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Local Baryon Number at the LHC

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Pith's one-line read The minimal theory in which baryon number is a local gauge symmetry predicts a long-lived charged fermion, $\rho^-$, that decays after about 5.6 cm and would show up as kinked tracks at the LHC, with current searches excluding masses…

desk verdict The kinked-track signature at the center of this paper does not survive a basic kinematics check; the decay pion is far too soft to be reconstructed, so the real signature is a disappearing track. The rest of the phenomenological analysis is solid and worth engaging. read the letter →

arxiv 2505.06341 v2 pith:3IU7WP3L submitted 2025-05-09 hep-ph hep-exhep-th

classification hep-phhep-exhep-th
keywords localbaryonnumberU(1)Bgaugesymmetryanomalycancellationlong-livedchargedfermionkinkedtracksleptophobicbosondarkmatterLHCphenomenology
topics Dark Matter
open problems Dark Matter
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

This paper argues that the simplest extension in which baryon number is a real gauge symmetry, rather than an accidental property of the Standard Model, leaves a concrete and testable imprint at the Large Hadron Collider. Adding only four new fermions to keep the theory mathematically consistent predicts that one of them, $\rho^-$, is long-lived: it travels about 5.6 cm before decaying mostly to a neutral partner and a soft pion, so its production would show up as 'kinked' charged tracks plus missing energy. The authors show that current LHC data exclude only part of the possible masses ($\rho^-$ below roughly 650 GeV, and the other charged fermion below a few hundred GeV in most decay scenarios), leaving a region the High-Luminosity LHC could probe. They also predict a rare decay of the 125 GeV Higgs into a photon and the new $Z_B$ boson, with a branching ratio near $10^{-6}$.

What carries the argument

The machine that drives the paper's most distinctive prediction is the anomaly-cancelling fermion sector: a chiral quartet that forces the mass of the charged $\rho^-$ to be split from the neutral $\rho^0$ by a one-loop effect of about 166 MeV. Because the splitting is so small, the charged state cannot decay to anything heavy; it goes almost exclusively to $\rho^0\pi^-$ with a width set by the pion decay constant and the splitting, producing a decay length $c\tau\approx 5.6$ cm and the 'kinked track' topology at the LHC. The paper also uses the fact that the new gauge boson $Z_B$ is leptophobic, coupling only to quarks, to set limits through Standard Model measurements, and a one-loop top-quark diagram to generate the effective $h\gamma Z_B$ coupling.

What would settle it

A dedicated search in existing LHC data for events with a charged track that kinks into a soft pion plus missing transverse momentum would settle the central prediction: if none are seen at the rate predicted for $\rho^-$ masses above 650 GeV, the long-lived-fermion claim is excluded. Alternatively, a direct computation of the $\rho^-$-$\rho^0$ mass splitting that moves it away from 166 MeV would change the decay length by orders of magnitude and invalidate the kinked-track signature.

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Extended reading notes

Core claim

The central claim is that the minimal local-baryon-number theory, a new $U(1)_B$ gauge symmetry spontaneously broken near the TeV scale with exactly four new fermions cancelling all anomalies, predicts new fermions light enough for LHC production. The $\rho^-$ fermion, as the charged member of an $SU(2)_L$ triplet, has its mass split from the neutral $\rho^0$ by about 166 MeV from one-loop corrections; this makes it long-lived, with $c\tau\approx 5.6$ cm, and it decays about 97% of the time to $\rho^0\pi^-$. Production of $\rho^+\rho^-$ and $\rho^0\rho^\pm$ therefore yields either two or one charged tracks that visibly kink when the soft pion emerges, together with missing energy from the neutral $\rho^0$; the same minimal spectrum contains a dark matter candidate. Reinterpreting published disappearing-chargino searches sets a lower bound $M_{\rho^-}>650$ GeV, while global comparisons of the model with Standard Model measurements exclude $\Psi^-$ masses below a few hundred GeV unless that fermion decays mostly to tau leptons. The same framework allows the 125 GeV Higgs to decay through a top-quark loop to $\gamma Z_B$ with branching ratio near $10^{-6}$ when $M_{Z_B}<125$ GeV.

Load-bearing premise

The kinked-track prediction rests on the assumed one-loop mass splitting of about 166 MeV between the charged and neutral components of the $\rho$ triplet, which fixes the 5.6 cm decay length, and on borrowing the 650 GeV bound from disappearing-chargino searches rather than a dedicated simulation of this model.

Editorial extensions

If this is right

  • Existing LHC data already force $M_{\rho^-}$ above about 650 GeV, so the discovery region for kinked tracks starts there and extends up to the TeV scale; a dedicated search would either confirm the bound or find the signal.
  • Observation of $\rho^+\rho^-\to \rho^0\rho^0\pi^+\pi^-$ would measure both the 5.6 cm decay length and the roughly 97% branching ratio to $\rho^0\pi^-$, giving a direct handle on the one-loop mass splitting.
  • The other charged fermion, $\Psi^-$, is excluded below roughly 350 to 480 GeV, depending on the $Z_B$ mass, when it decays to electrons or muons, but remains largely unconstrained when it decays to taus; that tau-dominated region is the main remaining target.
  • A $Z_B$ with mass near 360 GeV and gauge coupling around 0.25 can produce a top-pair cross-section excess near threshold at the level of about 9 pb, although the paper stresses that a full acceptance study is needed before claiming an explanation of the reported excess.
  • The rare decay $h\to \gamma Z_B$, at branching ratio near $10^{-6}$, would give roughly 146 events in a 3 ab$^{-1}$ HL-LHC dataset, but the QCD background makes it very hard to observe.

Reading between the lines

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

  • A dedicated kinked-track search with soft-pion identification, which the paper does not carry out, would determine whether the 650 GeV bound really applies to $\rho^-$ or is an artifact of borrowing wino limits.
  • The same 166 MeV mass splitting that sets the decay length also controls $\rho^+$-$\rho^0$ coannihilation in the early universe; computing the resulting relic density could tie the collider signature to the dark matter abundance, a connection the paper leaves implicit.
  • If $h\to \gamma Z_B$ is ever observed, the photon-plus-$Z_B$ invariant mass would pin down $M_{Z_B}$ precisely, turning the rare decay into a direct measurement of the new gauge sector rather than just an existence proof.
  • A vector $Z_B$ explanation of the top-threshold excess can be distinguished from the pseudoscalar bound-state hypothesis by measuring top-quark spin correlations and angular distributions, since the two possibilities have opposite parity.
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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 / 5 minor

Summary. The paper studies the collider phenomenology of a minimal SU(3)_C x SU(2)_L x U(1)_Y x U(1)_B theory in which baryon number is promoted to a local gauge symmetry and anomaly cancellation requires four new fermions. It computes ZB production and constraints using Contur, discusses the production and decay of the new fermions, and identifies two classes of signatures: multi-lepton events from Psi^+- decays, and long-lived charged rho^- decays that the authors claim produce 'kinked' tracks. It also computes the one-loop decay h -> gamma ZB and comments on a CMS top-pair threshold excess. The main quantitative claims are that current LHC data exclude M_rho^- below about 650 GeV, that Psi masses below a few hundred GeV are excluded in many leptonic channels, and that BR(h -> gamma ZB) is around 10^-6 when kinematically allowed, making the decay challenging but not impossible at the HL-LHC.

Significance. If the central signature claims were fully established, this would be a valuable paper: the model is minimal and UV-complete, the dark matter candidate is tied to anomaly cancellation, and the phenomenology is developed with modern tools (FeynRules/UFO, HERWIG, RIVET, Contur, Spey, Package-X). The h -> gamma ZB width is presented as a parameter-free one-loop prediction, and the ZB constraints use external ATLAS/CMS data in a reproducible way. The multi-lepton exclusion grids and the ZB coupling limits are useful additions to the literature. However, the most distinctive novelty, the 'kinked-track' signature, is currently not backed by a detector-level study, and the derived mass bound for rho^- relies on an unchecked reinterpretation of wino searches. With those points addressed, the paper would be a solid phenomenological contribution.

major comments (3)
  1. [Sec. 4, Eq. (13)-(16) and Fig. 1] The claim that rho^- -> rho^0 pi^- produces a visible 'kink' is not supported by kinematics. With Delta M = 166 MeV and m_pi = 140 MeV, the pion rest-frame momentum is p* ~ 90 MeV, and for a heavy rho^- with a mild boost the lab pT is bounded by approximately p* + (E*/M) pT_rho ~ 100 MeV for typical events at M_rho ~ 700 GeV. This is far below the standard LHC tracking threshold of about 0.5 GeV, and such a pion will stop in detector material before reaching the hadronic calorimeter. The depiction in Fig. 1 of the pion stopping in the hadronic calorimeter is therefore misleading. The actual observable signature is a disappearing charged track plus missing energy, not a resolvable kink. The paper should either perform a dedicated simulation with realistic track-reconstruction thresholds to quantify how often the soft pion can be seen, or remove the 'kinked-track' claim from the abstract and Sec. 4.
  2. [Sec. 4 and Fig. 5] The lower bound M_rho^- > 650 GeV is imported from ATLAS/CMS disappearing-chargino searches without a dedicated reinterpretation. The rho^- differs from a wino chargino in its production mechanism, its decay length, and the fate of the soft pion. If the soft pion is reconstructed, the event would fail a disappearing-track selection; if it is not reconstructed, the acceptance and trigger efficiencies still need to be mapped onto the rho^- production kinematics, which are Drell-Yan-like rather than electroweak-wino-like. The paper cites the experimental searches, but the simple statement in Sec. 4 and the dashed line in Fig. 5 do not establish the bound to the claimed precision. A fast or full detector simulation for the rho^- signal is needed, or the bound should be presented as approximate with the required caveats.
  3. [Sec. 2, Eq. (3), and Sec. 4] The long-lived rho^- and the associated kinked-track/disappearing-track signature depend on the dimension-five operators in Eq. (3) being negligible, yet these operators are allowed by the gauge symmetry. The paper itself states in Sec. 4 that 'this prediction could change if the higher-dimensional operators in Eq. (3) are allowed,' but it does not quantify the suppression scale or the resulting lifetimes. Since the spontaneous-breaking scenario with v_phi = 0 does not forbid these operators, the long-lived rho^- is not a generic prediction of the minimal model but rather a benchmark assumption. The authors should either demonstrate a natural mechanism that suppresses the operators, or explicitly frame the kinked-track and mass-bound results as conditional on that assumption.
minor comments (5)
  1. [Throughout] There are several typos and grammatical slips: 'contraints' in the abstract, 'sensivity' in Fig. 7, 'pararmeter' and 'additonal' in Sec. 6. These should be corrected in a revised version.
  2. [Sec. 3 and Fig. 6] The leading-order cross sections in Fig. 6 and Fig. 4 are shown without scale or PDF uncertainties, and the text does not state the factorization/renormalization scale choice. A sentence specifying the uncertainty treatment would help the reader judge the ZB sensitivity claims and the t-tbar excess discussion.
  3. [Sec. 5 B and Appendix B] The text should explicitly state that the coefficient A in Eq. (18) is the quantity defined in Eq. (B2), and it would be useful to include a numerical check reproducing the BR ~ 10^-6 value used in Eq. (19). The current presentation requires the reader to infer the connection between the width formula and the Appendix.
  4. [Sec. 3] The statement that a fit gives a maximum pp -> ZB -> t-tbar cross section of 9.2 pb at 95% CL using Spey is not described in enough detail. It would be helpful to state which measurement drives the limit and how the CLs value is computed.
  5. [Sec. 4] The mass splitting Delta M ~ 166 MeV is imported from Refs. [37,38] and is the key input for the decay length. Since the rho is an SU(2)_L triplet, the value is plausible, but the paper should verify explicitly that the U(1)_B and other interactions do not modify the splitting at a level that changes c tau.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central predictions are computed from the stated model Lagrangian with externally sourced one-loop quantities and are checked against independent LHC measurements.

full rationale

The paper's derivation chain is self-contained relative to its stated inputs. The anomalous fermion content is taken as the model definition from the authors' earlier construction (Ref. [10]), and the dark-matter/leptophobic-boson study in Ref. [11] provides boundary conditions for the present scans, but neither is used as evidence for the new quantitative claims. The long-lived rho- decay length follows from the externally calculated one-loop mass splitting Delta M about 166 MeV [37,38] inserted into standard two-body and leptonic width formulas (Eqs. 12-16); no fitted LHC quantity is renamed as a prediction. The M_rho- > 650 GeV exclusion is imported from ATLAS/CMS disappearing-chargino and heavy-charged-particle searches [39,40,42,43], i.e., from independent measurements, and the h -> gamma Z_B width is a parameter-free one-loop expression (Eqs. B1-B4) computed with Package-X. The Contur-based Z_B limits use external ATLAS and CMS standard-model measurements. Self-citations appear (Refs [10,11,12]) but they define the model and earlier scan framework rather than supplying the target results; the paper also explicitly caveats that the rho- long-lived prediction is altered by higher-dimensional operators in Eq. (3). Any concern about the observability of the soft-pion 'kink' is a detector-physics correctness issue rather than a circular reduction, so it does not affect this circularity score.

Assumptions & free parameters 8 free parameters · 6 assumptions · 6 invented entities

The paper's predictions rest on the existence of the U(1)_B gauge symmetry, the four-anomaly-fermion set, the scalar sector, and the v_phi = 0 DM scenario. None of these is independently derived here; they are imported from Refs [10,11]. The main new physics output is the set of LHC signatures and constraints derived from those inputs.

free parameters (8)
  • g_B = 0.25 (benchmark), 1e-6 (decoupled), constrained by Contur
    The U(1)_B gauge coupling sets ZB production, rho/Psi production, and h->gamma ZB rate; scans use 0.25 or 1e-6.
  • M_ZB = 360 GeV, 1 TeV, 3 TeV
    Chooses the ZB mass, either decoupled or motivated by ttbar threshold; affects fermion pair production near threshold.
  • M_Psi = 300, 400 GeV and scans up to 600 GeV
    The charged fermion mass is a free input from lambda_Psi vS; exclusions are presented as a function of it.
  • M_rho- = 700, 800 GeV in benchmarks; lower limit 650 GeV
    Mass of long-lived charged fermion from Yukawa coupling; production and decay kinematics depend on it.
  • M_chi = 100, 200, 500 GeV in figures
    Dark matter candidate mass from lambda_chi vS; affects ZB decay and exclusion limits.
  • M_phi = 50, 100 GeV in scans
    Scalar mass affects Psi decay kinematics; taken as benchmark.
  • sin_theta_B = 0.01
    Higgs mixing angle used for hB branching ratios; not scanned in this paper.
  • BR(Psi -> e/mu/tau phi) = scanned from 0 to 1
    Yukawa couplings lambda_i^e are free; the paper scans all branching ratio combinations and uses Contur to exclude regions.
assumptions (6)
  • domain assumption The U(1)_B gauge anomaly can be cancelled by exactly the four fermion representations listed in Sec. 2.
    Adopted from Ref [10] as the starting point; not re-derived here.
  • domain assumption The scalar sector contains S and phi with charges (1,1,0,3/2) and (1,1,0,3/4), and v_phi = 0 so the Z2 symmetry keeps a dark matter candidate.
    The v_phi = 0 scenario is chosen because the alternative has no DM candidate.
  • domain assumption Higher-dimensional operators in Eq. (3) are suppressed sufficiently that only one DM candidate remains.
    Needed so that rho0 and chi do not both contribute to missing energy in a way that changes the signatures.
  • domain assumption The rho- mass splitting Delta M about 166 MeV is the one-loop electroweak splitting of a wino-like triplet, taken from Refs [37,38].
    This value sets the decay length c tau about 5.6 cm, the basis of the kinked-track signature.
  • domain assumption The top quark dominates the h gamma ZB one-loop amplitude; only the top loop is included in Appendix B.
    Other SM fermion loops are neglected, which is standard but not explicitly justified in the text.
  • domain assumption Contur's reinterpretation of published ATLAS/CMS distributions is valid for the signals and uncertainties.
    The exclusions depend on this global re-interpretation framework and on the model being implemented correctly in the UFO files.
invented entities (6)
  • ZB gauge boson independent evidence
    purpose: mediator of local baryon number
    Its mass and coupling are constrained by dijet, dilepton, gamma+jet, ttbar, and missing-energy measurements via Contur, so it has a falsifiable handle.
  • hB (Cucuyo Higgs) / S scalar independent evidence
    purpose: breaks U(1)_B, gives ZB and fermion masses
    Ref [11] discusses its production and mass bounds; here diphoton branching ratios are computed.
  • chi dark matter fermion independent evidence
    purpose: neutral Majorana dark matter candidate
    Stability from Z2; missing-energy and gamma-line searches (Ref [12]) can test it.
  • rho- and rho0 independent evidence
    purpose: anomaly cancellation and kinked-track signatures
    Long-lived charged track searches (ATLAS/CMS) bound M_rho- > 650 GeV.
  • Psi- charged fermion independent evidence
    purpose: anomaly cancellation and multi-lepton signatures
    Dilepton, WW, and ditau measurements exclude parts of its mass/flavor plane.
  • phi scalar independent evidence
    purpose: allows Psi decays to charged leptons plus missing energy
    Neutral long-lived scalar contributes to missing-energy signatures and is constrained by inclusive MET measurements.

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Cite this review

Pith. "Pith review of Local Baryon Number at the LHC." pith.science (2026). https://pith.science/paper/3IU7WP3L

@misc{pith2026250506341,
  author       = {Pith},
  title        = {Pith review of: Local Baryon Number at the LHC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3IU7WP3L}},
  note         = {Machine review of arXiv:2505.06341}
}
abstract

The minimal theory in which baryon number is spontaneously broken at the low scale predicts new fermions, one of which is a dark matter candidate, from gauge anomaly cancellation. We discuss the production mechanisms and decays of these new fermions, which include channels with multi-leptons, and channels with long-lived charged fermions that can give rise to exotic signatures with 'kinked' tracks at the Large Hadron Collider. We evaluate the contraints on the theory from current LHC searches and measurements, and briefly comment on the excess in top pair production at threshold recently reported by CMS. We also discuss predictions for the $h \to \gamma Z_B$ decay, where $h$ is the SM-like Higgs and $Z_B$ is the new gauge boson associated with baryon number.

Figures

Figures reproduced from arXiv: 2505.06341 by the authors.

Figure 1
Figure 1. FIG. 1: Schematics of signatures from the production and decays of (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Branching ratios of the leptophobic gauge boson ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Exclusion limits in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Extra contribution to the production cross section of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Allowed parameter space for a charged long-lived particle (LLP). The red shaded region is [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Leading order Drell-Yan production cross sections of the new fermions at [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: (Left) Exclusion for each point in the grid of branching ratios, with interpolated excluded contours [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: BSM+SM vs SM only hypotheses for various distributions providing exclusion at parameter points [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Exclusion contour in the plane of the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: Branching ratios for [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Branching ratio for [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]

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Forward citations

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Reference graph

Works this paper leans on

71 extracted references · 14 canonical work pages · cited by 1 Pith paper

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    Local Baryon Number at the LHC

    INTRODUCTION After the discovery of the Brout-Englert-Higgs boson at the Large Hadron Collider (LHC) [1– 3], the Standard Model (SM) of Particle Physics stands as one of the most successful ever theo- ries in describing nature. The SM precisely explains how quarks and leptons interact via the electromagnetic, weak, and strong gauge forces. In this framewo...

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    MINIMAL THEORY FOR BARYON NUMBER In this theory, the Abelian global symmetry associated with baryon number in the SM is promoted to a local gauge symmetry and the theory is based on the gauge group [6–10]: SU (3)C⊗SU (2)L⊗U(1)Y⊗U(1)B. This implies an additional gauge boson,ZB, associated with theU(1)B symmetry. This boson must be given mass by spontaneous...

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