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dd¯ → W 0+W 0− ¯ 2 ) → W 0 − (q− ) + W 0 + (q+ ) goes through a t-channel exchange The subprocess d(p1 ) + d(p of the virtual top. The amplitude involves the vertex −g 0 W 0 µ t̄γ µ (gR PR )d, where a pure right-handed coupling is assumed. M = −(g 0 gR )2 v̄(p2 )γ ν p2t 6 pt γ µ PR u(p1 )ε∗− µ ε∗+ ν 2 − mt The fermion spin sum over probability gives a numerator factor 0 0 (g 0 gR )4 Tr (6 pt γ µ 6 p1 γ µ 6 pt γ ν 6 p2 γ ν PR ), where pt = p1 − q− = q+ − p2 . The vector boson polarization sum is done by the formula ε∗ µ εµ0 = −gµµ0 + qµ qµ0 /m0 2W . X g 0 4 gR4 |M| = 2 (pt − m2t )2 2 " t2 2+ 2m4W 0 ! t2 Tr (6 pt 6 p1 6 pt 6 p2 ) + 2 2 Tr (6 p2 6 p1 ) mW 0 # o g 0 4 gR4 n 2 4 2 2 2 2 (4 + t /m = 0 )[−(t − mW 0 ) − ts] + 4st /mW 0 W (t − m2t )2 i g 0 4 gR4 h 2 4 4 2 2 (4 + t /m = 0 )(ut − mW 0 ) + 4st /mW 0 W (t − m2t )2 The cross section becomes ! 1 1 X 1 β dΩ dσ = |M|2 4 3 2s 8π 4π | {z } | {z } | {z } | {z } spin color flux phasespace 1 where β = (1 − 4m2W 0 /s) 2 . The above formula agrees well with that by [1] (their E(s, t, u) in Eq.(3.10)). uū → Z 0 Z 0 a la Murayam et al. We can rescale Eq.(3.5) from [1] to approach the Z 0 Z 0 production via Murayama’s scenario of a off-diagonal new vertex −g 0 Z 0 µ t̄γ µ (gR PR )u. The transition probability becomes X T = + M = g 04 gR4 × T h i 1 2 4 4 2 2 (4 + t /m )(ut − m ) + 4st /m Z0 Z0 Z0 (t − m2t )2 h i 1 2 4 4 2 2 (4 + u /m )(ut − m ) + 4su /m 0 0 0 Z Z Z (u − m2t )2 " 4m2Z 0 s tu 1 2s 4ut − + − 2 + 2 2 4 (t − mt )(u − mt ) ut 2mZ 0 2 mZ 0 # The first and second lines are from the direct squares of the t and u channels. The third line from the interferece is obtained from rescaling those in Brown and Mikaelian[1]. The phase space integral has to be divided 2! because of the identical particle effect. 1 References [1] R. W. Brown and K. O. Mikaelian, Phys. Rev. D 19, 922 (1979). 2