Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
1.2. Electroweak Symmetry Break<strong>in</strong>g 16We note th<strong>at</strong> the s<strong>in</strong>ce the SU(2) and U(1) gauge factors commute <strong>with</strong> each other,they can have different coupl<strong>in</strong>g constants. We also note th<strong>at</strong> we have assigned acharge <strong>of</strong> 1/2 to the scalar under the U(1) symmetry and this is to eventually ensureth<strong>at</strong> the scalar rema<strong>in</strong>s electrically neutral. Assum<strong>in</strong>g th<strong>at</strong> the field acquires a vev<strong>of</strong> the form⎛〈φ〉 = √ 1 ⎝ 02 v⎞⎠, (1.43)then gauge transform<strong>at</strong>ions <strong>of</strong> the formφ → e iαa τ a e iβ/2 φ (1.44)<strong>with</strong> α 1 = α 2 = 0, α 3 = β leaves the vev <strong>in</strong>variant. It is this <strong>in</strong>variance to aparticular comb<strong>in</strong><strong>at</strong>ion <strong>of</strong> gener<strong>at</strong>ors which leaves one <strong>of</strong> the vector <strong>boson</strong>s massless.When we expand the quadr<strong>at</strong>ic terms <strong>in</strong> the Lagrangian we f<strong>in</strong>d,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)result<strong>in</strong>g <strong>in</strong> three massive vector <strong>boson</strong>s,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 rema<strong>in</strong><strong>in</strong>g comb<strong>in</strong><strong>at</strong>ion <strong>of</strong> 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 break<strong>in</strong>g symmetries can result <strong>in</strong> the spectrum<strong>of</strong> masses observed <strong>in</strong> n<strong>at</strong>ure. The unified theory <strong>of</strong> electroweak <strong>in</strong>teractionsmakes predictions about the rel<strong>at</strong>ionship between the W and Z <strong>boson</strong>, masses, <strong>in</strong>particular it produces a larger Z mass n<strong>at</strong>urally. To successfully break the symmetryone needed to <strong>in</strong>troduce a new scalar field <strong>in</strong>to the Standard Model. Thisfield transform<strong>in</strong>g <strong>in</strong> the SU(2) ×U(1) gauge group has a potential <strong>with</strong> the correctparameters to <strong>in</strong>troduce a non-zero vev to the theory. The physical manifest<strong>at</strong>ion <strong>of</strong>this new scalar is the <strong>Higgs</strong> <strong>boson</strong>. In the rema<strong>in</strong>der <strong>of</strong> this chapter we will discuss<strong>Higgs</strong> phenomenology <strong>at</strong> colliders and <strong>in</strong>troduce the gluon-<strong>Higgs</strong> effective coupl<strong>in</strong>g.