Davison E. Soper

portrait

Dave Soper works in elementary particle theory. Much of his recent work describes the theory of the strong interactions, quantum chromodynamics. He has been concerned with developing the methods that enable one to make predictions from the theory that can be compared with experiment. He is a member of the CTEQ Collaboration, which consists of both theorists and experimentalists from several experimental collaborations. CTEQ promotes research in quantum chromodynamics and runs an annual summer school. If you want to know more about him, you can look at his vita.

Soper's most recent work concerns the principles behind the construction of parton showers in Monte Carlo event generators. These event generators are computer programs that are used to simulate events at (for instance) the Large Hadron Collider (LHC) at the CERN laboratory in Geneva. Soper has worked with Z. Nagy of Desy laboratory in Hamburg on this subject. This work has concerned especially the influence of quantum interference on the behavior of parton showers. Quantum interference effects are especially important for the description of parton spin and SU(3) color. The general purpose of this work is to better understand the parton shower physics that is modeled in the event generators. The hope is that with better understanding, we will be able to do better modeling. This work has resulted in a parton shower event generator Deductor.

Another line of research has been developing methods for finding signals for new physics the LHC. Some small fraction of the collision events at the LHC may contain a new physics effect that we imagine might be present. However, there will be many more events that result from already known interactions. The problem is to find the features that make the exciting new physics events different from the standard events. The better that we are able to distinguish new physics events from standard events, the more likely we will be to discover the new physics in the data. With Michael Spannowsky of Durham University, Soper has developed algorithms for this purppse that go under the names "shower deconstruction" and "event deconstruction."

Soper has worked on performing next-to-leading order calculations of loop diagrams in quantum field theory by performing the integrations numerically. There is code available for this. The relevant papers on these subjects are in the list of recent publications below. You may also want to find out about Soper's earlier work on methods for doing calculations in quantum chromodynamics in which the integrals that represent virtual processes are performed using numerical integration. The latest versions of this code can also add parton showers to the calculation, while keeping the calculation correct to next-to-leading order. This allows for a more realistic representation of the final state than happens in standard next-to-leading order calculations.

Soper has worked with theorists from the University of Washington and the ETH in Zurich to calculate the cross section to produce "jets" of particles in high-energy colliding beam accelerators, such as the Large Hadron Collider near Geneva. Such jets are produced when high-energy quarks or gluons from the colliding proton and antiproton scatter. Each of the outgoing quarks or gluons materializes as a jet of particles (mostly pions), with its momentum distributed among the particles of the jet. Since jets with transverse momentum of over 1 TeV have been observed, the cross section provides a good window onto physics at very short distances. Information on the computer code for jet calculations in hadron-hadron collisions is available to anyone interested.

Soper has worked on organizing workshops on terascale physics, that is physics with an energy scale of tera electron volts. A list of these can be found at the website for these workshops.

Class notes for Soper's graduate courses on theoretical mechanics and quantum mechanics are available. You may also be interested in the class notes for his course in quantum field theory from 2001. There are also notes available for undergraduate quantum mechanics from Spring Quarter 2006. You might like to investigate his astronomy course for Spring Quarter 2002 (planets), Fall Quarter 2007 (stars), and Spring Quarter 1996 (galaxies).

Here is a list of Soper's most recent publications, with links to the abstracts at the e-Print Archives. From the abstracts, there are links to the electronic versions of the papers themselves. (For some of the entries, with titles in green, the papers are published on paper or will be published but were not submitted to the e-Print Archives.)

Journal Articles

  1. Diffractive Jet Production in a Simple Model with Applications to HERA, e-Print Archive: hep-ph/9403276, Phys. Rev. D 50, 4328 (1994), with A. Berera.
  2. Top Quark Contribution to Hadronic Decays of the Z Boson at alphas2 in QCD, e-Print Archive: hep-ph/9406407, Phys. Rev. Lett. 73, 2958 (1994), with L. Surguladze.
  3. Triply Differential Jet Cross Sections for Hadron Collisions at Order alphas3 in QCD, e-Print Archive: hep-ph/9412342, Phys. Rev. Lett. 74, 5182 (1995), with S. D. Ellis.
  4. Behavior of Diffractive Parton Distribution Functions, e-Print Archive: hep-ph/9509239, Phys. Rev. D 53, 6162 (1996), with A. Berera.
  5. On the QCD Perturbation Expansion for e+e- --> hadrons, e-Print Archive: hep-ph/9511258, Phys. Rev. D 54, 4566 (1996), with L. Surguladze.
  6. Semi-Inclusive Deeply Inelastic Scattering at Small qT, e-Print Archive: hep-ph/9511311, Phys. Rev. D 54, 1919 (1996), with R. Meng and F. I. Olness.
  7. Large Transverse Momentum Jet Production and the Gluon Distribution Inside the Proton, e-Print Archive: hep-ph/9511386, Phys. Rev. Lett. 77, 444 (1996), with J. Huston, E. Kovacs, S. Kuhlmann, H. L. Lai, J. F. Owens and W.-K. Tung.
  8. Improved Parton Distributions from Global Analysis of Recent Deep Inelastic Scattering and Inclusive Jet Data, e-Print Archive: hep-ph/9606399, Phys. Rev. D 55, 1280 (1997), with H. H. Lai, J. Huston, S. Kuhlmann, F. Olness, J. F. Owens, W.-K. Tung and H. Weerts.
  9. Probing the QCD Pomeron in e+ e- Collisions, e-Print Archive: hep-ph/9610260, Phys. Rev. Lett. 78, 803 (1997), Erratum -- ibid 79, 3544 (1997), with S. J. Brodsky and F. Hautmann.
  10. Virtual Photon Scattering at High Energies as a Probe of the Short Distance Pomeron, e-Print Archive: hep-ph/9706427, Phys. Rev. D 56, 6957 (1997). with S. J. Brodsky and F. Hautmann.
  11. Study of the Uncertainty of the Gluon Distribution, e-Print Archive: hep-ph/9801444, Phys. Rev. D 58, 114034 (1998), with J. Huston, S. Kuhlmann, H.L. Lai, F. Olness, J.F. Owens, and W.K. Tung.
  12. QCD Calculations by Numerical Integration, e-Print Archive: hep-ph/9804454, Phys. Rev. Lett. 81, 2638 (1998)
  13. Factorization is not violated, e-Print Archive: hep-ph/9806234, Phys. Lett. B438, 184 (1998), with John C. Collins and George Sterman.
  14. Diffractive deeply inelastic scatteering of hadronic states with small transverse size, e-Print Archive: hep-ph/9806298, Phys. Rev. Lett. 81, 3333 (1998), with F. Hautmann and Z. Kunszt.
  15. Hard scattering factorization and light cone hamiltonian aproach to diffractive processes, e-Print Archive: hep-ph/9906284, Nucl. Phys. B563, 153 (1999), with F. Hautmann and Z. Kunszt.
  16. Techniques for QCD calculations by numerical integration, e-Print Archive: hep-ph/9910292, Phys. Rev. D 62, 014009 (2000).
  17. Factorization scheme dependence of the NLO inclusive jet cross section, e-Print Archive: hep-ph/9912327, Phys. Rev. D 61, 094003 (2000), with P. Anandam.
  18. Treatment of heavy quarks in deeply inelastic scattering, e-Print Archive: hep-ph/0003035, Phys. Rev. D 62, 096007 (2000), with M. Kramer and F. I. Olness.
  19. Color transparency in deeply inelastic diffraction, e-Print Archive: hep-ph/0008224, Phys. Rev. D 63, 011501 (2000), with F. Hautmann.
  20. Choosing integration points for QCD calculations by numerical integration, e-Print Archive: hep-ph/0103262, Phys. Rev. D 64, 034018 (2001).
  21. Next-to-leading order numerical calculations in Coulomb gauge, e-Print Archive: hep-ph/0204113, Phys. Rev. D 66, 054017 (2002), with M. Kramer.
  22. Next-to-leading order QCD calculations with parton showers. I: Collinear singularities, e-Print Archive: hep-ph/0306222, Phys. Rev. D 69, 0504019 (2004), with M. Kramer.
  23. Next-to-leading order QCD calculations with parton showers. II: Soft singularities, e-Print Archive: hep-ph/0306268, Phys. Rev. D 69, 0504019 (2004).
  24. General subtraction method for numerical calculation of one-loop QCD matrix elements, e-Print Archive: hep-ph/0308127, JHEP 0309, 055 (2003), with Z. Nagy.
  25. Matching parton showers to NLO computations, e-Print Archive: hep-ph/0503053, JHEP 0510, 024 (2005), with Z. Nagy.
  26. Next-to-leading order QCD jet production with parton showers and hadronization, e-Print Archive: hep-ph/0509127, Phys. Rev. D 73, 014022 (2006), with M. Kramer, S. Mrenna.
  27. Numerical integration of one-loop Feynman diagrams for N-photon amplitudes, e-Print Archive:hep-ph/0610028, Phys. Rev. D 74, 093006 (2006), with Z. Nagy.
  28. Parton distribution function for quarks in an s-channel approach, e-Print Archive:hep-ph/0702077, Phys. Rev. D 75, 074020 (2007), with F. Hautmann.
  29. Parton showers with quantum interference, e-Print at arXiv:0706.0017 [hep-ph], JHEP 0709, 114 (2007) with Z. Nagy.
  30. Parton showers with quantum interference: leading color, spin averaged, e-Print at arXiv:0801.1917 [hep-ph], Phys. Rev. D 75, 074020 (2007), with Z. Nagy.
  31. Parton showers with quantum interference: leading color, with spin, e-Print at arXiv:0805.0216 [hep-ph], JHEP 0807, 025 (2008), with Z. Nagy.
  32. Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes, e-Print at arXiv:0812.3686 [hep-ph], Phys. Rev. D 79, 033005 (2009), with W. Gong and Z. Nagy.
  33. Final state dipole showers and the DGLAP equation, e-Print at arXiv:0901.3587 [hep-ph], JHEP 0905, 088 (2009), with Z. Nagy.
  34. Correlated theoretical uncertainties for the one-jet inclusive cross section, e-Print at arXiv:0907.5052 [hep-ph], Phys. Rev. D 81, 035018 (2010), with F. I. Olness.
  35. On the transverse momentum in Z-boson production in a virtuality ordered parton shower, e-Print at arXiv:0912.4534 [hep-ph], JHEP 1003, 097 (2010), with Z. Nagy.
  36. Combining subjet algorithms to enhance ZH detection at the LHC, e-Print at arXiv:1005.0417 [hep-ph], JHEP 1008, 029 (2010), with M. Spannowsky.
  37. Finding physics signals with shower deconstruction, e-Print at arXiv:1102.3480 [hep-ph], Phys. Rev. D 84, 074002 (2011), with M. Spannowsky.
  38. Parton shower evolution with subleading color, e-Print at arXiv:1202.4496 [hep-ph], JHEP 1206, 044 (2012), with Z. Nagy.
  39. MEKS: a program for computation of inclusive jet cross sections at hadron colliders, e-Print at arXiv:1207.0513 [hep-ph], Comput. Phys. Commun. 184, 1626 (2013), with J. Gao, Z. Liang, H. L. Lai, P. M. Nadolsky and C.-P. Yuan.
  40. Finding top quarks with shower deconstruction, e-Print at arXiv:1211.3140 [hep-ph], Phys. Rev. D 87, 054012 (2013), with M. Spannowsky.
  41. A parton shower based on factorization of the quantum density matrix, e-Print at arXiv:1401.6364 [hep-ph], JHEP 1406, 097 (2014), with Z. Nagy.
  42. Ordering variable for parton showers, e-Print at arXiv:1401.6366 [hep-ph], JHEP 1406, 178 (2014), with Z. Nagy.
  43. Parton distribution functions in the context of parton showers, e-Print at arXiv:1401.6368 [hep-ph], JHEP 1406, 179 (2014), with Z. Nagy.
  44. Finding physics signals with event deconstruction, e-Print at arXiv:1402.1189 [hep-ph], Phys. Rev. D 89, 094005 (2014), with M. Spannowsky.
  45. Scattering of dark particles with light mediators, e-Print at arXiv:1407.2623 [hep-ph], Phys. Rev. D 90, 115005 (2014), with M. Spannowsky, C. J. Wallace and T. M. P. Tait.
  46. Effects of subleading color in a parton shower, e-Print at arXiv:1501.00778 [hep-ph], JHEP 1507, 119 (2015), with Z. Nagy.
  47. Summing threshold logs in a parton shower, eprint at arXiv:1605.05845 [hep-ph], JHEP 1610, 019 (2016), with Z. Nagy.
  48. Quark-Gluon tagging with Shower Deconstruction: Unearthing dark matter and Higgs couplings, eprint at arXiv:1607.06031 [hep-ph], Phys. Rev. D 95, 034001 (2017), with D. Ferreira de Lima, P. Petrov, and M. Spannowsky.
  49. What is a parton shower?, eprint at arXiv:1705.08093 [hep-ph], Phys. Rev. D 98, 014034 (2018), with Z. Nagy.
  50. Jets and threshold summation in Deductor, eprint at arXiv:1711.02369 [hep-ph], Phys. Rev. D 98, 014035 (2018), with Z. Nagy.
  51. Parton showers with more exact color evolution, eprint at arXiv:1902.02105 [hep-ph], Phys. Rev. D 99, 054009 (2019), with Z. Nagy.
  52. Hadron structure in high-energy collisions, eprint at arXiv:1905.06957 [hep-ph], Rev. Mod. Phys. 92, 045003, (2020), with K. Kovarik and P. M. Nadolsky.
  53. Effect of color on rapidity gap survival, eprint at arXiv:1905.07176 [hep-ph], Phys. Rev. D 100, 074012 (2019) with with Z. Nagy.
  54. Sound waves move matter, eprint at arXiv:1908.07823 [physics.class-ph], Phys. Rev. Res. 2, 013258 (2020).
  55. Exponentiating virtual imaginary contributions in a parton shower, eprint at arXiv:1908.11420 [hep-ph], Phys. Rev. D 100, 074005 (2019), with with Z. Nagy.
  56. Evolution of parton showers and parton distribution functions, eprint at arXiv:2002.04125 [hep-ph], Phys. Rev. D 102, 014025 (2020), with with Z. Nagy.
  57. Summations of large logarithms by parton showers, eprint at arXiv:2011.04773 [hep-ph], Phys. Rev. D 104, 054049 (2021), with with Z. Nagy.
  58. Multivariable evolution in final state parton shower algorithms, eprint at arXiv:2201.08056 [hep-ph], Phys. Rev. D 105, 054012 (2022), with with Z. Nagy.
  59. Multivariable evolution in parton showers with initial state partons, eprint at arXiv:2204.05631 [hep-ph], Phys. Rev. D 106, 014024 (2022), with with Z. Nagy.
  60. Gauge choice for organizing infrared singularities in QCD, eprint at arXiv:2304.11736 [hep-ph], Phys. Rev. D 108, 074008 (2023), with with Z. Nagy.

Other publications

  1. Issues in the Determination of Parton Distribution Functions, e-Print Archive: hep-ph/9411214, (an electronic paper, not submitted to any journal), with J. C. Collins.
  2. Summary of the XXX Rencontre de Moriond QCD Session, e-Print Archive: hep-ph/9506218, in 30th Rencontre de Moriond: High Energy Hadronic Interactions, edited by J. Tran Thanh Van, Les Arcs, France, March 1995, (Editions Frontieres, Gif-sur-Yvette, France, 1995).
  3. Status of Perturbative QCD Evaluation of Hadronic Decay Rates of the Z and Higgs Bosons, e-Print Archive: hep-ph/9506244, in 30th Rencontre de Moriond: High Energy Hadronic Interactions, edited by J. Tran Thanh Van, Les Arcs, France, March 1995, (Editions Frontieres, Gif-sur-Yvette, France, 1995), with L. Surguladze.
  4. QCD and Beyond. Proceedings, Theoretical Advanced Sudy Institute in Elementary Particle Physics, TASI-95, Boulder, USA, June 1995, editor.
  5. Parton Distribution Functions, e-Print Archive: hep-lat/9609018, in Lattice '96 International Symposium on Lattice Field Theory, St. Louis, June 1996, edited by M. Golterman et al. (Elsevier Science, Amsterdam, 1997).
  6. Jets and Partons, e-Print Archive: hep-ph/9610434, talks in XXVIII International Conference on High Energy Physics, Warsaw, July 1996, edited by Z. Ajduk and A. K. Wroblewski (World Scientific, Singapore, 1997); Proceedings of QCD 96, Montpellier, July 1996, edited by S. Narison, published in Nucl. Phys. (Proc. Suppl.) 53, 69 (1997).
  7. Basics of QCD Perturbation Theory, e-Print Archive: hep-ph/9702203, lecture series in XXIV SLAC Summer Institute on Particle Physics, The Strong Interaction, from Hadrons to Patons , Stanford, August 1996, edited by L. DeProcel (SLAC, Stanford, 1997).
  8. Jet Observables in Theory and Reality, e-Print Archive: hep-ph/9706320, in 32nd Rencontre de Moriond: QCD and High Energy Hadronic Interactions, Les Arcs, France, March 1997, edited by J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, France, 1997).
  9. Diffraction in DIS and Elsewhere, e-Print Archive: hep-ph/9707384, in Deep Inelastic Scattering and QCD, 5th International Workshop, Chicago, April 1997, edited by J. Repond and D. Krakauer, AIP Conference Proceedings 407, 1997.
  10. Review of Particle Physics, One Hundred Years of Discoveries, by V. V. Ezhela et al., Am. J. Phys. 64, 932 (1997).
  11. BFKL Scattering at LEP2 and a Next e+e- Collider, e-Print Archive: hep-ph/9707444, in Deep Inelastic Scattering and QCD, 5th International Workshop, Chicago, April 1997, edited by J. Repond and D. Krakauer, AIP Conference Proceedings 407, 1997, and in InternationalConference on the Structure and the Interactions of the Photon (Photon 97), Egmond aan Zee, May 1997, with S. J. Brodsky and F. Hautmann.
  12. Study of the Uncertainty of the Gluon Distribution, in Proceedings of 6th International Workshop on Deep Indlastic Scattering and QCD (DIS 98), Brussels, Belgium, April 1998, edited by Gh.~Coremans and R.~Roosen (World Scientific, Singapore, 1998), with J. Huston, S. Kuhlmann, H.L. Lai, F. Olness, J.F. Owens, and W.K. Tung.
  13. Talk on QCD Calculations by Numerical Integration, e-Print Archive: hep-ph/9812324, in Radiative Corrections, Applications of Quantum Field Theory to Phenomenology, Proceedings of the 4th International Symposium on Radiative Corrections (RADCOR 98), Barcelona, Catalonia, Spain, September 1998, edited by Joan Sola (World Scientific, Singapore, 1999).
  14. Hard diffraction from small size color sources, e-Print Archive: hep-ph/9905218, in DPF 99, Proceedings of the Los Angeles Meeting, 1999 meeting of the Division of Particles and Fields of the American Physical Society, Los Angeles, California, January 1999, edited by K. Arisaka and Z. Bern, (University of California, Los Angeles, 1999, http://www.dpf99.library.ucla.edu), with F. Hautmann and Z. Kunszt.
  15. QCD calculations by numerical integration, in `99 QCD and High Energy Hadronic Interactions, Proceedings of the XXXIV Rencontre de Moriond, Les Arcs, France, March 1999, edited by J. Tran Thanh Van (The Gioi, Hanoi, 2001),
  16. Diffractive parton distributions for a small size hadron, in Proceedings of the 7th International Workshop on Deep Inelastic Scattering and QCD (DIS 99), Zeuthen, Germany, April 1999, Nucl. Phys. B (Proc. Sup.) 79, 260 (1999), with F. Hautmann and Z. Kunszt.
  17. QCD calculations by numerical integration, in Proceedings of the 7th International Workshop on Deep Inelastic Scattering and QCD (DIS 99), Zeuthen, Germany, April 1999, Nucl. Phys. B (Proc. Sup.) 79, 444 (1999), edited by J. Bluemlein and T. Riemann.
  18. Diffractive parton distributions in light cone QCD, e-Print Archive: hep-ph/9911278, in Proceedings of the 19th International Symposium on Multiparticle Dynamics (ISMD 99), Providence, Rhode Island, August 1999, edited by I. Sarcevic and T.-I. Tan, (World Scientific, Singapore, 2000), with F. Hautmann and Z. Kunszt.
  19. The QCD and standard model working group: summary report, e-Print Archive: hep-ph/0005114, from Les Houches Workshiop on Physics at TeV Colliders, June 1999, (unpublished), S. Catani et al., 30 authors in all.
  20. Heavy quark production, e-Print Archive: hep-ph/0005112 and hep-ph/0006300, from Parton distributions working group, edited by L. de Barbaro et al., in Physics at Run II: QCD and Weak Boson Physics Workshop, (Fermilab, Chicago, 2000), R. Dernina et al., 11 authors in all.
  21. QCD, e-Print Archive: hep-ph/0005025, in Standard model physics (and more) at the LHC, edited by G. Altareli and M. Mangano (CERN, Geneva, 2000), with S. Catani et al., 63 authors in all.
  22. Basics of QCD perturbation theory, e-Print Archive: hep-ph/0011256, in Advanced Study Institute in Elementary Particle Physics (TASI 2000): Flavor Physics for the Millennium, Boulder, 2000, edited by J. Bagger (World Scientific, Singapore, 2001).
  23. Letting real-virtual cancellations happen by themselves in QCD calculations, e-Print Archive: hep-ph/0102031, in Proceedings of the 5th International Symposium on Radiative Corrections (RADCOR-2000), Carmel, 2000, edited by H.~Haber, eConf C000911 (2001).
  24. Using Coulomb gauge for next-to-leading order numerical calculations, in Proceedings of the International Conference on High Energy Physics 2002, Amsterdam, July, 2002, (Elsvier Science BV, 2003).
  25. Partons and jets at the LHC, e-Print Archive: hep-ph/0308233, in Proceedings of the conference QCD 2002 , Indian Institute of Technology, Kanpur, India, November 2002, edited by P. Jain, Pramana 61, 785 (2003).
  26. QCD theory at the XL Rencontre de Moriond: Fish eyes and physics, e-Print Archive: hep-ph/0506069, to be published in 40th Rencontres de Moriond on QCD and High Energy Hadronic Interactions, La Thuile, Aosta Valley, Italy, 12-19 Mar 2005.
  27. A new parton shower algorithm: Shower evolution, matching at leading and next-to-leading order level, e-Print Archive: hep-ph/0601021, in Proceedings of Ringberg Workshop on New Trends in HERA Physics 2005, Ringberg Castle, Tegernsee, Germany, October 2005, with Z. Nagy.
  28. QCD and Monte Carlo event generators, in Deep Inelastic Scattering, DIS 2006 , Proceedings of the 14th International Workshop, Tsukuba, Japan, April 2006, edited by Masahiro Kuze, Kunihiro Nagano, and Katsuo Tokushuku (World Scientific, Singapore, 2007), e-Print Archive: hep-ph/0607046, with Z. Nagy.
  29. MSbar quark distribution and dipole scattering matrix elements at high energy, in Photon 2007 International Conference, Paris, France, July 2007, (to be published), e-Print at arXiv:0712.0526 [hep-ph], with F. Hautmann.
  30. The NLO multileg working group: summary report, in 5th Les Houches Workshop on Physics at TeV Colliders, Les Houches, France, June 2007, (published using arXiv), e-Print at arXiv:0803.0494 [hep-ph], with Z. Bern et al. (47 authors).
  31. Structure of parton showers including quantum interference, in 43rd Rencontres de Moriond on QCD and High Energy Interactions, La Thuile, Italy, March 2008, (to be published) e-Print at arXiv:0805.4371 [hep-ph], with Z. Nagy.
  32. Jet Substructure at the Tevatron and LHC: New results, new tools, new benchmarks, in Boost 2011 Workshop, Princeton, May 2011, e-Print at arXiv:1201.0008 [hep-ph], J. Phys. G 39, 063001 (2012), with A. Altheimer et al. (71 authors).
  33. Through a glass, darkly: theory summary, in 46th Rencontres de Moriond on QCD and High Energy Interactions, La Thuile, Italy, March 2012, E. Augé, J. Dumarchez, B. Pietrzyk and J. Trān Thanh Vān, eds., (ARISF, Paris, 2012), e-Print at arXiv:1206.5043 [hep-ph].
  34. Jets and QCD, in E. M. Henley and S. D. Ellis, eds., 100 Years of Subatomic Physics (World Scientific, Singapore, 2013), with S. D. Ellis.
  35. Deeply inelastic dark matter: Beam dumps as WIMP cannons, Frascati Phys. Ser. 56, 258 (2012), C. J. Wallace, M. Spannowsky and T. M. P. Tait.
  36. Towards an Understanding of the Correlations in Jet Substructure, e-print archive: 1504.00679 [hep-ph], Eur. Phys. J. C 75, no. 9, 409 (2015), Report of BOOST2013, hosted by the University of Arizona, 12-16 August 2013, with D. Adams and 84 other coauthors.
  37. DIS outlook: Into the woods with particle physics, 23rd International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2015), 27 Apr - 01 May 2015, Dallas, Texas, PoS DIS 2015, 024 (2015).
  38. Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report, e-print archive: arXiv:1605.04692 [hep-ph], with J. R. Andersen and 93 other coauthors.
  39. Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report, e-print archive: arXiv:2003.01700 [hep-ph], with S. Amoroso and 81 other coauthors.
  40. Future prospects for parton showers, 2022 Snowmass Summer Study, e-print archive: arXiv:2203.06799 [hep-ph], N.~Darvishi, J.~I.~M.~R.~Masouminia, Z.~Nagy, and P.~Richardson.
  41. Event Generators for High-Energy Physics Experiments, 2022 Snowmass Summer Study, e-print archive: arXiv:2203.11110 [hep-ph], J.~M.~Campbell et al.
  42. Proton structure at the precision frontier,, 2022 Snowmass Summer Study, e-print archive: arXiv:2203.13923 [hep-ph], S.~Amoroso et al.
  43. Theory Techniques for Precision Physics -- Snowmass 2021 TF06 Topical Group Report, e-print archive: 2209.10639 [hep-ph], R.~Boughezal et al.

Soper demonstrates the saddle point approximation. The path must avoid any essential singularities.