Abstract
We investigate the construction of tree-level MHV gluon amplitudes in multiplet bases using BCFW recursion. The multiplet basis decomposition can either be obtained by decomposing results derived in (for example) the DDM basis or by formulating the recursion directly in the multiplet basis. We focus on the latter approach and show how to efficiently deal with the color structure appearing in the recursion. For illustration, we also explicitly calculate the four-, five- and six-gluon amplitudes.
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F.A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans and T.T. Wu, Single Bremsstrahlung Processes in Gauge Theories, Phys. Lett. B 103 (1981) 124 [INSPIRE].
P. De Causmaecker, R. Gastmans, W. Troost and T.T. Wu, Multiple Bremsstrahlung in Gauge Theories at High-Energies. 1. General Formalism for Quantum Electrodynamics, Nucl. Phys. B 206 (1982) 53 [INSPIRE].
R. Kleiss and W.J. Stirling, Spinor Techniques for Calculating \( p\overline{p}\to {W}^{\pm }/{Z}^0 \) + Jets, Nucl. Phys. B 262 (1985) 235 [INSPIRE].
Z. Xu, D.-H. Zhang and L. Chang, Helicity Amplitudes for Multiple Bremsstrahlung in Massless Nonabelian Gauge Theories, Nucl. Phys. B 291 (1987) 392 [INSPIRE].
J.F. Gunion and Z. Kunszt, Improved Analytic Techniques for Tree Graph Calculations and the \( ggq\overline{q}l\overline{l} \) Subprocess, Phys. Lett. B 161 (1985) 333 [INSPIRE].
F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].
P. Cvitanovic, Group theory for Feynman diagrams in non-Abelian gauge theories, Phys. Rev. D 14 (1976) 1536 [INSPIRE].
P. Cvitanovic, P.G. Lauwers and P.N. Scharbach, Gauge Invariance Structure of Quantum Chromodynamics, Nucl. Phys. B 186 (1981) 165 [INSPIRE].
P. Dittner, Invariant tensors in SU(3). II, Commun. Math. Phys. 27 (1972) 44 [INSPIRE].
D. Zeppenfeld, Diagonalization of Color Factors, Int. J. Mod. Phys. A 3 (1988) 2175 [INSPIRE].
J.E. Paton and H.-M. Chan, Generalized veneziano model with isospin, Nucl. Phys. B 10 (1969) 516 [INSPIRE].
F.A. Berends and W. Giele, The Six Gluon Process as an Example of Weyl-Van Der Waerden Spinor Calculus, Nucl. Phys. B 294 (1987) 700 [INSPIRE].
M.L. Mangano, S.J. Parke and Z. Xu, Duality and Multi-Gluon Scattering, Nucl. Phys. B 298 (1988) 653 [INSPIRE].
M.L. Mangano, The Color Structure of Gluon Emission, Nucl. Phys. B 309 (1988) 461 [INSPIRE].
D.A. Kosower, Color Factorization for Fermionic Amplitudes, Nucl. Phys. B 315 (1989) 391 [INSPIRE].
Z. Nagy and D.E. Soper, Parton showers with quantum interference, JHEP 09 (2007) 114 [arXiv:0706.0017] [INSPIRE].
M. Sjodahl, Color structure for soft gluon resummation: A general recipe, JHEP 09 (2009) 087 [arXiv:0906.1121] [INSPIRE].
J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: Going Beyond, JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].
M. Sjodahl, ColorFull — a C++ library for calculations in SU(N C) color space, arXiv:1412.3967 [INSPIRE].
S. Platzer and M. Sjodahl, Subleading N c improved Parton Showers, JHEP 07 (2012) 042 [arXiv:1201.0260] [INSPIRE].
V. Del Duca, A. Frizzo and F. Maltoni, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit, Nucl. Phys. B 568 (2000) 211 [hep-ph/9909464] [INSPIRE].
V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [INSPIRE].
A. Kanaki and C.G. Papadopoulos, HELAC-PHEGAS: Automatic computation of helicity amplitudes and cross-sections, AIP Conf. Proc. 583 (2001) 169 [hep-ph/0012004] [INSPIRE].
F. Maltoni, K. Paul, T. Stelzer and S. Willenbrock, Color flow decomposition of QCD amplitudes, Phys. Rev. D 67 (2003) 014026 [hep-ph/0209271] [INSPIRE].
S. Keppeler and M. Sjodahl, Orthogonal multiplet bases in SU(NC) color space, JHEP 09 (2012) 124 [arXiv:1207.0609] [INSPIRE].
M. Sjödahl and J. Thorén, Decomposing color structure into multiplet bases, work in preparation.
B. Kol and R. Shir, Color structures and permutations, JHEP 11 (2014) 020 [arXiv:1403.6837] [INSPIRE].
S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [INSPIRE].
F. Cachazo and P. Svrček, Lectures on twistor strings and perturbative Yang-Mills theory, PoS(RTN2005)004 [hep-th/0504194] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, On-Shell Methods in Perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].
B. Feng and M. Luo, An Introduction to On-shell Recursion Relations, Front. Phys. 7 (2012) 533 [arXiv:1111.5759] [INSPIRE].
M.E. Peskin, Simplifying Multi-Jet QCD Computation, arXiv:1101.2414 [INSPIRE].
P. Benincasa, New structures in scattering amplitudes: a review, Int. J. Mod. Phys. A 29 (2014) 1430005 [arXiv:1312.5583] [INSPIRE].
R.K. Ellis, Z. Kunszt, K. Melnikov and G. Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, Phys. Rept. 518 (2012) 141 [arXiv:1105.4319] [INSPIRE].
H. Elvang and Y.-t. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
Z. Bern and D.A. Kosower, Color decomposition of one loop amplitudes in gauge theories, Nucl. Phys. B 362 (1991) 389 [INSPIRE].
B. Feng, R. Huang and Y. Jia, Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program, Phys. Lett. B 695 (2011) 350 [arXiv:1004.3417] [INSPIRE].
C.-H. Fu, Y.-J. Du and B. Feng, An algebraic approach to BCJ numerators, JHEP 03 (2013) 050 [arXiv:1212.6168] [INSPIRE].
M.G. Sotiropoulos and G.F. Sterman, Color exchange in near forward hard elastic scattering, Nucl. Phys. B 419 (1994) 59 [hep-ph/9310279] [INSPIRE].
N. Kidonakis, G. Oderda and G.F. Sterman, Evolution of color exchange in QCD hard scattering, Nucl. Phys. B 531 (1998) 365 [hep-ph/9803241] [INSPIRE].
A. Kyrieleis and M.H. Seymour, The colour evolution of the process qq → qqg, JHEP 01 (2006) 085 [hep-ph/0510089] [INSPIRE].
Y. Dokshitzer and G. Marchesini, Soft gluons at large angles in hadron collisions, JHEP 01 (2006) 007 [hep-ph/0509078] [INSPIRE].
M. Sjodahl, Color evolution of 2 → 3 processes, JHEP 12 (2008) 083 [arXiv:0807.0555] [INSPIRE].
M. Beneke, P. Falgari and C. Schwinn, Soft radiation in heavy-particle pair production: All-order colour structure and two-loop anomalous dimension, Nucl. Phys. B 828 (2010) 69 [arXiv:0907.1443] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
S. Stieberger, Open & Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].
H. Tye and Y. Zhang, Remarks on the identities of gluon tree amplitudes, Phys. Rev. D 82 (2010) 087702 [arXiv:1007.0597] [INSPIRE].
Y.-X. Chen, Y.-J. Du and B. Feng, A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory, JHEP 02 (2011) 112 [arXiv:1101.0009] [INSPIRE].
T. Sondergaard, New Relations for Gauge-Theory Amplitudes with Matter, Nucl. Phys. B 821 (2009) 417 [arXiv:0903.5453] [INSPIRE].
T. Melia, Getting more flavor out of one-flavor QCD, Phys. Rev. D 89 (2014) 074012 [arXiv:1312.0599] [INSPIRE].
M. Sjödahl, ColorMath — A package for color summed calculations in SU(NC), Eur. Phys. J. C 73 (2013) 2310 [arXiv:1211.2099] [INSPIRE].
P. Butera, G.M. Cicuta and M. Enriotti, Group Weight and Vanishing Graphs, Phys. Rev. D 21 (1980) 972 [INSPIRE].
P. Cvitanović, Classics Illustrated: Group Theory. Part I, Nordita, Copenhagen, (1984) [INSPIRE].
P. Cvitanović, Group Theory: Birdtracks, Lie’s, and Exceptional Groups, Princeton University Press, (2008), www.birdtracks.eu.
C. Duhr, S. Hoeche and F. Maltoni, Color-dressed recursive relations for multi-parton amplitudes, JHEP 08 (2006) 062 [hep-ph/0607057] [INSPIRE].
N. Arkani-Hamed and J. Kaplan, On Tree Amplitudes in Gauge Theory and Gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [INSPIRE].
A. Yutsis, I. Levinson and V. Vanagas, Theory of angular momentum, Israel Program for Scientific Translations, (1962).
D. Maître and P. Mastrolia, S@M, a Mathematica Implementation of the Spinor-Helicity Formalism, Comput. Phys. Commun. 179 (2008) 501 [arXiv:0710.5559] [INSPIRE].
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ArXiv ePrint: 1503.00530
On leave from Center for Field Theory and Particle Physics, Department of Physics, Fudan University. (Yi-Jian Du)
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Du, YJ., Sjödahl, M. & Thorén, J. Recursion in multiplet bases for tree-level MHV gluon amplitudes. J. High Energ. Phys. 2015, 119 (2015). https://doi.org/10.1007/JHEP05(2015)119
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DOI: https://doi.org/10.1007/JHEP05(2015)119