Global structure of curves from generalized unitarity cut of three-loop diagrams
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- 作者：Jonathan D. Hauenstein (1)
Rijun Huang (2)
Dhagash Mehta (1)
Yang Zhang (3)
1. Department of Applied and Computational Mathematics and Statistics ; University of Notre Dame ; Notre Dame ; IN ; 46556 ; U.S.A.
2. Institut de Physique Th茅orique ; CEA-Saclay ; F-91191 ; Gif-sur-Yvette Cedex ; France
3. Niels Bohr International Academy and Discovery Center ; The Niels Bohr Institute ; University of Copenhagen ; Blegdamsvej 17 ; DK-2100 ; Copenhagen ; Denmark - 关键词：Scattering Amplitudes ; Differential and Algebraic Geometry
- 刊名：Journal of High Energy Physics
- 出版年：2015
- 出版时间：February 2015
- 年：2015
- 卷：2015
- 期：2
- 全文大小：659 KB
- 参考文献：1. Brown, LM, Feynman, RP (1952) Radiative corrections to Compton scattering. Phys. Rev. 85: pp. 231 CrossRef
2. Passarino, G, Veltman, MJG (1979) One loop corrections for e+e鈭?annihilation into 渭+渭鈭?in the Weinberg model. Nucl. Phys. B 160: pp. 151 CrossRef
3. 鈥檛 Hooft, G, Veltman, MJG (1979) Scalar one loop integrals. Nucl. Phys. B 153: pp. 365 CrossRef
4. Stuart, RG (1988) Algebraic reduction of one loop Feynman diagrams to scalar integrals. Comput. Phys. Commun. 48: pp. 367 CrossRef
5. Stuart, RG, Gongora, A (1990) Algebraic reduction of one loop Feynman diagrams to scalar integrals. 2. Comput. Phys. Commun. 56: pp. 337 CrossRef
6. Landau, LD (1959) On analytic properties of vertex parts in quantum field theory. Nucl. Phys. 13: pp. 181 CrossRef
7. Mandelstam, S (1958) Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity. General theory. Phys. Rev. 112: pp. 1344 CrossRef
8. Mandelstam, S (1959) Analytic properties of transition amplitudes in perturbation theory. Phys. Rev. 115: pp. 1741 CrossRef
9. Cutkosky, RE (1960) Singularities and discontinuities of Feynman amplitudes. J. Math. Phys. 1: pp. 429 CrossRef
10. Bern, Z, Dixon, LJ, Dunbar, DC, Kosower, DA (1994) One loop n point gauge theory amplitudes, unitarity and collinear limits. Nucl. Phys. B 425: pp. 217 CrossRef
11. Bern, Z, Dixon, LJ, Dunbar, DC, Kosower, DA (1995) Fusing gauge theory tree amplitudes into loop amplitudes. Nucl. Phys. B 435: pp. 59 CrossRef
12. Bern, Z, Morgan, AG (1996) Massive loop amplitudes from unitarity. Nucl. Phys. B 467: pp. 479 CrossRef
13. Britto, R, Cachazo, F, Feng, B (2005) New recursion relations for tree amplitudes of gluons. Nucl. Phys. B 715: pp. 499 CrossRef
14. Britto, R, Cachazo, F, Feng, B, Witten, E (2005) Direct proof of tree-level recursion relation in Yang-Mills theory. Phys. Rev. Lett. 94: pp. 181602 CrossRef
15. Britto, R, Buchbinder, E, Cachazo, F, Feng, B (2005) One-loop amplitudes of gluons in SQCD. Phys. Rev. D 72: pp. 065012
16. Anastasiou, C, Britto, R, Feng, B, Kunszt, Z, Mastrolia, P (2007) D-dimensional unitarity cut method. Phys. Lett. B 645: pp. 213 CrossRef
17. Anastasiou, C, Britto, R, Feng, B, Kunszt, Z, Mastrolia, P (2007) Unitarity cuts and Reduction to master integrals in d dimensions for one-loop amplitudes. JHEP 03: pp. 111 CrossRef
18. Britto, R, Cachazo, F, Feng, B (2005) Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills. Nucl. Phys. B 725: pp. 275 CrossRef
19. Bern, Z, Dixon, LJ, Kosower, DA (1998) One loop amplitudes for e+e鈭?to four partons. Nucl. Phys. B 513: pp. 3 CrossRef
20. Ossola, G, Papadopoulos, CG, Pittau, R (2007) Reducing full one-loop amplitudes to scalar integrals at the integrand level. Nucl. Phys. B 763: pp. 147 CrossRef
21. Forde, D (2007) Direct extraction of one-loop integral coefficients. Phys. Rev. D 75: pp. 125019
22. Ellis, RK, Giele, WT, Kunszt, Z (2008) A numerical unitarity formalism for evaluating one-loop amplitudes. JHEP 03: pp. 003 CrossRef
23. W.B. Kilgore, / One-loop integral coefficients from generalized unitarity, arXiv:0711.5015 [INSPIRE].
24. Giele, WT, Kunszt, Z, Melnikov, K (2008) Full one-loop amplitudes from tree amplitudes. JHEP 04: pp. 049 CrossRef
25. Ossola, G, Papadopoulos, CG, Pittau, R (2008) On the rational terms of the one-loop amplitudes. JHEP 05: pp. 004 CrossRef
26. Badger, SD (2009) Direct extraction of one loop rational terms. JHEP 01: pp. 049 CrossRef
27. Gluza, J, Kajda, K, Kosower, DA (2011) Towards a basis for planar two-loop integrals. Phys. Rev. D 83: pp. 045012
28. Zhang, Y (2012) Integrand-level reduction of loop amplitudes by computational algebraic geometry methods. JHEP 09: pp. 042 CrossRef
29. Mastrolia, P, Mirabella, E, Ossola, G, Peraro, T (2012) Scattering amplitudes from multivariate polynomial division. Phys. Lett. B 718: pp. 173 CrossRef
30. Badger, S, Frellesvig, H, Zhang, Y (2012) Hepta-cuts of two-loop scattering amplitudes. JHEP 04: pp. 055 CrossRef
31. Feng, B, Huang, R (2013) The classification of two-loop integrand basis in pure four-dimension. JHEP 02: pp. 117 CrossRef
32. Kleiss, RHP, Malamos, I, Papadopoulos, CG, Verheyen, R (2012) Counting to one: reducibility of one- and two-loop amplitudes at the integrand level. JHEP 12: pp. 038 CrossRef
33. Badger, S, Frellesvig, H, Zhang, Y (2012) An integrand reconstruction method for three-loop amplitudes. JHEP 08: pp. 065 CrossRef
34. Mastrolia, P, Mirabella, E, Ossola, G, Peraro, T (2013) Integrand-reduction for two-loop scattering amplitudes through multivariate polynomial division. Phys. Rev. D 87: pp. 085026
35. P. Mastrolia et al., / On the one integrand reduction of one- and two-loop scattering amplitudes, PoS(LL2012)028.
36. Mastrolia, P, Mirabella, E, Ossola, G, Peraro, T (2013) Multiloop integrand reduction for dimensionally regulated amplitudes. Phys. Lett. B 727: pp. 532 CrossRef
37. Badger, S, Frellesvig, H, Zhang, Y (2013) A two-loop five-gluon helicity amplitude in QCD. JHEP 12: pp. 045 CrossRef
38. Deurzen, H (2014) Multi-leg one-loop massive amplitudes from integrand reduction via laurent expansion. JHEP 03: pp. 115 CrossRef
39. Tkachov, FV (1981) A theorem on analytical calculability of four loop renormalization group functions. Phys. Lett. B 100: pp. 65 CrossRef
40. Chetyrkin, KG, Tkachov, FV (1981) Integration by parts: the algorithm to calculate 尾-functions in 4 loops. Nucl. Phys. B 192: pp. 159 CrossRef
41. Laporta, S (2001) Calculation of master integrals by difference equations. Phys. Lett. B 504: pp. 188 CrossRef
42. Laporta, S (2000) High precision calculation of multiloop Feynman integrals by difference equations. Int. J. Mod. Phys. A 15: pp. 5087
43. Feng, B, Zhen, J, Huang, R, Zhou, K (2014) Integral reduction by unitarity method for two-loop amplitudes: a case study. JHEP 06: pp. 166 CrossRef
44. Henn, JM (2013) Multiloop integrals in dimensional regularization made simple. Phys. Rev. Lett. 110: pp. 251601 CrossRef
45. Caron-Huot, S, Henn, JM (2014) Iterative structure of finite loop integrals. JHEP 06: pp. 114 CrossRef
46. Kosower, DA, Larsen, KJ (2012) Maximal unitarity at two loops. Phys. Rev. D 85: pp. 045017
47. Larsen, KJ (2012) Global poles of the two-loop six-point N = 4 SYM integrand. Phys. Rev. D 86: pp. 085032
48. Caron-Huot, S, Larsen, KJ (2012) Uniqueness of two-loop master contours. JHEP 10: pp. 026 CrossRef
49. Johansson, H, Kosower, DA, Larsen, KJ (2013) Two-loop maximal unitarity with external masses. Phys. Rev. D 87: pp. 025030
50. S酶gaard, M (2013) Global residues and two-loop hepta-cuts. JHEP 09: pp. 116 CrossRef
51. Johansson, H, Kosower, DA, Larsen, KJ (2014) Maximal unitarity for the four-mass double box. Phys. Rev. D 89: pp. 125010
52. S酶gaard, M, Zhang, Y (2013) Multivariate residues and maximal unitarity. JHEP 12: pp. 008 CrossRef
53. Sogaard, M, Zhang, Y (2014) Unitarity cuts of integrals with doubled propagators. JHEP 07: pp. 112 CrossRef
54. M. Sogaard and Y. Zhang, / Massive nonplanar two-loop maximal unitarity, arXiv:1406.5044 [INSPIRE].
55. Huang, R, Zhang, Y (2013) On genera of curves from high-loop generalized unitarity cuts. JHEP 04: pp. 080 CrossRef
56. D.J. Bates et al., / Numerically solving polynomial systems with Bertini, Software, Environments, and Tools volume 25, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, U.S.A. (2013).
57. Mehta, D, He, Y-H, Hauenstein, JD (2012) Numerical algebraic geometry: a new perspective on string and gauge theories. JHEP 07: pp. 018 CrossRef
58. R. Hartshorne, / Algebraic geometry, Graduate Texts in Mathematics, Springer, U.S.A. (1977).
59. Maclean, C, Perrin, D (2007) Algebraic geometry: an introduction. Universitext, Springer, Germany
60. Bates, DJ (2011) Numerical computation of the genus of an irreducible curve within an algebraic set. J. Pure Appl. Algebra 215: pp. 1844 CrossRef
61. Hauenstein, JD, Sommese, AJ (2013) Membership tests for images of algebraic sets by linear projections. Appl. Math. Comput. 219: pp. 6809 CrossRef
62. Sommese, AJ, Wampler, CW (2005) The numerical solution of systems of polynomials. World Scientific Publishing Co. Pte. Ltd., Hackensack, U.S.A. CrossRef
63. Mehta, D (2011) Numerical polynomial homotopy continuation method and string vacua. Adv. High Energy Phys. 2011: pp. 263937 CrossRef
64. Hauenstein, J, He, Y-H, Mehta, D (2013) Numerical elimination and moduli space of vacua. JHEP 09: pp. 083 CrossRef
65. Hauenstein, JD, Wampler, CW (2013) Isosingular sets and deflation. Found. Comput. Math. 13: pp. 371 CrossRef
66. Hauenstein, JD, Sommese, AJ, Wampler, CW (2011) Regeneration homotopies for solving systems of polynomials. Math. Comp. 80: pp. 345 CrossRef
67. Hauenstein, JD, Sommese, AJ, Wampler, CW (2011) Regenerative cascade homotopies for solving polynomial systems. Appl. Math. Comput. 218: pp. 1240 CrossRef
68. Bates, DJ (2009) A numerical local dimensions test for points on the solution set of a system of polynomial equations. SIAM J. Numer. Anal. 47: pp. 3608 CrossRef
69. Sommese, AJ, Verschelde, J, Wampler, CW (2002) Symmetric functions applied to decomposing solution sets of polynomial systems. SIAM J. Numer. Anal. 40: pp. 2026 CrossRef
70. J.D. Hauenstein and C.W. Wampler, / Numerical algebraic intersection using regeneration, (2013).
71. D.J. Bates et al., / Homotopies to compute points on connected components, (2014).
72. D.R. Grayson and M.E. Stillman, / Macaulay2, a software system for research in algebraic geometry, http://www.math.uiuc.edu/Macaulay2/.
73. D.J. Bates, / Bertini: Software for numerical algebraic geometry, http://bertini.nd.edu.
74. Sturmfels, B (2002) Solving systems of polynomial equations. American Mathematical Society, U.S.A - 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Elementary Particles and Quantum Field Theory
Quantum Field Theories, String Theory - 出版者：Springer Berlin / Heidelberg
- ISSN：1029-8479
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