Abstract
Abstract A large enhancement of a factor of 1.5 - 2 in Higgs production and decay in the diphoton channel, with little deviation in the ZZ channel, can only plausibly arise from a loop of new charged particles with large couplings to the Higgs. We show that, allowing only new fermions with marginal interactions at the weak scale, the required Yukawa couplings for a factor of 2 enhancement are so large that the Higgs quartic coupling is pushed to large negative values in the UV, triggering an unacceptable vacuum instability far beneath the 10 TeV scale. An enhancement by a factor of 1.5 can be accommodated if the charged particles are lighter than 150 GeV, within reach of discovery in almost all cases in the 8 TeV run at the LHC, and in even the most difficult cases at 14 TeV. Thus if the diphoton enhancement survives further scrutiny, and no charged particles beneath 150 GeV are found, there must be new bosons far beneath the 10 TeV scale. This would unambiguously rule out a large class of fine-tuned theories for physics beyond the Standard Model, including split SUSY and many of its variants, and provide strong circumstantial evidence for a natural theory of electroweak symmetry breaking at the TeV scale. Alternately, theories with only a single fine-tuned Higgs and new fermions at the weak scale, with no additional scalars or gauge bosons up to a cutoff much larger than the 10 TeV scale, unambiguously predict that the hints for a large diphoton enhancement in the current data will disappear.
Highlights
We show that, allowing only new fermions with marginal interactions at the weak scale, the required Yukawa couplings for a factor of 2 enhancement are so large that the Higgs quartic coupling is pushed to large negative values in the UV, triggering an unacceptable vacuum instability far beneath the 10 TeV scale
If the diphoton enhancement survives further scrutiny, and no charged particles beneath 150 GeV are found, there must be new bosons far beneath the 10 TeV scale. This would unambiguously rule out a large class of fine-tuned theories for physics beyond the Standard Model, including split SUSY and many of its variants, and provide strong circumstantial evidence for a natural theory of electroweak symmetry breaking at the TeV scale
For a single set of new vector-like fermions, with electric charge |Q| ≤ 1 and large enough Yukawa couplings to give an enhancement of μγγ = 1.5, demanding that the tunneling rate through false vacuum bubbles of size Λ−UV1 ∼ (10 TeV)−1 is less than the age of the universe requires the existence of a new, un-colored, charged fermion lighter than about 115 GeV
Summary
A fermionic loop contribution enhancing the Higgs-diphoton coupling requires vector-like representations and large Yukawa couplings to the Higgs boson. This amounts to some fine-tuning of parameters: given μγγ, the product (yyc) is essentially fixed and so the cut-off scale is very sensitive to mismatch y = yc, as the Higgs quartic runs with (dλ/dt) ∝ y4+yc4 This result is clear, where, already for mild splitting y = 2yc, the pale gray band of ΛUV = 10 TeV excludes μγγ >∼ 1.4. A diphoton enhancement μγγ = 1.5 through a minimal vector-like set of fermions requires a light charged state with mass below 115 GeV, even when we allow a very low cut-off scale ΛUV = 10 TeV for the theory and judiciously tune the parameters to maximize the effect by setting φ = 0, ∆m = 0, and y = yc.
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