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Hierarchy problem and dimension-six effective operators

Ambalika Biswas
(
- Vivekananda Coll.
)
,
Anirban Kundu
(
- Calcutta U.
)
,
Poulami Mondal
(
- Calcutta U.
)

Jun 24, 2020

7 pages

Published in:

Phys.Rev.D 102 (2020) 7, 075022

Published: Oct 20, 2020

e-Print:

2006.13513 [hep-ph]

DOI:

10.1103/PhysRevD.102.075022

View in:

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Abstract: (APS)

Without any mechanism to protect its mass, the self-energy of the Higgs boson diverges quadratically, leading to the hierarchy or fine-tuning problem. One bottom-up solution is to postulate some yet-to-be-discovered symmetry which forces the sum of the quadratic divergences to be zero, or almost negligible; this is known as the Veltman condition. Even if one assumes the existence of some new physics at a high scale, the fine-tuning problem is not eradicated, although it is softer than what it would have been with a Planck scale momentum cutoff. We study such divergences in an effective theory framework and construct the Veltman condition with dimension-six operators. We show that there are two classes of diagrams, the one-loop and the two-loop ones, that contribute to quadratic divergences, but the contribution of the latter is suppressed by a loop factor of 1/16π2. There are only six dimension-six operators that contribute to the one-loop category, and the Wilson coefficients of these operators play an important role towards softening the fine-tuning problem. We find the parameter space for the Wilson coefficients that satisfies the extended Veltman condition, and also discuss why one need not bother about the d>6 operators. The parameter space is consistent with the theoretical and experimental bounds of the Wilson coefficients and should act as a guide to the model builders.

Note:

10 pages, 2 figures. v2: Corrected an error, added an Appendix. Version to be published in Physical Review D

Beyond the standard model
operator: higher-dimensional
operator: dimension: 6
operator: Wilson
renormalization group
Higgs particle: propagator
hierarchy
numerical calculations
new physics

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