Implications for New Physics from Fine-Tuning Arguments: I. Application to SUSY and Seesaw Cases

We revisit the standard argument to estimate the scale of new physics (NP)beyond the SM, based on the sensitivity of the Higgs mass to quadraticdivergences. Although this argument is arguably naive, the correspondingestimate, Lambda_SM < 2-3 TeV, works reasonably well in most cases and shouldbe considered a conservative bound, as it ignores other contributions to theHiggs mass which are potentially large. Besides, the possibility of anaccidental Veltman-like cancellation does not raise significantly Lambda_SM.One can obtain more precise implications from fine-tuning arguments in specificexamples of NP. Here we consider SUSY and right-handed (seesaw) neutrinos. SUSYis a typical example for which the previous general estimate is indeedconservative: the MSSM is fine-tuned a few %, even for soft masses of a fewhundred GeV. In contrast, other SUSY scenarios, in particular those withlow-scale SUSY breaking, can easily saturate the general bound on Lambda_SM.The seesaw mechanism requires large fine-tuning if M_R > 10^7 GeV, unless thereis additional NP (SUSY being a favourite option).Comment: 24 pages, LaTeX, 5 ps figure