Tracking the Higgs

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S - University of California, Santa Barbara

EWK Symmetry Breaking

Glashow Salam SU(2) ⊗U(1)

• µν ⋅ µν Weinberg

L=-¼W W µν -¼B B µν

µν ∂ W

ν

i=

µ i ∂

µ ν i +g♠ ijκ µ ν W jW k W - W

B µν = ∂

ν

B µ - ∂

µ

B ν

Add a scalar doublet field


φ † = 2 -1/2 (φ 1 -iφ 2 ,H-iφ ο with potential ) V(φ) = µ 2 φφ † + λ |φφ † | 2 λ > 0 ) (

– This is the most general SU(2) invariant and renormalizable potential

µ 2 > 0 (T > T c )

µ 2 < 0 ≠ 0.0 (T < T c )

L φ = (D µ φ) † (D µ φ) − V(φ)

– where D µ = ∂ µ + ig (τ/2)⋅W µ + ig′/2 Β µ

choose a gauge with φ † =2 -1/2 (0,v+H), 〈H〉 o = 0 This choice breaks the


symmetry!

Lagrangian now has 3 Massive Vector Gauge Bosons and massless photon:


W µ± =2 -1/2 (W µ1 W ± µ2 M ) = ¼ W2 g v 2 2

u

c

t

Z µο = (g 2 +g′ 2 ) -1/2 (-g′B µ +gW µ3 ) M Z2 = ¼ (g 2 +g′ 2 )v 2

A µ = (g 2 +g′ 2 ) -1/2 (gB µ +g′W µ3 ) M A2 = 0

d

s

b

High Energy Physics

Graduate Seminar at UCSB, March 3, 2006 J.Incandela, UC Santa Barbara 5

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