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Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality

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Abstract

The BCJ decomposition is a highly non-trivial property of gauge theories. In this paper we systematically construct an effective Lagrangian, whose Feynman rules automatically produce the BCJ numerators. The effective Lagrangian contains non-local terms. The difference between the standard Yang-Mills Lagrangian and the effective Lagrangian simplifies to zero.

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References

  1. Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  2. Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. Z. Bern and T. Dennen, A Color Dual Form for Gauge-Theory Amplitudes, Phys. Rev. Lett. 107 (2011) 081601 [arXiv:1103.0312] [INSPIRE].

    Article  ADS  Google Scholar 

  4. Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].

    ADS  Google Scholar 

  5. Z. Bern, S. Davies, T. Dennen, Y.-t. Huang and J. Nohle, Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops, arXiv:1303.6605 [INSPIRE].

  6. N. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. N. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes, JHEP 06 (2010) 003 [arXiv:1003.2403] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. N. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, Proof of Gravity and Yang-Mills Amplitude Relations, JHEP 09 (2010) 067 [arXiv:1007.3111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. N. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, The Momentum Kernel of Gauge and Gravity Theories, JHEP 01 (2011) 001 [arXiv:1010.3933] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. N. Bjerrum-Bohr, P.H. Damgaard, R. Monteiro and D. O’Connell, Algebras for Amplitudes, JHEP 06 (2012) 061 [arXiv:1203.0944] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. S. Stieberger, Open & Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].

  12. C.R. Mafra, O. Schlotterer, S. Stieberger and D. Tsimpis, A recursive method for SYM n-point tree amplitudes, Phys. Rev. D 83 (2011) 126012 [arXiv:1012.3981] [INSPIRE].

    ADS  Google Scholar 

  13. C.R. Mafra, O. Schlotterer and S. Stieberger, Explicit BCJ Numerators from Pure Spinors, JHEP 07 (2011) 092 [arXiv:1104.5224] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. C.R. Mafra, O. Schlotterer and S. Stieberger, Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation, Nucl. Phys. B 873 (2013) 419 [arXiv:1106.2645] [INSPIRE].

    Article  ADS  Google Scholar 

  15. C.R. Mafra, PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions, arXiv:1007.4999 [INSPIRE].

  16. P. Grassi, A. Mezzalira and L. Sommovigo, BCJ and KK Relations from BRST Symmetry and Supergravity Amplitudes, arXiv:1111.0544 [INSPIRE].

  17. T. Sondergaard, Perturbative Gravity and Gauge Theory Relations: A Review, Adv. High Energy Phys. 2012 (2012) 726030 [arXiv:1106.0033] [INSPIRE].

    MathSciNet  Google Scholar 

  18. 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].

    MathSciNet  ADS  Google Scholar 

  19. Y. Jia, R. Huang and C.-Y. Liu, U (1)-decoupling, KK and BCJ relations in \( \mathcal{N} \) = 4 SYM, Phys. Rev. D 82 (2010) 065001 [arXiv:1005.1821] [INSPIRE].

    ADS  Google Scholar 

  20. 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].

    Article  MathSciNet  ADS  Google Scholar 

  21. Y.-J. Du, B. Feng and C.-H. Fu, BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory, JHEP 08 (2011) 129 [arXiv:1105.3503] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. Y.-J. Du, B. Feng and C.-H. Fu, Note on Permutation Sum of Color-ordered Gluon Amplitudes, Phys. Lett. B 706 (2012) 490 [arXiv:1110.4683] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. C.-H. Fu, Y.-J. Du and B. Feng, An algebraic approach to BCJ numerators, JHEP 03 (2013) 050 [arXiv:1212.6168] [INSPIRE].

    Article  ADS  Google Scholar 

  24. Y.-J. Du, B. Feng and C.-H. Fu, The Construction of Dual-trace Factor in Yang-Mills Theory, arXiv:1304.2978 [INSPIRE].

  25. D. Vaman and Y.-P. Yao, Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes, JHEP 11 (2010) 028 [arXiv:1007.3475] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. R.H. Boels and R.S. Isermann, Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts, JHEP 03 (2012) 051 [arXiv:1110.4462] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. R.H. Boels, B.A. Kniehl, O.V. Tarasov and G. Yang, Color-kinematic Duality for Form Factors, JHEP 02 (2013) 063 [arXiv:1211.7028] [INSPIRE].

    Article  ADS  Google Scholar 

  28. R.H. Boels, R.S. Isermann, R. Monteiro and D. O’Connell, Colour-Kinematics Duality for One-Loop Rational Amplitudes, JHEP 04 (2013) 107 [arXiv:1301.4165] [INSPIRE].

    Article  ADS  Google Scholar 

  29. S. Oxburgh and C. White, BCJ duality and the double copy in the soft limit, JHEP 02 (2013) 127 [arXiv:1210.1110] [INSPIRE].

    Article  ADS  Google Scholar 

  30. R. Saotome and R. Akhoury, Relationship Between Gravity and Gauge Scattering in the High Energy Limit, JHEP 01 (2013) 123 [arXiv:1210.8111] [INSPIRE].

    Article  ADS  Google Scholar 

  31. J. Broedel and J.J.M. Carrasco, Virtuous Trees at Five and Six Points for Yang-Mills and Gravity, Phys. Rev. D 84 (2011) 085009 [arXiv:1107.4802] [INSPIRE].

    ADS  Google Scholar 

  32. J. Broedel and L.J. Dixon, Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators, JHEP 10 (2012) 091 [arXiv:1208.0876] [INSPIRE].

    Article  ADS  Google Scholar 

  33. F. Cachazo, Fundamental BCJ Relation in N = 4 SYM From The Connected Formulation, arXiv:1206.5970 [INSPIRE].

  34. R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].

    Article  ADS  Google Scholar 

  35. 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].

    Article  ADS  Google Scholar 

  36. R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099, Mainz, Germany

    Mathias Tolotti & Stefan Weinzierl

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  1. Mathias Tolotti
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  2. Stefan Weinzierl
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Correspondence to Stefan Weinzierl.

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ArXiv ePrint: 1306.2975

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Tolotti, M., Weinzierl, S. Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality. J. High Energ. Phys. 2013, 111 (2013). https://doi.org/10.1007/JHEP07(2013)111

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  • DOI: https://doi.org/10.1007/JHEP07(2013)111

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