Discovering Technicolor: Final Report for LHC School ... - CP3-Origins

10
VI.
LHC SIGNALS
There are several ways of looking for MWT signals at LHC and perhaps one of the
most promising chanels are looking for resonances in the invariant mass distributions corresponding
to the two heavy composite vector boson triplets of MWT called R ±/0
1 (light)
and R ±/0
2 (heavy) which mix the fundamental electroweak gauge fields W µ and B µ
with the composite vector bosons A µ
arising from the condensation of the techniquarks.
These mixed states can couple to the SM model fermions (see Figure 4) and can be seen
as resonances in the invariant mass distribution of both leptonic and hadronic final states.
q
l +
q
l + (¯ν)
q
¯q
R 0 1,2
R ± 1,2
R 1,2
¯q
l −
¯q
ν(l − )
¯q
q
q
q
q
l +
q ′
W
Z, W
R 1,2
q ′
¯q
R ± 1,2
Z
W ±
l −
l + (¯ν)
ν(l − )
FIG. 4: tree level diagrams due to exchange of R bosons (with ± corresponding to + (−) )
The standard model fermions do not couple directly to the TC vector bosons A µ
as can
be seen from the lagrangian (neglecting QCD) for the SM fermions
L fermion = ¯Ψ f /DΨ f + L(Ψ f , M) , D µ = ∂ µ + i 2 gLa W a µ + i 2 g′ ΥB µ
Where M = 1 √
2
(v + H + 2iπ a T a )
denotes the scalar content of MWT. The coupling is
due to the mixing of the gauge fields that occur in the bosonic lagranigan
L boson = − 1 2 Tr [W µνW µν ] − 1 4 B µνB µν − 1 2 Tr [F µνF µν ] + m 2 Tr [C µ C µ ] + L(C µ , M)
F µν = ∂ µ A ν − ∂ ν A µ − i˜g [A µ , A ν ] , C µ = A µ − g˜g
( )
gL a Wµ a + g ′ ΥB µ
When M aquires a VEV the bosonic lagrangian contains mixing matrices which gives rise
to mass eigenstates corresponding to the ordinary SM bosons and the six new composite
vector bosons R ±,0
1,2 which couple to the SM fermions through their lefthanded ( W ) and
hypercharge components ( B ). The mixing is determined by the elctroweak part of the