Veltman Criteria in Beyond Standard Model Effective Field Theory of Complex Scalar Triplet

Abstract: The Higgs mass is not protected by any symmetry in the Standard Model. Hence, the self-energy corrections to the Higgs mass become large due to the quadratic divergence terms. Veltman condition (V.C.) ensures that the coefficient of the quadratic divergent term either vanishes or becomes negligible. The non-observation of new physics has pushed the new physics scale to be larger than 1 TeV, making it impossible to satisfy the Veltman condition in the Standard Model without very large fine-tuning. Many attempts are made to satisfy the V.C. in Beyond Standard Model theories, but the V.C. is hard to achieve at a very large scale ($\Lambda$). Alternatively, it is possible that the new physics appears much above the Electroweak scale, and the effect of the new physics is observed in terms of the Wilson coefficients of the Standard Model Effective Field Theory (SMEFT) operators. The V.C. can be addressed in the SMEFT framework. In this paper, some specific new physics scenarios are considered at a very large scale. Below that scale, the effect of the new physics is observed as Beyond Standard Model Effective Field Theory (BSM-EFT). We particularly study the type-II seesaw model with the complex scalar triplet ($Y=1$) in the context of V.C. We found that this particular model is the minimal model to generate all SMEFT operators that appear in V.C. and satisfies V.C. We also examine the model parameter dependence of the Wilson coefficients in detail and show how the cancellation of the Wilson coefficients is highly dependent on some specific values of the model parameters.