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LHC Phenomenology of an Extended Standard Model with a Real Scalar Singlet

Vernon Barger, Paul Langacker, Mathew McCaskey, Michael J. Ramsey-Musolf, Gabe Shaughnessy

arXiv:0706.4311v1hep-ph

TL;DR

The paper asks how adding a real scalar singlet affects Higgs phenomenology at the LHC, including mixing and stable-singlet dark matter scenarios. It analyzes these cases and finds that mixing can relax scalar-mass constraints, while singlet decays can alter conventional Higgs discovery channels.

  • Problem

    The Standard Model has shortcomings including Higgs-mass fine tuning and no particle-physics explanation for dark matter, motivating study of how a singlet extension changes Higgs phenomenology.

    Source: §I · p. 2

  • Method

    The paper analyzes a real-singlet extension in mixed-Higgs and stable-singlet scenarios, examining electroweak precision constraints, LHC signatures, relic density, and direct detection.

    Source: §I · p. 3, §III · p. 10

  • Results

    The xSM relaxes the electroweak-precision and LEP tension, while singlet-pair decays can reduce conventional Higgs signals and alter discovery channels.

    Source: §VII · pp. 32–33

  • Takeaways & Limitations

    A Higgs discovery's mass and event rates can indicate mixing, and Higgs decays to stable singlets may require invisible-search channels.

    Source: §VII · pp. 32–33

Abstract

from arXiv · show

Gauge singlet extensions of the Standard Model (SM) scalar sector may help remedy its theoretical and phenomenological shortcomings while solving outstanding problems in cosmology. Depending on the symmetries of the scalar potential, such extensions may provide a viable candidate for the observed relic density of cold dark matter or a strong first order electroweak phase transition needed for electroweak baryogenesis. Using the simplest extension of the SM scalar sector with one real singlet field, we analyze the generic implications of a singlet-extended scalar sector for Higgs boson phenomenology at the Large Hadron Collider (LHC). We consider two broad scenarios: one in which the neutral SM Higgs and singlet mix and the other in which no mixing occurs and the singlet can be a dark matter particle. For the first scenario, we analyze constraints from electroweak precision observables and their implications for LHC Higgs phenomenology. For models in which the singlet is stable, we determine the conditions under which it can yield the observed relic density, compute the cross sections for direct detection in recoil experiments, and discuss the corresponding signatures at the LHC.

I. INTRODUCTION

The paper motivates a real-singlet extension as a simple framework for studying shortcomings of the Standard Model and its Higgs phenomenology at the LHC. It considers Higgs-singlet mixing and a stable singlet, using the xSM to examine these scenarios.

I. INTRODUCTION

  • The Standard Model leaves issues including Higgs-mass fine tuning and no particle-physics explanation for dark matter or the visible-matter excess.The passage also notes tension between electroweak precision fits favoring a light Higgs and the LEP-excluded mass region.Source: §I · p. 2
  • Adding a singlet scalar is presented as a simple extension that may help address these shortcomings.Singlet extensions have been studied in the SM.Source: §I · p. 2
  • The paper frames four LHC questions: how mixing affects discovery, how to distinguish singlet-like from SM-like scalars, and how stable-singlet dark matter affects Higgs searches and direct detection.Source: §I · p. 2
  • The xSM adds one real scalar singlet to the SM; its linear-term coefficient is chosen so the singlet has no vacuum expectation value.The authors focus on one singlet as a framework for generic LHC phenomenology, while noting that more singlets are possible.Source: §I · pp. 2–3
  • The parameter δ1 governs Higgs-singlet mixing, while without mixing the singlet mass is set by κ2 and δ2.Source: §I · p. 3

A. Higgs Mixing Case

In the mixing scenario, electroweak precision observables and LEP searches jointly constrain the scalar masses and mixing. The resulting mass, coupling, and decay patterns shape which neutral scalars and final states may be observable at the LHC.

A. Higgs Mixing Case

  • For the lighter scalar, SM decay branching ratios match those of an equal-mass SM Higgs, while its production rate is reduced by the squared mixing parameter.If H2 is more than twice as massive as H1, H2 → 2H1 can open and reduce its conventional SM decay branching ratios.Source: A. Higgs Mixing Case · p. 3
  • The xSM relaxes the tension between electroweak precision observables favoring light scalars with substantial SU(2) content and LEP limits on scalars below 114 GeV.At maximal mixing, the heavier scalar can reach about 220 GeV; away from maximal mixing, the SM-like scalar's upper bound decreases while the singlet-like scalar's can increase.Source: A. Higgs Mixing Case · p. 4
  • A mixed scalar can be heavier than an SM-like scalar under electroweak precision constraints, but this analysis changes if additional new physics significantly affects those observables.Such new physics could allow heavier scalars with significant SU(2) fraction.Source: A. Higgs Mixing Case · p. 4
  • A neutral scalar above about 160 GeV is likely to be the heavier mixed state, while one below that mass is most likely the SM-like lighter state.With at least 30 fb−1, event rates in ZZ → 4ℓ or WW → ℓνjj can constrain or determine mixing when the scalar's SU(2) fraction is at least about 40%.Source: A. Higgs Mixing Case · pp. 4–5
  • Higgs splitting can yield four-b or 2b + 2τ final states, but may suppress conventional H2 channels enough to prevent discovery through them.For a singlet-like H2, identifying these non-standard final states at the LHC appears challenging; for some models, hundreds of four-b events before cuts are possible, though backgrounds may prevent conclusive identification.Source: A. Higgs Mixing Case · p. 5

B. Dark matter singlet

With an exact Z2 symmetry, the singlet is stable and can be a dark matter candidate, with its parameter space constrained by the observed relic density. The paper connects this scenario to Higgs searches and direct-detection prospects.

B. Dark matter singlet

  • An exact Z2 symmetry, with δ1 = κ3 = 0, removes vertices containing an odd number of singlets and makes the singlet stable.The relic-density observations constrain the model's parameter space.Source: B. Dark matter singlet · p. 5
  • Higgs decays to singlet pairs can reduce discovery prospects in conventional channels, while invisible decays in weak-boson fusion or Z-Higgsstrahlung offer search routes.Source: B. Dark matter singlet · pp. 5–6
  • The predicted proton spin-independent recoil cross section is 10^-8–10^-9 pb, within the range of upcoming experiments.Because S has only scalar interactions with matter, it does not produce a spin-dependent signal in future dark-matter searches.Source: B. Dark matter singlet · p. 6
  • The paper organizes the dark-matter analysis around relic density and spin-independent scattering rates on nucleons.Source: B. Dark matter singlet · p. 6

II. THE SINGLET AS AN EXTRA HIGGS BOSON

The paper develops the mixed-scalar Higgs sector by relating its mass eigenstates and mixing to couplings and decays. It then examines how these properties affect LEP constraints and LHC discovery prospects.

II. THE SINGLET AS AN EXTRA HIGGS BOSON

  • Singlet mixing is also studied in the MSSM and in radion mixing scenarios.The passage cites prior xSM and MSSM work and Randall-Sundrum radion mixing.Source: §II · p. 6
  • The Higgs-sector mass matrix is diagonalized into mass-ordered states H1 and H2, with masses and mixing angle determined by the scalar-sector parameters.The paper's H1/H2 ordering differs from conventions in Refs. [33], where eigenstates denote SU(2)-like and singlet-like scalars.Source: §II · pp. 6–7
  • Mixing universally reduces each Higgs state's couplings to SM fields, leaving its SM-mode branching fractions unchanged when no additional decay mode is accessible.Source: §II · p. 7
  • The lighter Higgs usually satisfies the LEP lower limit of 114 GeV; exceptions include small cos²φ or a very light Higgs below the b¯b threshold.For a very light Higgs, B → HiX and Υ → Hiγ limits can severely restrict mixing.Source: §II · p. 7
  • If kinematically allowed, H2 → H1H1 changes H2 branching fractions to SM modes.Source: §II · p. 7
  • A reduction in production strength and branching fractions relative to the SM can lower the statistical significance of Higgs discovery.Source: §II · p. 8
  • The authors scan xSM parameter space over ranges broad enough to show varied scalar states at a few-hundred-GeV scale.The dimensionless parameter ranges are broadly consistent with perturbativity, while electroweak precision constraints narrow the ranges for λ and λS.Source: §II · p. 8
  • A light Higgs below the LEP limit can occur through strong mixing or when the lightest state is dominantly singlet, weakening its coupling to SM fields.Very light Higgs mixing may be constrained by B and Υ decays.Source: §II · p. 8

III. ELECTROWEAK PRECISION CONSTRAINTS

The section evaluates how singlet–Higgs mixing affects electroweak precision observables (EWPO), using oblique parameters to constrain scalar masses and mixing. The fit favors lighter scalars as mixing increases, while vacuum stability may further restrict some surviving models.

III. ELECTROWEAK PRECISION CONSTRAINTS

  • Figure 1 presents the Higgs signal reduction as a function of scalar mass, with the right panel including EWPO constraints and the left panel omitting them.The section uses the figure to show the impact of EWPO constraints on signal reduction.Source: Figure 1 · p. 9, §III · pp. 9, 13
  • For scalars near the electroweak scale, S, T, and U alone are not guaranteed to approximate the full EWPO effects; the V parameter may also matter.The analysis nevertheless first uses the leading derivative-expansion terms S, T, and U to obtain a reasonable picture.Source: §III · p. 10
  • The fit uses Z-pole, W-mass, and low-energy measurements to extract S, T, and U, and defines its 95% C.L. ellipsoid by Δχ² < 7.815.The reported central values and ranges are consistent with the PDG, with a slight shift attributed to a more recent top-quark mass.Source: §III · p. 11
  • The scalar contributions to T are weighted by cos²φ and sin²φ for the two mass eigenstates, with logarithmic mass dependence for very heavy scalars.The expression generalizes to more than one real scalar by enlarging the mixing matrix.Source: §III · pp. 12–13
  • At maximal mixing, EWPO favor m2 ≲220 GeV at 95% C.L.; increasing mixing also favors a lighter H2 and a relatively light H1.With a heavy H2 and small mixing, the dependence on H1 is close to that of a pure SU(2) Higgs, leaving H2 minimally constrained by EWPO.Source: §III · p. 13
  • Most surviving models have a light, strongly SM-like scalar and a heavy scalar that mixes very weakly, though moderately mixed scalars around 200–300 GeV are possible.The fit also leaves a few points with a light singlet-like scalar.Source: §III · p. 13
  • Some models that survive the EWPO constraints may still be incompatible with vacuum stability, which the paper does not analyze in detail.The lower Higgs-mass bound depends on the top-quark mass and especially on the theory cutoff scale.Source: §III · p. 14

IV. OBSERVATION OF A SINGLET MIXED HIGGS BOSON AT THE LHC

The analysis finds that CMS could discover at least one mixed-sector Higgs in nearly all considered cases using traditional channels, although EWPO constrain which masses and couplings are allowed. Higgs splitting may weaken conventional signals while offering exotic final states, and measured rates can probe reduced Higgs couplings.

IV. OBSERVATION OF A SINGLET MIXED HIGGS BOSON AT THE LHC

  • With 30 fb−1 at CMS, nearly all cases yield at least one Higgs above 5σ in traditional modes; exceptions fall below the quoted range or discovery threshold.Figure 3 compares discovery significance with LEP constraints alone and with EWPO constraints applied.Source: Figure 3 · p. 15, §IV · p. 15
  • Discovering both Higgs states requires nearly maximal singlet-Higgs mixing, whereas neither may be discovered when the SM-like Higgs dominantly decays to a light singlet-like Higgs.The latter decay reduces branching fractions to conventional search modes; prospects improve with luminosity beyond 30 fb−1.Source: §IV · pp. 16–17
  • EWPO restrict the lightest Higgs mass, while an observable H1 requires ξ2 near 1 and a mass below about 160 GeV.Consistency with EWPO makes discovery of at least one state likely, with an exception when a light SM-like Higgs dominantly decays to a light singlet-like Higgs.Source: §IV · pp. 16–17
  • Many EWPO-allowed ≥5σ cases have a SM-like H1 with MH1 ≲160 GeV, while the extended sector can also permit discovery of a Higgs heavier than a pure SM Higgs.The bottom-right panel of Figure 4 contains numerous ≥5σ H2 cases, though the supplied passage does not complete its mass range.Source: Figure 4 · p. 16, §IV · p. 17
  • At CMS with 30 fb−1, scalars of mass ≳150 GeV could yield ≥5σ significance for ξ2 as low as ∼0.4; across most allowed masses, coupling could be identified as reduced from the SM Higgs.At mH = 170 GeV, the ZZ mode weakens because Higgs decay becomes dominated by H →WW.Source: Figure 5 · p. 18, §IV · p. 18
  • H2→H1H1 can suppress conventional decays yet yield 4b, bbττ, or bbγγ signatures; singlet-like H2 prospects are less certain and need dedicated feasibility study.The study estimates several hundred pre-cut four-b-jet events for singlet-like H2 at 30 fb−1, but says practical LHC observability requires further analysis.Source: §IV · pp. 19–20

V. THE SINGLET AS DARK MATTER

The paper studies a Z2-symmetric real-singlet scenario in which the stable singlet can be dark matter. It determines relic-density-compatible parameter regions, direct-detection recoil cross sections, and implications for LHC Higgs searches.

V. THE SINGLET AS DARK MATTER

  • A Z2 symmetry makes the singlet stable and a viable particle dark-matter candidate.The parameter space is constrained to accommodate the relic density implied by cosmological and astrophysical observations.Source: §V · p. 20
  • Assuming thermal production and standard cosmology, the analysis identifies xSM parameters that reproduce the observed dark-matter relic density.The relevant parameters govern the singlet mass and its coupling to the SM Higgs.Source: §V · p. 20
  • The study computes nuclear-recoil direct-detection cross sections and examines implications for Higgs-boson searches at the LHC.Source: §V · p. 20

A. Relic density

The relic-density analysis relates thermal singlet annihilation to Higgs-mediated processes and constrains the coupling and mass parameters. The observed density spans a broad mass range, while small or large Higgs-singlet coupling can respectively produce over- or under-density.

A. Relic density

  • The observed relic density is ΩDMh2 = 0.111 ± 0.006, and thermal abundance is roughly inversely related to the total annihilation cross section.The paper integrates the Boltzmann equation to calculate the singlet relic density.Source: A. Relic density · pp. 20–21
  • A strong first-order electroweak phase transition is difficult in this dark-matter case unless many light singlets are present.Source: A. Relic density · p. 20
  • The thermally averaged annihilation cross section sums Higgs-mediated processes, with δ2 and λ governing the key interactions.The SS→h→hh channel is expected to be suppressed because its intermediate Higgs is far off shell.Source: A. Relic density · p. 21, Figure 6
  • The relic-density parameter regions are shown with and without EWPO constraints; the SM Higgs mass constraint used for the EWPO case is Mh < 150 GeV.The open region with small |δ2| and large κ2 corresponds to models with relic dark-matter over-density.Source: Figure 7 · p. 21, A. Relic density · pp. 21–22
  • The observed relic-density region spans a wide range of singlet masses, but below about 50 GeV off-shell Higgs annihilation is suppressed and the minimum relic density rises sharply.Source: A. Relic density · p. 22
  • Small |δ2| yields excess relic singlet dark matter through insufficient annihilation, whereas large |δ2| yields under-density assuming thermal production.As singlet mass increases, |δ2| must increase to maintain the annihilation rate associated with a fixed relic density.Source: A. Relic density · pp. 22–23

B. Direct Detection of Singlet Scalar Dark Matter: Elastic Scattering

Singlet dark matter scatters from nucleons mainly through t-channel Higgs exchange, linking direct-detection rates to Higgs-sector parameters. The expected experimental reach depends on resonance effects and the assumed cosmology, while the calculated cross section has a substantial hadronic uncertainty.

Elastic scattering

  • Spin-dependent scattering vanishes in the xSM, so a future positive spin-dependent signal would rule out this model as a viable dark-matter scenario.The singlet has no vector-like interactions connecting it to matter.Source: B. Direct Detection of Singlet Scalar… · p. 24
  • T-channel Higgs exchange dominates spin-independent scattering, proton and neutron cross sections are similar, and hadronic matrix elements contribute an uncertainty of about 60%.The analysis therefore calculates scattering on protons.Source: B. Direct Detection of Singlet Scalar… · pp. 24–25

Direct-detection reach

  • Expected SuperCDMS sensitivity covers most scanned parameter space consistent with EWPO, except models annihilating through the Higgs s-channel near MS ≈ 100–150 GeV.The exception appears below the expected SuperCDMS limit.Source: B. Direct Detection of Singlet Scalar… · p. 25

Resonant annihilation

  • Near the Higgs resonance, mH ≈ 2MS, annihilation can yield ΩSh² ≤ 0.123 with a small coupling and suppress direct-detection rates below 10⁻⁹ pb.Away from resonance, the same coupling can produce excessive relic density; the analysis finds this effect does not arise for MS ≳ 150 GeV.Source: B. Direct Detection of Singlet Scalar… · p. 26

Constraints and cosmology

  • With EWPO constraints, the allowed cross-section range below current bounds shrinks, and current direct-detection experiments may cover a sizable part of the parameter space.A non-standard cosmology can instead make the singlet account for the local dark-matter density without scaling the cross section; a null signal would not eliminate all such models.Source: B. Direct Detection of Singlet Scalar… · pp. 26–27

C. Impact on LHC searches for Higgs bosons

If Higgs decays to singlet pairs are open, invisible decays can weaken conventional LHC search signals, while invisible searches may recover sensitivity. The paper also considers effects on Higgs-width measurements and displaced-decay signatures.

Invisible Higgs decays

  • For light Higgs masses, singlet decays can dominate fermionic modes, making usual SM searches insufficient; WBF searches use missing energy and forward-jet azimuthal correlations.Z-Higgstrahlung is also noted as an alternative invisible-decay search.Source: C. Impact on LHC searches for Higgs… · pp. 27–28
  • Opening h → SS reduces conventional Higgs-search significance, and the cases below 5σ in the CMS study are covered by the ATLAS invisible search via WBF.For these models, the invisible branching fraction is dominant, at 60–100%.Source: C. Impact on LHC searches for Higgs… · pp. 27–28, Figure 11 · p. 28

Higgs-width measurements

  • At Mh = 300 GeV, a significant invisible width can approach twice the width to SM modes and reduce the 4l rate, potentially spoiling width resolution.The cited ATLAS width uncertainty is 10% with 300 fb⁻¹, and an extreme width may make signal reconstruction difficult.Source: C. Impact on LHC searches for Higgs… · pp. 28–29

Displaced decays

  • For φ ∼ O(10⁻⁶), a light singlet-like state may travel a detector-scale distance before decaying, producing displaced decay products.In this small-mixing regime, the singlet decays before freeze-out and cannot be a dark-matter candidate.Source: C. Impact on LHC searches for Higgs… · p. 29

VI. SPECIFIC MODEL ILLUSTRATIONS

The representative models show how Higgs discovery prospects vary across mixing and stable-singlet dark-matter scenarios. Some points suppress conventional signals, while others allow discovery through multiple channels.

Mixing case A1

  • In mixing case A1, ξ2² = 0.001 suppresses traditional decay-mode production of the heavy SM-like Higgs, while the light state also has a reduced rate from its singlet composition.The heavy state dominantly decays to two light scalars.Source: §VI · p. 29

Mixing case A2

  • In mixing case A2, sufficiently large mixing makes both Higgs states discoverable, with unchanged SM branching fractions because the splitting decay is kinematically closed.The representative model has enough mixing for both states to exceed the required discovery significance.Source: §VI · pp. 29–30

Stable-singlet case B1

  • Stable-singlet case B1 is consistent with the observed relic density and Xenon10 limits, but its SM-mode Higgs production rate is about one-quarter of the SM expectation.Its approximately 75% branching fraction to stable singlets makes an indirect invisible-decay search possible.Source: §VI · pp. 30–31

Stable-singlet case B2

  • Stable-singlet case B2 has a weaker singlet branching fraction and yields 3.8σ evidence, with discovery through direct and indirect channels potentially possible at higher luminosity.The model illustrations assume 30 fb⁻¹ of CMS data.Source: Table II · p. 30, §VI · p. 31

VII. CONCLUSIONS

The xSM adds a real scalar singlet and yields distinct Higgs-phenomenology outcomes depending on whether the singlet mixes with the Higgs or is stable. Mixing can accommodate a strong first-order electroweak phase transition, while a stable singlet can account for the relic abundance of cold dark matter.

VII. CONCLUSIONS

  • Electroweak precision and LEP 2 constraints limit mixing scenarios; the SM-like state has an upper mass bound of 220 GeV, while the singlet-like state can generally be heavier.A large singlet fraction can also allow the light Higgs mass below the LEP bound for an SM Higgs.Source: §VII · p. 32
  • Higgs discovery remains viable, but depends on which scalar is SU(2)-like: CMS may discover a lighter state below about 180 GeV or a heavier state as massive as ~220 GeV with 30 fb−1.A Higgs scalar above 150 GeV would point toward an augmented scalar sector.Source: §VII · p. 32
  • If H2 → H1H1 is allowed, nonstandard 4b or 2b + 2τ final states can reduce conventional H2 branching fractions enough to preclude discovery in those channels.Direct observation of these final states may be feasible for an SU(2)-like H2, but appears challenging for a singlet-like H2.Source: §VII · p. 32
  • With Z2 symmetry forbidding mixing, the stable singlet can be a dark-matter candidate, but matching the observed relic density tightly constrains the model.Its annihilation rate is controlled by the Higgs-singlet coupling, Higgs self-coupling, and singlet mass.Source: §VII · p. 33
  • When Higgs-to-singlet-pair decay is open, it reduces rates to conventional SM modes and can suppress discovery significance below 5σ; invisible decays via weak boson fusion may still reveal the Higgs.For EWPO-allowed models that do not overproduce relic dark matter, the SM Higgs may be discoverable only through invisible decays.Source: §VII · p. 33
  • If Z2 symmetry is approximate, a singlet-dominated state can be long-lived; for mixing angles O(10−6), its decay length can be comparable to LHC detector scales, producing displaced vertices.The xSM examines both mixing and stable-singlet scenarios and their implications for Higgs phenomenology and cosmology.Source: §VII · pp. 31, 33, 34

APPENDIX A: HIGGS CORRECTIONS TO GAUGE BOSON PROPAGATORS

The appendix gives the singlet-induced W- and Z-boson propagator functions and specifies their regularization and renormalization conventions.

APPENDIX A: HIGGS CORRECTIONS TO GAUGE BOSON PROPAGATORS

  • The added neutral singlet affects only the W- and Z-boson propagator functions, for which the appendix provides unrenormalized expressions including divergent and finite parts.The expressions are computed in Feynman gauge using dimensional regularization in 4 − 2ε dimensions.Source: Appendix A · p. 34
  • The renormalized propagator functions are obtained by subtracting 1/ε − γ + ln 4π and choosing μ = MZ.The expressions use MW and MZ for the charged and neutral would-be Goldstone boson propagators in Feynman gauge.Source: Appendix A · p. 35
  • The expressions reduce to the Standard Model results in Ref. and can be extended to one complex SU(2) doublet with N real scalars.The extension is made by expanding the dimension of the V_ij matrix.Source: Appendix A · p. 35
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