Abstract
We compute the contributions to the N3LO inclusive Higgs boson cross-section from the square of one-loop amplitudes with a Higgs boson and three QCD partons as external states. Our result is a Taylor expansion in the dimensional regulator ϵ, where the coefficients of the expansion are analytic functions of the ratio of the Higgs boson mass and the partonic center of mass energy and they are valid for arbitrary values of this ratio. We also perform a threshold expansion around the limit of soft-parton radiation in the final state. The expressions for the coefficients of the threshold expansion are valid for arbitrary values of the dimension. As a by-product of the threshold expansion calculation, we have developed a soft expansion method at the integrand level by identifying the relevant soft and collinear regions for the loop-momentum.
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C. Anastasiou, S. Buehler, F. Herzog and A. Lazopoulos, Inclusive Higgs boson cross-section for the LHC at 8 TeV, JHEP 04 (2012) 004 [arXiv:1202.3638] [INSPIRE].
S. Buehler and A. Lazopoulos, Scale dependence and collinear subtraction terms for Higgs production in gluon fusion at N 3 LO, JHEP 10 (2013) 096 [arXiv:1306.2223] [INSPIRE].
P. Baikov, K. Chetyrkin, A. Smirnov, V. Smirnov and M. Steinhauser, Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002 [arXiv:0902.3519] [INSPIRE].
T. Gehrmann, E. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [arXiv:1004.3653] [INSPIRE].
T. Gehrmann, E. Glover, T. Huber, N. Ikizlerli and C. Studerus, The quark and gluon form factors to three loops in QCD through to O(𝜖 2 ), JHEP 11 (2010) 102 [arXiv:1010.4478] [INSPIRE].
A. Pak, M. Rogal and M. Steinhauser, Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders, JHEP 09 (2011) 088 [arXiv:1107.3391] [INSPIRE].
C. Anastasiou, S. Buehler, C. Duhr and F. Herzog, NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization, JHEP 11 (2012) 062 [arXiv:1208.3130] [INSPIRE].
M. Höschele, J. Hoff, A. Pak, M. Steinhauser and T. Ueda, Higgs boson production at the LHC: NNLO partonic cross sections through order ǫ and convolutions with splitting functions to N 3 LO, Phys. Lett. B 721 (2013) 244 [arXiv:1211.6559] [INSPIRE].
C. Anastasiou, C. Duhr, F. Dulat and B. Mistlberger, Soft triple-real radiation for Higgs production at N 3 LO, JHEP 07 (2013) 003 [arXiv:1302.4379] [INSPIRE].
C. Duhr and T. Gehrmann, The two-loop soft current in dimensional regularization, arXiv:1309.4393 [INSPIRE].
Y. Li and H.X. Zhu, Single soft gluon emission at two loops, JHEP 11 (2013) 080 [arXiv:1309.4391] [INSPIRE].
C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys. B 646 (2002) 220 [hep-ph/0207004] [INSPIRE].
C. Anastasiou, L.J. Dixon and K. Melnikov, NLO Higgs boson rapidity distributions at hadron colliders, Nucl. Phys. Proc. Suppl. 116 (2003) 193 [hep-ph/0211141] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD, Phys. Rev. Lett. 91 (2003) 182002 [hep-ph/0306192] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [hep-ph/0312266] [INSPIRE].
A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998) 497 [arXiv:1105.2076] [INSPIRE].
K.T. Chen, Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977) 831.
F.C. Brown, Multiple zeta values and periods of moduli spaces \( {{\mathfrak{M}}_{0,n }} \), Annales Sci. Ecole Norm. Sup. 42 (2009) 371 [math/0606419] [INSPIRE].
A. Goncharov, A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 [INSPIRE].
A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].
C. Duhr, H. Gangl and J.R. Rhodes, From polygons and symbols to polylogarithmic functions, JHEP 10 (2012) 075 [arXiv:1110.0458] [INSPIRE].
A. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry, Duke Math. J. 128 (2005) 209 [math/0208144] [INSPIRE].
F. Brown, On the decomposition of motivic multiple zeta values, arXiv:1102.1310 [INSPIRE].
C. Duhr, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, JHEP 08 (2012) 043 [arXiv:1203.0454] [INSPIRE].
P. Baikov and K. Chetyrkin, Top quark mediated Higgs boson decay into hadrons to order \( \alpha_s^5 \), Phys. Rev. Lett. 97 (2006) 061803 [hep-ph/0604194] [INSPIRE].
E. Furlan, Gluon-fusion Higgs production at NNLO for a non-standard Higgs sector, JHEP 10 (2011) 115 [arXiv:1106.4024] [INSPIRE].
C. Anastasiou, R. Boughezal and E. Furlan, The NNLO gluon fusion Higgs production cross-section with many heavy quarks, JHEP 06 (2010) 101 [arXiv:1003.4677] [INSPIRE].
K. Chetyrkin, B.A. Kniehl and M. Steinhauser, Hadronic Higgs decay to order \( \alpha_S^4 \), Phys. Rev. Lett. 79 (1997) 353 [hep-ph/9705240] [INSPIRE].
M. Krämer, E. Laenen and M. Spira, Soft gluon radiation in Higgs boson production at the LHC, Nucl. Phys. B 511 (1998) 523 [hep-ph/9611272] [INSPIRE].
D. Graudenz, M. Spira and P. Zerwas, QCD corrections to Higgs boson production at proton proton colliders, Phys. Rev. Lett. 70 (1993) 1372 [INSPIRE].
S. Dawson, Radiative corrections to Higgs boson production, Nucl. Phys. B 359 (1991) 283 [INSPIRE].
A. Djouadi, M. Spira and P. Zerwas, Production of Higgs bosons in proton colliders: QCD corrections, Phys. Lett. B 264 (1991) 440 [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
R.V. Harlander and W.B. Kilgore, Next-to-next-to-leading order Higgs production at hadron colliders, Phys. Rev. Lett. 88 (2002) 201801 [hep-ph/0201206] [INSPIRE].
V. Ravindran, J. Smith and W.L. van Neerven, NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nucl. Phys. B 665 (2003) 325 [hep-ph/0302135] [INSPIRE].
E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
T. Gehrmann and E. Remiddi, Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun. 141 (2001) 296 [hep-ph/0107173] [INSPIRE].
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun. 167 (2005) 177 [hep-ph/0410259] [INSPIRE].
D. Maître, Extension of HPL to complex arguments, Comput. Phys. Commun. 183 (2012) 846 [hep-ph/0703052] [INSPIRE].
D. Maître, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [INSPIRE].
S. Buehler and C. Duhr, CHAPLIN — complex harmonic polylogarithms in fortran, arXiv:1106.5739 [INSPIRE].
(RV) 2 Higgs boson cross-section webpage, http://www.phys.ethz.ch/~pheno/HN3LO/RVsq/.
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
J. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
C. Anastasiou, E.N. Glover and C. Oleari, The two loop scalar and tensor pentabox graph with lightlike legs, Nucl. Phys. B 575 (2000) 416 [Erratum ibid. B 585 (2000) 763] [hep-ph/9912251] [INSPIRE].
C. Anastasiou, T. Gehrmann, C. Oleari, E. Remiddi and J. Tausk, The tensor reduction and master integrals of the two loop massless crossed box with lightlike legs, Nucl. Phys. B 580 (2000) 577 [hep-ph/0003261] [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [hep-ph/0404258] [INSPIRE].
C. Anastasiou, E.N. Glover and C. Oleari, Application of the negative dimension approach to massless scalar box integrals, Nucl. Phys. B 565 (2000) 445 [hep-ph/9907523] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
A. Pak and A. Smirnov, Geometric approach to asymptotic expansion of Feynman integrals, Eur. Phys. J. C 71 (2011) 1626 [arXiv:1011.4863] [INSPIRE].
B. Jantzen, Foundation and generalization of the expansion by regions, JHEP 12 (2011) 076 [arXiv:1111.2589] [INSPIRE].
S. Coleman and R. Norton, Singularities in the physical region, Nuovo Cim. 38 (1965) 438 [INSPIRE].
G.F. Sterman, Mass divergences in annihilation processes. 1. Origin and nature of divergences in cut vacuum polarization diagrams, Phys. Rev. D 17 (1978) 2773 [INSPIRE].
K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
F. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [INSPIRE].
C.W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symbol. Comput. 33 (2002) 1 [cs/0004015].
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
A. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett. B 254 (1991) 158 [INSPIRE].
T. Huber and D. Maˆıtre, HypExp 2, expanding hypergeometric functions about half-integer parameters, Comput. Phys. Commun. 178 (2008) 755 [arXiv:0708.2443] [INSPIRE].
S. Moch, P. Uwer and S. Weinzierl, Nested sums, expansion of transcendental functions and multiscale multiloop integrals, J. Math. Phys. 43 (2002) 3363 [hep-ph/0110083] [INSPIRE].
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ArXiv ePrint: 1311.1425
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Anastasiou, C., Duhr, C., Dulat, F. et al. Real-virtual contributions to the inclusive Higgs cross-section at N3LO. J. High Energ. Phys. 2013, 88 (2013). https://doi.org/10.1007/JHEP12(2013)088
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DOI: https://doi.org/10.1007/JHEP12(2013)088