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Dual identities inside the gluon and the graviton scattering amplitudes

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Abstract

Recently, Bern, Carrasco and Johansson conjectured dual identities inside the gluon tree scattering amplitudes. In this paper, we use the properties of the heterotic string and open string tree scattering amplitudes to refine and derive these dual identities. These identities can be carried over to loop amplitudes using the unitarity method. Furthermore, given the M-gluon (as well as gluon-gluino) tree amplitudes, M-graviton (as well as graviton-gravitino) tree scattering amplitudes can be written down immediately, avoiding the derivation of Feynman rules and the evaluation of Feynman diagrams for graviton scattering amplitudes.

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References

  1. D. Zhu, Zeros in scattering amplitudes and the structure of non-Abelian gauge theories, Phys. Rev. D 22 (1980) 2266 [SPIRES].

    Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  3. 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].

    Article  MathSciNet  ADS  Google Scholar 

  4. Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [SPIRES].

    Article  ADS  Google Scholar 

  5. P. Cvitanovic, Group Theory for Feynman Diagrams in Nonabelian Gauge Theories: Exceptional Groups, Phys. Rev. D 14 (1976) 1536 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  6. 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 [SPIRES].

    Article  ADS  Google Scholar 

  7. M.L. Mangano, S.J. Parke and Z. Xu, Duality and Multi - Gluon Scattering, Nucl. Phys. B 298 (1988) 653 [SPIRES].

    Article  ADS  Google Scholar 

  8. M.L. Mangano, The Color Structure of Gluon Emission, Nucl. Phys. B 309 (1988) 461 [SPIRES].

    Article  ADS  Google Scholar 

  9. C.R. Mafra, Simplifying the Tree-level Superstring Massless Five-point Amplitude, JHEP 01 (2010) 007 [arXiv:0909.5206] [SPIRES].

    Article  Google Scholar 

  10. D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, Heterotic String Theory. 1. The Free Heterotic String, Nucl. Phys. B 256 (1985) 253 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, Heterotic String Theory. 2. The Interacting Heterotic String, Nucl. Phys. B 267 (1986) 75 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. J. Polchinski, String theory. Vol.1: An introduction to the bosonic string, Cambridge Univ. Press, Cambridge U.K. (1998).

    Google Scholar 

  14. J. Polchinski, String theory. Vol.2: Superstring theory and beyond, Cambridge Univ. Press, Cambridge U.K. (1998).

    Google Scholar 

  15. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. M.L. Mangano and S.J. Parke, Multi-Parton Amplitudes in Gauge Theories, Phys. Rept. 200 (1991) 301 [hep-th/0509223] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

  19. E. Plahte, Symmetry properties of dual tree-graph n-point amplitudes, Nuovo Cim. A 66 (1970) 713 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. 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] [SPIRES].

    Article  ADS  Google Scholar 

  21. L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker, The Conformal Field Theory of Orbifolds, Nucl. Phys. B 282 (1987) 13 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. See also N.E.J. Bjerrum-Bohr and O.T. Engelund, Gravitino Interactions from Yang-Mills Theory, Phys. Rev. D 81 (2010) 105009 [1002.2279] [SPIRES].

    ADS  Google Scholar 

  23. 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 [SPIRES].

    ADS  Google Scholar 

  24. 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 [SPIRES].

    Article  ADS  Google Scholar 

  25. R. Kleiss and W.J. Stirling, Spinor Techniques for Calculating \( p\overline p \) → W + −/Z0+ Jets, Nucl. Phys. B 262 (1985) 235 [SPIRES].

    Article  ADS  Google Scholar 

  26. R. Gastmans and T.T. Wu, The Ubiquitous Photon: Helicity Method for QED and QCD, Clarendon Press, Oxford U.K. (1990).

    Google Scholar 

  27. Z. Xu, D.-H. Zhang and L. Chang, Helicity Amplitudes for Multiple Bremsstrahlung in Massless Nonabelian Gauge Theories, Nucl. Phys. B 291 (1987) 392 [SPIRES].

    Article  ADS  Google Scholar 

  28. J.F. Gunion and Z. Kunszt, Improved Analytic Techniques for Tree Graph Calculations and the G g q anti-q Lepton anti-Lepton Subprocess, Phys. Lett. B 161 (1985) 333 [SPIRES].

    ADS  Google Scholar 

  29. D. Spehler and S.F. Novaes, Helicity wave functions for massless and massive spin-2 particles, Phys. Rev. D 44 (1991) 3990 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. C.J. Goebel, F. Halzen and J.P. Leveille, Angular zeros of Brown, Mikaelian, Sahdev and Samuel and the factorization of tree amplitudes in gauge theories, Phys. Rev. D 23 (1981) 2682 [SPIRES].

    ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratory for Elementary Particle Physics, Cornell University, Ithaca, NY, 14853, U.S.A.

    S.-H. Henry Tye & Yang Zhang

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  1. S.-H. Henry Tye
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  2. Yang Zhang
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Correspondence to Yang Zhang.

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ArXiv ePrint: 10031732

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Henry Tye, SH., Zhang, Y. Dual identities inside the gluon and the graviton scattering amplitudes. J. High Energ. Phys. 2010, 71 (2010). https://doi.org/10.1007/JHEP06(2010)071

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  • DOI: https://doi.org/10.1007/JHEP06(2010)071

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