Vacuum stability bounds on Higgs coupling deviations in the absence of new bosons

Received: February stability bounds on Higgs coupling deviations in the absence of new bosons Kfir Blum 0 2 Raffaele Tito D'Agnolo 0 2 JiJi Fan 0 1 Open Access 0 c The Authors. 0 0 Princeton , NJ 08540 , U.S.A 1 Department of Physics, Syracuse University 2 Institute for Advanced Study We analyze the constraints imposed by Higgs vacuum stability on models with new fermions beyond the Standard Model. We focus on the phenomenology of Higgs couplings accessible at the Large Hadron Collider. New fermions that affect Higgs couplings lead to vacuum instability of the Higgs potential. Above the scale of vacuum instability, bosonic states must stabilize the potential, implying a cut-off to the pure fermion model. Conservatively tuning the models to produce the maximal cut-off for a given Higgs coupling effect, we show that observing a deviation in the Htt, H-diphoton, or H-digluon coupling, larger than 20%, would require that new bosons exist in order to stabilize the Higgs potential below about 100 TeV. For generic parameter configurations, and unless the new fermions are made as light as they can possibly be given current experimental constraints, observing a 10% deviation in any of these couplings would suggest an instability cut-off below 10-100 TeV. Similarly, if new bosons are absent up to a high scale, then a deviation in the Hbb or H coupling, larger than about 20%, should be accompanied by a sizable deviation in the Zbb or Z couplings that can be conclusively tested with electroweak precision measurements at planned lepton colliders. in; the; absence; of; new; bosons; Higgs Physics; Beyond Standard Model 3 Higgs couplings to massless gauge bosons 4 Conclusions A The effective potential C Collider constraints C.1 Colored particles B EFT analysis of deviations in Z and Higgs couplings to SM fermions Numerical verification for very light vector-like states 1 Introduction 2 Higgs couplings to fermions 2.1 2.2 2.3 States decaying promptly to first and second generation quarks States decaying promptly to third generation quarks Prompt decays to charged first and second generation leptons Prompt decays to charged third generation leptons Prompt decays to a W and missing energy C.2.5 Prompt cascade decays of Q = 2 fermions The large hadron collider (LHC) Run-I gave us the Higgs boson, but the weak scale hierarchy problem does not seem closer to a solution than it did decades ago. This may change with new experimental information in Run-II, of which improved Higgs coupling measurements [16] are a guaranteed outcome. A natural question to ask, is whether this Higgs particle that was found is the only one of its kind, namely, the only scalar particle up to very high energies. Indeed, proposed solutions to the hierarchy problem include new bosonic states beyond the Standard Model (SM). Examples are the scalar super-partners of the SM fields in supersymmetry [7] and the bosonic resonances in composite Higgs models [8, 9]. In these examples, the scale at which the new bosonic states become dynamical marks the cut-off of the quadratic divergence in the quantum corrections to the Higgs mass. In this paper we show that measuring deviations in Higgs couplings at the LHC can establish the presence of new bosonic states, even if these bosons do not directly affect any Higgs coupling and are beyond reach of direct production. To show this, we proceed by elimination: we analyze the possibility that Higgs coupling modifications arise due to new To explain the logic, note that the only way to couple new fermions to the Higgs is through Yukawa couplings. New Yukawa interactions can certainly affect Higgs couplings or mixing with the SM leptons or quarks at tree level. However, as we shall show, the new Yukawa couplings must be sizable to generate a measurable deviation. Large Yukawa couplings have a definite effect in the renormalization group evolution (RGE) of the Higgsself quartic coupling, driving the quartic negative and leading to an instability in the effective potential [10]. To fix this instability, at least within the domain of validity of a perturbative analysis, new bosonic states are needed.1 Vacuum stability has been invoked as a constraint on the SM effective theory in the past (for an early review see, e.g. [11]). A point that drew much attention in the days prior to the Higgs discovery and the precise measurement of the top quark mass, was the fact that measuring a heavy top quark or a light Higgs would have indirectly but robustly (then plausible) values of mt and mh, could have been within reach of collider experiments such as the (then futuristic) LHC [1218]. Our paper can be thought of as an update circa-2015 of this logic. Today, having measured both the top and the Higgs masses to impressive accuracy (establishing that the SM Higgs potential is consistent with vacuum stability up to very high scales [1921]), the missing crucial experimental information is the precise values of the Higgs couplings. By the end of the LHC 14 TeV program we expect uncertainties in the ballpark of 5more details to the body of the paper, our generic quantitative statement here is that a resolution of planned GigaZ machines such as the international linear collider (ILC) or 1An alternative logical possibility is that the Higgs scalar itself ceases to exist as a fundamental state in which this happens without new bosonic degrees of freedom (fundamental or composite) becoming dynamical close to the same scale. circular electron-positron colliders in China or at CERN; ruling out this corresponding Zpole deviation would rule out pure fermion models. In addition, while we do not report a detailed analysis of this point here, applying our results to the HW W and HZZ couplings suggests strong vacuum stability constraints, strong enough to imply that observing a deviation in one of these channels at the LHC would rule out pure fermion models. Our results can be turned around to serve as generic prediction for the Higgs couplings in theories that do not contain new bosonic states up to very high scales, such as split supersymmetry [2326] and its variants. According to our analysis, this general class of models predicts that Higgs coupling modifications will not be discoverable (or just very barely) at the LHC. This is not a trivial point because low-lying fermions, protected by chiral symmetries, could in principle be accommodated in these theories and couple to Our results are relevant to the high-luminosity LHC as well as to a future lepton collider such as the ILC, the electron-positron mode of the future circular collider FCC-ee (formerly known as TLEP) and the circular electron positron collider (CEPC), that promise percent and even sub-percent accuracy on Higgs coupling measurements [22, 2731]. be inferred from measuring a deviation in the Higgs couplings to SM states. Since our derivation requires that we add only new fermions but no scalars or vector bosons, and since exot (...truncated)