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arxiv: 1907.05158 · v1 · pith:7NRFMI73new · submitted 2019-07-11 · ✦ hep-ph

Flavour anomalies and (fundamental) partial compositeness

Peter Stangl This is my paper

Pith reviewed 2026-05-24 23:09 UTC · model grok-4.3

classification ✦ hep-ph
keywords flavour anomaliespartial compositenessB-meson decayslepton flavour universalitycomposite Higgsnaturalness problem
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The pith

Partial compositeness explains the deviations from lepton flavour universality in rare B-meson decays.

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

The paper shows that partial compositeness, in which Standard Model fermions mix with composite states, produces lepton flavour universality violation that matches the pattern of anomalies seen in rare B decays. A simple model based on this mechanism fits the observed deviations. The minimal fundamental partial compositeness model is then examined in detail, demonstrating that the same structure can simultaneously address the naturalness problem of the Standard Model. Updated results incorporate recent measurements of the relevant decay observables. This approach ties the flavour anomalies directly to the dynamics of a composite Higgs sector.

Core claim

Partial compositeness generically produces lepton flavour universality violation, enabling both a simple model and the minimal fundamental partial compositeness model to account for the anomalies in rare B-meson decays while the latter also solves the naturalness problem of the Standard Model.

What carries the argument

partial compositeness, the mixing of elementary fermions with composite operators that induces flavour-dependent couplings and lepton flavour universality violation.

If this is right

  • The minimal fundamental partial compositeness model explains both the flavour anomalies and the naturalness problem.
  • Flavour observables in the model must satisfy all existing constraints beyond the B anomalies.
  • Updated experimental inputs on rare B decays refine the allowed parameter space of the model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Predictions for other rare decays or electroweak observables could provide additional tests of the same mixing structure.
  • The approach suggests examining whether partial compositeness patterns appear in related flavour processes at current or future experiments.
  • Collider signatures of the composite states could be correlated with the B decay fits to strengthen or refute the explanation.

Load-bearing premise

The partial compositeness structure generates the precise pattern of deviations seen in the B decay data while remaining consistent with all other flavour and electroweak constraints.

What would settle it

New measurements of B decay ratios such as R_K or R_K* falling outside the ranges predicted by the minimal fundamental partial compositeness model.

Figures

Figures reproduced from arXiv: 1907.05158 by Peter Stangl.

Figure 1
Figure 1. Figure 1: Illustration of the Higgs coupling to composite fermions and the mixing between ele [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Tree-level contributions to b → s ` +` − (a) and Bs mixing (b). chosen to be flavour universal and the complete flavour structure is then contained in the mixing terms. Due to the mixing terms, the mass eigenstates in the model are actually superpositions of elementary and composite fields. The light SM-like mass eigenstates are mainly elementary, but still partially composite. The size of the mixing terms… view at source ↗
Figure 3
Figure 3. Figure 3: Contours of constant C µ 9 −C µ 10 when assuming a 10% shift in ∆Ms (green lines) and contours of constant relative shift in the Fermi constant δGF/GF (red lines). The shaded areas correspond to the 1σ (dark green) and 2σ (light green) regions around the best-fit value of a global fit [30] in a scenario with a NP contribution to C µ 9 = −C µ 10. • Electroweak precision tests (EWPTs): The presence of a non-… view at source ↗
Figure 4
Figure 4. Figure 4: Predictions for LFU observables RD(∗). Gray points are excluded by LEP data. Blue points are allowed by all constraints. The plot also shows the 1-5σ contours of the experimental world combination as presented at Moriond 2019 [18]. – A numerical minimization of χ 2 mass,CKM is performed for 100 k random starting points. – The regions around the local minima of χ 2 mass,CKM are sampled using Markov Chains f… view at source ↗
Figure 5
Figure 5. Figure 5: Left: Predictions for LFU observables RK(∗) in the MFPC model for points allowed by all constraints. Right: Generic predictions in several NP scenarios. Unprimed Wilson coefficients are varied between −1.5 and 1.5; primed coefficients are varied between −0.15 and 0.15. RD∗ would require a huge degree of compositeness of the τ lepton, which is excluded by the LEP measurements of Z partial widths. However, t… view at source ↗
read the original abstract

Several measurements of B-meson decay observables show deviations from Standard Model (SM) predictions, some of them hinting at violation of lepton flavour universality (LFU). I discusses how the anomalies in rare B decays can be explained by partial compositeness. Partial compositeness is a key ingredient of models with a composite Higgs boson and generically leads to violation of LFU. After presenting a simple model with partial compositeness that is able to explain the anomalies in rare B decays, the flavour phenomenology of a minimal UV completion of a composite Higgs model with partial compositeness is discussed: the minimal fundamental partial compositeness (MFPC) model. A virtue of the MFPC model is its capability of serving both as a solution to the naturalness problem of the SM and as an explanation of the flavour anomalies in rare B-meson decays. In view of recent new measurements, the results on which this proceedings contribution is based are updated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that partial compositeness, a generic feature of composite-Higgs scenarios, produces lepton-flavour-universality violation that can account for the observed deviations in rare B-meson decays (R_K, R_K*, etc.). It first constructs a simple partial-compositeness model that reproduces the anomalies, then examines the flavour phenomenology of its minimal UV completion—the minimal fundamental partial compositeness (MFPC) model—asserting that the same framework simultaneously solves the SM naturalness problem and explains the flavour data. Results are updated with the most recent measurements.

Significance. A concrete demonstration that the MFPC mixing angles and compositeness scale simultaneously fit the B-decay anomalies while remaining consistent with all other flavour and electroweak bounds would constitute a non-trivial unification of the hierarchy problem and the flavour anomalies, elevating the phenomenological interest of fundamental partial-compositeness constructions.

major comments (2)
  1. [section presenting the simple model] The central assertion that the simple partial-compositeness model 'is able to explain the anomalies' (abstract and dedicated section) is load-bearing; the manuscript must exhibit at least one explicit parameter point (or scan) in which the generated four-fermion operators reproduce the measured R_K and R_K* central values within 1–2 σ while the same parameters keep ΔF=2 observables, B_s→μμ, and electroweak precision parameters inside current limits. Generic statements that partial compositeness 'leads to violation of LFU' are insufficient.
  2. [MFPC model section] In the MFPC phenomenology discussion, the claim that the model serves 'both as a solution to the naturalness problem … and as an explanation of the flavour anomalies' requires an explicit check that the minimal spectrum and mixing angles needed for the anomalies do not push any other observable outside experimental bounds; without such a demonstration the dual-purpose virtue remains unestablished.
minor comments (2)
  1. [abstract] The abstract contains the grammatical error 'I discusses'; correct to 'It discusses'.
  2. [model definitions] Notation for the partial-compositeness mixing angles and the compositeness scale should be defined once at first use and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed report and the opportunity to clarify the manuscript. We address the two major comments below. Where the comments correctly identify the need for more explicit demonstrations, we will revise the text accordingly.

read point-by-point responses

  1. Referee: [section presenting the simple model] The central assertion that the simple partial-compositeness model 'is able to explain the anomalies' (abstract and dedicated section) is load-bearing; the manuscript must exhibit at least one explicit parameter point (or scan) in which the generated four-fermion operators reproduce the measured R_K and R_K* central values within 1–2 σ while the same parameters keep ΔF=2 observables, B_s→μμ, and electroweak precision parameters inside current limits. Generic statements that partial compositeness 'leads to violation of LFU' are insufficient.

    Authors: We agree that an explicit benchmark point strengthens the claim. The simple model section will be expanded with one concrete parameter choice (including the relevant mixing angles and compositeness scale) that reproduces the central values of R_K and R_K* within 1–2σ while satisfying the listed flavour and electroweak constraints. The revised manuscript will include this point together with the resulting Wilson coefficients. revision: yes

  2. Referee: [MFPC model section] In the MFPC phenomenology discussion, the claim that the model serves 'both as a solution to the naturalness problem … and as an explanation of the flavour anomalies' requires an explicit check that the minimal spectrum and mixing angles needed for the anomalies do not push any other observable outside experimental bounds; without such a demonstration the dual-purpose virtue remains unestablished.

    Authors: We accept that the dual-purpose statement requires a more explicit verification. In the MFPC section we will add a short paragraph (or table) showing that the mixing angles and compositeness scale chosen to fit the anomalies remain compatible with the most relevant ΔF=2, B_s→μμ, and electroweak precision observables. If the existing parameter space already satisfies the bounds, this will be stated with the relevant references; otherwise the scan range will be restricted accordingly. revision: yes

Circularity Check

0 steps flagged

No circularity: model construction and phenomenology are independent of fitted inputs

full rationale

The paper constructs a simple partial-compositeness model and the MFPC UV completion, then discusses how their parameters can accommodate the observed B-decay deviations while respecting other bounds. No step reduces a claimed prediction to a fit by definition, nor does any load-bearing premise rest solely on self-citation chains or imported uniqueness theorems. The central virtue claim (simultaneous naturalness solution plus anomaly explanation) is presented as a consequence of the model's structure and parameter choices, not as a tautology. The derivation chain is therefore self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review; the ledger is populated from statements that partial compositeness 'generically leads to' LFU violation and that the MFPC model simultaneously solves naturalness and anomalies. No explicit free parameters, axioms, or invented entities are enumerated in the abstract.

axioms (1)
  • domain assumption Partial compositeness generically produces lepton flavour universality violation in B decays
    Stated directly in the abstract as a key property used to explain the anomalies.
invented entities (1)
  • Minimal fundamental partial compositeness (MFPC) model no independent evidence
    purpose: Simultaneous solution to naturalness and B-flavour anomalies
    Introduced in the abstract as the UV completion under discussion; no independent evidence supplied.

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discussion (0)

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Reference graph

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