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 two subjects.
 One subject is 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 in the past few years 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 nexttoleading 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 nexttoleading order. This allows for a more
realistic representation of the final state than happens in standard
nexttoleading 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 highenergy colliding beam accelerators,
such as the Large Hadron Collider near Geneva. Such jets are produced
when
highenergy 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 hadronhadron 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 ePrint 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 ePrint Archives.)
Journal Articles

Diffractive Jet Production in a Simple Model with Applications
to HERA,
ePrint Archive: hepph/9403276,
Phys. Rev. D 50, 4328 (1994), with A. Berera.

Top Quark Contribution to Hadronic Decays of the Z Boson at
alpha_{s}^{2} in QCD,
ePrint Archive: hepph/9406407,
Phys. Rev. Lett. 73, 2958 (1994),
with L. Surguladze.

Triply Differential Jet Cross Sections for Hadron Collisions
at Order alpha_{s}^{3} in QCD,
ePrint Archive: hepph/9412342,
Phys. Rev. Lett. 74, 5182 (1995),
with S. D. Ellis.

Behavior of Diffractive Parton Distribution Functions,
ePrint Archive: hepph/9509239,
Phys. Rev. D 53, 6162 (1996),
with A. Berera.

On the QCD Perturbation Expansion for e^{+}e^{}
> hadrons,
ePrint Archive: hepph/9511258,
Phys. Rev. D 54, 4566 (1996),
with L. Surguladze.

SemiInclusive Deeply Inelastic Scattering at Small q_{T},
ePrint Archive: hepph/9511311,
Phys. Rev. D 54, 1919 (1996),
with R. Meng and F. I. Olness.

Large Transverse Momentum Jet Production and the
Gluon Distribution Inside the Proton,
ePrint Archive: hepph/9511386,
Phys. Rev. Lett. 77, 444 (1996),
with J. Huston, E. Kovacs, S. Kuhlmann, H. L. Lai, J. F. Owens
and W.K. Tung.

Improved Parton Distributions from Global Analysis of
Recent Deep Inelastic Scattering and Inclusive Jet Data,
ePrint Archive: hepph/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.

Probing the QCD Pomeron in e^{+} e^{} Collisions,
ePrint Archive: hepph/9610260,
Phys. Rev. Lett. 78, 803 (1997),
Erratum  ibid 79, 3544 (1997),
with S. J. Brodsky and F. Hautmann.

Virtual Photon Scattering at High Energies as a Probe of the
Short Distance Pomeron,
ePrint Archive: hepph/9706427,
Phys. Rev. D 56, 6957 (1997).
with S. J. Brodsky and F. Hautmann.

Study of the Uncertainty of the Gluon Distribution,
ePrint Archive: hepph/9801444,
Phys. Rev. D 58, 114034 (1998),
with J. Huston, S. Kuhlmann, H.L. Lai, F. Olness,
J.F. Owens, and W.K. Tung.

QCD Calculations by Numerical Integration,
ePrint Archive: hepph/9804454,
Phys. Rev. Lett. 81, 2638 (1998)

Factorization is not violated,
ePrint Archive: hepph/9806234,
Phys. Lett. B438, 184 (1998),
with John C. Collins and George Sterman.

Diffractive deeply inelastic scatteering of hadronic states with small transverse size,
ePrint Archive: hepph/9806298,
Phys. Rev. Lett. 81, 3333 (1998),
with F. Hautmann and Z. Kunszt.

Hard scattering factorization and light cone hamiltonian
aproach to diffractive processes,
ePrint Archive: hepph/9906284,
Nucl. Phys. B563, 153 (1999),
with F. Hautmann and Z. Kunszt.

Techniques for QCD calculations by numerical integration,
ePrint Archive: hepph/9910292,
Phys. Rev. D 62, 014009 (2000).

Factorization scheme dependence of the NLO inclusive jet cross section,
ePrint Archive: hepph/9912327,
Phys. Rev. D 61, 094003 (2000),
with P. Anandam.

Treatment of heavy quarks in deeply inelastic scattering,
ePrint Archive: hepph/0003035,
Phys. Rev. D 62, 096007 (2000),
with M. Kramer and F. I. Olness.

Color transparency in deeply inelastic diffraction,
ePrint Archive: hepph/0008224,
Phys. Rev. D 63, 011501 (2000),
with F. Hautmann.

Choosing integration points for QCD calculations by numerical integration,
ePrint Archive: hepph/0103262,
Phys. Rev. D 64, 034018 (2001).

Nexttoleading order numerical calculations in Coulomb gauge,
ePrint Archive: hepph/0204113,
Phys. Rev. D 66, 054017 (2002),
with M. Kramer.

Nexttoleading order QCD calculations with parton showers. I: Collinear
singularities,
ePrint Archive: hepph/0306222,
Phys. Rev. D 69, 0504019 (2004),
with M. Kramer.

Nexttoleading order QCD calculations with parton showers. II: Soft
singularities,
ePrint Archive: hepph/0306268,
Phys. Rev. D 69, 0504019 (2004).

General subtraction method for numerical calculation of oneloop QCD matrix
elements,
ePrint Archive: hepph/0308127,
JHEP 0309, 055 (2003),
with Z. Nagy.

Matching parton showers to NLO computations,
ePrint Archive: hepph/0503053,
JHEP 0510, 024 (2005),
with Z. Nagy.

Nexttoleading order QCD jet production with parton showers and
hadronization,
ePrint Archive: hepph/0509127,
Phys. Rev. D 73, 014022 (2006),
with M. Kramer, S. Mrenna.

Numerical integration of oneloop Feynman diagrams for Nphoton
amplitudes,
ePrint Archive:hepph/0610028,
Phys. Rev. D 74, 093006 (2006),
with Z. Nagy.

Parton distribution function for quarks in an schannel approach,
ePrint Archive:hepph/0702077,
Phys. Rev. D 75, 074020 (2007),
with F. Hautmann.

Parton showers with quantum interference,
ePrint at arXiv:0706.0017 [hepph],
JHEP 0709, 114 (2007)
with Z. Nagy.

Parton showers with quantum interference: leading color, spin averaged,
ePrint at arXiv:0801.1917 [hepph],
Phys. Rev. D 75, 074020 (2007),
with Z. Nagy.

Parton showers with quantum interference: leading color, with spin,
ePrint at arXiv:0805.0216 [hepph],
JHEP 0807, 025 (2008),
with Z. Nagy.

Direct numerical integration of oneloop Feynman diagrams for Nphoton
amplitudes,
ePrint at arXiv:0812.3686 [hepph],
Phys. Rev. D 79, 033005 (2009),
with W. Gong and Z. Nagy.

Final state dipole showers and the DGLAP equation,
ePrint at arXiv:0901.3587 [hepph],
JHEP 0905, 088 (2009),
with Z. Nagy.

Correlated theoretical uncertainties for the onejet inclusive cross
section,
ePrint at arXiv:0907.5052 [hepph],
Phys. Rev. D 81, 035018 (2010),
with F. I. Olness.

On the transverse momentum in Zboson production in a virtuality ordered
parton shower,
ePrint at arXiv:0912.4534 [hepph],
JHEP 1003, 097 (2010),
with Z. Nagy.

Combining subjet algorithms to enhance ZH detection at the LHC,
ePrint at arXiv:1005.0417 [hepph],
JHEP 1008, 029 (2010),
with M. Spannowsky.

Finding physics signals with shower deconstruction,
ePrint at arXiv:1102.3480 [hepph],
Phys. Rev. D 84, 074002 (2011),
with M. Spannowsky.

Parton shower evolution with subleading color,
ePrint at arXiv:1202.4496 [hepph],
JHEP 1206, 044 (2012),
with Z. Nagy.

MEKS: a program for computation of inclusive jet cross sections at hadron colliders,
ePrint at arXiv:1207.0513 [hepph],
Comput. Phys. Commun. 184, 1626 (2013),
with J. Gao, Z. Liang, H. L. Lai, P. M. Nadolsky and C.P. Yuan.

Finding top quarks with shower deconstruction,
ePrint at arXiv:1211.3140 [hepph],
Phys. Rev. D 87, 054012 (2013),
with M. Spannowsky.

A parton shower based on factorization of the quantum density matrix,
ePrint at arXiv:1401.6364 [hepph],
JHEP 1406, 097 (2014),
with Z. Nagy.

Ordering variable for parton showers,
ePrint at arXiv:1401.6366 [hepph],
JHEP 1406, 178 (2014),
with Z. Nagy.

Parton distribution functions in the context of parton showers,
ePrint at arXiv:1401.6368 [hepph],
JHEP 1406, 179 (2014),
with Z. Nagy.

Finding physics signals with event deconstruction,
ePrint at arXiv:1402.1189 [hepph],
Phys. Rev. D 89, 094005 (2014),
with M. Spannowsky.

Scattering of dark particles with light mediators,
ePrint at arXiv:1407.2623 [hepph],
Phys. Rev. D 90, 115005 (2014),
with M. Spannowsky, C. J. Wallace and T. M. P. Tait.

Effects of subleading color in a parton shower,
ePrint at arXiv:1501.00778 [hepph],
JHEP 1507, 119 (2015),
with Z. Nagy.

Summing threshold logs in a parton shower,
eprint at arXiv:1605.05845 [hepph],
JHEP 1610, 019 (2016),
with Z. Nagy.

QuarkGluon tagging with Shower Deconstruction:
Unearthing dark matter and Higgs couplings,
eprint at arXiv:1607.06031 [hepph],
Phys. Rev. D 95, 034001 (2017),
with D. Ferreira de Lima, P. Petrov, and M. Spannowsky.

What is a parton shower?,
eprint at arXiv:1705.08093 [hepph],
Phys. Rev. D 98, 014034 (2018),
with Z. Nagy.

Jets and threshold summation in Deductor,
eprint at arXiv:1711.02369 [hepph],
Phys. Rev. D 98, 014035 (2018),
with Z. Nagy.

Parton showers with more exact color evolution,
eprint at arXiv:1902.02105 [hepph],
Phys. Rev. D 99, 054009 (2019),
with Z. Nagy.

Hadron structure in highenergy collisions,
eprint at arXiv:1905.06957 [hepph],
Rev. Mod. Phys. 92, 045003, (2020),
with K. Kovarik and P. M. Nadolsky.

Effect of color on rapidity gap survival,
eprint at arXiv:1905.07176 [hepph],
Phys. Rev. D 100, 074012 (2019)
with with Z. Nagy.

Sound waves move matter,
eprint at arXiv:1908.07823 [physics.classph],
Phys. Rev. Res. 2, 013258 (2020).

Exponentiating virtual imaginary contributions in a parton shower,
eprint at arXiv:1908.11420 [hepph],
Phys. Rev. D 100, 074005 (2019),
with with Z. Nagy.

Evolution of parton showers and parton distribution functions,
eprint at arXiv:2002.04125 [hepph],
Phys. Rev. D 102, 014025 (2020),
with with Z. Nagy.
Other publications

Issues in the Determination of Parton Distribution Functions,
ePrint Archive: hepph/9411214, (an electronic
paper, not submitted to any journal),
with J. C. Collins.

Summary of the XXX Rencontre de Moriond QCD Session,
ePrint Archive: hepph/9506218,
in 30th Rencontre de Moriond: High Energy Hadronic Interactions,
edited by J. Tran Thanh Van,
Les Arcs, France, March 1995,
(Editions Frontieres, GifsurYvette, France, 1995).

Status of Perturbative QCD Evaluation of Hadronic Decay Rates of the
Z and Higgs Bosons,
ePrint Archive: hepph/9506244,
in 30th Rencontre de Moriond: High Energy Hadronic Interactions,
edited by J. Tran Thanh Van,
Les Arcs, France, March 1995,
(Editions Frontieres, GifsurYvette, France, 1995),
with L. Surguladze.

QCD and Beyond.
Proceedings, Theoretical Advanced Sudy Institute
in Elementary Particle Physics, TASI95, Boulder, USA, June 1995, editor.

Parton Distribution Functions,
ePrint Archive: heplat/9609018,
in
Lattice '96 International Symposium on Lattice Field Theory,
St. Louis, June 1996,
edited by M. Golterman et al.
(Elsevier Science, Amsterdam, 1997).

Jets and Partons,
ePrint Archive: hepph/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).

Basics of QCD Perturbation Theory,
ePrint Archive: hepph/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).

Jet Observables in Theory and Reality,
ePrint Archive: hepph/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, GifsurYvette, France, 1997).

Diffraction in DIS and Elsewhere,
ePrint Archive: hepph/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.

Review of Particle Physics, One Hundred Years of Discoveries,
by V. V. Ezhela et al., Am. J. Phys. 64, 932 (1997).

BFKL Scattering at LEP2 and a Next e^{+}e^{} Collider,
ePrint Archive: hepph/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.

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.

Talk on QCD Calculations by Numerical Integration,
ePrint Archive: hepph/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).

Hard diffraction from small size color sources,
ePrint Archive: hepph/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.

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),

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.

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.

Diffractive parton distributions in light cone QCD,
ePrint Archive: hepph/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.

The QCD and standard model working group: summary report,
ePrint Archive: hepph/0005114,
from Les Houches Workshiop on Physics at TeV Colliders,
June 1999,
(unpublished),
S. Catani et al.,
30 authors in all.

Heavy quark production,
ePrint Archive: hepph/0005112 and hepph/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.

QCD,
ePrint Archive: hepph/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.

Basics of QCD perturbation theory,
ePrint Archive: hepph/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).

Letting realvirtual cancellations happen by themselves in QCD
calculations,
ePrint Archive: hepph/0102031,
in Proceedings of the 5th International Symposium on
Radiative Corrections (RADCOR2000), Carmel, 2000,
edited by H.~Haber,
eConf C000911 (2001).

Using Coulomb gauge for nexttoleading order numerical
calculations,
in Proceedings of the International
Conference on High Energy Physics 2002,
Amsterdam, July, 2002,
(Elsvier Science BV, 2003).

Partons and jets at the LHC,
ePrint Archive: hepph/0308233,
in
Proceedings of the conference QCD 2002 ,
Indian Institute of Technology, Kanpur, India, November 2002,
edited by P. Jain,
Pramana 61, 785 (2003).

QCD theory at the XL Rencontre de Moriond: Fish eyes and physics,
ePrint Archive: hepph/0506069,
to be published in
40th Rencontres de Moriond on QCD and High Energy Hadronic Interactions, La Thuile, Aosta Valley, Italy, 1219 Mar 2005.

A new parton shower algorithm: Shower evolution, matching at leading and
nexttoleading order level,
ePrint Archive: hepph/0601021, in
Proceedings of Ringberg Workshop on New Trends in HERA Physics 2005,
Ringberg Castle, Tegernsee, Germany, October 2005,
with Z. Nagy.

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),
ePrint Archive: hepph/0607046,
with Z. Nagy.

MSbar quark distribution and dipole scattering matrix elements at high energy,
in Photon 2007 International Conference,
Paris, France, July 2007,
(to be published),
ePrint at arXiv:0712.0526 [hepph],
with F. Hautmann.

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),
ePrint at arXiv:0803.0494 [hepph],
with Z. Bern et al. (47 authors).

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)
ePrint at arXiv:0805.4371 [hepph],
with Z. Nagy.

Jet Substructure at the Tevatron and LHC: New results, new tools, new benchmarks,
in Boost 2011 Workshop,
Princeton, May 2011,
ePrint at arXiv:1201.0008 [hepph],
J. Phys. G 39, 063001 (2012),
with A. Altheimer et al. (71 authors).

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),
ePrint at arXiv:1206.5043 [hepph].

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.

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.

Towards an Understanding of the Correlations in Jet Substructure,
eprint archive: 1504.00679 [hepph],
Eur. Phys. J. C 75, no. 9, 409 (2015),
Report of BOOST2013, hosted by the University of Arizona, 1216 August 2013,
with D. Adams and 84 other coauthors.

DIS outlook: Into the woods with particle physics,
23rd International Workshop on DeepInelastic Scattering and Related Subjects (DIS 2015),
27 Apr  01 May 2015, Dallas, Texas,
PoS DIS 2015, 024 (2015).

Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report,
eprint archive: arXiv:1605.04692 [hepph],
with J. R. Andersen and 93 other coauthors.

Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report,
eprint archive: arXiv:2003.01700 [hepph],
with S. Amoroso and 81 other coauthors.
Soper demonstrates the saddle point approximation. The path
must avoid any essential singularities.