[Paper Review] No Higgs at the LHC

J.J. van der Bij|ArXiv.org|Apr 22, 2008

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper explores the possibility that the Higgs boson may not be discovered at the LHC due to invisible decays or mixing with singlet scalar fields, leading to a broadened or invisible Higgs resonance. It proposes that higher-dimensional models with extra spatial dimensions can naturally produce such a spread-out Higgs propagator, consistent with LEP-200 data anomalies, implying the Higgs could be hidden from the LHC but detectable via precision measurements at the ILC.

ABSTRACT

I discuss the question whether it is possible that the LHC will find no signal for the Higgs particle. It is argued that in this case singlet scalars should be present that could move in extra, even fractional, dimensions. A critical view at the existing electroweak data shows that this possibility might be favored over the simplest standard model. In this case one needs the ILC in order to study the Higgs sector.

Motivation & Objective

• To investigate whether the LHC could fail to detect the Higgs boson despite its existence, challenging the 'no-lose theorem' of new physics at hadron colliders.
• To analyze inconsistencies in electroweak precision data, particularly the tension between the forward-backward asymmetry in bottom quarks and other measurements, which suggest a non-standard Higgs sector.
• To propose a minimal extension of the Standard Model using singlet scalar fields that can hide the Higgs via invisible decays or mixing into fractional Higgs states.
• To explore higher-dimensional models (up to six dimensions) where the Higgs propagator acquires a continuum structure, making it undetectable at the LHC.
• To reconcile the model with LEP-200 data anomalies, including a 2.3σ excess at 98 GeV and a 1.7σ excess at 115 GeV, interpreting them as signatures of a broadened Higgs resonance.

Proposed method

• Introduces a singlet scalar extension of the Higgs sector with a superrenormalizable interaction $ H\Phi^\dagger\Phi $, which avoids generating $ H^3 $, $ H^4 $, or $ H^2\Phi^\dagger\Phi $ terms at quantum level, preserving renormalizability.
• Uses the Källén-Lehmann spectral representation to model the Higgs propagator as a sum or integral over states: $ D_{\sigma\sigma}(k^2) = \int ds\, \rho(s)/(k^2 + s - i\epsilon) $, allowing for a broad or continuum-like resonance.
• Constructs a higher-dimensional model where the Higgs field propagates in $ d > 4 $ dimensions, leading to a modified propagator: $ D_{\sigma\sigma}(q^2) = \left[q^2 + M^2 - \mu_{\text{lhd}}^{8-d}(q^2 + m^2)^{(d-6)/2}\right]^{-1} $, with $ d=5 $ or $ 6 $.
• Performs a fit to LEP-200 data, treating the 98 GeV and 115 GeV excesses as a delta peak and a continuum component, respectively, within the spectral density framework.
• Analyzes the invisible branching ratio as a function of invariant mass, allowing for a complete suppression of the sharp Higgs peak at the LHC while preserving standard model branching ratios.
• Compares the $ d=5 $ and $ d=6 $ models, finding that $ d=5 $ fits the data more robustly within experimental uncertainties.

Experimental results

Research questions

• RQ1 Can the LHC fail to detect the Higgs boson even if it exists, due to invisible decays or mixing with singlet scalars?
• RQ2 Is the observed tension in electroweak precision data—particularly the discrepancy between $ A_{FB}(b) $ and other measurements—explainable by an extended Higgs sector?
• RQ3 Can a higher-dimensional Higgs model with $ d=5 $ or $ d=6 $ dimensions produce a broad or invisible Higgs resonance consistent with LEP-200 data?
• RQ4 Does the presence of a continuum Higgs propagator, arising from extra dimensions, make the Higgs undetectable at the LHC but still measurable at the ILC?
• RQ5 Can the LEP-200 anomalies at 98 GeV and 115 GeV be interpreted as evidence for a spread-out Higgs resonance in a higher-dimensional model?

Key findings

• The $ d=5 $ model fits the LEP-200 data well within uncertainties, yielding allowed ranges: $ 95 < m < 101 $ GeV, $ 111 < M < 121 $ GeV, and $ 26 < \mu_{\text{lhd}} < 49 $ GeV.
• The $ d=6 $ model fits only in a restricted range: $ 95 < m < 101 $ GeV, $ 106 < M < 111 $ GeV, and $ 22 < \mu_{\text{lhd}} < 27 $ GeV, indicating it is less favored than the $ d=5 $ case.
• The model predicts a Higgs boson with a broad or invisible resonance that would evade detection at the LHC, despite being consistent with electroweak precision data.
• The 2.3σ excess at 98 GeV in LEP-200 data is interpreted as a delta peak in the Källén-Lehmann spectral density, while the 1.7σ excess at 115 GeV is attributed to the continuum component of the propagator.
• The model allows for a dark matter candidate via a stable, weakly interacting singlet scalar, consistent with the invisible decay channel.
• The paper concludes that the LHC may see no Higgs signal, but the ILC would be essential to probe the Higgs sector in detail if such a scenario holds.