Hadronic production of a Higgs boson in association with two jets at ...

1.2. Electroweak Symmetry Breaking 16We note that the since the SU(2) and U(1) gauge factors commute with each other,they can have different coupling constants. We also note that we have assigned acharge of 1/2 to the scalar under the U(1) symmetry and this is to eventually ensurethat the scalar remains electrically neutral. Assuming that the field acquires a vevof the form⎛〈φ〉 = √ 1 ⎝ 02 v⎞⎠, (1.43)then gauge transformations of the formφ → e iαa τ a e iβ/2 φ (1.44)with α 1 = α 2 = 0, α 3 = β leaves the vev invariant. It is this invariance to aparticular combination of generators which leaves one of the vector bosons massless.When we expand the quadratic terms in the Lagrangian we find,L mass = 1 v 22 4 [g2 (A 1 µ )2 + g 2 (A 2 µ )2 + (−gA 3 µ + g′ B µ ) 2 ], (1.45)resulting in three massive vector bosons,W ± µ = 1 √2(A 1 µ ± iA 2 µ), m W = g v 2 , (1.46)andZ 0 µ = 1√g2 + g ′2(gA3 µ − g′ B µ ), m Z = √ g 2 + g ′2v 2 . (1.47)The remaining combination of vector fields is the massless photon,A µ =1√g2 + g ′2(gA3 µ + g ′ B µ ) m A = 0 (1.48)We have seen how spontaneously breaking symmetries can result in the spectrumof masses observed in nature. The unified theory of electroweak interactionsmakes predictions about the relationship between the W and Z boson, masses, inparticular it produces a larger Z mass naturally. To successfully break the symmetryone needed to introduce a new scalar field into the Standard Model. Thisfield transforming in the SU(2) ×U(1) gauge group has a potential with the correctparameters to introduce a non-zero vev to the theory. The physical manifestation ofthis new scalar is the Higgs boson. In the remainder of this chapter we will discussHiggs phenomenology at colliders and introduce the gluon-Higgs effective coupling.