HATHOR – HAdronic Top and Heavy quarks crOss section calculatoR

HATHOR is a fast performance tool with different options to choos (like order of calculation, PDF used, collider type etc) to calculate hadronic pair production cross sections of heavy quarks (top, b', t') up to NNLO in proton-proton (pp) or proton-antiproton (ppbar) collisions. All the necessary information about Hathor can be found from the following links:

1) S.Moch's talk in the Top20120 conference.

2) The tool is available also under links:

http://www-zeuthen.desy.de/~moch/hathor

http://www.physik.hu-berlin.de/pep/tools/

3) You may also directly contact P.Uwer or S.Moch to get the package.

How it works

Functionality of HATHOR is based on the use of the expression:

\[ \sigma_{pp\rightarrow q\bar{q}}(\sqrt{s},m_q)=\sum_{i,j=q,\bar{q},g} \int dx_idx_jf^A_i(x_i,\mu_f^2) f^B_j(x_j,\mu_f^2) \sigma_{ij\rightarrow q\bar{q}}(\rho,m^2_q,x_i,x_j,\alpha_s,\mu_r,\mu_f). \]

where $\sigma_{ij\rightarrow q\bar{q}}$ is a quark-antiquark pair production cross sections induced by i-th and j-th partons interaction, $f_i^A(x_i,\mu_f^2)$ and $f_j^B(x_j,\mu_f^2)$ are $i$-th and $j$-th partons distribution functions (PDF) in the A-th and B-th incoming nucleons correspondingly, $\mu_f$ and $\mu_r$ are factorization and renormalization scales, and $x_i$ and $x_j$ momentum fraction of each interacting parton in incoming nucleons A and B.

In order to calculate the central value factorization $\mu_f$ and renormalization $\mu_r$ scale parameters are set to a heavy quark mass, i.e. $\mu_f=\mu_r=m_q$. Along with central value the tool calculates also errors. There are two kind of errors: 1) errors coming from factorization $\mu_f$ and renormalization $\mu_r$ scales and 2) PDFs errors.

1) Scale errors are calculated by setting $\mu_f=\mu_r=m_q/2$ and $\mu_f=\mu_r=2m_q$ in order to get upper and lower deviations from the central value respectively.

2) PDF errors can be calculated in two ways: a) in a simplified way, where upper and lower deviations from the central value are calculated as averaged, according to the formula $\Delta = \frac{1}{2}\sqrt{\sum_{i=1}^N[max(\sigma_i^+-\sigma_i^-)]^2}$ and thus errors are symmetric; b) in a more general way, where deviations from the central value are calculated according to the formula $\Delta \sigma_{max}^+=\sqrt{\sum^N_{i=1}[max(\sigma_i^+-\sigma_0,\sigma_i^--\sigma_0,0)]^2}$, for the upper deviation, and formula $\Delta \sigma_{max}^-=\sqrt{\sum^N_{i=1}[max(\sigma_0-\sigma_i^+,\sigma_0-\sigma_i^-,0)]^2}$, for the lower deviation, so that the errors are asymmetric.

To read more on the subject, go to References.

Validation

Validation of the tool is done comparing heavy quarks pair production cross sections calculated using this tool with ones obtained from other open official sources, first of all from different articles.

Below Top quark pair production cross sections in proton-proton (pp) and proton-antiproton (ppb) collisions calculated by this tool (in red) are compared with ones obtained from arXiv/hep-ph/0804.2800 (in blue). PDF errors are calculated in the asymmetric way. Cross sections are given in picobarns (pb).

  • $\sigma_{NLO}$ (pp, Mt=171 GeV, CME=14 TeV, CTEQ6.5) = 875+102-100(scales) +30-29(PDFs)
  • CS_nlo(pp, Mt=171 GeV, CME=14 TeV, CTEQ6.5) = 875+102-101(scales)+30-29(PDFs)

  • CS_lo (pp, Mt=171 GeV, CME=14 TeV, CTEQ6.5) = 583+165-120(scales)+20-19(PDFs)
  • CS_lo (pp, Mt=171 GeV, CME=14 TeV, CTEQ6.5) = 582+164-120(scales)+20-19(PDFs)

  • CS_nlo(pp, Mt=171 GeV, CME=14 TeV, MRST2006nnlo) = 927+109-107(scales)+11-12(PDFs)
  • CS_nlo(pp, Mt=171 GeV, CME=14 TeV, MRST2006nnlo) = 925+113-109(scales)+12-11(PDFs)

  • CS_lo (pp, Mt=171 GeV, CME=14 TeV, MRST2006nnlo) = 616+172-126(scales)+7-8(PDFs)
  • CS_lo (pp, Mt=171 GeV, CME=14 TeV, MRST2006nnlo) = 634+178-130(scales)+7-8(PDFs)

  • CS_nlo(ppb, Mt=171 GeV, CME=1.96 TeV, CTEQ6.5) = 7.35+0.38-0.80(scales)+0.49-0.34(PDFs)
  • CS_nlo(ppb, Mt=171 GeV, CME=1.96 TeV, CTEQ6.5) = 7.45+0.43-0.83(scales)+0.49-0.34(PDFs)

  • CS_lo (ppb, Mt=171 GeV, CME=1.96 TeV, CTEQ6.5) = 5.92+2.34-1.54(scales)+0.32-0.24(PDFs)
  • CS_lo (ppb, Mt=171 GeV, CME=1.96 TeV, CTEQ6.5) = 5.92+2.34-1.54(scales)+0.32-0.24(PDFs)

  • CS_nlo(ppb, Mt=171 GeV, CME=1.96 TeV, MRST2006nnlo) = 7.62 + 0.45 - 0.88 (scales) + 0.23 - 0.18 (PDFs)
  • CS_nlo(ppb, Mt=171 GeV, CME=1.96 TeV, MRST2006nnlo) = 7.70 + 0.53 - 0.93 (scales) + 0.23 - 0.18 (PDFs)

  • CS_lo (ppb, Mt=171 GeV, CME=1.96 TeV, MRST2006nnlo) = 6.05 + 2.47 - 1.61 (scales) + 0.16 - 0.13 (PDFs)
  • CS_lo (ppb, Mt=171 GeV, CME=1.96 TeV, MRST2006nnlo) = 6.04 + 2.49 - 1.62 (scales) + 0.16 - 0.13 (PDFs)

Here Top quark pair production cross sections in proton-proton (pp) and proton-antiproton (ppb) collisions calculated by this tool (in red) are compared with ones obtained from arXiv/hep-ph/0906.5273 (in green). PDF errors are calculated in the symmetric way (as given in the source).

  • CS_nnlo(pp, Mt=173 GeV, CME=14 TeV, CTEQ6.6) = 874 + 9 - 33(scales) + 28 - 28(PDFs)
  • CS_nlo(pp, Mt=173 GeV, CME=14 TeV, CTEQ6.5) = 833 + 96 - 97(scales) + 28 - 28(PDFs)

  • CS_nnlo(pp, Mt=173 GeV, CME=14 TeV, MSTW2008) = 887 + 9 - 33(scales) + 15 - 15(PDFs)
  • CS_nlo(pp, Mt=173 GeV, CME=14 TeV, CTEQ6.5) = 846 + 98 - 98(scales) + 15 - 15(PDFs)

  • CS_nnlo(ppb, Mt=173 GeV, CME=1.96 TeV, CTEQ6.6) = 7.34 + 0.24 - 0.38 (scales) + 0.41 - 0.41 (PDFs)
  • CS_nlo(ppb, Mt=173 GeV, CME=1.96 TeV, CTEQ6.6) = 6.88 + 0.40 - 0.77 (scales) + 0.44?? - 0.33?? (PDFs)

  • CS_nnlo(ppb, Mt=173 GeV, CME=1.96 TeV, MSTW2008) = 7.04 + 0.24 - 0.36 (scales) + 0.14 - 0.14 (PDFs)
  • CS_nlo(ppb, Mt=173 GeV, CME=1.96 TeV, MSTW2008) = 6.60 + 0.37 - 0.73 (scales) + 0.14 - 0.14 (PDFs)

Some cross section numbers

This section represents some heavy (or top) quark pair production cross sections numbers. Under Scale errors renormalization and factorization errors are understood. Cross sections are given in picobarns (pb).

Top pair production

NLO cross sections

This section gives some cross sections for Top pair production in pp collisions. All NLO cross sections are calculated using CTEQ6.6 PDF set.

Top cross sections for 7 TeV
Top Mass (GeV) Central value Scale errors PDF errors
170 162.7 + 19.6 - 21.1 + 11.8 - 10.6
171 157.8 + 19.0 - 20.5 + 11.4 - 10.6
172 153.1 + 18.5 - 19.9 + 11.4 - 10.2
173 148.5 + 17.8 - 19.2 + 11.2 - 09.8
174 144.2 + 17.3 - 18.7 + 10.8 - 09.6
175 139.9 + 16.7 - 18.1 + 10.9 - 09.3

Top cross sections for 10 TeV
Top Mass (GeV) Central value Scale errors PDF errors
170 408.6 + 48.9 - 49.9 + 20.1 - 18.5
171 397.4 + 47.4 - 48.8 + 18.8 - 18.7
172 386.4 + 45.6 - 47.6 + 17.9 - 18.8
173 375.6 + 44.3 - 46.5 + 17.7 - 18.7
174 364.9 + 43.1 - 45.0 + 17.7 - 17.5
175 354.7 + 42.3 - 43.5 + 17.6 - 17.0

Top cross sections for 14 TeV
Top Mass (GeV) Central value Scale errors PDF errors
170 903.4 + 105.5 - 105.8 + 26.7 - 31.5
171 877.9 + 103.3 - 102.2 + 28.3 - 28.2
172 855.0 + 100.2 - 99.2 + 25.8 - 29.0
173 833.1 + 96.4 - 97.2 + 26.9 - 28.3
174 810.9 + 93.5 - 94.9 + 24.9 - 29.0
175 788.6 + 92.3 - 90.7 + 27.7 - 25.4

4th generation quarks pair production

NLO cross sections

In this section you can find some cross section numbers for heavy quark pair production in pp and ppbar collisions.

1.96 TeV cross sections for ppbar (Tevatron) collisions

Quark mass (GeV) Central value Scale errors PDF errors  
160 10.41 + 0.62 - 1.17 + 0.70 - 0.54 x 1
180 5.55 + 0.32 - 0.62 + 0.35 - 0.26 x 1
200 3.08 + 0.18 - 0.35 + 0.18 - 0.14 x 1
220 1.76 + 0.11 - 0.20 + 0.10 - 0.08 x 1
240 [ 10.25 + 0.66 - 1.22 + 0.56 - 0.47 ] x 0.1
260 [ 6.05 + 0.42 - 0.74 + 0.34 - 0.28 ] x 0.1
280 [ 3.60 + 0.27 - 0.45 + 0.21 - 0.18 ] x 0.1
300 [ 2.16 + 0.17 - 0.28 + 0.14 - 0.12 ] x 0.1
320 [ 1.30 + 0.11 - 0.17 + 0.09 - 0.08 ] x 0.1
340 [ 7.79 + 0.71 - 1.07 + 0.60 - 0.52 ] x 0.01
360 [ 4.67 + 0.46 - 0.66 + 0.41 - 0.34 ] x 0.01
380 [ 2.80 + 0.29 - 0.41 + 0.27 - 0.23 ] x 0.01
400 [ 1.66 + 0.19 - 0.25 + 0.18 - 0.15 ] x 0.01
420 [ 0.98 + 0.12 - 0.15 + 0.12 - 0.10 ] x 0.01
440 [ 5.77 + 0.72 - 0.92 + 0.77 - 0.62 ] x 0.001
460 [ 3.36 + 0.44 - 0.55 + 0.50 - 0.40 ] x 0.001
480 [ 1.93 + 0.27 - 0.32 + 0.32 - 0.25 ] x 0.001
500 [ 1.10 + 0.16 - 0.19 + 0.20 - 0.16 ] x 0.001
520 [ 6.18 + 0.96 - 1.09 + 1.24 - 0.97 ] x 0.0001
540 [ 3.41 + 0.56 - 0.62 + 0.76 - 0.60 ] x 0.0001
560 [ 1.85 + 0.32 - 0.35 + 0.46 - 0.36 ] x 0.0001
580 [ 0.99 + 0.18 - 0.19 + 0.27 - 0.21 ] x 0.0001
600 [ 5.15 + 0.97 - 1.02 + 1.56 - 1.23 ] x 0.00001

7 TeV cross sections for pp (LHC) collisions

Quark mass (GeV) central value Scale errors PDF errors  
300 7.32 + 0.77 - 0.92 + 0.96 - 0.77 x 1
325 4.59 + 0.47 - 0.58 + 0.62 - 0.52 x 1
350 2.95 + 0.30 - 0.37 + 0.44 - 0.35 x 1
375 1.94 + 0.19 - 0.24 + 0.30 - 0.24 x 1
400 1.31 + 0.13 - 0.16 + 0.21 - 0.17 x 1
450 [ 6.21 + 0.59 - 0.77 + 1.09 - 0.84 ] x 0.1
500 [ 3.11 + 0.29 - 0.38 + 0.59 - 0.44 ] x 0.1
550 [ 1.63 + 0.15 - 0.20 + 0.33 - 0.24 ] x 0.1
600 [ 0.89 + 0.08 - 0.11 + 0.19 - 0.14 ] x 0.1
650 [ 4.95 + 0.46 - 0.62 + 1.11 - 0.79 ] x 0.01
700 [ 2.83 + 0.27 - 0.36 + 0.67 - 0.47 ] x 0.01
750 [ 1.65 + 0.16 - 0.21 + 0.42 - 0.28 ] x 0.01
800 [ 0.98 + 0.09 - 0.13 + 0.26 - 0.18 ] x 0.01
850 [ 5.93 + 0.57 - 0.77 + 1.65 - 1.11 ] x 0.001
900 [ 3.61 + 0.36 - 0.47 + 1.07 - 0.71 ] x 0.001
950 [ 2.23 + 0.22 - 0.30 + 0.69 - 0.46 ] x 0.001
1000 [ 1.38 + 0.14 - 0.19 + 0.46 - 0.30 ] x 0.001

10 TeV cross sections for pp (LHC) collisions

Quark mass (GeV) central value Scale errors PDF errors  
300 22.3 + 2.3 - 2.7 + 2.1 - 1.8 x 1
350 9.60 + 0.97 - 1.14 + 1.04 - 0.89 x 1
400 4.53 + 0.44 - 0.54 + 0.55 - 0.46 x 1
450 2.29 + 0.22 - 0.27 + 0.31 - 0.25 x 1
500 1.23 + 0.11 - 0.14 + 0.18 - 0.14 x 1
550 [ 6.88 + 0.62 - 0.80 + 1.08 + 0.85 ] x 0.1
600 [ 4.00 + 0.36 - 0.47 + 0.66 - 0.51 ] x 0.1
650 [ 2.40 + 0.21 - 0.28 + 0.41 - 0.32 ] x 0.1
700 [ 1.48 + 0.13 - 0.17 + 0.27 - 0.20 ] x 0.1
750 [ 0.93 + 0.08 - 0.11 + 0.18 - 0.13 ] x 0.1
800 [ 5.97 + 0.51 - 0.69 + 1.19 - 0.86 ] x 0.01
850 [ 3.90 + 0.33 - 0.45 + 0.81 - 0.57 ] x 0.01
900 [ 2.58 + 0.22 - 0.30 + 0.55 - 0.39 ] x 0.01
950 [ 1.73 + 0.15 - 0.20 + 0.39 - 0.27 ] x 0.01
1000 [ 1.17 + 0.10 - 0.14 + 0.27 - 0.19 ] x 0.01

14 TeV cross sections for pp (LHC) collisions

Quark mass (GeV) central value Scale errors PDF errors  
300 57.2 + 5.9 - 6.6 + 3.7 - 3.6 x 1
350 25.8 + 2.6 - 2.9 + 2.0 - 1.8 x 1
400 12.8 + 1.2 - 1.5 + 1.1 - 1.0 x 1
450 6.77 + 0.64 - 0.76 + 0.68 - 0.58 x 1
500 3.78 + 0.35 - 0.42 + 0.42 - 0.36 x 1
550 2.21 + 0.20 - 0.25 + 0.26 + 0.22 x 1
600 1.34 + 0.12 - 0.15 + 0.17 - 0.14 x 1
650 [ 8.42 + 0.73 - 0.93 + 1.14 - 0.94 ] x 0.1
700 [ 5.41 + 0.46 - 0.59 + 0.78 - 0.62 ] x 0.1
750 [ 3.56 + 0.30 - 0.39 + 0.54 - 0.42 ] x 0.1
800 [ 2.39 + 0.20 - 0.26 + 0.38 - 0.30 ] x 0.1
850 [ 1.63 + 0.13 - 0.18 + 0.27 - 0.21 ] x 0.1
900 [ 1.13 + 0.09 - 0.12 + 0.19 - 0.15 ] x 0.1
950 [ 7.98 + 0.64 - 0.87 + 1.40 - 1.06 ] x 0.01
1000 [ 5.68 + 0.45 - 0.62 + 1.04 - 0.76 ] x 0.01

NNLO cross sections

The following NNLO approximate cross sections are calculated using MSTW2008nnlo68cl NNLO PDF.

7 TeV cross sections for pp (LHC) collisions

Quark mass (GeV) central value Scale errors PDF errors  
200 [ 76.52 + 1.65 - 4.35 + 2.23 - 2.24 ] x 1
225 [ 40.48 + 0.95 - 2.31 + 1.25 - 1.25 ] x 1
250 [ 22.60 + 0.56 - 1.31 + 0.73 - 0.73 ] x 1
275 [ 13.19 + 0.34 -0.76 + 0.44 - 0.44 ] x 1
300 [ 7.99 + 0.22 - 0.47 + 0.28 - 0.27 ] x 1
325 [ 4.99 + 0.14 - 0.29 + 0.18 - 0.18 ] x 1
350 [ 3.20 + 0.10 - 0.19 + 0.12 - 0.12 ] x 1
375 [ 2.10 + 0.07 - 0.12 + 0.08 - 0.08 ] x 1
400 [ 1.41 + 0.05 - 0.08 + 0.05 - 0.05 ] x 1
425 [ 9.57 + 0.32 - 0.57 + 0.38 - 0.37 ] x 0.1
450 [ 6.62 + 0.22 - 0.39 + 0.27 - 0.26 ] x 0.1
475 [ 4.64 + 0.16 - 0.29 + 0.19 - 0.18 ] x 0.1
500 [ 3.30 + 0.12 - 0.20 + 0.14 - 0.13 ] x 0.1
525 [ 2.37 + 0.09 - 0.14 + 0.10 - 0.10 ] x 0.1
550 [ 1.71 + 0.06 - 0.10 + 0.08 - 0.07 ] x 0.1
575 [ 12.53 + 0.49 - 0.77 + 0.58 - 0.54 ] x 0.01
600 [ 9.23 + 0.37 - 0.57 + 0.44 - 0.40 ] x 0.01
650 [ 5.11 + 0.21 - 0.32 + 0.26 - 0.23 ] x 0.01
700 [ 2.90 + 0.12 - 0.18 + 0.16 - 0.14 ] x 0.01
750 [ 1.68 + 0.07 - 0.11 + 0.10 - 0.09 ] x 0.01
800 [ 9.88 + 0.45 - 0.63 + 0.66 - 0.55 ] x 0.001
850 [ 5.89 + 0.28 - 0.38 + 0.43 - 0.35 ] x 0.001
900 [ 3.55 + 0.17 - 0.24 + 0.29 - 0.23 ] x 0.001
950 [ 2.16 + 0.11 - 0.15 + 0.19 - 0.15 ] x 0.001
1000 [ 1.33 + 0.07 - 0.09 + 0.13 - 0.10 ] x 0.001

8 TeV cross sections for pp (LHC) collisions

Quark mass (GeV) central value Scale errors PDF errors  
300 [12.34 + 0.30 - 0.69 + 0.40 - 0.40 ] x 1
325 [ 7.81   ] x1
350 [ 5.08 + 0.14 - 0.29 + 0.18 - 0.17 ] x 1
375 [ 3.37   ] x1
400 [ 2.30 + 0.07 - 0.13 + 0.08 - 0.08 ] x 1
425 [ 15.87   ] x0.1
450 [ 11.13 + 0.34 - 0.63 + 0.42 - 0.41 ] x 0.1
475 [ 7.92   ] x0.1
500 [ 5.70 + 0.19 - 0.33 + 0.22 - 0.22 ] x 0.1
525 [ 4.16   ] x0.1
550 [ 3.06 + 0.10 - 0.18 + 0.12 - 0.12 ] x 0.1
575 [ 2.27   ] x0.1
600 [ 16.96 + 0.59 - 0.99 + 0.73 - 0.69 ] x 0.01
625 [ 12.80   ] x0.01
650 [ 9.71 + 0.36 - 0.57 + 0.44 - 0.41 ] x 0.01
675 [ 7.43   ] x0.01
700 [ 5.69 + 0.22 - 0.34 + 0.28 - 0.25 ] x 0.01
725 [ 4.40   ] x0.01
750 [ 3.41 + 0.14 - 0.20 + 0.18 - 0.15 ] x 0.01
775 [ 2.65   ] x0.01
800 [ 2.08 + 0.08 - 0.13 + 0.12 - 0.10 ] x 0.01
825 [ 16.32   ] x0.001
850 [ 12.85   ] x0.001
875 [ 10.17   ] x0.001
900 [ 8.05   ] x0.001
925 [ 6.40   ] x0.001
950 [ 5.12   ] x0.001
975 [ 4.10   ] x0.001
1000 [ 3.28   ] x0.001
1025 [ 2.62   ] x0.001
1050 [ 2.11   ] x0.001
1075 [ 16.97   ] x0.0001
1100 [ 13.69   ] x0.0001
1125 [ 11.03   ] x0.0001
1150 [ 8.93   ] x0.0001
1175 [ 7.19   ] x0.0001
1200 [ 5.85   ] x0.0001
1225 [ 4.75   ] x0.0001
1250 [ 3.85   ] x0.0001
1275 [ 3.11   ] x0.0001
1300 [ 2.54   ] x0.0001
1325 [ 2.06   ] x0.0001
1350 [ 16.75   ] x0.00001
1375 [ 13.61   ] x0.00001
1400 [ 11.04   ] x0.00001
1425 [ 8.99   ] x0.00001
1450 [ 7.30   ] x0.00001
1475 [ 5.94   ] x0.00001
1500 [ 4.81   ] x0.00001

References

1. J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis

2. P.M. Nadolsky et al., Implications of CTEQ global analysis for collider observables

3. S. Moch and P. Uwer, Theoretical status and prospects for top-quark pair production at hadron colliders

4. S. Moch and P. Uwer, Heavy-quark pair production at two loops in QCD

5. U. Langenfeld, S. Moch and P. Uwer, New results for ttbar production at hadron colliders

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Unknown file formatext Makefile r1 manage 17.3 K 2010-02-11 - 14:44 UnknownUser  
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PDFpdf NasonDawsonEllis.pdf r1 manage 1349.2 K 2010-02-17 - 18:26 UnknownUser  
Unknown file formateps c1.eps r1 manage 22.3 K 2010-06-24 - 19:02 MalikAliev  
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This topic: Sandbox > CrossSectionsCalculationTool
Topic revision: r60 - 2013-06-27 - MalikAliev
 
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