two-loopcalculations in the eikonal approximation. Resummation is controlled by a soft anomalousdimension matrix, ΓS [15], which can be calculated by the evaluation of dimensionallyregularized graphs with Wilson lines.5pik2pjk1pik2pjk1piklpjpilkpjpik1k2pjpilkpjpiklpjpiklpjpiklpjFig. 7. Two-loop diagrams with heavy-quark eikonal lines.Figure 7 shows some typical two-loop diagrams with heavy-quark lines; there are addi-tional graphs not shown here including heavy-quark self-energies and one-loop countert-erms. For massless quarks ΓS was calculated at two loops in Ref. [16] and shown to beproportional to the one-loop result. The mass makes the corresponding calculation forheavy quarks more difficult but several results for the required integrals have appeared inRefs. [17,18] and work is ongoing. It is clear that the two-loop CFnf terms in the massivecase obey the same relation with respect to the one-loop result as in the massless case,but the CFCA terms are more challenging.References[1] N. Kidonakis and R. Vogt, Phys. Rev. D 78, 074005 (2008), arXiv:0805.3844 [hep-ph].[2] CDF Collaboration, Phys. Rev. Lett. 96, 202002 (2006) [hep-ex/0603043]; Phys. Rev. D 74,072006 (2006) [hep-ex/0607035]; D 74, 072005 (2006) [hep-ex/0607095]; D 76, 072009 (2007),arXiv:0706.3790 [hep-ex].[3] D0 Collaboration, Phys. Rev. D 74, 112004 (2006) [hep-ex/0611002]; D 76, 072007 (2007)[hep-ex/0612040]; D 76, 092007 (2007), arXiv:0705.2788 [hep-ex]; D 76, 052006 (2007),arXiv:0706.0458 [hep-ex]; Phys. Rev. Lett. 100, 192004 (2008), arXiv:0803.2779 [hep-ex].[4] A.D. Martin, W.J. Stirling, R.S. Thorne, and G. Watt, Phys. Lett. B 652, 292 (2007),arXiv:0706.0459 [hep-ph].[5] P.M. Nadolsky et. al., Phys. Rev. D 78, 013004 (2008), arXiv:0802.0007 [hep-ph].[6] N. Kidonakis and R. Vogt, Phys. Rev. D 68, 114014 (2003) [hep-ph/0308222].[7] D0 Collaboration, Phys. Rev. Lett. 98, 181802 (2007) [hep-ex/0612052]; Phys. Rev. D 78,012005 (2008), arXiv:0803.0739 [hep-ex]; CDF Collaboration, Phys. Rev. Lett. 101, 252001 (2008),arXiv:0809.2581 [hep-ex].[8] N. Kidonakis, Phys. Rev. D 74, 114012 (2006) [hep-ph/0609287].[9] N. Kidonakis, Phys. Rev. D 75, 071501(R) (2007) [hep-ph/0701080].[10] N. Kidonakis, Acta Phys. Polon. B 39, 1593 (2008), arXiv:0802.3381 [hep-ph].[11] A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S. Thorne, Phys. Lett. B 604, 61 (2004)[hep-ph/0410230].[12] N. Kidonakis and R. Vogt, Eur. Phys. J. C 36, 201 (2004) [hep-ph/0401056].[13] A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S. Thorne, Eur. Phys. J. C 28, 455 (2003)[hep-ph/0211080].[14] HERA-B Collaboration, Phys. Rev. D 73, 052005 (2006) [hep-ex/0512030]; Phys. Lett. B 650, 103(2007) [hep-ex/0612024].[15] N. Kidonakis and G. Sterman, Nucl. Phys. B 505, 321 (1997) [hep-ph/9705234].[16] S.M. Aybat, L.J. Dixon, and G. Sterman, Phys. Rev. D 74, 074004 (2006) [hep-ph/0607309].[17] N. Kidonakis, A. Sabio Vera, and P. Stephens, arXiv:0802.4240 [hep-ph].[18] N. Kidonakis and P. Stephens, in DIS 2008, arXiv:0805.1193 [hep-ph], and in preparation.6

Heavy-Flavor Production at Accelerators

https://digitalcommons.kennesaw.edu/cgi/viewcontent.cgi?article=1224&amp;context=facpubs

Heavy-Flavor Production at Accelerators

Abstract

Similar works

Full text

Available Versions

Crossref

DigitalCommons@Kennesaw State University