Abstract
Without proper control of numerical and methodological errors in theoretical predictions at the per mille level it is not possible to study the effect of input parameters in current hadron-collider measurements at the required precision. We present the new version of the parton-level code MCFM-9.0 that achieves this requirement through its highly-parallelized nature, significant performance improvements and new features. An automatic differential jettiness slicing cutoff extrapolation is introduced to assess the cutoff dependence of all results, thus ensuring their reliability and potentially improving fixed- cutoff results by an order of magnitude. The efficient differential study of PDF uncertainties and PDF set differences at NNLO, for multiple PDF sets simultaneously, is achieved by exploiting correlations. We use these improvements to study uncertainties and PDF sensitivity at NNLO, using 371 PDF set members. The work described here permits NNLO studies that were previously prohibitively expensive, and lays the groundwork necessary for a future implementation of NNLO calculations with a jet at Born level in MCFM.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett.103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett.98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
M. Grazzini, NNLO predictions for the Higgs boson signal in the H → WW → lνlν and H → ZZ → 4l decay channels, JHEP02 (2008) 043 [arXiv:0801.3232] [INSPIRE].
M. Grazzini and H. Sargsyan, Heavy-quark mass effects in Higgs boson production at the LHC, JHEP09 (2013) 129 [arXiv:1306.4581] [INSPIRE].
R.V. Harlander, S. Liebler and H. Mantler, SusHi: A program for the calculation of Higgs production in gluon fusion and bottom-quark annihilation in the Standard Model and the MSSM, Comput. Phys. Commun.184 (2013) 1605 [arXiv:1212.3249] [INSPIRE].
R.V. Harlander, S. Liebler and H. Mantler, SusHi Bento: Beyond NNLO and the heavy-top limit, Comput. Phys. Commun.212 (2017) 239 [arXiv:1605.03190] [INSPIRE].
M. Bonvini, R.D. Ball, S. Forte, S. Marzani and G. Ridolfi, Updated Higgs cross section at approximate N 3LO, J. Phys.G 41 (2014) 095002 [arXiv:1404.3204] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys.B 724 (2005) 197 [hep-ph/0501130] [INSPIRE].
C. Anastasiou, S. Bucherer and Z. Kunszt, HPro: A NLO Monte-Carlo for Higgs production via gluon fusion with finite heavy quark masses, JHEP10 (2009) 068 [arXiv:0907.2362] [INSPIRE].
M. Cacciari, F.A. Dreyer, A. Karlberg, G.P. Salam and G. Zanderighi, Fully Differential Vector-Boson-Fusion Higgs Production at Next-to-Next-to-Leading Order, Phys. Rev. Lett.115 (2015) 082002 [Erratum ibid.120 (2018) 139901] [arXiv:1506.02660] [INSPIRE].
F.A. Dreyer and A. Karlberg, Fully differential Vector-Boson Fusion Higgs Pair Production at Next-to-Next-to-Leading Order, Phys. Rev.D 99 (2019) 074028 [arXiv:1811.07918] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett.108 (2012) 072001 [Erratum ibid.117 (2016) 089901] [arXiv:1110.2375] [INSPIRE].
R. Gavin, Y. Li, F. Petriello and S. Quackenbush, FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order, Comput. Phys. Commun.182 (2011) 2388 [arXiv:1011.3540] [INSPIRE].
R. Gavin, Y. Li, F. Petriello and S. Quackenbush, W Physics at the LHC with FEWZ 2.1, Comput. Phys. Commun.184 (2013) 208 [arXiv:1201.5896] [INSPIRE].
Y. Li and F. Petriello, Combining QCD and electroweak corrections to dilepton production in FEWZ, Phys. Rev.D 86 (2012) 094034 [arXiv:1208.5967] [INSPIRE].
S. Alioli, C.W. Bauer, C. Berggren, F.J. Tackmann and J.R. Walsh, Drell-Yan production at NNLL’+NNLO matched to parton showers, Phys. Rev.D 92 (2015) 094020 [arXiv:1508.01475] [INSPIRE].
M. Grazzini, S. Kallweit and M. Wiesemann, Fully differential NNLO computations with MATRIX, Eur. Phys. J.C 78 (2018) 537 [arXiv:1711.06631] [INSPIRE].
J. Bellm et al., Jet Cross Sections at the LHC and the Quest for Higher Precision, arXiv:1903.12563 [INSPIRE].
J.M. Campbell and R.K. Ellis, An Update on vector boson pair production at hadron colliders, Phys. Rev.D 60 (1999) 113006 [hep-ph/9905386] [INSPIRE].
J.M. Campbell, R.K. Ellis and W.T. Giele, A Multi-Threaded Version of MCFM, Eur. Phys. J.C 75 (2015) 246 [arXiv:1503.06182] [INSPIRE].
R. Boughezal et al., Color singlet production at NNLO in MCFM, Eur. Phys. J.C 77 (2017) 7 [arXiv:1605.08011] [INSPIRE].
J.M. Campbell, D. Wackeroth and J. Zhou, Study of weak corrections to Drell-Yan, top-quark pair and dijet production at high energies with MCFM, Phys. Rev.D 94 (2016) 093009 [arXiv:1608.03356] [INSPIRE].
T. Neumann and Z.E. Sullivan, Off-Shell Single-Top-Quark Production in the Standard Model Effective Field Theory, JHEP06 (2019) 022 [arXiv:1903.11023] [INSPIRE].
S. Catani, D. de Florian, G. Ferrera and M. Grazzini, Vector boson production at hadron colliders: transverse-momentum resummation and leptonic decay, JHEP12 (2015) 047 [arXiv:1507.06937] [INSPIRE].
G. Bozzi, S. Catani, G. Ferrera, D. de Florian and M. Grazzini, Production of Drell-Yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy, Phys. Lett.B 696 (2011) 207 [arXiv:1007.2351] [INSPIRE].
D. de Florian, G. Ferrera, M. Grazzini and D. Tommasini, Higgs boson production at the LHC: transverse momentum resummation effects in the H → 2γ, H → W W → lνlν and H → Z Z → 4l decay modes, JHEP06 (2012) 132 [arXiv:1203.6321] [INSPIRE].
L. Arpino, A. Banfi, S. Jäger and N. Kauer, BSM W W production with a jet veto, JHEP08 (2019) 076 [arXiv:1905.06646] [INSPIRE].
T. Carli et al., A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: The APPLGRID Project, Eur. Phys. J.C 66 (2010) 503 [arXiv:0911.2985] [INSPIRE].
J. Gao, C.S. Li and H.X. Zhu, Top Quark Decay at Next-to-Next-to Leading Order in QCD, Phys. Rev. Lett.110 (2013) 042001 [arXiv:1210.2808] [INSPIRE].
T. Melia, K. Melnikov, R. Rontsch, M. Schulze and G. Zanderighi, Gluon fusion contribution to W+W- + jet production, JHEP08 (2012) 115 [arXiv:1205.6987] [INSPIRE].
I. Anderson et al., Constraining Anomalous HVV Interactions at Proton and Lepton Colliders, Phys. Rev.D 89 (2014) 035007 [arXiv:1309.4819] [INSPIRE].
G.P. Lepage, Vegas: an adaptive multidimensional integration program, (1980) [INSPIRE].
R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP02 (2008) 002 [arXiv:0712.1851] [INSPIRE].
S. Carrazza, R.K. Ellis and G. Zanderighi, QCDLoop: a comprehensive framework for one-loop scalar integrals, Comput. Phys. Commun.209 (2016) 134 [arXiv:1605.03181] [INSPIRE].
T. Gehrmann and E. Remiddi, Numerical evaluation of two-dimensional harmonic polylogarithms, Comput. Phys. Commun.144 (2002) 200 [hep-ph/0111255] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J.C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
G.P. Lepage, A New Algorithm for Adaptive Multidimensional Integration, J. Comput. Phys.27 (1978) 192 [INSPIRE].
P. Bratley and B. Fox, Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator, ACM Trans. Math. Software14 (1988) 88.
B. Fox, Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators, ACM Trans. Math. Software12 (1986) 362.
Antonov and Saleev, An economic method of computing LPτ-sequences, USSR Comput. Math. Math. Phys.19 (1980) 252.
I. Sobol, Uniformly distributed sequences with an additional uniform property, USSR Comput. Math. Math. Phys.16 (1977) 236.
I.M. Sobol and Y.L. Levitan, The Production of Points Uniformly Distributed in a Multidimensional Cube (in Russian), Preprint IPM Akad. Nauk SSSR (1976).
J.M. Campbell, R.K. Ellis and C. Williams, Driving missing data at the LHC: NNLO predictions for the ratio of γ + j and Z + j, Phys. Rev.D 96 (2017) 014037 [arXiv:1703.10109] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and D.M. Walker, Vector Boson Production in Association with a Jet at Forward Rapidities, Eur. Phys. J.C 79 (2019) 526 [arXiv:1901.11041] [INSPIRE].
T. Kluge, K. Rabbertz and M. Wobisch, FastNLO: Fast pQCD calculations for PDF fits, in Deep inelastic scattering. Proceedings, 14th International Workshop, DIS 2006, Tsukuba, Japan, 20–24 April 2006, pp. 483–486 (2006) [DOI:https://doi.org/10.1142/9789812706706_0110] [hep-ph/0609285] [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys.G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].
A. Accardi et al., A Critical Appraisal and Evaluation of Modern PDFs, Eur. Phys. J.C 76 (2016) 471 [arXiv:1603.08906] [INSPIRE].
NNPDF collaboration, A first determination of parton distributions with theoretical uncertainties, Eur. Phys. J.C (2019) 79:838 [arXiv:1905.04311] [INSPIRE].
T. Hahn, CUBA: A Library for multidimensional numerical integration, Comput. Phys. Commun.168 (2005) 78 [hep-ph/0404043] [INSPIRE].
J.F. Koksma, A general theorem from the theory of uniform distribution modulo 1, Mathematica, Zutphen. B.11 (1942) 7.
E. Hlawka, Funktionen von beschränkter Variation in der Theorie der Gleichverteilung, Ann. Mat. Pura Appl.54 (1961) 325.
D. van Vugt and K. Beljaars, Modern fortran implementation of a Sobol sequence, https://github.com/Exteris/sobseq (2016).
S. Joe and F.Y. Kuo, Sobol sequence direction numbers, https://web.maths.unsw.edu.au/∼fkuo/sobol/ (2010).
S. Joe and F. Kuo, Constructing sobol sequences with better two-dimensional projections, SIAM J. Sci. Comput.30 (2008) 2635.
S. Joe and F.Y. Kuo, Remark on algorithm 659: Implementing sobol’s quasirandom sequence generator, ACM Trans. Math. Softw.29 (2003) 49.
Z. Nagy and Z. Trócsányi, Next-to-leading order calculation of four jet observables in electron positron annihilation, Phys. Rev.D 59 (1999) 014020 [Erratum ibid.D 62 (2000) 099902] [hep-ph/9806317] [INSPIRE].
Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev.D 68 (2003) 094002 [hep-ph/0307268] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, A. Huss and T.A. Morgan, NNLO QCD corrections for Z boson plus jet production, PoS(RADCOR2015)075 (2016) [arXiv:1601.04569] [INSPIRE].
A. Canty and B. Ripley, Functions and datasets for bootstrapping from the book “Bootstrap Methods and Their Application”, https://cran.r-project.org/web/packages/boot/index.html (2019).
A.C. Davison and D.V. Hinkley, Bootstrap Methods and Their Application, Cambridge University Press (1997).
B. Efron, Jackknife-after-bootstrap standard errors and influence functions (with Discussion), J. Roy. Statist. Soc.B (1992) 83.
R. Boughezal, C. Focke, X. Liu and F. Petriello, W -boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett.115 (2015) 062002 [arXiv:1504.02131] [INSPIRE].
J. Gaunt, M. Stahlhofen, F.J. Tackmann and J.R. Walsh, N-jettiness Subtractions for NNLO QCD Calculations, JHEP09 (2015) 058 [arXiv:1505.04794] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N-Jettiness: An Inclusive Event Shape to Veto Jets, Phys. Rev. Lett.105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].
I. Moult, L. Rothen, I.W. Stewart, F.J. Tackmann and H.X. Zhu, Subleading Power Corrections for N-Jettiness Subtractions, Phys. Rev.D 95 (2017) 074023 [arXiv:1612.00450] [INSPIRE].
J.M. Campbell, T. Neumann and C. Williams, Z γ Production at NNLO Including Anomalous Couplings, JHEP11 (2017) 150 [arXiv:1708.02925] [INSPIRE].
M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Power Corrections for N-Jettiness Subtractions at 𝒪(αs ), JHEP12 (2018) 084 [arXiv:1807.10764] [INSPIRE].
J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP07 (2016) 148 [arXiv:1603.02663] [INSPIRE].
J. Burkardt, MINPACK, a Fortran90 implementation, https://people.sc.fsu.edu/∼jburkardt/f src/minpack/minpack.html (2010).
J. More, B. Garbow and K. Hillstrom, User Guide for MINPACK-1, Technical Report ANL-80-74, Argonne National Laboratory (1980).
J. More, D. Sorenson, B. Garbow and K. Hillstrom, The MINPACK Project, in Sources and Development of Mathematical Software, Prentice-Hall (1984).
S. Catani and M.H. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys.B 485 (1997) 291 [Erratum ibid.B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
C. Anastasiou et al., High precision determination of the gluon fusion Higgs boson cross-section at the LHC, JHEP05 (2016) 058 [arXiv:1602.00695] [INSPIRE].
LHCb collaboration, Measurement of forward W and Z boson production in pp collisions at \( \sqrt{s}=8\kern0.33em TeV, \)JHEP01 (2016) 155 [arXiv:1511.08039] [INSPIRE].
LHCb collaboration, Measurement of forward W → eν production in pp collisions at \( \sqrt{s}=8\kern0.33em TeV, \)JHEP10 (2016) 030 [arXiv:1608.01484] [INSPIRE].
LHCb collaboration, Measurement of the forward Z boson production cross-section in pp collisions at \( \sqrt{s}=13\kern0.33em TeV, \)JHEP09 (2016) 136 [arXiv:1607.06495] [INSPIRE].
LHCb collaboration, Measurement of the forward Z boson production cross-section in pp collisions at \( \sqrt{s}=7\kern0.33em TeV, \)JHEP08 (2015) 039 [arXiv:1505.07024] [INSPIRE].
S. Alekhin, J. Blümlein, S. Moch and R. Placakyte, Parton distribution functions, αs and heavy-quark masses for LHC Run II, Phys. Rev.D 96 (2017) 014011 [arXiv:1701.05838] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev.D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J.C 75 (2015) 204 [arXiv:1412.3989] [INSPIRE].
NNPDF collaboration, Parton distributions for the LHC Run II, JHEP04 (2015) 040 [arXiv:1410.8849] [INSPIRE].
NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J.C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
CMS collaboration, Inclusive search for a highly boosted Higgs boson decaying to a bottom quark-antiquark pair, Phys. Rev. Lett.120 (2018) 071802 [arXiv:1709.05543] [INSPIRE].
R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, JHEP06 (2013) 072 [arXiv:1302.6216] [INSPIRE].
X. Chen, T. Gehrmann, E.W.N. Glover and M. Jaquier, Precise QCD predictions for the production of Higgs + jet final states, Phys. Lett.B 740 (2015) 147 [arXiv:1408.5325] [INSPIRE].
R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order, Phys. Rev. Lett.115 (2015) 082003 [arXiv:1504.07922] [INSPIRE].
R. Boughezal, C. Focke, W. Giele, X. Liu and F. Petriello, Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett.B 748 (2015) 5 [arXiv:1505.03893] [INSPIRE].
F. Caola, K. Melnikov and M. Schulze, Fiducial cross sections for Higgs boson production in association with a jet at next-to-next-to-leading order in QCD, Phys. Rev.D 92 (2015) 074032 [arXiv:1508.02684] [INSPIRE].
X. Chen, J. Cruz-Martinez, T. Gehrmann, E.W.N. Glover and M. Jaquier, NNLO QCD corrections to Higgs boson production at large transverse momentum, JHEP10 (2016) 066 [arXiv:1607.08817] [INSPIRE].
J.M. Campbell, R.K. Ellis and S. Seth, H + 1 jet production revisited, JHEP10 (2019) 136 [arXiv:1906.01020] [INSPIRE].
S.P. Jones, M. Kerner and G. Luisoni, Next-to-Leading-Order QCD Corrections to Higgs Boson Plus Jet Production with Full Top-Quark Mass Dependence, Phys. Rev. Lett.120 (2018) 162001 [arXiv:1802.00349] [INSPIRE].
T. Neumann, NLO Higgs+jet production at large transverse momenta including top quark mass effects, J. Phys. Comm.2 (2018) 095017 [arXiv:1802.02981] [INSPIRE].
T. Neumann and C. Williams, The Higgs boson at high p T , Phys. Rev.D 95 (2017) 014004 [arXiv:1609.00367] [INSPIRE].
ATLAS collaboration, Precision measurement and interpretation of inclusive W +, W −and Z/γ ∗production cross sections with the ATLAS detector, Eur. Phys. J.C 77 (2017) 367 [arXiv:1612.03016] [INSPIRE].
S. Alioli et al., Precision studies of observables in pp → W → lν land pp → γ, Z → l +l −processes at the LHC, Eur. Phys. J.C 77 (2017) 280 [arXiv:1606.02330] [INSPIRE].
S. Frixione and G. Ridolfi, Jet photoproduction at HERA, Nucl. Phys.B 507 (1997) 315 [hep-ph/9707345] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at the LHC: a QCD study up to NNLO, JHEP04 (2018) 142 [arXiv:1802.02095] [INSPIRE].
J. Teunissen, config fortran — A configuration file parser for Fortran, https://github.com/jannisteunissen/config fortran/ (2019).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1909.09117
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Campbell, J., Neumann, T. Precision phenomenology with MCFM. J. High Energ. Phys. 2019, 34 (2019). https://doi.org/10.1007/JHEP12(2019)034
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2019)034