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Associated $Z^\prime$ production in the flavorful $U(1)$ scenario for $R_{K^{(*)}}$

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The flavorful $Z'$ boson proposed to explain the $B$-meson anomalies would be discoverable at the 14 TeV proton-proton collider in the dimuon-plus-$b$-jet channel with 5-sigma significance for masses up to 500 GeV with 300 fb$^{-1}$ of…

desk verdict Solid Z' phenomenology with an internal tension: the 5-sigma b-channel projection is for parameter space already excluded by ATLAS dimuon data at 300-500 GeV. read the letter →

arxiv 1908.03031 v2 pith:LGL24755 submitted 2019-08-08 hep-ph

Siddharth Dwivedi , Adam Falkowski , Dilip Kumar Ghosh , Nivedita Ghosh This is my paper · ORCID
classification hep-ph
keywords flavorfulZ'modelB-mesonanomaliesR_KanomalyR_K^*leptonflavoruniversalityassociatedproductiondimuonresonancesearchhigh-luminositycolliderdiscoveryprospects
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the same new particle---a massive neutral vector boson, the flavorful $Z'$, with couplings mainly to bottom quarks, strange quarks, and muons---that can explain the observed deficits in $R_K$ and $R_{K^*}$ should be directly visible in the next runs of the 14 TeV proton-proton collider. It defines the region of coupling space consistent both with the 2019 global fit to $b\to s\mu^+\mu^-$ data and with low-energy constraints from neutrino trident production and $B_s$ mixing. It then simulates two associated-production signatures: $Z'$ radiated off a bottom quark, giving $\mu^+\mu^-$ plus one or two $b$-jets, and $Z'$ radiated off a muon or neutrino, giving three muons plus missing energy. In the first channel, a 5-$\sigma$ discovery is projected for $M_{Z'} \lesssim 500$ GeV with 300 fb$^{-1}$, with benchmark significances of 8.35 (26.4) at $M_{Z'}=200$ GeV and 6.8 (21.5) at 500 GeV for 300 (3000) fb$^{-1}$. If true, this would provide a concrete way to confirm the new-physics interpretation of the $B$-meson anomalies and identify the responsible model.

What carries the argument

The load-bearing relation is the anti-correlation between the $Z'$ couplings to bottom quarks and muons: $g_{bb}g_{\mu\mu}/M_{Z'}^2 = 1/(6.9\,\mathrm{TeV})^2$ at 68% CL from the fit to $b\to s\mu^+\mu^-$ data, together with the neutrino-trident bound $g_{\mu\mu}^2/M_{Z'}^2 \lesssim 1/(330\,\mathrm{GeV})^2$ and the quark-mixing comparison bound $g_{bb}^2/M_{Z'}^2 \lesssim 1/(11.5\,\mathrm{TeV})^2$; these leave a narrow window of allowed couplings for each mass. The collider mechanism is associated production: a $b$-quark line radiates the $Z'$, which decays to $\mu^+\mu^-$, producing the distinctive $\mu^+\mu^- + b$-jet final state; alternatively the $Z'$ is radiated from a muon or neutrino in $W$-boson production, giving $3\mu+\not{E}_T$. The discriminating variables are the high-transverse-momentum muons, the small ratio $R=\not{E}_T/M_{\mu^+\mu^-}$ (which separates the signal from top-pair backgrounds), and the dimuon invariant-mass window $|M_{\mu^+\mu^-}-M_{Z'}|<6\Gamma_{Z'}$.

What would settle it

The decisive test is a direct search in the $\mu^+\mu^-+b$-jet channel at 14 TeV with 300 fb$^{-1}$: with the benchmark couplings $g_{\mu\mu}=0.20$, $g_{bb}=4.2\times10^{-3}$, $M_{Z'}=200$ GeV, the paper reports 0.92 fb of signal and 6.27 fb of background after all selection cuts (before $k$-factors), corresponding to $S=8.35$ at 300 fb$^{-1}$; observing no resonance-like excess in that final state with this sensitivity would refute the central claim. More broadly, the complete absence of a dimuon resonance below about 500 GeV in the full high-luminosity 14 TeV dataset would falsify the model's anomaly-favored parameter space.

Watch

Extended reading notes

Core claim

The central claim is that the flavorful $Z'$ model proposed to explain $R_{K^{(*)}}$ predicts a collider signature with discovery-level significance in the near term. In this model the $Z'$ couples to left-handed $b$ quarks, $s$ quarks, and muons, with $g_{bs}=V_{ts}g_{bb}$; the product $g_{bb}g_{\mu\mu}/M_{Z'}^2$ is fixed by the best-fit new-physics contribution $C_9^\mu=-C_{10}^\mu=-0.53\pm 0.09$, while $g_{\mu\mu}^2/M_{Z'}^2$ and $g_{bb}^2/M_{Z'}^2$ are bounded by neutrino trident production and by comparing $B_s$ mixing with $B\to D^*\ell\nu$ decays. Within this allowed region, the process $pp\to Z'+1b(2b)\to\mu^+\mu^-+1b(2b)$, with cuts on muon transverse momenta, on $R=\not{E}_T/M_{\mu^+\mu^-}<0.2$, and on the dimuon invariant mass around the $Z'$ resonance, yields significances exceeding $5\sigma$ for $M_{Z'}\lesssim 500$ GeV at 300 fb$^{-1}$ and $3\sigma$ sensitivity up to about 1 TeV. The complementary $3\mu+\not{E}_T$ channel, governed solely by $g_{\mu\mu}$, reaches $5\sigma$ only at 3000 fb$^{-1}$ for $M_{Z'}=200$ GeV. Together the two channels cover the low-energy-favored parameter space for $200\lesssim M_{Z'}\lesssim 500$ GeV, and the paper shows that existing dimuon resonance limits already exclude part of that space, with the new channels offering comparable and complementary coverage.

Load-bearing premise

The projected discovery reach rests on the assumption that the $B$-meson anomalies are genuinely caused by this $Z'$ with the coupling pattern used here, in particular that the product of its couplings to $b$ quarks and muons divided by its mass squared equals the 2019 best-fit value; if the anomalies have a different origin, the benchmark couplings and all projected significances change.

Editorial extensions

If this is right

  • With 300 fb$^{-1}$ at 14 TeV, the $\mu^+\mu^-+b$-jet channel is projected to give a $5\sigma$ detection for $M_{Z'}\lesssim 500$ GeV at the couplings preferred by low-energy data.
  • The same channel gives $3\sigma$ sensitivity up to about $M_{Z'}=1$ TeV with 300 fb$^{-1}$, so the absence of a signal there would exclude a large part of the anomaly-favored parameter space.
  • The $\mu^+\mu^-+b$-jet channel and generic dimuon resonance searches cover overlapping parameter regions, so observing both would be strong evidence for the flavorful-$Z'$ interpretation rather than for a generic dilepton resonance.
  • The $3\mu+\not{E}_T$ channel probes the complementary large-$g_{\mu\mu}$ region and, combined with the other searches, could exclude essentially all of the low-energy-favored parameter space for $M_{Z'}\lesssim 500$ GeV.
  • Heavier $Z'$ bosons with $M_{Z'}\gtrsim 1$ TeV would likely remain out of reach at the high-luminosity 14 TeV collider in the parameter region preferred by the $B$-meson anomalies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension is to use the same $\mu^+\mu^-+b$-jet selection to distinguish the flavorful $Z'$ from other $Z'$ models, since the presence of associated bottom quarks directly tags the $b$-quark coupling that the anomaly fit requires.
  • Because the model also couples to the left-handed top-bottom doublet, the analysis could be extended to $Z'$ production off top quarks, which would give a $\mu^+\mu^- + t\bar{t}$-like signature and could extend the mass reach beyond the $b$-jet channel.
  • If a future global fit shifts the central value of $C_9^\mu=-C_{10}^\mu$, the benchmark couplings and therefore the projected significances would rescale roughly as the shift in the product $g_{bb}g_{\mu\mu}$; the same collider cuts would remain the appropriate test.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies LHC signatures of a flavorful Z′ model proposed to address the R_K and R_K* anomalies, with couplings g_bb to left-handed third-generation quarks, g_μμ to left-handed muons, and g_bs = V_ts g_bb. Equation (2.2) fixes the product g_bb g_μμ / M_Z′^2 from the global b→s μμ fit, while neutrino trident and Δm_Bs/CKM constraints leave finite coupling intervals. Using MadGraph5, Pythia 8, and Delphes 3 with LO parton-level events and k-factors, the authors analyze pp→Z′+1b(2b)→μ+μ−+1b(2b) and pp→Z′μ±+MET→3μ+MET, reporting projected significances. They find that a 5σ discovery is possible in the first channel for M_Z′ ≲ 500 GeV at 300 fb−1 and 14 TeV in the parameter region preferred by the anomalies. Section 4 then compares with the ATLAS 139 fb−1 dimuon resonance search and states that for M_Z′ = 300 and 500 GeV the region preferred by the global fit is excluded by the LHC, leaving only a 2σ-allowed chunk of parameter space.

Significance. The study provides a transparent cut-flow analysis, explicit benchmark points, and a useful demonstration that the associated-production channels 2μ+b and 3μ+MET probe complementary coupling regions. The authors are also candid in Section 4 about the tension with current dimuon searches. However, the headline discovery claim is internally inconsistent with that candor: the 5σ curves and benchmarks are computed without imposing the ATLAS dimuon exclusion that the paper itself identifies. If the analysis is revised to present the projection in the currently surviving parameter space, the paper would be a valuable sensitivity study for HL-LHC; as written, the abstract and Section 3.1 overstate the discovery potential. The central methodology is defensible but the main claim needs substantial revision.

major comments (3)
  1. [Abstract; Section 3.1, Eq. (3.4); Section 4, Fig. 13] The abstract and Section 3.1 claim 5σ discovery in the parameter space "preferred by the b→s μμ anomalies and allowed by low-energy constraints," with benchmarks in Eq. (3.4) lying on the central hyperbola of Eq. (2.2). However, Section 4 (Fig. 13) states explicitly that for M_Z′ = 300 and 500 GeV the region preferred by the global fit is excluded at 95% CL by the ATLAS 139 fb−1 dimuon search. Because the significance curves in Fig. 8 are computed with g_bb fixed by Eq. (2.2) along this same band, the discovery claim is made in parameter space that the paper itself shows is excluded. Please recompute the discovery projections with the current dimuon limit imposed, report the significance only in the surviving 2σ-allowed region, and restate the abstract and Section 5 accordingly. If the projection is meant to be hypothetical (i.e., in the absence of current limits), that must be stated clearly and the claim "consistent with all other experimental constraints" must be removed.
  2. [Section 3.1, Eq. (3.3); Tables 2 and 3; Figures 8 and 12] The main significances use the purely statistical formula in Eq. (3.3) and the cut-flow tables list no systematic uncertainties. The dashed curves in Figures 8 and 12 are described only as "including systematics ∼10% in the background estimates," but the text does not explain how the 10% is propagated into the significance or which backgrounds it applies to. Since the paper's central claim is a 5σ discovery, please provide systematics-inclusive significances for at least the benchmark points in Eq. (3.4) and describe the procedure used to obtain the dashed bands.
  3. [Section 3.1 and Section 3.2, k-factors] All signal and background samples are generated at leading order and the NLO corrections are approximated by k-factors taken from other processes, with no uncertainty assigned. In particular, the 1.25 signal k-factor for the 3μ+MET channel is cited to Ref. [70], which reports an ATLAS search for doubly-charged Higgs bosons and does not appear to contain a k-factor for pp→Z′μν. Please justify each k-factor choice for the specific process, or provide a scale/PDF uncertainty estimate, because the projected significances in Eqs. (3.4) and (3.8) depend directly on these factors.
minor comments (4)
  1. [Section 3.1, page 10] The sentence "the discovery potential in this final state is more more pronounced for lower g_μμ" contains a duplicated word "more" and should be corrected.
  2. [Section 3.2, Table 3 caption] The caption reads "after each cut described in the next" and is incomplete; it should say "in the text" or refer to the specific paragraphs describing the cuts.
  3. [Section 3.2, Eq. (3.6)] The invariant-mass veto M_OSD < 75 GeV or M_OSD > 105 GeV is stated without mentioning how events with M_OSD near the Z′ mass are treated when M_Z′ is close to the Z mass; the assumption M_Z′ > M_Z is made in the text but should be stated explicitly at the point where the cut is introduced.
  4. [Section 4, Fig. 13] The figure would be easier to interpret if the 2σ-allowed chunk mentioned in the text were explicitly shaded or outlined in the (g_μμ, M_Z′) plane, since the subsequent discussion of future LHC runs relies on the location of this surviving region.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LHC reach is a Monte Carlo projection evaluated at couplings imported from external low-energy fits, not a fit relabeled as a prediction.

full rationale

The derivation chain starts from the flavorful Z' Lagrangian (Eq. 2.1), adopted from Ref. [37], with g_bb and g_mumu constrained by the external b->s mu mu global fit (Eq. 2.2, Ref. [5]), the neutrino-trident bound (Eq. 2.3), and the CKM-consistency analysis of Ref. [53] (Eq. 2.4). These are imported inputs, not results derived in this paper. The collider analysis computes signal and background cross sections with MadGraph/PYTHIA/Delphes and evaluates significances via Eq. (3.3); the benchmark couplings in Eq. (3.4) are chosen on the central-fit hyperbola of Eq. (2.2). No fitted low-energy parameter is renamed as a collider prediction; the significances are genuine Monte Carlo outputs conditional on those couplings. The authors' self-citations (Refs. [37], [51], [53]) are not load-bearing in a circular sense: they are published, empirically anchored analyses that define the adopted model and constraints, and no uniqueness claim from the authors is invoked to exclude alternatives. The paper itself flags the main external limitation in Section 4, noting that 'the region preferred by the global fit to low-energy data is excluded by the LHC' for M=300-500 GeV; this is a consistency check against ATLAS dimuon data, not a circular step. While this exclusion undercuts the central-fit benchmarks in Eq. (3.4), it does not make the derivation equivalent to its inputs. The reach projections and the exclusion are both functions of the same imported couplings, but that is a conditional sensitivity statement rather than circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central collider-reach claim rests on three model parameters (g_mu_mu, g_bb, M_Z') plus the model Lagrangian and the low-energy constraints that define the allowed parameter space. All of these are taken from earlier fits or chosen as benchmarks; the paper itself contributes the Monte Carlo projection, not a derivation of the parameters.

free parameters (3)
  • g_mu_mu (Z' coupling to left-handed muons) = Table 1 ranges: 0.040-0.61 for M_Z'=200 GeV up to 0.20-3.0 for M_Z'=1000 GeV
    Scanned as a free variable; constrained by the B-anomaly fit Eq. (2.2) and the trident bound Eq. (2.3); directly controls the 3mu channel rate and the Z' decay into muons.
  • g_bb (Z' coupling to left-handed b/t doublet) = Fixed via Eq. (2.2) to the central anomaly-fit value; 99% CL ranges 0.0016-0.017 (200 GeV) to 0.0080-0.087 (1000 GeV)
    Not independently fitted in this paper; set by the B-anomaly relation and constrained by Delta m_Bs via Eq. (2.4). The 2mu+b signal scales as g_bb^2, so the reach claim depends directly on it.
  • M_Z' (Z' mass) = Benchmarks: 200, 300, 500, 750, 1000 GeV
    Chosen by hand as representative masses; the projected significance is a strong function of M_Z', and the paper's central conclusion is mass-dependent.
assumptions (5)
  • domain assumption The flavorful Z' Lagrangian of Eq. (2.1) with couplings only to q_L=(t_L,b_L) and L_L=(nu_mu,mu_L), and no other BSM states at LHC energies.
    Taken from Ref. [37]; the paper explicitly assumes only the Z' is produced at accessible energies (Section 2).
  • domain assumption g_bs = |V_ts| g_bb and sign(g_bb)=sign(g_mu_mu), with |V_ts| ~ 0.04.
    Imposed in Section 2 based on the UV structure of the model; it reduces the parameter space from three couplings to two.
  • domain assumption The global fit C9_mu = -C10_mu = -0.53 +/- 0.09 maps to Eq. (2.2): g_bb g_mu_mu / M_Z'^2 = 1.00 +/- 0.17 / (6.9 TeV)^2.
    Input from Ref. [5]; defines the band of parameter space that the collider study probes.
  • domain assumption The trident and Delta m_Bs constraints of Eqs. (2.3)-(2.4), including the CKM-comparison analysis of Ref. [53], correctly characterize the low-energy bounds.
    The paper argues that comparing Delta m_Bs with B->D* l nu is the consistent way to bound g_bb; the reach projections assume this treatment is correct.
  • standard math The simulation chain (NNPDF23LO1 PDFs, Pythia8, Delphes3, CMS b-tag functions) approximates the LHC detector response and background rates.
    Standard tooling in Section 3; the paper validates only the WZ background against CMS and otherwise relies on customary fast-simulation performance.
invented entities (1)
  • Z' boson independent evidence
    purpose: Mediator that generates the b->s mu mu four-fermion operator and explains R_K and R_K*; the paper computes LHC signatures for it.
    The Z' is inherited from Ref. [37], not introduced here. It has falsifiable handles: predicted dimuon resonances and associated-production cross sections that ATLAS and CMS can test.

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Cite this review

Pith. "Pith review of Associated $Z^\prime$ production in the flavorful $U(1)$ scenario for $R_{K^{(*)}}$." pith.science (2026). https://pith.science/paper/LGL24755

@misc{pith2026190803031,
  author       = {Pith},
  title        = {Pith review of: Associated $Z^\prime$ production in the flavorful $U(1)$ scenario for $R_K^(*)$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LGL24755}},
  note         = {Machine review of arXiv:1908.03031}
}
abstract

The flavorful $Z^\prime$ model with its couplings restricted to the left-handed second generation leptons and third generation quarks can potentially resolve the observed anomalies in $R_K$ and $R_{K^*}$. After examining the current limits on this model from various low-energy processes, we probe this scenario at 14 TeV high-luminosity run of the LHC using two complementary channels: one governed by the coupling of $Z'$ to $b$-quarks and the other to muons. We also discuss the implications of the latest LHC high mass resonance searches in the dimuon channel on the model parameter space of our interest.

Figures

Figures reproduced from arXiv: 1908.03031 by the authors.

Figure 1
Figure 1. The parameter space in the (gµµ, gbb) plane for MZ0 = 200 GeV preferred at 68% CL by the b → s`+` − anomalies (parabolic green band). We also show the regions excluded at 99% CL. by trident neutrino production (vertical orange band), and by the analysis Ref. [53] comparing the ∆mBs and B → D∗ `ν probes of the CKM elements (horizontal grey band). flavor observables (see e.g. [52]). These fits always include the Bs me… view at source ↗
Figure 2
Figure 2. Leading Feynman diagrams for the Z 0 + 1b(2b) final state. the detector level simulation using Delphes3 [59], with the jets reconstructed using the anti-kT jet algorithm [60]. In our analysis we ignore Z 0 production proceeding via the Z 0 -b-s coupling, which is suppressed due to the smallness of that coupling in our model, gbs/gbb ∼ |Vts| = O(10−2 ). 3.1 pp → Z 0 + 1b(2b) → µ +µ − + 1b(2b) channel In this channel … view at source ↗
Figure 3
Figure 3. Leading Feynman diagrams for the Z 0µ ± ✚E✚T final state. of each signal cross-section curve are due to the finite allowed range of the couplings gbb and gµµ as shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The signal cross-section as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Normalized transverse momentum (pT ) distributions of the leading (left) and sub-leading (right) muons for the signal (MZ0 = 200 and 500 GeV) and relevant SM backgrounds. The values of gµµ and gbb are 0.20(0.48) and 4.2 × 10−3 (1.10 × 10−2 ) for MZ0 = 200(500) GeV, res…
Figure 6
Figure 6. Figure 6: Normalized R = ET Mµ+µ− distribution for signal and backgrounds. where ΓZ0 is the width of the Z 0 resonance. This cut is instrumental in further reducing the µ +µ − + jets background as for these process the invariant mass of the muon pair peaks around the Z boson mas…
Figure 7
Figure 7. Figure 7: Normalized invariant mass distributions of the muon-pair for signal and backgrounds. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Significance vs. gµµ for MZ0 = 200(8a), 300(8b), 500(8c), 750(8d) and 1000(8e) GeV for µ +µ − + 1b(2b) channel at √ s = 14 TeV. The dashed lines represent the error band in Significance curves after including systematics ∼ 10% in the background estimates. The dark shad…
Figure 9
Figure 9. Figure 9: Signal cross-section at √ s = 14 TeV for 3µ + ET channel as a function of gµµ for MZ0 = 200, 300 and 500 GeV. To optimize our signal versus background discrimination, we demand our final state to be comprised of exactly three muons with two muons of the same sign and t…
Figure 10
Figure 10. Figure 10: Normalized transverse momentum (pT ) distributions of the leading (10a), sub-leading (10b) and sub-sub-leading (10c) muons for the 3µ + ET final state. Signal distributions are for MZ0 = 200 GeV, gµµ = 0.20, gbb = 4.2×10−3 , and for MZ0 = 500 GeV, gµµ = 0.48, gbb = 1.…
Figure 11
Figure 11. Figure 11: Normalized missing energy (ET ) distribution for the 3µ + ET final state. We show the distribution for the signal for MZ0 = 200 GeV, gµµ = 0.20, gbb = 4.2×10−3 , and for MZ0 = 500 GeV, gµµ = 0.48, gbb = 1.1 × 10−2 . We also show the analogous distributions for the W Z…
Figure 12
Figure 12. Figure 12: Significance in the 3µ + ET channel as a function of gµµ for MZ0 = 200(12a), 300(12b) and 500(12c) GeV for √ s = 14 TeV. The dashed lines represent the error band for the significance curves after including systematics ∼ 10% in the background estimates. The dark shade…
Figure 13
Figure 13. Figure 13: The parameter range of our model excluded at 95% CL by the ATLAS dimuon resonance [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

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