Abstract
samurai is a tool for the automated numerical evaluation of one-loop corrections to any scattering amplitudes within the dimensional-regularization scheme. It is based on the decomposition of the integrand according to the OPP -approach, extended to accommodate an implementation of the generalized d-dimensional unitarity-cuts technique, and uses a polynomial interpolation exploiting the Discrete Fourier Transform. samurai can process integrands written either as numerator of Feynman diagrams or as product of tree-level amplitudes. We discuss some applications, among which the 6-and 8-photon scattering in QED, and the 6-quark scattering in QCD. samurai has been implemented as a Fortran90 library, publicly available, and it could be a useful module for the systematic evaluation of the virtual corrections oriented towards automating next-to-leading order calculations relevant for the LHC phenomenology.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Stelzer and W.F. Long, Automatic generation of tree level helicity amplitudes, Comput. Phys. Commun. 81 (1994) 357 [hep-ph/9401258] [SPIRES].
F. Maltoni and T. Stelzer, MadEvent: automatic event generation with MadGraph, JHEP 02 (2003) 027 [hep-ph/0208156] [SPIRES].
J. Alwall et al., MadGraph/MadEvent v4: the new web generation, JHEP 09 (2007) 028 [arXiv:0706.2334] [SPIRES].
CompHEP collaboration, E. Boos et al., CompHEP 4.4: automatic computations from Lagrangians to events, Nucl. Instrum. Meth. A 534 (2004) 250 [hep-ph/0403113] [SPIRES].
A. Pukhov, Calchep 2.3: MSSM, structure functions, event generation, 1 and generation of matrix elements for other packages, hep-ph/0412191 [SPIRES].
T. Gleisberg et al., SHERPA 1.alpha, a proof-of-concept version, JHEP 02 (2004) 056 [hep-ph/0311263] [SPIRES].
T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [SPIRES].
W. Kilian, T. Ohl and J. Reuter, WHIZARD: simulating multi-particle processes at LHC and ILC, arXiv:0708.4233 [SPIRES].
M.L. Mangano, M. Moretti, F. Piccinini, R. Pittau and A.D. Polosa, ALPGEN, a generator for hard multiparton processes in hadronic collisions, JHEP 07 (2003) 001 [hep-ph/0206293] [SPIRES].
A. Kanaki and C.G. Papadopoulos, HELAC: a package to compute electroweak helicity amplitudes, Comput. Phys. Commun. 132 (2000) 306 [hep-ph/0002082] [SPIRES].
A. Cafarella, C.G. Papadopoulos and M. Worek, Helac-Phegas: a generator for all parton level processes, Comput. Phys. Commun. 180 (2009) 1941 [arXiv:0710.2427] [SPIRES].
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] [SPIRES].
J.M. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2 jet and Z + 2 jet production at hadron colliders, Phys. Rev. D 65 (2002) 113007 [hep-ph/0202176] [SPIRES].
Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [SPIRES].
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [SPIRES].
S. Frixione and B.R. Webber, The MC@NLO 3.3 event generator, hep-ph/0612272 [SPIRES].
P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [SPIRES].
P. Nason and G. Ridolfi, A positive-weight next-to-leading-order Monte Carlo for Z pair hadroproduction, JHEP 08 (2006) 077 [hep-ph/0606275] [SPIRES].
O. Latunde-Dada, S. Gieseke and B. Webber, A positive-weight next-to-leading-order Monte Carlo for e + e − annihilation to hadrons, JHEP 02 (2007) 051 [hep-ph/0612281] [SPIRES].
S. Frixione, P. Nason and G. Ridolfi, A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction, JHEP 09 (2007) 126 [arXiv:0707.3088] [SPIRES].
S. Alioli, P. Nason, C. Oleari and E. Re, NLO vector-boson production matched with shower in POW HEG, JHEP 07 (2008) 060 [arXiv:0805.4802] [SPIRES].
K. Hamilton, P. Richardson and J. Tully, A positive-weight next-to-leading order Monte Carlo simulation of Drell-Yan vector boson production, JHEP 10 (2008) 015 [arXiv:0806.0290] [SPIRES].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [SPIRES].
W.T. Giele and E.W.N. Glover, Higher order corrections to jet cross-sections in e + e − annihilation, Phys. Rev. D 46 (1992) 1980 [SPIRES].
R.K. Ellis, D.A. Ross and A.E. Terrano, The perturbative calculation of jet structure in e + e − annihilation, Nucl. Phys. B 178 (1981) 421 [SPIRES].
Z. Kunszt and D.E. Soper, Calculation of jet cross-sections in hadron collisions at order alpha-S 3, Phys. Rev. D 46 (1992) 192 [SPIRES].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [SPIRES].
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] [SPIRES].
S. Catani, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [SPIRES].
T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J. C 53 (2008) 501 [arXiv:0709.2881] [SPIRES].
M.H. Seymour and C. Tevlin, TeVJet: a general framework for the calculation of jet observables in NLO QCD, arXiv:0803.2231 [SPIRES].
M. Czakon, C.G. Papadopoulos and M. Worek, Polarizing the Dipoles, JHEP 08 (2009) 085 [arXiv:0905.0883] [SPIRES].
K. Hasegawa, S. Moch and P. Uwer, AutoDipole – automated generation of dipole subtraction terms, arXiv:0911.4371 [SPIRES].
R. Frederix, T. Gehrmann and N. Greiner, Automation of the dipole subtraction method in MadGraph/MadEvent, JHEP 09 (2008) 122 [arXiv:0808.2128] [SPIRES].
R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: the FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [SPIRES].
R. Frederix, T. Gehrmann and N. Greiner, Integrated dipoles with MadDipole in the MadGraph framework, JHEP 06 (2010) 086 [arXiv:1004.2905] [SPIRES].
D.A. Kosower, Antenna factorization of gauge-theory amplitudes, Phys. Rev. D 57 (1998) 5410 [hep-ph/9710213] [SPIRES].
J.M. Campbell, M.A. Cullen and E.W.N. Glover, Four jet event shapes in electron positron annihilation, Eur. Phys. J. C 9 (1999) 245 [hep-ph/9809429] [SPIRES].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [SPIRES].
A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [SPIRES].
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [SPIRES].
A. Denner, S. Dittmaier, M. Roth and L.H. Wieders, Electroweak corrections to charged-current e + e − → 4 fermion processes: technical details and further results, Nucl. Phys. B 724 (2005) 247 [hep-ph/0505042] [SPIRES].
C.F. Berger et al., Precise predictions for W + 3 jet production at hadron colliders, Phys. Rev. Lett. 102 (2009) 222001 [arXiv:0902.2760] [SPIRES].
C.F. Berger et al., Next-to-leading Order QCD predictions for W+3-jet distributions at hadron colliders, Phys. Rev. D 80 (2009) 074036 [arXiv:0907.1984] [SPIRES].
R.K. Ellis, K. Melnikov and G. Zanderighi, Generalized unitarity at work: first NLO QCD results for hadronic W + 3jet production, JHEP 04 (2009) 077 [arXiv:0901.4101] [SPIRES].
R. Keith Ellis, K. Melnikov and G. Zanderighi, W+3 jet production at the Tevatron, Phys. Rev. D 80 (2009) 094002 [arXiv:0906.1445] [SPIRES].
C.F. Berger et al., Next-to-leading order QCD predictions for Z, γ +3 -jet distributions at the Tevatron, arXiv:1004.1659 [SPIRES].
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to \( pp \to t\bar{t}b\bar{b} + X \) at the LHC, Phys. Rev. Lett. 103 (2009) 012002 [arXiv:0905.0110] [SPIRES].
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results, JHEP 03 (2010) 021 [arXiv:1001.4006] [SPIRES].
G. Bevilacqua, M. Czakon, C.G. Papadopoulos, R. Pittau and M. Worek, A ssault on the NLO wishlist: pp → ttbb, JHEP 09 (2009) 109 [arXiv:0907.4723] [SPIRES].
G. Bevilacqua, M. Czakon, C.G. Papadopoulos and M. Worek, Dominant QCD backgrounds in higgs boson analyses at the LHC: a study of \( pp \to t\bar{t} + 2 \) jets at next-to-leading order, Phys. Rev. Lett. 104 (2010) 162002 [arXiv:1002.4009] [SPIRES].
T. Binoth et al., Next-to-leading order QCD corrections to \( pp \to b\bar{b}b\bar{b} + X \) at the LHC: the quark induced case, Phys. Lett. B 685 (2010) 293 [arXiv:0910.4379] [SPIRES].
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [SPIRES].
R. Britto, E. Buchbinder, F. Cachazo and B. Feng, One-loop amplitudes of gluons in SQCD, Phys. Rev. D 72 (2005) 065012 [hep-ph/0503132] [SPIRES].
R. Britto, B. Feng and P. Mastrolia, The cut-constructible part of QCD amplitudes, Phys. Rev. D 73 (2006) 105004 [hep-ph/0602178] [SPIRES].
P. Mastrolia, On triple-cut of scattering amplitudes, Phys. Lett. B 644 (2007) 272 [hep-th/0611091] [SPIRES].
D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [SPIRES].
N.E.J. Bjerrum-Bohr, D.C. Dunbar and W.B. Perkins, Analytic structure of three-mass triangle coefficients, JHEP 04 (2008) 038 [arXiv:0709.2086] [SPIRES].
W.B. Kilgore, One-loop integral coefficients from generalized unitarity, arXiv:0711.5015 [SPIRES].
S.D. Badger, Direct extraction of one loop rational terms, JHEP 01 (2009) 049 [arXiv:0806.4600] [SPIRES].
P. Mastrolia, Double-cut of scattering amplitudes and Stokes’ Theorem, Phys. Lett. B 678 (2009) 246 [arXiv:0905.2909] [SPIRES].
P. Mastrolia, Unitarity-cuts and Berry’s phase, Lett. Math. Phys. 91 (2010) 199 [arXiv:0906.3789] [SPIRES].
C.F. Berger, V. Del Duca and L.J. Dixon, Recursive construction of Higgs+multiparton loop amplitudes: the last of the ϕ-nite loop amplitudes, Phys. Rev. D 74 (2006) 094021 [Erratum ibid. D 76 (2007) 099901] [hep-ph/0608180] [SPIRES].
S.D. Badger and E.W.N. Glover, One-loop helicity amplitudes for H → gluons: the all-minus configuration, Nucl. Phys. Proc. Suppl. 160 (2006) 71 [hep-ph/0607139] [SPIRES].
S.D. Badger, E.W.N. Glover and K. Risager, One-loop ϕ-MHV amplitudes using the unitarity bootstrap, JHEP 07 (2007) 066 [arXiv:0704.3914] [SPIRES].
E.W.N. Glover, P. Mastrolia and C. Williams, One-loop ϕ-MHV amplitudes using the unitarity bootstrap: the general helicity case, JHEP 08 (2008) 017 [arXiv:0804.4149] [SPIRES].
S. Badger, E.W. Nigel Glover, P. Mastrolia and C. Williams, One-loop Higgs plus four gluon amplitudes: full analytic results, JHEP 01 (2010) 036 [arXiv:0909.4475] [SPIRES].
L.J. Dixon and Y. Sofianatos, Analytic one-loop amplitudes for a Higgs boson plus four partons, JHEP 08 (2009) 058 [arXiv:0906.0008] [SPIRES].
S. Badger, J.M. Campbell, R.K. Ellis and C. Williams, Analytic results for the one-loop NMHV Hqqgg amplitude, JHEP 12 (2009) 035 [arXiv:0910.4481] [SPIRES].
G. Passarino and M.J.G. Veltman, One loop corrections for e + e − annihilation into μ + μ − in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [SPIRES].
G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365 [SPIRES].
G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596] [SPIRES].
T. Binoth, J.P. Guillet, G. Heinrich, E. Pilon and T. Reiter, Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs, Comput. Phys. Commun. 180 (2009) 2317 [arXiv:0810.0992] [SPIRES].
A. Lazopoulos, Multi-gluon one-loop amplitudes numerically, arXiv:0812.2998 [SPIRES].
J.-C. Winter and W.T. Giele, Calculating gluon one-loop amplitudes numerically, arXiv:0902.0094 [SPIRES].
C.F. Berger et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev. D 78 (2008) 036003 [arXiv:0803.4180] [SPIRES].
W.T. Giele and G. Zanderighi, On the numerical evaluation of one-loop amplitudes: the gluonic case, JHEP 06 (2008) 038 [arXiv:0805.2152] [SPIRES].
A. van Hameren, C.G. Papadopoulos and R. Pittau, Automated one-loop calculations: a proof of concept, JHEP 09 (2009) 106 [arXiv:0903.4665] [SPIRES].
F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals, JHEP 07 (2004) 017 [hep-ph/0404120] [SPIRES].
G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [SPIRES].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop n-point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [SPIRES].
C.F. Berger and D. Forde, Multi-parton scattering amplitudes via on-shell methods, arXiv:0912.3534 [SPIRES].
G. Mahlon, One loop multi-photon helicity amplitudes, Phys. Rev. D 49 (1994) 2197 [hep-ph/9311213] [SPIRES].
Z. Bern and A.G. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys. B 467 (1996) 479 [hep-ph/9511336] [SPIRES].
C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, D-dimensional unitarity cut method, Phys. Lett. B 645 (2007) 213 [hep-ph/0609191] [SPIRES].
C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes, JHEP 03 (2007) 111 [hep-ph/0612277] [SPIRES].
W.T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes, JHEP 04 (2008) 049 [arXiv:0801.2237] [SPIRES].
R.K. Ellis, W.T. Giele, Z. Kunszt and K. Melnikov, Masses, fermions and generalized D-dimensional unitarity, Nucl. Phys. B 822 (2009) 270 [arXiv:0806.3467] [SPIRES].
G. Ossola, C.G. Papadopoulos and R. Pittau, Numerical evaluation of six-photon amplitudes, JHEP 07 (2007) 085 [arXiv:0704.1271] [SPIRES].
Z. Bern, L.J. Dixon and D.A. Kosower, Bootstrapping multi-parton loop amplitudes in QCD, Phys. Rev. D 73 (2006) 065013 [hep-ph/0507005] [SPIRES].
G. Ossola, C.G. Papadopoulos and R. Pittau, On the rational terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876] [SPIRES].
P. Draggiotis, M.V. Garzelli, C.G. Papadopoulos and R. Pittau, Feynman rules for the rational part of the QCD 1-loop amplitudes, JHEP 04 (2009) 072 [arXiv:0903.0356] [SPIRES].
M.V. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the electroweak 1-loop amplitudes, JHEP 01 (2010) 040 [arXiv:0910.3130] [SPIRES].
P. Mastrolia, G. Ossola, C.G. Papadopoulos and R. Pittau, Optimizing the reduction of one-loop amplitudes, JHEP 06 (2008) 030 [arXiv:0803.3964] [SPIRES].
R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851] [SPIRES].
T. Binoth et al., NLO cross sections for the LHC using GOLEM: status and prospects, PoS(RADCOR2009)026 [arXiv:1001.4905] [SPIRES].
SM and NLO Multileg Working Group collaboration, J.R. Andersen et al., The SM and NLO multileg working group: Summary report, arXiv:1003.1241 [SPIRES].
T. Binoth et al., A proposal for a standard interface between Monte Carlo tools and one-loop programs, Comput. Phys. Commun. 181 (2010) 1612 [arXiv:1001.1307] [SPIRES].
K. Melnikov and M. Schulze, NLO QCD corrections to top quark pair production in association with one hard jet at hadron colliders, arXiv:1004.3284 [SPIRES].
R. Pittau, A simple method for multi-leg loop calculations, Comput. Phys. Commun. 104 (1997) 23 [hep-ph/9607309] [SPIRES].
R. Kleiss, W.J. Stirling and S.D. Ellis, A new Monte Carlo treatment of multiparticle phase space at high-energies, Comput. Phys. Commun. 40 (1986) 359 [SPIRES].
G.J. Gounaris, P.I. Porfyriadis and F.M. Renard, The γγ → γγprocess in the standard and SUSY models at high energies, Eur. Phys. J. C 9 (1999) 673 [hep-ph/9902230] [SPIRES].
C. Bernicot, Light-light amplitude from generalized unitarity in massive QED, arXiv:0804.0749 [SPIRES].
Z. Nagy and D.E. Soper, Numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev. D 74 (2006) 093006 [hep-ph/0610028] [SPIRES].
T. Binoth, G. Heinrich, T. Gehrmann and P. Mastrolia, Six-photon amplitudes, Phys. Lett. B 649 (2007) 422 [hep-ph/0703311] [SPIRES].
W. Gong, Z. Nagy and D.E. Soper, Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev. D 79 (2009) 033005 [arXiv:0812.3686] [SPIRES].
C. Bernicot and J.P. Guillet, Six-photon amplitudes in scalar QED, JHEP 01 (2008) 059 [arXiv:0711.4713] [SPIRES].
C. Bernicot, The six-photon amplitude, arXiv:0804.1315 [SPIRES].
T. Binoth, J.P. Guillet and G. Heinrich, Algebraic evaluation of rational polynomials in one-loop amplitudes, JHEP 02 (2007) 013 [hep-ph/0609054] [SPIRES].
S. Badger, N.E.J. Bjerrum-Bohr and P. Vanhove, Simplicity in the structure of QED and gravity amplitudes, JHEP 02 (2009) 038 [arXiv:0811.3405] [SPIRES].
G. Altarelli, R.K. Ellis and G. Martinelli, Leptoproduction and Drell-Yan processes beyond the leading approximation in chromodynamics, Nucl. Phys. B 143 (1978) 521 [Erratum ibid. B 146 (1978) 544] [SPIRES].
G. Altarelli, R.K. Ellis and G. Martinelli, Large perturbative corrections to the Drell-Yan process in QCD, Nucl. Phys. B 157 (1979) 461 [SPIRES].
B.W. Harris, E. Laenen, L. Phaf, Z. Sullivan and S. Weinzierl, The Fully differential single top quark cross-section in next to leading order QCD, Phys. Rev. D 66 (2002) 054024 [hep-ph/0207055] [SPIRES].
Z. Bern, L.J. Dixon and D.A. Kosower, One-loop amplitudes for e + e − to four partons, Nucl. Phys. B 513 (1998) 3 [hep-ph/9708239] [SPIRES].
Z. Bern, L.J. Dixon and D.A. Kosower, New QCD results from string theory, hep-th/9311026 [SPIRES].
Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower, One loop N gluon amplitudes with maximal helicity violation via collinear limits, Phys. Rev. Lett. 72 (1994) 2134 [hep-ph/9312333] [SPIRES].
A. Brandhuber, S. McNamara, B.J. Spence and G. Travaglini, Loop amplitudes in pure Yang-Mills from generalised unitarity, JHEP 10 (2005) 011 [hep-th/0506068] [SPIRES].
S.D. Badger, E.W.N. Glover, V.V. Khoze and P. Svrček, Recursion relations for gauge theory amplitudes with massive particles, JHEP 07 (2005) 025 [hep-th/0504159] [SPIRES].
T. Binoth, G. Ossola, C.G. Papadopoulos and R. Pittau, NLO QCD corrections to tri-boson production, JHEP 06 (2008) 082 [arXiv:0804.0350] [SPIRES].
S. Actis, P. Mastrolia and G. Ossola, NLO QED corrections to Hard-Bremsstrahlung emission in Bhabha scattering, Phys. Lett. B 682 (2010) 419 [arXiv:0909.1750] [SPIRES].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [SPIRES].
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [SPIRES].
T. Reiter, Optimising code generation with haggies, Comput. Phys. Commun. 181 (2010) 1301 [arXiv:0907.3714] [SPIRES].
T. Reiter, Automated evaluation of one-loop six-point processes for the LHC, arXiv:0903.0947 [SPIRES].
S. Kretzer, H.L. Lai, F.I. Olness and W.K. Tung, CTEQ6 parton distributions with heavy quark mass effects, Phys. Rev. D 69 (2004) 114005 [hep-ph/0307022] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Mastrolia, P., Ossola, G., Reiter, T. et al. Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level. J. High Energ. Phys. 2010, 80 (2010). https://doi.org/10.1007/JHEP08(2010)080
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2010)080