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A panoramic study of K-factors for 111 processes at the 14 TeV LHC

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Abstract

In this comprehensive study, we investigate K-factors (\(K=\sigma _{\text {NLO}}/\sigma _{\text {LO}}\equiv 1+\delta K\)) for a broad array of Standard Model processes at the 14 TeV LHC, which are pivotal for background assessments in Beyond the Standard Model (BSM) searches. Using MadGraph5_aMC@NLO, we calculate the leading-order and next-to-leading-order (NLO) cross-sections and compute the corresponding K-factors for 111 processes. Our analysis reveals K-factors ranging from 1.005 for \(pp \rightarrow jjj\) to 4.221 for \(pp\rightarrow W^\pm \gamma \gamma \gamma \). Key findings include: (i) processes involving photons display significantly high K-factors, attributed to gluon-initiated processes at NLO; (ii) processes with multiple particle productions, particularly those involving vector bosons, exhibit elevated K-factors due to multiple real emission processes; (iii) there exists an inverse correlation between the number of jets and \(\delta K\), indicating that the addition of jets generally leads to a decrease in \(\delta K\). In addition, our investigation into differential K-factors relative to transverse momentum and invariant mass shows notable increases with higher \(p_T\), but minimal changes with invariant mass. This study highlights the indispensable role of precise K-factor evaluations for accurate interpretations of BSM search outcomes.

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Notes

  1. Concerns may arise regarding processes with high scale uncertainty, exemplified by \(pp \rightarrow \gamma \gamma j\). At LO, this process yields a cross section of \(17.56^{+17.92\%}_{-15.77\%} ~\text{pb}\), while at NLO, it is \(41.11^{+16.15\%}_{-14.38\%}~\text{ pb }\). These computations follow the standard approach, considering nine choices for \(\mu _R\) and \(\mu _F\): \((\mu _R,\mu _F) = (\mu _0/2,\mu _0/2)\), \((\mu _0/2,\mu _0)\), \((\mu _0/2, 2\mu _0)\), \((\mu _0,\mu _0/2)\), \((\mu _0,\mu _0)\), \((\mu _0, 2\mu _0)\), \((2\mu _0,\mu _0/2)\), \((2\mu _0,\mu _0)\), \((2\mu _0, 2\mu _0)\). However, the uncertainty in the \(K\)-factor is remarkably reduced: \(K(\gamma \gamma j) = 2.34^{+5.66\%}_{-3.54\%}\)

  2. For the sake of simplicity in our discussions, contributions from \(c\bar{s} \rightarrow \gamma W^+\), while not negligible, are not mentioned

  3. The \(p_T^j\) dependence of \(K\)-factor was extensively studied in Ref. [56]

  4. Event counts at the \(p_T\) threshold were adjusted to align with the differential cross sections.

References

  1. ATLAS collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1–29, (2012) [arXiv:1207.7214]

  2. CMS collaboration, S. Chatrchyan et al., Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B 716, 30–61, (2012) [arXiv:1207.7235]

  3. J.F. Navarro, C.S. Frenk, S.D.M. White, The structure of cold dark matter halos. Astrophys. J. 462, 563–575 (1996). [arXiv:astro-ph/9508025]

    Article  ADS  Google Scholar 

  4. G. Bertone, D. Hooper, J. Silk, Particle dark matter: evidence, candidates and constraints. Phys. Rept. 405, 279–390 (2005). [arXiv:hep-ph/0404175]

    Article  ADS  Google Scholar 

  5. G. Degrassi, S. Di Vita, J. Elias-Miro, J.R. Espinosa, G.F. Giudice, G. Isidori et al., Higgs mass and vacuum stability in the Standard Model at NNLO. JHEP 08, 098 (2012). [arXiv:1205.6497]

    Article  ADS  Google Scholar 

  6. S. Dimopoulos, G.F. Giudice, Naturalness constraints in supersymmetric theories with nonuniversal soft terms. Phys. Lett. B 357, 573–578 (1995). [arXiv:hep-ph/9507282]

    Article  ADS  Google Scholar 

  7. K.L. Chan, U. Chattopadhyay, P. Nath, Naturalness, weak scale supersymmetry and the prospect for the observation of supersymmetry at the Tevatron and at the CERN LHC. Phys. Rev. D 58, 096004 (1998). [arXiv:hep-ph/9710473]

    Article  ADS  Google Scholar 

  8. N. Craig, A. Katz, M. Strassler, R. Sundrum, Naturalness in the dark at the LHC. JHEP 07, 105 (2015). arXiv:1501.05310

  9. SLAC-SP-017 collaboration, J.E. Augustin et al., Discovery of a narrow resonance in \(e^+ e^-\) annihilation, Phys. Rev. Lett. 33, 1406–1408 (1974)

  10. E598 collaboration, J. J. Aubert et al., Experimental observation of a heavy particle \(J\), Phys. Rev. Lett. 33, 1404–1406 (1974)

  11. V. Hankele, D. Zeppenfeld, QCD corrections to hadronic WWZ production with leptonic decays. Phys. Lett. B 661, 103–108 (2008). [arXiv:0712.3544]

    Article  ADS  Google Scholar 

  12. F. Campanario, C. Englert, M. Rauch, S. Sapeta, D. Zeppenfeld, Di-boson and Tri-boson production at the LHC, PoS DIS2013 154, (2013) [arXiv:1307.2261]

  13. A. Jueid, J. Kim, S. Lee, J. Song, D. Wang, Exploring lepton flavor violation phenomena of the Z and Higgs bosons at electron-proton colliders. Phys. Rev. D 108, 055024 (2023). arXiv:2305.05386

  14. M. Spira, QCD effects in Higgs physics. Fortsch. Phys. 46, 203–284 (1998). arXiv:hep-ph/9705337

    Article  ADS  Google Scholar 

  15. C. Anastasiou, K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD. Nucl. Phys. B 646, 220–256 (2002). arXiv:hep-ph/0207004

    Article  ADS  Google Scholar 

  16. V. Ahrens, T. Becher, M. Neubert, L.L. Yang, Renormalization-Group Improved Prediction for Higgs Production at Hadron Colliders. Eur. Phys. J. C 62, 333–353 (2009). arXiv:0809.4283

    Article  ADS  Google Scholar 

  17. C. Anastasiou, C. Duhr, F. Dulat, F. Herzog, B. Mistlberger, Higgs Boson gluon-fusion production in QCD at three loops. Phys. Rev. Lett. 114, 212001 (2015). arXiv:1503.06056

  18. M. Spira, Higgs Boson production and decay at Hadron colliders. Prog. Part. Nucl. Phys. 95, 98–159 (2017). arXiv:1612.07651

  19. J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. JHEP 07, 079 (2014). arXiv:1405.0301

    Article  ADS  Google Scholar 

  20. A. Ghosh, B. Nachman, T. Plehn, L. Shire, T.M.P. Tait, D. Whiteson, Statistical patterns of theory uncertainties. SciPost Phys. Core 6, 045 (2023). arXiv:2210.15167

  21. S. Alioli, P. Nason, C. Oleari, E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX. JHEP 06, 043 (2010). arXiv:1002.2581

    Article  ADS  Google Scholar 

  22. S. Frixione, V. Hirschi, D. Pagani, H.S. Shao, M. Zaro, Weak corrections to Higgs hadroproduction in association with a top-quark pair. JHEP 09, 065 (2014). arXiv:1407.0823

    Article  ADS  Google Scholar 

  23. Y. Zhang, W.-G. Ma, R.-Y. Zhang, C. Chen, L. Guo, QCD NLO and EW NLO corrections to \(t\bar{t}H\) production with top quark decays at hadron collider. Phys. Lett. B 738, 1–5 (2014). arXiv:1407.1110

    Article  ADS  Google Scholar 

  24. S. Kallweit, J.M. Lindert, P. Maierhofer, S. Pozzorini, M. Schönherr, NLO QCD+EW predictions for V + jets including off-shell vector-boson decays and multijet merging. JHEP 04, 021 (2016). arXiv:1511.08692

  25. S. Frixione, V. Hirschi, D. Pagani, H.S. Shao, M. Zaro, Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons. JHEP 06, 184 (2015). arXiv:1504.03446

  26. M. Czakon, D. Heymes, A. Mitov, D. Pagani, I. Tsinikos, M. Zaro, Top-pair production at the LHC through NNLO QCD and NLO EW. JHEP 10, 186 (2017). arXiv:1705.04105

  27. S. Frixione, Z. Kunszt, A. Signer, Three jet cross-sections to next-to-leading order. Nucl. Phys. B 467, 399–442 (1996). arXiv:hep-ph/9512328

    Article  ADS  Google Scholar 

  28. S. Frixione, A general approach to jet cross-sections in QCD. Nucl. Phys. B 507, 295–314 (1997). arXiv:hep-ph/9706545

    Article  ADS  Google Scholar 

  29. G. Ossola, C.G. Papadopoulos, R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level. Nucl. Phys. B 763, 147–169 (2007). [arXiv:hep-ph/0609007]

    Article  ADS  MathSciNet  Google Scholar 

  30. G. Passarino, M.J.G. Veltman, One loop corrections for e+ e-annihilation Into mu+ mu- in the Weinberg model. Nucl. Phys. B 160, 151–207 (1979)

    Article  ADS  Google Scholar 

  31. S. Frixione, B.R. Webber, Matching NLO QCD computations and Parton shower simulations. JHEP 06, 029 (2002). [arXiv:hep-ph/0204244]

    Article  ADS  Google Scholar 

  32. NNPDF collaboration, R.D. Ball et al., Parton distributions from high-precision collider data, Eur. Phys. J. C 77 663, (2017). arXiv:1706.00428

  33. S. Catani, Y.L. Dokshitzer, M.H. Seymour, B.R. Webber, Longitudinally invariant \(K_t\) clustering algorithms for hadron hadron collisions. Nucl. Phys. B 406, 187–224 (1993)

    Article  ADS  Google Scholar 

  34. S.D. Ellis, D.E. Soper, Successive combination jet algorithm for hadron collisions. Phys. Rev. D 48, 3160–3166 (1993). arXiv:hep-ph/9305266

    Article  ADS  Google Scholar 

  35. S. Frixione, Isolated photons in perturbative QCD. Phys. Lett. B 429, 369–374 (1998). arXiv:hep-ph/9801442

    Article  ADS  Google Scholar 

  36. J.M. Campbell, R.K. Ellis, D.L. Rainwater, Next-to-leading order QCD predictions for \(W\) + 2 jet and \(Z\) + 2 jet production at the CERN LHC. Phys. Rev. D 68, 094021 (2003). arXiv:hep-ph/0308195

    Article  ADS  Google Scholar 

  37. J.M. Campbell, R.K. Ellis, An Update on vector boson pair production at hadron colliders. Phys. Rev. D 60, 113006 (1999). arXiv:hep-ph/9905386

    Article  ADS  Google Scholar 

  38. F. Cascioli, T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhöfer, A. von Manteuffel et al., ZZ production at hadron colliders in NNLO QCD. Phys. Lett. B 735, 311–313 (2014). arXiv:1405.2219

    Article  ADS  Google Scholar 

  39. T. Binoth, G. Ossola, C.G. Papadopoulos, R. Pittau, NLO QCD corrections to tri-boson production. JHEP 06, 082 (2008). arXiv:0804.0350

    Article  ADS  Google Scholar 

  40. S. Dittmaier, A. Huss, G. Knippen, Next-to-leading-order QCD and electroweak corrections to WWW production at proton-proton colliders. JHEP 09, 034 (2017). arXiv:1705.03722

  41. CMS collaboration, A. Tumasyan et al., Measurements of the pp \(\rightarrow \) W\(^\pm \gamma \gamma \)and pp \(\rightarrow \) Z\(\gamma \gamma \)cross sections at\(\sqrt{s} =\) 13 TeV and limits on anomalous quartic gauge couplings, JHEP 10, 174, (2021). arXiv:2105.12780

  42. S. Catani, S. Devoto, M. Grazzini, S. Kallweit, J. Mazzitelli, Bottom-quark production at hadron colliders: fully differential predictions in NNLO QCD. JHEP 03, 029 (2021). arXiv:2010.11906

  43. N. Kidonakis, Higher-order corrections for \(t{\bar{t}}\) production at high energies, in Snowmass 2021, 3, (2022). arXiv:2203.03698

  44. P. Nason, S. Dawson, R.K. Ellis, The total cross-section for the production of heavy quarks in hadronic collisions. Nucl. Phys. B 303, 607–633 (1988)

    Article  ADS  Google Scholar 

  45. W. Beenakker, W.L. van Neerven, R. Meng, G.A. Schuler, J. Smith, QCD corrections to heavy quark production in hadron hadron collisions. Nucl. Phys. B 351, 507–560 (1991)

    Article  ADS  Google Scholar 

  46. M. Czakon, A. Mitov, Top++: a program for the calculation of the top-pair cross-section at hadron colliders. Comput. Phys. Commun. 185, 2930 (2014). arXiv:1112.5675

    Article  ADS  Google Scholar 

  47. N. Kidonakis, Top-quark double-differential distributions at approximate N\(^3\)LO. Phys. Rev. D 101, 074006 (2020). arXiv:1912.10362

  48. G. Bevilacqua, M. Worek, Constraining BSM Physics at the LHC: four top final states with NLO accuracy in perturbative QCD. JHEP 07, 111 (2012). arXiv:1206.3064

    Article  ADS  Google Scholar 

  49. ATLAS collaboration, G. Aad et al., Observation of four-top-quark production in the multilepton final state with the ATLAS detector, Eur. Phys. J. C 83, 496, (2023). arXiv:2303.15061. [Erratum: Eur.Phys.J.C 84, 156 (2024)]

  50. CMS collaboration, A. Hayrapetyan et al., Observation of four top quark production in proton-proton collisions at s=13TeV, Phys. Lett. B 847, 138290, (2023). arXiv:2305.13439

  51. A. Bredenstein, A. Denner, S. Dittmaier, S. Pozzorini, NLO QCD corrections to pp —> t anti-t b anti-b + X at the LHC. Phys. Rev. Lett. 103, 012002 (2009). arXiv:0905.0110

    Article  ADS  Google Scholar 

  52. S. Badger, J.M. Campbell, R.K. Ellis, QCD corrections to the hadronic production of a heavy quark pair and a W-Boson including decay correlations. JHEP 03, 027 (2011). arXiv:1011.6647

    Article  ADS  Google Scholar 

  53. R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau, P. Torrielli, W and \(Z/\gamma *\) boson production in association with a bottom-antibottom pair. JHEP 09, 061 (2011). arXiv:1106.6019

    Article  ADS  Google Scholar 

  54. S. Blasi, F. Maltoni, A. Mariotti, K. Mimasu, D. Pagani, S. Tentori, Top-philic ALP phenomenology at the LHC: the elusive mass-window, arXiv:2311.16048

  55. Anisha, D. Azevedo, L. Biermann, C. Englert, M. Mühlleitner, Effective 2HDM Yukawa interactions and a strong first-order electroweak phase transition. JHEP 02, 045 (2024)

    Article  Google Scholar 

  56. M. Rubin, G.P. Salam, S. Sapeta, Giant QCD K-factors beyond NLO. JHEP 09, 084 (2010)

    Google Scholar 

  57. T. Sjöstrand, S. Ask, J.R. Christiansen, R. Corke, N. Desai, P. Ilten et al., An introduction to PYTHIA 8.2. Comput. Phys. Commun. 191, 159–177 (2015). arXiv:1410.3012

  58. CMS collaboration, A. Hayrapetyan et al., Search for narrow trijet resonances in proton-proton collisions at\(\sqrt{s}\) = 13 TeV, arXiv:2310.14023

  59. K. Huitu, J. Maalampi, A. Pietila, M. Raidal, Doubly charged Higgs at LHC. Nucl. Phys. B 487, 27–42 (1997). arXiv:hep-ph/9606311

    Article  ADS  Google Scholar 

  60. K.S. Agashe, J. Collins, P. Du, S. Hong, D. Kim, R.K. Mishra, LHC signals from cascade decays of warped vector resonances. JHEP 05, 078 (2017). arXiv:1612.00047

  61. K. Agashe, M. Ekhterachian, D. Kim, D. Sathyan, LHC Signals for KK Graviton from an Extended Warped Extra Dimension. JHEP 11, 109 (2020). arXiv:2008.06480

  62. U. Baur, M. Spira, P.M. Zerwas, Excited Quark and Lepton Production at Hadron Colliders. Phys. Rev. D 42, 815–824 (1990)

    Article  ADS  Google Scholar 

  63. ATLAS collaboration, G. Aad et al., Search for short- and long-lived axion-like particles in\(H\rightarrow a a \rightarrow 4\gamma \)decays with the ATLAS experiment at the LHC, arXiv:2312.03306

  64. D. Wang, J.-H. Cho, J. Kim, S. Lee, P. Sanyal, J. Song, Probing light fermiophobic Higgs boson via diphoton jets at the HL-LHC. Phys. Rev. D 109, 015017 (2024). arXiv:2310.17741

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Acknowledgements

This paper was supported by Konkuk University in 2023.

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  1. Department of Physics, Konkuk University, Seoul, 05029, Republic of Korea

    Dongjoo Kim, Soojin Lee, Hanseok Jung, Dongchan Kim, Jinheung Kim & Jeonghyeon Song

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  1. Dongjoo Kim
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Kim, D., Lee, S., Jung, H. et al. A panoramic study of K-factors for 111 processes at the 14 TeV LHC. J. Korean Phys. Soc. (2024). https://doi.org/10.1007/s40042-024-01072-0

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