Radion effects on unitarity in gauge-boson scattering(5)

The scalar field associated with fluctuations in the positions of the two branes, the ``radion'', plays an important role determining the cosmology and collider phenomenology of the Randall-Sundrum solution to the hierarchy problem. It is now well known th

W+L

W−L

γ/Z

W+L

W−L

(a)

γ/Z

(b)

(c)

h

(d)

h

(e)

Figure1:Tree-level Feynman diagrams for W W scattering in the SM.

of all2→2electroweak gauge boson scattering processes in the SM.The Feynman diagrams are shown in Fig.1.At high energies,the wave-function of a longitudinal gauge boson can be written as

ǫW L µ(p)=

pµ

E ,(8)

This indicates that the longitudinally polarized gauge bosons are behaving as their eaten Gold-stone boson counterparts with corrections of order M W/E where E is the gauge boson energy.

With this substitution,the contributions from the diagrams in Fig.1(a),(b),or(c)indi-vidually leads to a contribution O(s2/M4W),but these terms cancel among each other due to electroweak gauge symmetry.The leading order result for the sum of these three diagrams, neglecting O(M2W/s)terms,is

−i M=−u

32π 1−1d cosθ(−i M)=−s

2

,(11) then one obtains the bound

√