REVIEW
Diphoton decay for a $750$ GeV scalar boson in an $U(1)_{X}$ model
High Energy Physics - Phenomenology · Submitted 17 Dec 2015 · 34 references
Pith's verdict: A competent scan of the authors' own anomaly-free U(1)_X model against a signal that was already dying when v4 appeared, with one real derivation slip in the ξχhh decoupling that a referee should force them to fix.
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Referee report
The paper
The paper claims
A 750 GeV scalar can reach the diphoton rate through heavy-quark loops in a U(1) extension
The reading
What carries the argument
The load-bearing device is the one-loop triangle amplitude for a CP-even scalar coupling to two gauge bosons, written in the paper's compact form: each fermion or charged scalar in the loop contributes $h_i N_i Q_i^2 F_i$ with $F_{1/2} = -sqrt{tau}[1 + (1-tau) f(tau)]$ and $F_0 = sqrt{tau}[1 - tau f(tau)]$, $f(tau) = [arcsin(1/sqrt{tau})]^2$, $tau_i = 4 m_i^2 / m_{xi_chi}^2$. Because all relevant loop masses exceed $375$ GeV, the form factors stay in the real branch and the amplitudes are computable without imaginary parts. The second piece of machinery is the decoupling construction in Eqs. (18)-(20): the authors set $lambda_6 S_alpha^2 + lambda_7 C_alpha^2 approx 0$ to suppress $xi_chi h h$ (which is tightly bounded) while demanding $lambda_6 S_beta^2 + lambda_7 C_beta^2 = lambda$, so that a free effective coupling $lambda$ to $H^+ H^-$ survives to feed the photon loop. This is what lets the contour plots in $Gamma_{Zgamma}/Gamma_{gamma gamma}$ versus $Gamma_{ZZ}/Gamma_{gamma gamma}$ be drawn as a function of only $m_T$ and $lambda_{rm eff}$.
Extended reading notes
Core claim
The paper's central claim is that in the nonuniversal $U(1)_X$ model of its earlier work, the real component $xi_chi$ of the singlet $chi$ is a viable 750 GeV diphoton resonance. The decay $xi_chi to gamma gamma$ proceeds at one loop through two bottom-like singlets $J_n$, one top-like singlet $T$, and the charged Higgs $H^pm$; the same loops generate $gg$, $Zgamma$ and $ZZ$ channels, and the paper computes all four widths from a common form-factor expression with $F_{1/2}$ for fermions and $F_0$ for the scalar. The production cross section is obtained from the standard narrow-width formula $sigma(pp to xi_chi to gamma gamma) = C_{gg}, Gamma(xi_chi to gg), Gamma(xi_chi to gamma gamma) / (m_{xi_chi} Gamma)$, with the gluon-gluon luminosity integral taken as $C_{gg} = 2137$ at 13 TeV. Three treatments of the total width are scanned: loop-only, the ATLAS-motivated $Gamma = 45$ GeV, and dark-matter dominance via $xi_chi to sigma^* sigma$. The authors report that for exotic quark masses between 900 GeV and 3 TeV, and with the trilinear coupling $lambda_{rm eff}$ and Yukawa $h$ chosen appropriately, the predicted cross section falls inside the combined ATLAS and CMS range of 2-8 fb, while the ratio bounds $Gamma_{Zgamma} < 20, Gamma_{gamma gamma}$ and $Gamma_{ZZ} < 10, Gamma_{gamma gamma}$ cut off the large-coupling end of the scan.
Load-bearing premise
The argument needs the 750 GeV singlet to be switched off from the highly constrained $hh$ channel while keeping a freely adjustable, sizeable coupling to $H^+ H^-$; the paper obtains this by imposing two conditions and then solving them under the approximation $alpha approx beta$, which is the step that makes the free coupling possible.
Editorial extensions
If this is right
- If the mechanism holds, a 750 GeV resonance in this model would come with correlated rates in $Zgamma$ and $ZZ$, not photons alone, so the ratios $Gamma_{Zgamma}/Gamma_{gamma gamma}$ and $Gamma_{ZZ}/Gamma_{gamma gamma}$ become the discriminating observables rather than the diphoton yield by itself.
- The exotic quark masses are bounded from above by the same fit: with a 45 GeV width the model is excluded above $m_T approx 965$ GeV at 99% CL, and with dark-matter-dominated width the excluded region moves to roughly 2.7 TeV, 2.0 TeV, 1.3 TeV or 0.98 TeV depending on $lambda_8$ and $m_{H^pm}$.
- A scalar dark matter particle $sigma$ with $0.15 leq lambda_8 leq 3$ would give $xi_chi$ a width between about 1.2 and 23 GeV, so the observed width of the resonance would itself be a measurement of the dark-sector coupling.
- Because the same singlet-quark content is required by anomaly cancellation, a confirmed diphoton resonance at this mass would simultaneously be evidence for the extended quark sector that the $U(1)_X$ charge assignment demands.
Reading between the lines
- The decoupling step deserves a direct algebraic check: if the approximation $alpha approx beta$ of Eq. (7) is taken exactly, then Eqs. (18) and (19) coincide and together force $lambda = 0$ rather than leaving $lambda$ free up to 5, so the Fig. 3 scan over $lambda_{rm eff}$ rests on a condition that the paper's own approximation does not actually permit. A reader wanting to use these contours shou
- The framework predicts a specific partner signature that the paper does not pursue: the same $T$ and $J_n$ quarks that feed the photon loop should be produced in pairs at the LHC and decay through the $Z'$ and the extra Higgs states, so the 900 GeV lower bound used here is a moving target that future heavy-quark searches will tighten independently of the diphoton channel.
- Since the width is the least constrained ingredient, the three scenarios scanned here are effectively three different theories; a measurement of the resonance width, even a loose one, would select among them and could rule out the loop-only case, whose branching ratios the paper puts at roughly 42% to $gamma gamma$, 33% to $Zgamma$ and 25% to $ZZ$.
- The dark matter singlet is introduced with a global $U(1)$ to forbid odd terms, but the paper notes that spontaneous symmetry breaking can regenerate them; whether the symmetry survives the $U(1)_X$ breaking is a separate stability question that the diphoton fit does not test.
Original abstract
In the context of a nonuniversal and anomaly free $U(1)_{X}$ extension of the standard model, we examine the decay of a $750$GeV scalar singlet state, $\xi_{\chi}$, as a possible explanation of the observed diphoton excess announced by the ATLAS and CMS collaborations at CERN-LHC collider. One-loop decay to photons is allowed through three heavy singlet quarks and one charged Higgs boson into the loop. We obtain, for different width approximations and for masses of the exotic singlet quarks in the region $[900,\,3000]$ GeV, a production cross section $\sigma(pp\to\xi_{\chi}\to\gamma\gamma)$ compatible with ATLAS and CMS collaborations data. We also include another scalar singlet, $\sigma$, as a dark matter candidate that may couple with the 750 GeV scalar at tree level with production cross sections in agreement with ATLAS and CMS.
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
In the context of a nonuniversal and anomaly free $U(1)_{X}$ extension of the standard model, we examine the decay of a $750$GeV scalar singlet state, $\xi_{\chi}$, as a possible explanation of the observed diphoton excess announced by the ATLAS and CMS collaborations at CERN-LHC collider. One-loop decay to photons is allowed through three heavy singlet quarks and one charged Higgs boson into the loop. We obtain, for different width approximations and for masses of the exotic singlet quarks in the region $[900,\,3000]$ GeV, a production cross section $\sigma(pp\to\xi_{\chi}\to\gamma\gamma)$ compatible with ATLAS and CMS collaborations data. We also include another scalar singlet, $\sigma$, as a dark matter candidate that may couple with the 750 GeV scalar at tree level with production cross sections in agreement with ATLAS and CMS.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the context of a nonuniversal and anomaly free $U(1)_{X}$ extension of the standard model, we examine the decay of a $750$GeV scalar singlet state, $\xi_{\chi}$, as a possible explanation of the observed diphoton excess announced by the ATLAS and CMS collaborations at CERN-LHC collider. | contribution 0.78 | 0.55 | 0.12 | hedged possibility 0.96 |
| s1 | One-loop decay to photons is allowed through three heavy singlet quarks and one charged Higgs boson into the loop. | method 0.95 | 0.39 | 0.05 | asserted 0.97 |
| s2 | We obtain, for different width approximations and for masses of the exotic singlet quarks in the region $[900,\,3000]$ GeV, a production cross section $\sigma(pp\to\xi_{\chi}\to\gamma\gamma)$ compatible with ATLAS and CMS collaborations data. | result 1.00 | 0.94 | 0.63 | asserted 0.78 |
| s3 | We also include another scalar singlet, $\sigma$, as a dark matter candidate that may couple with the 750 GeV scalar at tree level with production cross sections in agreement with ATLAS and CMS. | contribution 0.72 | 0.87 | 0.14 | hedged possibility 0.96 |
What was examined, and what was not
- arXiv listing abstract v4
- 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:1512.05617 by the authors.
References
How the literature uses it
55 arXiv papers cite this in 62 sentences
Papers citing it · 16 sentences without a confident label
Contests it 1 paper
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In the validation process of this work, we identified several results in the literature that deviate, often by an order of magnitude or more, in comparison to our results [ref] .
Precision tools and models to narrow in on the 750 GeV diphoton resonance · The diphoton and digluon rates beyond leading order · contest 0.82
Cites it as background 43 papers
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In one of the most studied types, the $750$ GeV particle is a scalar or pseudoscalar $s$ that is produced and decays via loops of vector-like exotic fermions [ref] .
String Consistency, Heavy Exotics, and the 750 GeV Diphoton Excess at the LHC: Addendum · Introduction · 0.99
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This could be an argument against the reality of the diphoton excess, meaning nothing but a statistical fluctuations; but if taken seriously, it put strong constraint on the implied model building [ref] [ Refs. [ref] on this subject appeared at the same time as this work.].
The Minimal Scalar-Stealth Top Interpretation of the Diphoton Excess · Introduction · 0.85
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Although many attempts [ref] have already been made in the context of a scalar resonance coupled to vector-like fermions, our prime goal in this paper is to show that the vector-like fermions assisting the production and decay of the scalar can be related to a possible dark sector.
750 GeV Di-photon excess at CERN LHC from a dark sector assisted scalar decay · Introduction · 0.81
What it cites · 26 sentences without a confident label
Uses the method or tool of 1 paper
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When we apply the minimum conditions $∂⟨V⟩/∂υ_i=0$ for each scalar VEV $υ_i=υ_1,2,χ$, following [ref] we obtain at dominant order
Scalar Dark Matter with CERN-LEP data and $Z'$ search at the LHC in an $U(1)'$ Model · Higgs potential · 0.92
Uses data or values from 5 papers
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For the analysis, we take the combined results for the cross section from ATLAS and CMS, $σ(pp→ξ_χ→γγ)=(2-8) fb$ equally valid for $√(s)=8$ TeV and $C_gg=174$ [ref] .
On the Interpretation of a Possible $\sim 750$ GeV Particle Decaying into $\gamma \gamma$ · Production cross section · 1.00
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Also, the lower bound of 900 GeV for $m_T$ corresponds to the reported value in recent searches on top- and bottom-like heavy quarks from ATLAS and CMS Collaborations [ref] and the upper bound of 3 TeV corresponds to the asymptotic value obtained from the fermionic form factor $F_1/2$.
Search for single production of vector-like quarks decaying into $Wb$ in $pp$ collisions at $\sqrt{s} =$ 8 TeV with the ATLAS detector · Production cross section · 0.98
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At the scale $μ=m_ξ_χ=750$ GeV, and center-of-mass energy $√(s)=13 TeV$, this integral gives $C_gg=2137$ [ref] .
Parton distributions for the LHC · Production cross section · 0.86
Cites as background 2 papers
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Authors in [ref] and [ref] have studied general cases for different possible models.
On the Interpretation of a Possible $\sim 750$ GeV Particle Decaying into $\gamma \gamma$ · Introduction · 0.92
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Authors in [ref] and [ref] have studied general cases for different possible models.
Precision tools and models to narrow in on the 750 GeV diphoton resonance · Introduction · 0.92
Discussion
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