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1
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0000872388
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Reviews may be found in articles by P. Van Nieuwenhuizen
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(1981)
Phys. Rep.
, vol.68
, pp. 189
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10
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0003041676
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A review has been made by, 145, 2, A. B. Lahanas, D. V. Nanopoulos, Phys. Rep.
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(1983)
Phys. Lett.
, vol.133 B
, pp. 61
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Cremmer, E.1
Ferrara, S.2
Kounnas, C.3
Nanopoulos, D.V.4
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15
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24444437248
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1C P. Fayet
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(1977)
Phys. Lett.
, vol.69 B
, pp. 489
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16
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84927413557
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See, for example, R. Godbole, in Supersymmetry and Supergravity/Nonperturbative QCD, edited by P. Roy and V. Singh, Lecture Notes in Physics Vol. 206 (Springer-Verlag, Berlin, 1984).
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18
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84927413556
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J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).
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19
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84927413555
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The sum of the contributions from the three diagrams is - lcurl 4-1 mark "" i κ2 u ¯λ2 ( k2 ) σ μν γλ ( k2 - p2 - mγ̃ )-1 γρ σ αβ uρ1 ( k1 ) p 2 μ epsilon 2 ν p 1 β epsilon 1 α + ( p2 , epsilon2 <-> p1 , epsilon1 ) rcurl lineup - i sqrt 2 κ lcurl ( 2 p1[μ epsilon 1 ρ] p 2[ν epsilon 2 λ] η ρλ + μ <-> ν ) - p 1[ρ epsilon 1 τ] p2 "" [ρ epsilon2 "" τ] η μν rcurl 2 i p-2 R times κ ( 2 sqrt 2 )-1 u ¯α2 ( k2 ) lcurl epsilonαλβ(μ γ5 γ ν) ( k2 - k1 )λ + 2-1 i epsilon αλβ(μ γ5 [ γλ , σ ν)ζ ]+ pζ rcurl vβ1 ( k1 ) , which leads to Eq. (2). Gauge invariance with respect to each photon is explicit and the gravitino gauge invariance (in the supersymmetric limit) can be checked by replacement of either the gravitino spinors by its momentum. For a discussion of the graviton propagator, see M. Veltman, in Methods in Field Theory, Proceedings of the Les Houches Summer School, Session XXVIII, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam, 1976).
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20
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84927413554
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For the present case of double gravitino emission, one gets [vide Eq. (3)] two terms: one proportional to mγ̃ 4 and another to mγ̃ 2. This is since partialμx ^ partialνy < 0 | T S ¯μ ( x ) Sν ( y ) | γ γ in > = < 0 | T partialμx S ¯μ ( x ) partialνy Sν ( y ) + δ ( x0 - y0 ) lcurl S ¯0 ( x ) , partialν Sν ( y ) rcurl - δ ( x0 - y0 ) lcurl partialμ S ¯μ ( x ) , S0 ( y ) rcurl | γ γ in > and partial cdot S generates one mγ̃^ .
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21
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84927413553
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C. Itzykson and J. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
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22
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84927413552
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For instance, there is a contribution to our process from a box graph with the following four internal lines: two gamma's, one γ ̃ and one z. We can estimate its magnitude in terms of a cutoff LAMBDA. We find that it overtakes the tree-level terms when sqrt s exceeds apeq 48 π κ-2 m3/22 mγ̃ -2 Λ-1. Taking m3/2 apeq 10-6 eV, mγ̃ apeq 10 GeV, and LAMBDA to be at least 1 order of magnitude higher than sqrt s, this corresponds to an ( Ec.m. ) γγ crit apeq 1 TeV.
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