Modelling Hadronic Collisions Beyond Leading Order: (N)NLO Monte Carlo Tools for the LHC

• Applicant: Professor Dr. Michal Czakon
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 160780747

• Final Report Year: 2015

Final Report Abstract

The main purpose of this project was to improve the precision of theoretical predictions for hadron collider processes in general and for the main processes at the LHC in particular. Three large scale problems have been studied: 1) hadronic top quark pair production at next-to-next-to leading order; 2) automated software for real radiation at next-to-next-to leading order; 3) next-to-leading order tools with showering effects. Substantial successes have been achieved in each of the topics. In top-quark physics, we were able to provide the first complete predictions for the total hadronic production cross section with next-to-next-to-leading order accuracy without any approximations. These show an excellent agreement with the most recent Large Hadron Collider (LHC) data, and have been used for several applications. While others have extracted fundamental parameters such as the top-quark mass and the strong coupling constant form top-quark data, we exploited the achieved precision to improve exclusion limits for supersymmetric partners of the top-quark, and to constrain the gluon parton distribution function. The technical advances necessary to perform the required calculations turned out to be useful in other ways. For example, it has been possible to improve the analytic expansion of the total cross section in the threshold limit. Beyond inclusive predictions, we were able to derive differential distributions for the Tevatron and, in particular, to evaluate first non-trivial QCD corrections to the famous forward-backward asymmetry. Our results removed theory ambiguities and at the same time brought the theory and experiment to excellent agreement. Efforts on both sides thus led to the resolution of one of the most persistent anomalies in recent measurements. Further results on differential distributions at the LHC are being prepared for publication. The second topic of our research was more technical and involved the development and implementation of a subtraction scheme for next-to-next-to-leading order calculations. While the necessary novel ideas for this problem had their origin in top-quark cross section calculations, they turned out to provide a general solution for arbitrary processes. As a result of this project, we were able to give a four-dimensional formulation of the scheme. In consequence, this is the first scheme to be specified in all generality at this order of perturbation theory. We were able to implement it in the form of a C++ library and provide first results. Our software will be made publicly available in the nearest future once more tests have been performed. A third subproject was concerned with the development of Monte Carlo tools including a matching between next-to-leading order calculations and a parton shower with quantum interference invented by Z. Nagy and D. Soper. Accurate Monte Carlo tools are of major importance to the whole LHC research program due to the number of processes, which must be understood precisely to discriminate between Standard Model behaviour and New Physics signals. In a first step, we have developed and implemented a new subtraction scheme based on the parton shower splitting kernels. We used it to study four-b-jet production at the LHC, a process of relevance to Higgs physics among others. Finally, we formulated a matching procedure based on the well-known MC@NLO concept and included it in the leading color approximation within the Monte Carlo system H ELAC. A first promising validation of our work appeared in the form of a study of top-quark pair production with a jet. The results of this project were featured as highlight in Physical Review Letters. Furthermore, they have been used numerous times by experimental groups for comparison with data. They have also spawned a research program for several years ahead and led to three PhD theses.

Publications

• “NNLO corrections to top pair production at hadron colliders: the all-fermionic scattering channels”, JHEP 1212 (2012) 054
  M. Czakon and A. Mitov
  
• 4 “Total top quark pair production cross section at hadron colliders through O(αs )”, Phys. Rev. Lett. 110 (2013) 252004
  M. Czakon, P. Fiedler and A. Mitov
  
• Quantifying quark mass effects at the LHC: A study of pp -> b anti-b b anti-b + X at next-to-leading order. JHEP 1307 (2013) 095
  G. Bevilacqua, M. Czakon, M. Krämer, M. Kubocz and M. Worek
  
• “Complete Nagy-Soper subtraction for next-to-leading order calculations in QCD”, JHEP 1310 (2013) 204
  G. Bevilacqua, M. Czakon, M. Kubocz and M. Worek
  
• “Constraints on the gluon PDF from top quark pair production at hadron colliders”, JHEP 1307 (2013) 167
  M. Czakon, M. L. Mangano, A. Mitov and J. Rojo
  
• “NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction”, JHEP 1301 (2013) 080
  M. Czakon and A. Mitov
  
• “Closing the stop gap”, Phys. Rev. Lett. 113 (2014) 20, 201803
  M. Czakon, A. Mitov, M. Papucci, J. T. Ruderman and A. Weiler
  
• “Four-dimensional formulation of the sector-improved residue subtraction scheme”, Nucl. Phys. B 890 (2014) 152
  M. Czakon and D. Heymes
  
• “Matching the Nagy-Soper parton shower at next-to-leading order”, JHEP 1506 (2015) 033
  M. Czakon, H. B. Hartanto, M. Kraus and M. Worek
  
• “Resolving the Tevatron top quark forward-backward asymmetry puzzle: fully differential nextto-next-to-leading-order calculation”, Phys. Rev. Lett. 115 (2015) 5, 052001
  M. Czakon, P. Fiedler and A. Mitov