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Cheung, J. Gunion, T. Han, G. Ladinsky, R. -P. Yuan, Phys. Rev. D49, 1246 (1994); ibid, D52, 3878 (1995). [39] V. N. Phillips, and D. Zeppenfeld, Phys. Lett. B346, 106 (1995); D. Rainwater, D. Zeppenfeld, and K. Hagiwara, Phys. Rev. D59, 014037 (1999). [40] P. Langacker, R. W. Robinett and J. L. Rosner, Phys. Rev. D30, 1470 (1984); V. D. Barger, N. G. Deshpande, J. L. Rosner and K. Whisnant, Phys. Rev. D35, 2893 (1987); J. L. Rosner, Phys. Rev. D54, 1078 (1996). [41] T. E. -T. Wang, arXiv:hep-ph/0506313.

Consider an unstable particle V produced by a + b and decaying to 1 + 2 + ... + n. For a weakly coupled particle ΓV ≪ MV , according to the Breit-Wigner resonance Eq. (B1), the amplitude develops a kinematical peak near the pole mass value at n (pa + pb )2 = ( i pi )2 ≈ MV2 . (41) This is called the invariant mass, and is the most effective observable for discovering a resonance if either the initial momenta or the final momenta can be fully reconstructed. As a simple example of a two-body decay, consider Z → e+ e− , m2ee = (pe+ + pe− )2 ≈ 2pe+ · pe− ≈ 2Ee+ Ee− (1 − cos θe+ e− ) ≈ MZ2 , 30 (42) which is invariant in any Lorentz frame, and leads to Ee ≈ MZ /2 in the Z-rest frame.

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