PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

interaction with the Higgs as λ f Hff, contributes to the one loop correction to the Higgs
mass as [11,12]
δm 2 H = −|λ f| 2
8π 2 Λ2 UV
+..., (1.16)
where Λ UV is the cut-off scale beyond which the new physics is expected. Considering
the validity of the standard model upto the Planck scale, the Higgs mass gets a quantum
correction O(10 18 ). Cancellation of this divergences with the bare mass parameter would
require fine-tuning of order one part in 10 −18 , rendering the theory unnatural [11,12].
This huge quantum correction due to fermionic contribution is cancelled by the scalar
contribution, if we introduce scalar particle ˜f with the quartic interaction λ˜f|H| 2 |˜f| 2 and
with the property λ˜f
= |λ f | 2 . Supersymmetry is the desired symmetry which naturally
introducesascalarparticle ˜f forthefermionicfieldf withthesamemassandthenecessary
criteria between the couplings λ˜f
= |λ f | 2 . The contribution of the ˜f scalar to the one
loop correction of the Higgs mass is the following,
δm 2 H = (λ˜f)
8π 2 Λ2 UV . (1.17)
The total contribution to quadratic divergence of the Higgs mass in this case would be,
and hence will naturally vanish for λ˜f
= |λ f | 2 .
δm 2 H = (λ˜f −|λ f | 2 )
8π 2 Λ 2 UV , (1.18)
The operator Q that generates a supersymmetric transformation is an anticommuting
spinor, with
and
Q|Boson〉 = |Fermion〉, (1.19)
Q|Fermion〉 = |Boson〉 (1.20)
The hermitian conjugate of Q i.e Q † is also a supersymmetry generator. Supersymmetry
is a space-time symmetry and the possible form of supersymmetry is restricted by
Haag-Lopuszanski-Sohnius extension of the Coleman-Mandula theorem [24]. For realistic
theories like standard model, the theorem implies these following anticommutation and
commutation relations between the different generators,
{Q,Q † } = P µ (1.21)
{Q,Q} = {Q † ,Q † } = 0
[P µ ,Q] = [P µ ,Q † ] = 0,
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