REVIEW
The Anatomy of Electro-Weak Symmetry Breaking. I: The Higgs boson in the Standard Model
High Energy Physics - Phenomenology · Submitted 17 Mar 2005 · 300 references
Pith's verdict: A review that earned its place as the standard quantitative reference for SM Higgs decays and production, with 2005-vintage inputs and no error bands on the summary plots — both minor for the genre.
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Referee report
The paper
The paper claims
Fix one number — the Higgs mass — and every other Higgs prediction follows
The reading
What carries the argument
The load-bearing object is the proportionality of every Higgs coupling to the mass of the particle it couples to, inherited from the single scalar doublet and its vacuum expectation value. Because the same $v$ sets the $W$ mass, the Fermi constant and the fermion Yukawa couplings, the Higgs has no independent coupling constants to adjust — this is what converts 'one unknown mass' into 'all observables predicted'. The machinery that makes the prediction usable is the renormalization-group treatment of the hadronic channels: large logarithms $α_s^n log^n(m_q/M_H)$ are absorbed by evaluating running $overline{MS}$ quark masses and $α_s$ at the scale $M_H$, which is why the $b$ and $c$ partial widths are computed with $m_b(M_H)$ and $m_c(M_H)$ rather than pole masses. The second piece of machinery is the set of loop amplitudes for $Hγγ$, $HZγ$ and $Hgg$, dominated by the $W$ boson and the top quark, which give the Higgs its only coupling to massless gauge bosons and hence its main production route at a hadron collider.
Extended reading notes
Core claim
The claim the review is built to establish is that the Standard Model Higgs sector has no free shape, only a free scale. The couplings are fixed by the particle masses through $g_{Hf f} = m_f/v$ and $g_{HVV} = 2M_V^2/v$ with $v = (1/2^{1/2}G_μ)^{-1/2} = 246$ GeV, so a single input, $M_H$, determines the whole profile: which decay channel dominates in which mass window, how the total width grows, and how large each production cross section is at a given machine energy. The review works this out channel by channel. Below the $WW$ threshold the $b$ quark width dominates but is suppressed by the running mass at the scale $M_H$; above roughly 130 GeV the three-body $H → WW^*$ overtakes it; above the real $WW$ and $ZZ$ thresholds the width grows as $M_H^3$ until the Higgs becomes too broad to be called a resonance. Loop-induced decays into $γγ$, $γZ$ and $gg$ are kept because they do not decouple as the loop mass grows, making them a window on particles heavier than the Higgs itself, and because the gluon fusion rate built on the same vertex is the dominant production mechanism at the LHC. Alongside this, the review assembles the constraints: the precision electroweak fit gives $M_H = 114^{+69}_{-45}$ GeV with a 95% upper bound of 260 GeV, the direct LEP search gives $M_H > 114.4$ GeV, and the theoretical requirements of perturbative unitarity, positivity of the quartic coupling up to a cut-off, and tolerable fine-tuning bound the allowed region from above and below.
Load-bearing premise
Every number in the review is computed with one fixed set of electroweak inputs — a top mass of 178 GeV, $α_s(M_Z) = 0.1172$, and running quark masses evaluated at the scale of the Higgs — and the summary plots do not propagate the uncertainties on those inputs into the quoted rates.
Editorial extensions
If this is right
- A measured Higgs mass alone yields a complete set of predicted branching ratios and cross sections, so any single measured rate can be checked against the rest of the table without further theoretical input.
- The gluon fusion cross section, built from the same top-quark loop that mediates $H → gg$, is the largest production channel at the LHC and therefore the primary discovery mode over most of the allowed mass range.
- Because the $b\bar b$ and $c\bar c$ widths depend sensitively on the running masses, a percent-level measurement of hadronic branching ratios would translate into a constraint on $α_s$ and the quark masses rather than on the Higgs sector.
- The loop-induced $γγ$ and $Zγ$ rates are sensitive to any new charged or coloured particle whose mass comes from the Higgs mechanism, so a deviation from the tabulated values would be evidence for physics beyond the Standard Model before any such particle is produced directly.
- The theoretical bounds — unitarity failing around 700 GeV, the triviality and stability window narrowing as the cut-off rises — mean that if the Higgs is absent or heavier than about 1 TeV, new phenomena must appear in the TeV range to restore unitarity in longitudinal gauge-boson scattering.
Reading between the lines
- The review's tables are usable as a null hypothesis only to the extent that the electroweak inputs are held fixed; a reader who wants to test the Standard Model rather than confirm it would need the input-parameter uncertainties folded into the quoted rates, which the summary plots do not attempt.
- The same coupling-to-mass proportionality that makes the predictions rigid also makes them fragile in one direction: any particle that acquires its mass from the Higgs enters the loop-induced $γγ$ and $gg$ rates even if it is far too heavy to produce, so those two channels carry more sensitivity to unknown physics than their small branching fractions suggest.
- The precision-electroweak preference for a light Higgs sits close to the direct-search exclusion line, which means the two constraints are not independent confirmations but a near-coincidence; a shift in the top mass or in the hadronic vacuum-polarization input moves the fit region by tens of GeV.
- The CP-discrimination material — azimuthal correlations in $H → τ^+τ^-$ and $H → t\bar t$ — is presented as a template rather than a measurement, and it defines the observable that a future lepton collider would need in order to distinguish a scalar from a pseudoscalar once a state is found.
Original abstract
This review is devoted to the study of the mechanism of electroweak symmetry breaking and this first part focuses on the Higgs particle of the Standard Model. The fundamental properties of the Higgs boson are reviewed and its decay modes and production mechanisms at hadron colliders and at future lepton colliders are described in detail.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
This review is devoted to the study of the mechanism of electroweak symmetry breaking and this first part focuses on the Higgs particle of the Standard Model. The fundamental properties of the Higgs boson are reviewed and its decay modes and production mechanisms at hadron colliders and at future lepton colliders are described in detail.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This review is devoted to the study of the mechanism of electroweak symmetry breaking and this first part focuses on the Higgs particle of the Standard Model. | contribution 0.81 | 0.32 | 0.08 | asserted 0.87 |
| s1 | The fundamental properties of the Higgs boson are reviewed and its decay modes and production mechanisms at hadron colliders and at future lepton colliders are described in detail. | contribution 0.98 | 0.17 | 0.08 | asserted 0.97 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:hep-ph/0503172 by the authors.
References
How later papers used it
419 later papers cite it
12 later papers by other authors are listed below: 7 used its method or tool, 3 used its data or values and 2 compared their own results with it.
Uses its method or tool 7 of 34 papers with this label
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Computed production cross sections for fusion processes by including the full NLO QCD corrections as in this paper.
Spontaneous Mirror Parity Violation, Common Origin of Matter and Dark Matter, and the LHC Signatures (2011) · 1.00 · paraphrased: the licence does not allow quoting
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For this partial rate, we apply the 4-body decay formula Eq. (2.35) of [ref] and work in the heavy $W_R$ limit.
Anatomy of Diluted Dark Matter in the Minimal Left-Right Symmetric Model (2023) · Majorana Higgs dilutor · 1.00
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Computed the partial widths mostly following this paper, to an intended accuracy of about 10% including NLO QCD corrections to decays into light-flavor quarks.
Cosmological Signals of a Mirror Twin Higgs (2016) · 1.00 · paraphrased: the licence does not allow quoting
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Employed this paper's full one-loop result for the digluon decay width with a top quark mass of 172 and neglected the bottom quark contribution.
Interpretation of 750 GeV Diphoton Excess at LHC in Singlet Extension of Color-octet Neutrino Mass Model (2016) · 0.93 · paraphrased: the licence does not allow quoting
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Used this paper's count of the number of particles of the (3)_C representation in the loop in its decay width formula for s to gg.
Diphoton channel at the LHC experiments to find a hint for a new heavy gauge boson (2015) · 0.83 · paraphrased: the licence does not allow quoting
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Included QCD corrections in the H to q qbar rates as in this paper when evaluating the quantities and the sum of partial widths.
Hints of Standard Model Higgs Boson at the LHC and Light Dark Matter Searches (2011) · 0.90 · paraphrased: the licence does not allow quoting
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The basic integrals $I_1$ and $I_2$ are taken in [ref] and presented in term of $f$, $g$ functions as follows: [equation] Two complex functions $f, g$ can be expressed as follows: [equation]
One-loop expressions for $h\rightarrow l\bar{l}\gamma$ in Higgs extensions of the Standard Model (2023) · The basic integrals $I_1, I_2$ · 0.80
Uses its data or values 3 of 32 papers with this label
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Applied the decay width Gamma_Z gamma obtained from the exact formulas given in this paper.
The LHC upper bounds for $pp \to \text{diboson}$, $t\bar t$ cross section on fermionic dark matter (2016) · 0.99 · paraphrased: the licence does not allow quoting
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Used the gluon-gluon fusion estimate of 800(80) fb from this paper as one of two estimates.
A hidden, heavier resonance of the Higgs field (2021) · 0.98 · paraphrased: the licence does not allow quoting
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Considered the lower value lambda_l of about 0.186 at the electroweak scale, which saturates the stability bound of this paper.
Cosmological Perturbations in the New Higgs Inflation (2010) · 0.93 · paraphrased: the licence does not allow quoting
Compares with it 2 of 13 papers with this label
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Compared its own calculated total SM Higgs width with this paper's width, which includes higher-order corrections, to show the error from including only leading terms.
Top quark rare decays in a two Higgs doublet model for the top (2007) · 1.00 · paraphrased: the licence does not allow quoting
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Compared its own tree-level total SM Higgs width with this paper's width calculated including higher-order corrections to show the role of radiative corrections.
Scalar FCNC and rare top decays in a two Higgs doublet model "for the top" (2008) · 0.98 · paraphrased: the licence does not allow quoting
How the literature uses it
387 arXiv papers cite this in 517 sentences
Papers citing it · 280 sentences without a confident label
Contests it 1 paper
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This relation, which includes the Higgs and $Z$ boson masses $m_H$ and $m_Z$, respectively, is in agreement with the formulae available in the literature[We would like to point out that there is a misprint in Eq. (7) of Ref. [ref] , which has to be multiplied by $1/4$.] [ref] .
Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics · Kinematics and Notation · contest 0.73
Builds on it 3 papers
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Now, in close analogy to the Higgs boson decay [ref] we can calculate the decay width of the dark particles $χ$.
Minimal extension of the Standard Model with a mirror symmetry between fundamental fermions and a possible origin of dark matter · Cosmological stability of dark matter · 0.82
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Adapting the expression for the Higgs decay to two photons from Ref. [ref] , the $H →γγ$ partial width including the two additional charged fermions becomes [equation] where $G_F$ is the Fermi constant, $M_H$ is the Higgs mass of 125 GeV, and we include the dominant contributions from the top quark, bottom quark, the $W$ boson, and the two new fermions.
Probing new $U(1)$ gauge symmetries via exotic $Z \to Z' \gamma$ decays · Collider searches for anomalons · 0.80
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The following expressions for the loop-induced decays into $γγ, γZ, gg$ are modified from Sec. 2.3 in [ref] .
Characterizing LHC-Resonances in extended HEFT: information on the nature of extended scalar sectors · Loop-induced Decay from $D_c = 2$ Operators · 0.91
Uses its method or tool 29 papers
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The decay widths of $h$ into $γγ, γZ and gg$ are given explicitly by [ref] [equation] with $v̂_f= 2 I_f^3 -4Q_f s^2_W$ and $v_H ^±_i=2c_W^2-1/c_W$.
Loop induced $h \rightarrow \gamma \gamma, Z\gamma, gg $ decays in 3-Higgs doublet models · LOOP INDUCED DECAYS INTO $γγ, γZ, gg$ · 0.84
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The cross section of $gg →ϕ$ is estimated by CalcHEP_3.8 [ref] implementing the effective interaction for $ϕ$-gluon-gluon, and we get $σ(gg →ϕ) ≃sin^2 α×250$ pb applying K-factor 1.6 [ref] for $m_ϕ=$ 50 GeV and $√(s) = 13$ TeV case.
Multi-$Z'$ signatures of spontaneously broken local $U(1)'$ symmetry · Middle mass case: ${m_Z', m_ϕ} = {20, 50}$ GeV · 1.00
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It is computed in the code [ref] using the following formula: [equation] where $A_SUSY^h_s g g, q$ and $A_SUSY^h_s g g, q̃$ represent the contributions to the $h_s g g$ coupling from quark loops and squark loops, respectively [ref] . $A_SM^h_s g g, q$ denotes the quark loop contribution in the SM with the formulation available in Ref. [ref] . $C_h_s q q̅^tree$ is the tree-level coupling between $h_s$ and quarks. $m_q (Q)$ and $m_q (pole)$ represent the running mass of the quark at scale $Q ≈m_h_s$ and the quark pole mass, respectively.
95GeV Excesses in the $\mathbb{Z}_3$-symmetric Next-to Minimal Supersymmetric Standard Model · and signals · 1.00
Uses its data or values 30 papers
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Therefore, by using the conventional estimate for $M_h=$ 700 GeV [ref] Γ^conv( M_h →ZZ)∼56.7 GeVand from Eq.([ref]) Γ( M_h →ZZ)∼m^2_h /M^2_h Γ^conv(M_h →ZZ)we could insert a given value for $m_h$ and compute Γ( M_h →ZZ)∼m^2_h/(700 GeV)^2 56.7 GeVWith the tentative identification $m_h= 125$ GeV, this gives Γ( M_h →ZZ)∼1.8 GeV Afterward, to obtain the total width, we will maintain exactly the other contributions reported in the literature [ref] for $M_h=$ 700 GeV, namely [The quoted value refers to a top-quark mass of 173.7 which averages between the two determinations 173.2(6) GeV and 174.2(1.4) GeV reported by the Particle Data Group [ref] and replaces the values 171.4 and 172.5 GeV used respectively in [ref] [ref] .] Γ(M_h→fermions+ gluons+ photons...)∼28 GeV and the same ratio Γ( M_h →WW)/Γ( M_h →ZZ) ∼2.03 These input numbers, which have very small uncertainties, produce a total decay
A resonance of the Higgs field at 700 GeV and a new phenomenology · A new phenomenology · 0.99
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(The branching fraction of a SM-like Higgs boson of similar mass would be $BR(H_SM →γγ)≃0.15%$ [ref] .)
Enhanced di-photon Higgs signal in the Next-to-Minimal Supersymmetric Standard Model · Properties of light Higgs bosons in the NMSSM · 0.96
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For $M_h=$ 700 GeV, where $Γ^conv( M_h →ZZ)∼56.7 GeV$ [ref] , fixing $m_h=125$ GeV gives Γ( M_h →ZZ)∼m^2_h/(700 GeV)^2 56.7 GeV∼1.8 GeV Afterward, by maintaining the other contributions for $M_h=$ 700 GeV [ref] Γ(M_h→fermions+ gluons+ photons...)∼28 GeVand with the same ratio $Γ( M_h →WW)/Γ( M_h →ZZ)∼$ 2.03, we find a total width Γ( M_h →all) ∼28 GeV + 3.03 Γ(M_h →ZZ) ∼33.5 GeV and a fraction $B( M_h →ZZ)∼(1.8 / 33.5) ∼0.054$.
A hidden, heavier resonance of the Higgs field · Comparison with 4-lepton data · 0.96
Compares with it 11 papers
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Our results reduce to the SM result found in the literature [ref] when the KK modes are removed and agree with the result in [ref] when we use tree-level KK masses in mUED.
Testing Minimal Universal Extra Dimensions Using Higgs Boson Searches at the LHC · Evaluation of amplitudes for Higgs production and decay in mUED · 0.99
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The decay rate is: [equation] in agreement with the result in Ref. [ref] .
Higgs decay into a lepton pair and a photon: a roadmap to $\mathbf{H\to Z\gamma}$ discovery and probes of new physics · Resonant contribution and the Narrow-Width Approximation · 0.96
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[ref] only if the branches of the piecewise function $g(τ)$ in eq.
The decay $h\to Z \gamma$ in the Standard-Model Effective Field Theory · $h→Zγ$ in the Standard Model and the input parameters scheme · 0.92
Cites it as background 138 papers
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The recent discovery of Higgs-Boson at the Large Hadron Collider (LHC) [ref] is quite crucial as it provides mass to the constituent particles of the Standard Model (SM) [ref] , which has been a successful theory in experiments.
Investigating non-minimal flavour-violating CMSSM in the light of Higgs-Boson mass using information theory · Introduction · 0.90
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Precision predictions for the respective production rates are a key ingredient in the experimental searches, the higher-order radiative corrections usually being known to next-to-next-to-leading order (NNLO) in QCD and to next-to-leading order (NLO) as far as electro-weak corrections are concerned (see e.g. [ref] ).
Higher order constraints on the Higgs production rate from fixed-target DIS data · Introduction · 0.93
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The partial width reads [ref] [equation] where $τ_i$ = $4m_i^2/m_H^2$, and the spin form factors are [equation] and the universal scaling function $f(τ)$ is [equation] Supersymmetry corrects this partial width [ref] by factors involving the Higgs mixing angle $α$ and $β$ arising from the two Higgs doublets.
Gluino-driven Radiative Breaking, Higgs Boson Mass, Muon $\mathbf{g-2}$, and the Higgs Diphoton Decay in SUGRA Unification · Higgs Diphoton Decay · 0.85
Discussion
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