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

4
and two right-handed techniquark singlets:
( ) U
Q a a
L = L
, UR, a DR a (1)
D a L
where a ∈ {1, 2, 3} denotes the techniquark family. To remove the Witten anomaly [2], it
is necessary to add a fourth fermion family, weakly charged but a singlet under technicolor:
L L =
(
NL
E L
)
, N R , E R . (2)
Gauge anomalies are cancelled with the following hypercharge assignment:
Y (Q L ) = y ( y + 1
2 , Y (U R, D R ) =
2 , y − 1 )
,
2
Y (L L ) = − 3 ( ) −3y + 1
2 y, Y (N R, E R ) =
. (3)
2
Due to the assignment Q = T 3 + Y with T 3 being the weak isospin, one obtains the SM
hypercharge from Eq. (3) for y = 1/3 and the presence of a technigaugino for y = 1.
The full Lagrangian of Minimal Walking Technicolor Theory then contains the Standard
Model Lagrangian (without the Higgs part) and in addition Technicolor terms as follows:
L = L SM − L H + L T C ,
L T C = − 1 4 F µνF a aµν + i ¯Q L γ µ D µ Q L + iŪRγ µ D µ U R + i ¯D R γ µ D µ D R
+ i¯L L γ µ D µ L L + iĒRγ µ D µ E R + i ¯N R γ µ D µ N R
where F a µν = ∂ µ A a ν − ∂ ν A a µ + g T C ɛ abc A b µA c ν is the field strength tensor for techni-gauge
bosons A µ (a, b, c ∈ {1, 2, 3}) and the left-handed covariant derivative is
D µ Q L =
(δ ac ∂ µ + g T C ɛ abc A b µ − i g 2 ⃗ W µ · ⃗τδ ac − ig ′ y 2 B µδ ac )
Q c L. (4)
Note that in the above formula ⃗ W µ and B µ are the gauge bosons of the Standard Model,
τ a are Pauli matrices and ɛ abc is the fully antisymmetric tensor.
Electroweak symmetry breaking is obtained by means of techniquark condensation, anal-