Singletop and topantitop cross sections
Abstract
I present highorder calculations, including softgluon corrections, for singletop and topantitop production cross sections and differential distributions. For singletop production, results are presented for the three different channels in the Standard Model, for associated production with a charged Higgs, and for processes involving anomalous couplings. For topantitop pair production, total cross sections and topquark transversemomentum and rapidity distributions are presented for various LHC energies.
Singletop and topantitop cross sections
Nikolaos Kidonakis^{}^{}email: nkidonak@kennesaw.edu
\@textsuperscript1Department of Physics, Kennesaw State University, Kennesaw, GA 30144, USA

Abstract.
1 Introduction
Higherorder softgluon corrections have been calculated through NLO for topquark production via various processes; see Ref. [1] for a review. Here I present the latest results for channel and channel singletop production, and production, production via anomalous couplings, and production. For all these processes QCD corrections are very significant and are dominated by softgluon corrections.
I calculate and resum these soft corrections at nexttonexttoleading logarithm (NNLL) accuracy for the doubledifferential cross section, which is then used to calculate topquark transversemomentum and rapidity distributions and total cross sections. Finiteorder expansions at approximate NNLO (aNNLO) and approximate NLO (aNLO), matched to exact results, provide the best predictions for these quantities.
We calculate softgluon corrections for partonic processes of the form
and we define , , , and . At partonic threshold . The thorder softgluon corrections appear as where .
Moments of the partonic cross section, , can be written in factorized form
in dimensions, where is a hard function and is a softgluon function. satisfies the renormalization group equation
where the soft anomalous dimension controls the evolution of the soft function, giving the exponentiation of logarithms of . To achieve NNLL accuracy we need to calculate the relevant soft anomalous dimensions at two loops.
2 Singletop production
We now provide results for singletop production in the channel, channel, and via production. Fixedorder results for these processes are known at NNLO for the channel [2, 3, 4] and channel [5], and at NLO for production [6]. Here we provide results with softgluon corrections at aNNLO for  and channel production [7], and at aNLO for production [8]; these results are obtained from NNLL resummation [7, 8, 9]. We use MMHT2014 NNLO pdf [10].
We begin with channel production at aNNLO. In the left plot of Fig. 1 we display total channel cross sections as functions of collider energy at the LHC and (inset) at the Tevatron. Results are given for the singletop cross section, the singleantitop cross section, and their sum. We observe very good agreement of the aNNLO theory curves [7, 11] with all available data from the LHC and the Tevatron at various energies. The right plot of Fig. 1 shows the aNNLO normalized topquark distributions at 8 TeV LHC energy, which describe the corresponding data from CMS [19] quite well.
We continue with channel production at aNNLO. In the left plot of Fig. 2 we show cross sections for singletop and singleantitop channel production, and their sum, as functions of energy at the LHC and (inset) at the Tevatron. We again observe very good agreement of the aNNLO theory curves [7, 11] with available data at LHC and Tevatron energies.
3 production
We continue with production in the MSSM or other twoHiggsdoublet models [29]. We use MMHT2014 NNLO pdf [10] for our numerical results.
In the left plot of Fig. 3 we show the aNLO total cross section for production [11] as a function of chargedHiggs mass at LHC energies of 7, 8, 13, and 14 TeV. We use . The softgluon corrections are large for this process. Topquark and rapidity distributions in this process have also been presented in [29].
4 production via anomalous couplings
Next, we discuss softgluon corrections in production in models with anomalous  couplings [30, 31]. The NLO corrections for this process were calculated in Ref. [32]. The complete NLO corrections are very well approximated by the softgluon corrections at that order.
We use CT14 pdf [33] for our numerical results in this process. In the right plot of Fig. 3 we plot the aNNLO total cross section for production as a function of topquark mass at LHC energies of 7, 8, 13, and 14 TeV.
The factors shown in the inset plot show that the aNNLO corrections are large and significantly enhance the NLO cross section, especially at lower energies. This is important in providing theoretical input to experimental limits on the couplings [34, 35]. Topquark differential distributions in this process have been presented in Ref. [31].
Similar results have more recently been presented for production via anomalous couplings in Ref. [36].
5 Topantitop pair production
Finally, we discuss topantitop pair production [37, 38]. The soft anomalous dimensions are matrices for the channel, and matrices for the channel.
At one loop for , the elements of the matrix in an channel singletoctet color basis are
At two loops for , the elements of the matrix are
See also Ref. [1] for more details. Here is the cusp anomalous dimension [39].
The softgluon corrections are large and they are excellent approximations to the complete corrections at both NLO and NNLO. The additional corrections at aNLO provide further significant enhancements and must be included for precision physics. Another approach for the aNLO corrections has appeared recently in Ref. [40].
In our numerical results below we use the MMHT2014 NNLO pdf [10]. The total topantitop cross sections at aNLO [38] are shown in Fig. 4 and compared with data at Tevatron and LHC energies. We find remarkable agreement between theory and data at all energies.
The aNLO topquark normalized distributions in production are shown in Fig. 5 at 13 TeV (left plot) and 8 TeV (right plot) and compared with CMS and ATLAS data respectively. We find excellent agreement of the theoretical predictions with the data.
The aNLO topquark normalized rapidity distributions in production are shown in Fig. 6 at 13 TeV (left plot) and 8 TeV (right plot) and compared with CMS data. Again, we find that the theory curves provide an excellent description of the data.
6 Summary
We have discussed cross sections and distributions for various topquark production processes. Softgluon corrections are important in all cases. We have shown results for channel and channel singletop production at aNNLO, production at aNLO, production at aNLO, production via anomalous couplings at aNNLO, and production at aNLO. We find excellent agreement with available collider data. The higherorder corrections are very significant and need to be included for better theoretical predictions.
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. PHY 1519606.
References
 [1] N. Kidonakis, Int. J. Mod. Phys. A 33, 1830021 (2018) [arXiv:1806.03336 [hepph]].
 [2] M. Brucherseifer, F. Caola, and K. Melnikov, Phys. Lett. B 736, 58 (2014) [arXiv:1404.7116 [hepph]].
 [3] E.L. Berger, J. Gao, C.P. Yuan, and H.X. Zhu, Phys. Rev. D 94, 071501 (2016) [arXiv:1606.08463 [hepph]].
 [4] E.L. Berger, J. Gao, and H.X. Zhu, JHEP 1711, 158 (2017) [arXiv:1708.09405 [hepph]].
 [5] Z. Liu and J. Gao, arXiv:1807.03835 [hepph].
 [6] S.H. Zhu, Phys. Lett. B 524, 283 (2002) [Erratum: ibid. 537, 351 (2002)] [hepph/0109269].
 [7] N. Kidonakis, Phys. Rev. D 81, 054028 (2010) [arXiv:1001.5034 [hepph]]; 83, 091503(R) (2011) [arXiv:1103.2792 [hepph]]; 88, 031504(R) (2013) [arXiv:1306.3592 [hepph]]; 93, 054022 (2016) [arXiv:1510.06361 [hepph]].
 [8] N. Kidonakis, Phys. Rev. D 96, 034014 (2017) [arXiv:1612.06426 [hepph]]; in Proceedings of DPF 2017, eConf C170731 [arXiv:1709.06975 [hepph]].
 [9] N. Kidonakis, Phys. Rev. D 82, 054018 (2010) [arXiv:1005.4451 [hepph]].
 [10] L.A. HarlandLang, A.D. Martin, P. Molytinski, and R.S. Thorne, Eur. Phys. J. C 75, 204 (2015) [arXiv:1412.3989 [hepph]].
 [11] N. Kidonakis, in Proceedings of CIPANP2018 [arXiv:1808.02934 [hepph]].
 [12] CMS Collab., JHEP 1212, 035 (2012) [arXiv:1209.4533 [hepex]].
 [13] ATLAS Collab., Phys. Rev. D 90, 112006 (2014) [arXiv:1406.7844 [hepex]].
 [14] CMS Collab., JHEP 1406, 090 (2014) [arXiv:1403.7366 [hepex]].
 [15] ATLAS Collab., Eur. Phys. J. C 77, 531 (2017) [arXiv:1702.02859 [hepex]].
 [16] ATLAS Collab., JHEP 1704, 086 (2017) [arXiv:1609.03920 [hepex]].
 [17] CMS Collab., Phys. Lett. B 772, 752 (2017) [arXiv:1610.00678 [hepex]].
 [18] CDF and D0 Collab., Phys. Rev. Lett. 115, 152003 (2015) [arXiv:1503.05027 [hepex]].
 [19] CMS Collab., CMSPASTOP14004.
 [20] ATLAS Collab., ATLASCONF2011118.
 [21] CMS Collab., JHEP 1609, 027 (2016) [arXiv:1603.02555 [hepex]].
 [22] ATLAS Collab., Phys. Lett. B 756, 228 (2016) [arXiv:1511.05980 [hepex]].
 [23] CDF and D0 Collab., Phys. Rev. Lett. 112, 231803 (2014) [arXiv:1402.5126 [hepex]].
 [24] ATLAS Collab., Phys. Lett. B 716, 142 (2012) [arXiv:1205.5764 [hepex]].
 [25] CMS Collab., Phys. Rev. Lett. 110, 022003 (2013) [arXiv:1209.3489 [hepex]].
 [26] ATLAS and CMS Collab., ATLASCONF2016023, CMSPASTOP15019.
 [27] ATLAS Collab., JHEP 1801, 063 (2018) [arXiv:1612.07231 [hepex]].
 [28] CMS Collab., arXiv:1805.07399 [hepex].
 [29] N. Kidonakis, JHEP 0505, 011 (2005) [hepph/0412422]; Phys. Rev. D 94, 014010 (2016) [arXiv:1605.00622 [hepph]].
 [30] A. Belyaev and N. Kidonakis, Phys. Rev. D 65, 037501 (2002) [hepph/0102072]; N. Kidonakis and A. Belyaev, JHEP 0312, 004 (2003) [hepph/0310299].
 [31] N. Kidonakis, Phys. Rev. D 97, 034028 (2018) [arXiv:1712.01144 [hepph]].
 [32] B.H. Li, Y. Zhang, C.S. Li, J. Gao, and H.X. Zhu, Phys. Rev. D 83, 114049 (2011) [arXiv:1103.5122 [hepph]].
 [33] S. Dulat, T.J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, and C.P. Yuan, Phys. Rev. D 93, 033006 (2016) [arXiv:1506.07443 [hepph]].
 [34] CMS Collaboration, JHEP 1707, 003 (2017) [arXiv:1702.01404 [hepex]].
 [35] ATLAS Collaboration, ATLASCONF2017070.
 [36] M. Forslund and N. Kidonakis, arXiv:1808.09014 [hepph].
 [37] N. Kidonakis, Phys. Rev. D 82, 114030 (2010) [arXiv:1009.4935 [hepph]]; in Physics of Heavy Quarks and Hadrons, HQ2013 [arXiv:1311.0283 [hepph]].
 [38] N. Kidonakis, Phys. Rev. D 90, 014006 (2014) [arXiv:1405.7046 [hepph]]; 91, 031501(R) (2015) [arXiv:1411.2633 [hepph]]; 91, 071502(R) (2015) [arXiv:1501.01581 [hepph]].
 [39] N. Kidonakis, Phys. Rev. Lett. 102, 232003 (2009) [arXiv:0903.2561 [hepph]]; Int. J. Mod. Phys. A 31, 1650076 (2016) [arXiv:1601.01666 [hepph]].
 [40] J. Piclum and C. Schwinn, JHEP 1803, 164 (2018) [arXiv:1801.05788 [hepph]].
 [41] CMS Collab., JHEP 1803, 115 (2018) [arXiv:1711.03143 [hepex]].
 [42] ATLAS Collab., Eur. Phys. J. C 74, 3109 (2014) [Addendum: ibid. 76, 642 (2016)] [arXiv:1406.5375 [hepex]].
 [43] CMS Collab., JHEP 1608, 029 (2016) [arXiv:1603.02303 [hepex]].
 [44] ATLAS Collab., Eur. Phys. J. C 78, 487 (2018) [arXiv:1712.06857 [hepex]].
 [45] ATLAS Collab., Phys. Lett. B 761, 136 (2016) [Erratum: ibid. 772, 879 (2017)] [arXiv:1606.02699 [hepex]].
 [46] CMS Collab., JHEP 1709, 051 (2017) [arXiv:1701.06228 [hepex]].
 [47] CDF Collab., Phys. Rev. D 64, 032002 (2001) [Erratum: ibid. 67, 119901 (2003)] [hepex/0101036].
 [48] D0 Collab., Phys. Rev. D 67, 012004 (2003) [hepex/0205019].
 [49] CDF and D0 Collab., Phys. Rev. D 89, 072001 (2014) [arXiv:1309.7570 [hepex]].
 [50] CMS Collab., JHEP 1804, 060 (2018) [arXiv:1708.07638 [hepex]].
 [51] ATLAS Collab., Eur. Phys. J. C 76, 538 (2016) [arXiv:1511.04716 [hepex]].
 [52] CMS Collab., Eur. Phys. J. C 75, 542 (2015) [arXiv:1505.04480 [hepex]].