Changes between Initial Version and Version 1 of SingleTopNLO


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Timestamp:
Mar 20, 2012, 4:15:59 PM (12 years ago)
Author:
trac
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  • SingleTopNLO

    v1 v1  
     1
     2
     3== t-channel single top production at NLO ==
     4
     5
     6
     7=== Motivation ===
     8There are two ways to calculate t-channel single top production. The first is using a 2->2 process where the b-quark is taken in the initial state. By taking the b-quark from the PDF and setting the factorization scale equal to the top mass, the logarithms %$\log(m_b/m_t)$% will be resummed to all orders.
     9T-channel single top production can also be calculated without the b-quark PDF by including the gluon splitting into the diagram. The process becomes then a 2->3 process with also a massive b-quark in the final state. The goal is to calculate the the NLO corrections to the 2->3 process and provide in this way reliable predictions for the kinematics of this b-quark.
     10
     11=== Talks ===
     12
     13[:SingleTopTalks:Single top talks]
     14
     15=== Results ===
     16The parameters used are
     17   * %$m_t=172$% GeV
     18   * %$m_b=4.7$% GeV
     19   * %$m_W=80.419$% GeV
     20   * %$m_Z=91.118$% GeV
     21   * %$\mu_R=\mu_F=m_t$%
     22   * PDF is CTEQ6L (LO) and CTEQ6M (NLO)
     23   * Jet definition: kT jet algorithm, with ptjetmin=15 GeV, etajetmax=8, Rcut=0.7, Inclusive.
     24   * no cuts whatsoever are applied
     25if not stated otherwise.
     26
     27==== total cross section ====
     28Default scale choices:
     29   * For %$2\to 2$% we choose %$\mu_R^l=\mu_F^l=\mu_R^h=\mu_F^h=m_t$%.
     30   * For %$2\to 3$% we choose %$\mu_R^l=\mu_F^l=m_t/2$% and %$\mu_R^h=\mu_F^h=m_t/4$%.
     31
     32||  %$\sigma(2\to 2)$%  ||  '''LO'''  ||  '''NLO'''  ||  '''k-factor'''  ||
     33||Tevatron (fb)  ||  809.1 +- 0.6  ||  891.9 +- 0.7  ||  1.10  ||
     34||LHC top  (pb)  ||  142.1 +- 0.1  ||  146.8 +- 0.1  ||  1.03  ||
     35||LHC anti-top (pb)  ||  81.93 +- 0.05  ||  86.43 +- 0.06  ||  1.05  ||
     36
     37||  %$\sigma(2\to 3)$%  ||  '''LO'''  ||  '''NLO'''  ||  '''k-factor'''  ||
     38||Tevatron  (fb)  ||  595.8 +- 0.7  ||  800 +- 1  ||  1.34  ||
     39||LHC top  (pb)  ||  132.8 +- 0.3  ||  132.0 +- 0.5  ||  0.99  ||
     40||LHC anti-top  (pb) ||  74.85 +- 0.15  ||  76.3 +- 2  ||  1.02  ||
     41
     42Note in particular the small k-factor for the 2->2 process and the large k-factor for the 2->3 at the tevatron. In the PDF's a bottom mass of 4.5 GeV is used. Lowering the bottom mass will slightly increase the cross section for the 2->3 process.
     43
     44==== scale dependence ====
     45As the central choices for the renormalization and factorization scales we have chosen:
     46   * for the heavy line: %$\mu_{F,R}^{h}=m_t/4$%. This is chosen from the previous runs, where for %$m_t/4$% the total cross section for the 2->3 is closest to the 2->2 and also the LO is very close to the NLO.
     47   * for the light line: %$\mu_{F,R}^{l}=m_t/2$%. This is close to the average value for the %$Q^2$% of the W boson, which would be the natural choice for the massless line if we could use event-by-event scale choises. Also here the LO is very close to the NLO.
     48
     49The results for the scale dependence can be found in the tables below:
     50
     51
     52||  light quark line %$\mu_0=m_t/2$%  ||||  heavy quark line %$\mu_0=m_t/4$% ||||  '''2->3 at NLO, LHC top'''  ||||  '''2->3 at NLO, LHC anti-top'''  ||||  '''2->3 at NLO, Tevatron top'''  ||||
     53||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||
     54||  1  ||  1  ||  1  ||  1  ||  LHCt_89  ||  132.0 +- 0.5  ||  LHCa_89  ||  76.0 +- 0.3  ||  tev_89  ||  800 +- 1  ||
     55||  1  ||  1  ||  1  ||  1  ||  LHCt_90  ||  131.1 +- 0.6  ||  LHCa_90  ||  76.5 +- 0.4  ||  tev_90  ||  800 +- 1  ||
     56||  1  ||  1  ||  1  ||  1  ||  LHCt_91  ||  131.6 +- 0.6  ||  LHCa_91  ||  76.0 +- 0.3  ||  tev_91  ||  800 +- 1  ||
     57||  1  ||  1  ||  1  ||  1  ||  LHCt_92  ||  131.8 +- 0.5  ||  LHCa_92  ||  76.6 +- 0.3  ||  tev_92  ||  800 +- 1  ||
     58||  1  ||  1/2  ||  1  ||  1  ||  LHCt_L1  ||  131.3 +- 0.5  ||  LHCa_L1  ||  74.9 +- 0.4  ||  tev_L1  ||  779 +- 1  ||
     59||  1/2  ||  1/2  ||  1  ||  1  ||  LHCt_L2  ||  130.7 +- 0.5  ||  LHCa_L2  ||  74.9 +- 0.3  ||  tev_L2  ||  778 +- 1  ||
     60||  2  ||  1  ||  1  ||  1  ||  LHCt_L3  ||  131.8 +- 0.5  ||  LHCa_L3  ||  76.1 +- 0.3  ||  tev_L3  ||  799 +- 1  ||
     61||  1/2  ||  1  ||  1  ||  1  ||  LHCt_L4  ||  130.8 +- 0.6  ||  LHCa_L4  ||  76.1 +- 0.3  ||  tev_L4  ||  803 +- 1  ||
     62||  2  ||  2  ||  1  ||  1  ||  LHCt_L5  ||  131.3 +- 0.5  ||  LHCa_L5  ||  76.9 +- 0.3  ||  tev_L5  ||  813 +- 1  ||
     63||  1  ||  2  ||  1  ||  1  ||  LHCt_L6  ||  132.5 +- 0.6  ||  LHCa_L6  ||  76.7 +- 0.4  ||  tev_L6  ||  815 +- 1  ||
     64||  1  ||  1  ||  1  ||  1/2  ||  LHCt_H1  ||  133.1 +- 0.8  ||  LHCa_H1  ||  78.0 +- 0.4  ||  tev_H1  ||  860 +- 1  ||
     65||  1  ||  1  ||  1/2  ||  1/2  ||  LHCt_H2  ||  138.1 +- 0.8  ||  LHCa_H2  ||  79.1 +- 0.4  ||  tev_H2  ||  901 +- 2  ||
     66||  1  ||  1  ||  2  ||  1  ||  LHCt_H3  ||  126.3 +- 0.4  ||  LHCa_H3  ||  73.7 +- 0.3  ||  tev_H3  ||  752 +- 1  ||
     67||  1  ||  1  ||  1/2  ||  1  ||  LHCt_H4  ||  133.7 +- 0.7  ||  LHCa_H4  ||  76.8 +- 0.7  ||  tev_H4  ||  846 +- 1  ||
     68||  1  ||  1  ||  2  ||  2  ||  LHCt_H5  ||  125.7 +- 0.4  ||  LHCa_H5  ||  73.1 +- 0.3  ||  tev_H5  ||  704 +- 1  ||
     69||  1  ||  1  ||  1  ||  2  ||  LHCt_H6  ||  130.2 +- 0.6  ||  LHCa_H6  ||  76.0 +- 0.3  ||  tev_H6  ||  752 +- 1  ||
     70||  1/4  ||  1/4  ||  1  ||  1  ||  LHCt_Ls1  ||  130.2 +- 0.6  ||  LHCa_Ls1  ||  74.6 +- 0.3  ||  tev_Ls1  ||  729 +- 1  ||
     71||  1/8  ||  1/8  ||  1  ||  1  ||  LHCt_Ls2  ||  128.2 +- 0.6  ||  LHCa_Ls2  ||  74.8 +- 0.4  ||  tev_Ls2  ||  640 +- 2  ||
     72||  4  ||  4  ||  1  ||  1  ||  LHCt_Ls3  ||  132.1 +- 0.5  ||  LHCa_Ls3  ||  77.5 +- 0.4  ||  tev_Ls3  ||  812 +- 1  ||
     73||  8  ||  8  ||  1  ||  1  ||  LHCt_Ls4  ||  132.6 +- 0.5  ||  LHCa_Ls4  ||  78.8 +- 0.3  ||  tev_Ls4  ||  810 +- 1  ||
     74||  1  ||  1  ||  1/4  ||  1/4  ||  LHCt_Hs1  ||  143.3 +- 0.9  ||  LHCa_Hs1  ||  83.4 +- 0.8  ||  tev_Hs1  ||  972 +- 2  ||
     75||  1  ||  1  ||  4  ||  4  ||  LHCt_Hs2  ||  120.6 +- 0.4  ||  LHCa_Hs2  ||  69.2 +- 0.2  ||  tev_Hs2  ||  616 +- 1  ||
     76||  1  ||  1  ||  8  ||  8  ||  LHCt_Hs3  ||  114.9 +- 0.3  ||  LHCa_Hs3  ||  65.9 +- 0.2  ||  tev_Hs3  ||  542 +- 1  ||
     77||  1  ||  1  ||  16  ||  16  ||  LHCt_Hs4  ||  109.6 +- 0.3  ||  LHCa_Hs4  ||  62.5 +- 0.2  ||  tev_Hs4  ||  480 +- 1  ||
     78||  1/8  ||  1/8  ||  1/4  ||  1/4  ||  LHCt_LH1  ||  135.5 +- 0.9  ||  LHCa_LH1  ||  75.8 +- 0.5  ||  tev_LH1  ||  564 +- 2  ||
     79||  1/4  ||  1/4  ||  1/2  ||  1/2  ||  LHCt_LH2  ||  134.8 +- 0.7  ||  LHCa_LH2  ||  76.9 +- 0.5  ||  tev_LH2  ||  784 +- 2  ||
     80||  2  ||  2  ||  4  ||  4  ||  LHCt_LH3  ||  120.3 +- 0.4  ||  LHCa_LH3  ||  69.5 +- 0.2  ||  tev_LH3  ||  617 +- 1  ||
     81||  4  ||  4  ||  8  ||  8  ||  LHCt_LH4  ||  113.8 +- 0.3  ||  LHCa_LH4  ||  66.1 +- 0.2  ||  tev_LH4  ||  534 +- 1  ||
     82||  8  ||  8  ||  16  ||  16  ||  LHCt_LH5  ||  107.5 +- 0.3  ||  LHCa_LH5  ||  62.3 +- 0.2  ||  tev_LH5  ||  462 +- 1  ||
     83
     84
     85||  light quark line %$\mu_0=m_t/2$%  ||||  heavy quark line %$\mu_0=m_t/4$% ||||  '''2->3 at LO, LHC top'''  ||||  '''2->3 at LO, LHC anti-top'''  ||||  '''2->3 at LO, Tevatron top'''  ||||
     86||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||
     87||  1/8  ||  1/8  ||  1/4  ||  1/4  ||  LHCt_1  ||  194.8 +- 0.5  ||  LHCa_1  ||  108.4 +- 0.2  ||  tev_1  ||  1368 +- 2  ||
     88||  1/4  ||  1/4  ||  1/2  ||  1/2  ||  LHCt_2  ||  162.0 +- 0.4  ||  LHCa_2  ||  90.37 +- 0.19  ||  tev_2  ||  916.0 +- 1.1  ||
     89||  1/2  ||  1/2  ||  1  ||  1  ||  LHCt_3  ||  136.7 +- 0.3  ||  LHCa_3  ||  76.05 +- 0.14  ||  tev_3  ||  645.6 +- 0.8  ||
     90||  1  ||  1  ||  2  ||  2  ||  LHCt_4  ||  116.2 +- 0.3  ||  LHCa_4  ||  64.74 +- 0.12  ||  tev_4  ||  473.7 +- 0.6  ||
     91||  2  ||  2  ||  4  ||  4  ||  LHCt_5  ||  100.7 +- 0.2  ||  LHCa_5  ||  55.81 +- 0.10  ||  tev_5  ||  358.7 +- 0.4  ||
     92||  4  ||  4  ||  8  ||  8  ||  LHCt_6  ||  87.13 +- 0.18  ||  LHCa_6  ||  48.49 +- 0.09  ||  tev_6  ||  279.5 +- 0.3  ||
     93||  8  ||  8  ||  16  ||  16  ||  LHCt_7  ||  76.56 +- 0.15  ||  LHCa_7  ||  42.52 +- 0.08  ||  tev_7  ||  222.1 +- 0.3  ||
     94||  1/8  ||  1/8  ||  1  ||  1  ||  LHCt_L1  ||  146.5 +- 0.4  ||  LHCa_L1  ||  78.46 +- 0.17  ||  tev_L1  ||  782.1 +- 1.0  ||
     95||  1/4  ||  1/4  ||  1  ||  1  ||  LHCt_L2  ||  141.0 +- 0.3  ||  LHCa_L2  ||  77.21 +- 0.16  ||  tev_L2  ||  705.3 +- 0.9  ||
     96||  1  ||  1  ||  1  ||  1  ||  LHCt_L3  ||  132.8 +- 0.3  ||  LHCa_L3  ||  74.85 +- 0.15  ||  tev_L3  ||  595.8 +- 0.7  ||
     97||  2  ||  2  ||  1  ||  1  ||  LHCt_L4  ||  129.1 +- 0.3  ||  LHCa_L4  ||  73.46 +- 0.14  ||  tev_L4  ||  554.6 +- 0.7  ||
     98||  4  ||  4  ||  1  ||  1  ||  LHCt_L5  ||  125.9 +- 0.3  ||  LHCa_L5  ||  72.42 +- 0.14  ||  tev_L5  ||  518.6 +- 0.6  ||
     99||  8  ||  8  ||  1  ||  1  ||  LHCt_L6  ||  122.8 +- 0.3  ||  LHCa_L6  ||  71.36 +- 0.13  ||  tev_L6  ||  488.3 +- 0.6  ||
     100||  1  ||  1  ||  1/4  ||  1/4  ||  LHCt_H1  ||  180.0 +- 0.4  ||  LHCa_H1  ||  105.6 +- 0.2  ||  tev_H1  ||  1050 +- 1  ||
     101||  1  ||  1  ||  1/2  ||  1/2  ||  LHCt_H2  ||  153.0 +- 0.4  ||  LHCa_H2  ||  87.85 +- 0.18  ||  tev_H2  ||  773.4 +- 0.9  ||
     102||  1  ||  1  ||  1  ||  1  ||  LHCt_H3  ||  132.8 +- 0.3  ||  LHCa_H3  ||  74.85 +- 0.15  ||  tev_H3  ||  595.8 +- 0.7  ||
     103||  1  ||  1  ||  4  ||  4  ||  LHCt_H4  ||  103.5 +- 0.2  ||  LHCa_H4  ||  56.88 +- 0.11  ||  tev_H4  ||  386.9 +- 0.5  ||
     104||  1  ||  1  ||  8  ||  8  ||  LHCt_H5  ||  92.68 +- 0.22  ||  LHCa_H5  ||  50.59 +- 0.10  ||  tev_H5  ||  322.0 +- 0.4  ||
     105||  1  ||  1  ||  16  ||  16  ||  LHCt_H6  ||  83.93 +- 0.18  ||  LHCa_H6  ||  45.23 +- 0.09  ||  tev_H6  ||  272.3 +- 0.3  ||
     106
     107
     108
     109||  For both quark lines %$\mu_0=m_t$%, massive b-quark  ||||  '''2->2 at NLO, LHC top'''  ||||  '''2->2 at NLO, LHC anti-top'''  ||||  '''2->2 at NLO, Tevatron top'''  ||||
     110||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||
     111||  1/16  ||  1/16  ||  LHCt_1  ||  195.7 +- 0.5  ||  LHCa_1  ||  110.3 +- 0.2  ||  tev_1  ||  1241 +- 2  ||
     112||  1/8  ||  1/8  ||  LHCt_2  ||  170.5 +- 0.4  ||  LHCa_2  ||  96.65 +- 0.19  ||  tev_2  ||  927.6 +- 1.1  ||
     113||  1/4  ||  1/4  ||  LHCt_3  ||  157.1 +- 0.3  ||  LHCa_3  ||  89.10 +- 0.14  ||  tev_3  ||  833.3 +- 0.8  ||
     114||  1/2  ||  1/2  ||  LHCt_4  ||  150.7 +- 0.3  ||  LHCa_4  ||  85.87 +- 0.12  ||  tev_4  ||  823.4 +- 0.6  ||
     115||  1  ||  1  ||  LHCt_5  ||  149.9 +- 0.2  ||  LHCa_5  ||  85.46 +- 0.10  ||  tev_5  ||  841.4 +- 0.4  ||
     116||  2  ||  2  ||  LHCt_6  ||  151.0 +- 0.2  ||  LHCa_6  ||  86.79 +- 0.09  ||  tev_6  ||  868.2 +- 0.3  ||
     117||  4  ||  4  ||  LHCt_7  ||  154.7 +- 0.2  ||  LHCa_7  ||  89.24 +- 0.08  ||  tev_7  ||  891.0 +- 0.3  ||
     118||  1  ||  1/2  ||  LHCt_8  ||  156.5 +- 0.2  ||  LHCa_8  ||  89.19 +- 0.12  ||  tev_8  ||  822.4 +- 0.5  ||
     119||  2  ||  1  ||  LHCt_9  ||  148.5 +- 0.2  ||  LHCa_9  ||  85.29 +- 0.10  ||  tev_9  ||  841.8 +- 0.4  ||
     120||  1/2  ||  1  ||  LHCt_10  ||  142.3 +- 0.2  ||  LHCa_10  ||  81.07 +- 0.11  ||  tev_10  ||  843.0 +- 0.5  ||
     121||  1  ||  2  ||  LHCt_11  ||  151.0 +- 0.2  ||  LHCa_11  ||  86.36 +- 0.10  ||  tev_11  ||  870.1 +- 0.4  ||
     122
     123
     124
     125||  For both quark lines %$\mu_0=m_t$%  ||||  '''2->2 at NLO, LHC top'''  ||||  '''2->2 at NLO, LHC anti-top'''  ||||  '''2->2 at NLO, Tevatron top'''  ||||
     126||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||
     127||  1/16  ||  1/16  ||  LHCt_1  ||  167.6 +- 0.1  ||  LHCa_1  ||  99.02 +- 0.07  ||  tev_1  ||  1257.3 +- 1.0  ||
     128||  1/8  ||  1/8  ||  LHCt_2  ||  153.3 +- 0.1  ||  LHCa_2  ||  90.58 +- 0.07  ||  tev_2  ||  977.7 +- 0.8  ||
     129||  1/4  ||  1/4  ||  LHCt_3  ||  146.6 +- 0.1  ||  LHCa_3  ||  86.51 +- 0.06  ||  tev_3  ||  890.7 +- 0.7  ||
     130||  1/2  ||  1/2  ||  LHCt_4  ||  145.1 +- 0.1  ||  LHCa_4  ||  85.47 +- 0.06  ||  tev_4  ||  877.9 +- 0.7  ||
     131||  1  ||  1  ||  LHCt_5  ||  146.8 +- 0.1  ||  LHCa_5  ||  86.43 +- 0.06  ||  tev_5  ||  891.9 +- 0.7  ||
     132||  2  ||  2  ||  LHCt_6  ||  150.6 +- 0.1  ||  LHCa_6  ||  88.65 +- 0.07  ||  tev_6  ||  911.0 +- 0.7  ||
     133||  4  ||  4  ||  LHCt_7  ||  155.5 +- 0.1  ||  LHCa_7  ||  91.64 +- 0.07  ||  tev_7  ||  929.2 +- 0.7  ||
     134||  1  ||  1/2  ||  LHCt_8  ||  144.2 +- 0.1  ||  LHCa_8  ||  84.93 +- 0.06  ||  tev_8  ||  877.7 +- 0.7  ||
     135||  2  ||  1  ||  LHCt_9  ||  147.3 +- 0.1  ||  LHCa_9  ||  86.68 +- 0.06  ||  tev_9  ||  891.0 +- 0.7  ||
     136||  1/2  ||  1  ||  LHCt_10  ||  146.3 +- 0.1  ||  LHCa_10  ||  86.17 +- 0.07  ||  tev_10  ||  892.1 +- 0.7  ||
     137||  1  ||  2  ||  LHCt_11  ||  149.2 +- 0.1  ||  LHCa_11  ||  87.91 +- 0.07  ||  tev_11  ||  914.3 +- 0.7  ||
     138
     139
     140||  For both quark lines %$\mu_0=m_t$%  ||||  '''2->2 at LO, LHC top'''  ||||  '''2->2 at LO, LHC anti-top'''  ||||  '''2->2 at LO, Tevatron top'''  ||||
     141||  '''ren. scale'''  ||  '''fac. scale'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||  '''tag'''  ||  '''cross section'''  ||
     142||  1/16  ||  1/16  ||  LHCt_1  ||  51.98 +- 0.03  ||  LHCa_1  ||  29.28 +- 0.02  ||  tev_1  ||  512.9 +- 0.4  ||
     143||  1/8  ||  1/8  ||  LHCt_2  ||  83.35 +- 0.06  ||  LHCa_2  ||  47.35 +- 0.03  ||  tev_2  ||  692.0 +- 0.5  ||
     144||  1/4  ||  1/4  ||  LHCt_3  ||  107.8 +- 0.1  ||  LHCa_3  ||  61.65 +- 0.04  ||  tev_3  ||  774.8 +- 0.6  ||
     145||  1/2  ||  1/2  ||  LHCt_4  ||  127.0 +- 0.1  ||  LHCa_4  ||  73.01 +- 0.05  ||  tev_4  ||  806.5 +- 0.6  ||
     146||  1  ||  1  ||  LHCt_5  ||  142.1 +- 0.1  ||  LHCa_5  ||  81.94 +- 0.05  ||  tev_5  ||  809.1 +- 0.6  ||
     147||  2  ||  2  ||  LHCt_6  ||  154.1 +- 0.1  ||  LHCa_6  ||  89.04 +- 0.06  ||  tev_6  ||  797.4 +- 0.6  ||
     148||  4  ||  4  ||  LHCt_7  ||  163.4 +- 0.1  ||  LHCa_7  ||  94.65 +- 0.06  ||  tev_7  ||  776.1 +- 0.6  ||
     149||  1  ||  1/2  ||  LHCt_8  ||  127.0 +- 0.1  ||  LHCa_8  ||  73.01 +- 0.05  ||  tev_8  ||  806.5 +- 0.6  ||
     150||  2  ||  1  ||  LHCt_9  ||  142.1 +- 0.1  ||  LHCa_9  ||  81.94 +- 0.05  ||  tev_9  ||  809.1 +- 0.6  ||
     151||  1/2  ||  1  ||  LHCt_10  ||  142.1 +- 0.1  ||  LHCa_10  ||  81.94 +- 0.05  ||  tev_10  ||  809.1 +- 0.6  ||
     152||  1  ||  2  ||  LHCt_11  ||  154.1 +- 0.1  ||  LHCa_11  ||  89.04 +- 0.06  ||  tev_11  ||  797.4 +- 0.6  ||
     153
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     156
     157The 2->2 at LO the cross section is independent of the ren. scale.
     158
     159
     160<br />
     161<br />
     162<br />
     163<br />
     164<br />
     165<br />
     166<br />
     167
     168Old results without the interference terms:
     169<br />
     170<img src="%ATTACHURLPATH%/scale--TeV.png" alt="scale--TeV.png" width='300'/>
     171<img src="%ATTACHURLPATH%/scale--LHCtop.png" alt="scale--LHCtop.png" width='300'/>
     172<img src="%ATTACHURLPATH%/scale--LHCantitop.png" alt="scale--LHCantitop.png" width='300'/>
     173
     174The above plots show the cross section as a function of the scales. The renormalization and factorization scales are set equal to eachother and varied simultaneously. For the 2->2 processes (in particular at NLO) the scale dependence is extremely small over a very large range of scale choices. The dependence for the 2->3 is slightly larger, but is still small and very reasonable. At LO the cross sections for the 2->2 and 2->3 process become equal for small scale choices. For the NLO this is no longer the case. The difference between the 2->2 and 2->3 at NLO is large over the whole range of scales.
     175   * A tarball with all the plots (including sources) can be found here: [attachment:scale.tar.gz scale.tar.gz]
     176
     177Normalized:
     178<br />
     179     <img src="%ATTACHURLPATH%/scale-norm2--TeV.png" alt="scale-norm2--TeV.png" width='300' />
     180     <img src="%ATTACHURLPATH%/scale-norm2--LHCtop.png" alt="scale-norm2--LHCtop.png" width='300' />
     181
     182
     183scale dependence at the LHC for independent scale variations for light and heavy fermion lines: <br />
     184     <img src="%ATTACHURLPATH%/scaleLH--LHCtop.png" alt="scaleLH--LHCtop.png" width='300'/>
     185
     186The above plot shows the scale dependence for the 2->3 process at NLO. In this plot the renormalization scale is set equal to the factorization scale %$\mu_R=\mu_F$%, but the scale for the heavy fermion line is varied independently from the scale of the light fermion line. The ''black'' curves show the scale variation of the heavy fermion line, i.e. the scales for the light line are fixed, and vice versa for the ''red'' line. The value to which the scales are fixed for a particular curve can be read of from the point where this black (or red) line crosses a red (or black) line in a point.
     187   * It is obvious that the total scale dependence, i.e. the ''blue'' curve (which is the same as the blue curve in the plots above), is totally coming from the scale variations in the '''heavy''' fermion line.
     188
     189
     190
     191
     192==== b-mass dependence ====
     193<br />
     194     <img src="%ATTACHURLPATH%/bmass--TeV.png" alt="bmass--TeV.png" width='300'/>
     195     <img src="%ATTACHURLPATH%/bmass--LHCtop.png" alt="bmass--LHCtop.png" width='300'/>
     196     <img src="%ATTACHURLPATH%/bmass--LHCantitop.png" alt="bmass--LHCantitop.png" width='300'/>
     197
     198In the above plots the cross section is plotted as a function of the mass of the (anti-)b quark (for the 2->3 process). From these plots it is clear the cross section is quite sensitive to the mass of the b-quark. In particular, using the running mass at the scale of the top quark or at the scale of the bottom quark could enhance the cross section by over 10-15%. We should figure out to which mass we should let the b-mass run. Note that the CTEQ6 PDF sets assume a bottom mass of 4.5 GeV.
     199   * The NLO plots lie perfectly on a straight line (within the statistical MC errors). This suggests that the 'large logarithms' at NLO (that would be the terms proportional to %$\alpha_s^2\log^2(m_b/m_t)$%) do not play an important role and that using the resummed calculation with the b-quark PDF is not the best estimation for this process.
     200
     201
     202
     203===== scale dependence for %$m_b=m_c$%  =====
     204<br />
     205     <img src="%ATTACHURLPATH%/scale-mb=mc--TeV.png" alt="scale-mb=mc--TeV.png" width='300'/>
     206     <img src="%ATTACHURLPATH%/scale-mb=mc--LHCtop.png" alt="scale-mb=mc--LHCtop.png" width='300'/>
     207     <img src="%ATTACHURLPATH%/scale-mb=mc--LHCantitop.png" alt="scale-mb=mc--LHCantitop.png" width='300'/>
     208
     209In the above plots the cross section as a function of the scales is plotted. The mass of the bottom quark is set equal to the mass of the charm. The scale dependence for the NLO calculation is still very small, but the k-factors are much larger as compared to the %$m_b=4.7\textrm{ GeV}$%.
     210
     211Unfortunaly the 'wrong' charm mass has been used for the 2->3 process: for the 2->2 process the charm PDF has been used which has a charm mass of 1.3 GeV. For the 2->3 process the a charm mass of 1.5 GeV was used. Using a charm mass of 1.3 also for the 2->3 process would increase this cross section slightly. The wobbly lines for the 2->3 at NLO at the LHC are entirely due to lack of statistics. Due to the small bottom numerical instabilities start playing a role and numerical convergence becomes more difficult.
     212   * '''The NLO 2->3 processes are wrong''', because the old version with the bug was used.
     213   * All the plots (including sources) for the b-mass dependence can be downloaded here: [attachment:bmass.tar.gz bmass.tar.gz]. This includes also some plots for the 2->3 process with scale dependence for a 50 GeV b quark mass. The dependence on the scales is very similar as using the normal b-quark mass.
     214
     215
     216==== final state particle kinematics ====
     217   * [attachment:all--TeV.pdf all--TeV.pdf]: pt, eta of the t and bbar quarks at the tevatron
     218   * [attachment:all--LHCtop.pdf all--LHCtop.pdf]: pt, rapidity of the t and bbar quarks at the LHC
     219   * [attachment:all--LHCantitop.pdf all--LHCantitop.pdf]: pt, rapidity of the tbar and b quarks at the LHC
     220
     221
     222
     223=== To do ===
     224   1. '''Analytic Check of Born amplitude''' <br>
     225   We need to understand what is the analytic dependence of the short distance cross section as a function of the bmass.
     226   1. '''Check of the calculation''' <br>
     227   We check the calculation inderectly by evaluating the s-channel top qq>W*>tbg at NLO. The idea is then to set mb=mt and compare with Oleari's NLO calculation for    e+e-> Z/gamma>bb~ g.
     228   1.  '''Check the mass effects in the 2->2 calculation''' <br> Just to be sure, it would be useful to also compare with the 2->2 calculation at NLO, where the 2->3 contribution is calculated with a finite mass for the b. This can be done by using the collinear subtraction in the massive MSbar scheme, as we have done for W+jets and in the W+c calculation.
     229   1. '''Allow for different event-by-event scales in the process''' <br> 
     230   We need to be able to check all possible factorization and renormalization scales. The main point is that we can treat the light quark line and the heavy quark line independently, since as  in the 2->2 there is no talking between the lines. The aim is to have four scales: muf_light, mur_light, muf_heavy, mur_heavy. So first thing is to assess the real scale dependence of the results by varying these scale independently. Scott suggested that we used a dynamical scale for the heavy line. After some thought I think that min(mT(b),mT(t)) =~ mT(b) should be used. By doing so we will slightly overestimate the diagrams where the initial gluon splits into a ttbar pair. However this contribution is anyway very small and should have no impact on the final result. This is also similar to the choice made by PS MC.
     231
     232<img src="%ATTACHURLPATH%/63.png" alt="63.png" width='300'/>
     233
     234
     235   * [attachment:MCFM-Stopb.tar.gz MCFM-Stopb.tar.gz]: Latest version of MCFM including the 2->3 t-channel single top (updated with interference terms)
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