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arxiv: 2606.03510 · v1 · pith:FN7PJKCQnew · submitted 2026-06-02 · ✦ hep-ex

Analysis of the C\!P structure of the Yukawa coupling between the Higgs boson and tau leptons in proton-proton collisions at sqrt{s} = 13.6 TeV

CMS Collaboration This is my paper

Pith reviewed 2026-06-28 07:54 UTC · model grok-4.3

classification ✦ hep-ex
keywords Higgs bosontau leptonsCP mixing angleYukawa couplingproton-proton collisionsCMS experimentangular correlations
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The pith

CMS measures the CP mixing angle of the Higgs-tau Yukawa coupling as 7 ± 16 degrees in combined data.

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

The paper measures the charge-parity structure of the Yukawa coupling between the Higgs boson and tau leptons in proton-proton collisions at 13.6 TeV. Angular correlations in the decay products of taus from Higgs decays are used to constrain an effective mixing angle that describes any admixture of scalar and pseudoscalar couplings. The new dataset alone yields a value consistent with the Standard Model expectation of zero mixing, and the combination with earlier 13 TeV data produces a tighter constraint that remains consistent with the Standard Model. This approach directly tests whether the Higgs interaction with taus respects CP symmetry.

Core claim

The analysis determines the CP mixing angle α^{H au au} to be (36^{+33}_{-30})° from 62.4 fb^{-1} of 13.6 TeV data, compared with an expected value of (0 ± 19)° under the Standard Model. When combined with the previous CMS measurement from 138 fb^{-1} at 13 TeV, the mixing angle is (7 ± 16)°, with an expected value of (0 ± 14)°.

What carries the argument

The effective CP mixing angle α^{H au au} that parameterizes the admixture of scalar and pseudoscalar couplings in the Higgs-tau Yukawa interaction, extracted by fitting angular correlations between tau decay products.

If this is right

  • The combined uncertainty on the mixing angle reaches ±16°.
  • The result remains consistent with a pure scalar coupling under the Standard Model.
  • The measurement sets the current best expected precision on this CP property by any experiment.

Where Pith is reading between the lines

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

  • The same angular-correlation method could be applied to other Higgs decay channels if sufficient statistics become available.
  • Any future deviation from zero would point to CP-violating new physics in the Higgs sector.
  • The result provides a benchmark for theoretical models that extend the Standard Model with additional CP-odd components.

Load-bearing premise

The analysis assumes that angular correlations between tau decay products are accurately modeled in simulation and that all relevant backgrounds and detector effects have been correctly accounted for when fitting for the mixing angle.

What would settle it

A statistically significant deviation of the fitted mixing angle from zero in the combined dataset, or a clear mismatch between observed and simulated angular distributions that cannot be explained by background or detector uncertainties.

Figures

Figures reproduced from arXiv: 2606.03510 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: Illustration of the reconstruction of ϕCP. The frame is defined such that the sum of the ⃗P ∗± vectors is zero. The ϕCP angle is reconstructed from ⃗R ∗± ⊥ and⃗P ∗± . The corresponding unit vectors are used to define the angle ϕ ∗ : ϕ ∗ = arccos(Rˆ ∗+ ⊥ · Rˆ ∗− ⊥ ), (5) and the CP-odd triple product correlation O∗ observable: O ∗ = Pˆ ∗− · (Rˆ ∗+ ⊥ × Rˆ ∗− ⊥ ). (6) The acoplanarity angle ϕCP is then define… view at source ↗
Figure 2
Figure 2. Figure 2: The post-fit BDT score distributions for the Genuine (left) and Mis-ID (right) cate [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: shows the data and background distributions, with the expected scalar and pseu￾doscalar signal templates overlaid, for the most sensitive decay mode combinations (ρρ, πρ, and ρa 3pr 1 ). The distributions highlight the effectiveness of the BDT discriminant in optimizing the signal over background ratio, as well as the CP-sensitivity of the measurement that follows from the visibly different phases of the C… view at source ↗
Figure 4
Figure 4. Figure 4: Negative log-likelihood scan for the combination of the [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Negative log-likelihood scan for the combination of the [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The ϕCP distributions for the ρρ, πρ, µρ, and eρ channels in 13 and 13.6 TeV data, and the ρa 3pr 1 , ρa 1pr 1 + a 1pr 1 a 1pr 1 , µa 3pr 1 , and ea3pr 1 channels in 13.6 TeV data, are weighed by A S/(S + B) and combined. The upper plot includes only the 13.6 TeV data, while the lower plot shows the combination of the 13 and 13.6 TeV data. Events are included from all BDT score bins in the signal categorie… view at source ↗
Figure 7
Figure 7. Figure 7: Observed scan of −2∆ ln L for µ against α Hτ τ for the combination of the 13 and 13.6 TeV measurements. The red marker indicates the SM prediction, and the white marker indicates the best fit to the data. -2 -1 0 1 2 -2 -1 0 1 2 = 1 200 fb 1 CMS (13 and 13.6 TeV) 68.3% CL 95.5% CL 99.7% CL SM Best fit 0 5 10 15 20 25 2 ln L [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Observed scan of −2∆ ln L for the reduced CP-odd (κeτ ) coupling against the re￾duced CP-even (κτ ) coupling for the combination of the 13 and 13.6 TeV measurements. The red marker indicates the SM prediction, and the white markers indicate the best fits to the data [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Projections of the expected likelihood scans to an integrated luminosity of 3 ab [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
read the original abstract

This paper presents a measurement of the charge-parity ($C\!P$) structure of the Yukawa coupling between the Higgs boson (H) and tau leptons, using proton-proton collision data at $\sqrt{s}$ = 13.6 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 62.4 fb$^{1}$. Angular correlations between the decay products of tau leptons produced in H $\to$ $\tau\tau$ decays are exploited to constrain the effective $C\!P$ mixing angle $\alpha^{\mathrm{H}\tau\tau}$, which parameterizes the admixture of scalar and pseudoscalar couplings. The mixing angle is measured to be $\alpha^{\mathrm{H}\tau\tau}$ = (36$^{+33}_{-30}$)$^\circ$, compared with an expected value of (0 $\pm$ 19)$^\circ$ under the standard model hypothesis. When combined with the previous CMS measurement using data collected at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$, the mixing angle is determined to be (7 $\pm$ 16)$^\circ$, with an expected value of (0 $\pm$ 14)$^\circ$. This result represents the most precise measurement by CMS of the $C\!P$ nature of the Higgs boson coupling to tau leptons, with an expected precision that is the best achieved by any experiment to date.

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

1 major / 0 minor

Summary. The manuscript reports a measurement of the CP-mixing angle α^{Hττ} parameterizing the scalar-pseudoscalar admixture in the Higgs-tau Yukawa coupling. Using 62.4 fb^{-1} of 13.6 TeV pp collision data recorded with CMS, angular correlations in H→ττ decays yield α^{Hττ} = (36^{+33}_{-30})°, consistent with the SM expectation of (0 ± 19)°. Combination with the prior 13 TeV CMS result (138 fb^{-1}) gives (7 ± 16)° (expected (0 ± 14)°), stated to be the most precise CMS result and the best expected precision achieved by any experiment.

Significance. If the modeling assumptions hold, the result supplies the tightest CMS constraint to date on possible CP violation in the Hττ coupling and achieves the best expected precision reported by any experiment. The combined measurement is statistics-limited, so further luminosity would directly improve the bound.

major comments (1)
  1. [Analysis and fit procedure (as described in the body)] The extraction of α^{Hττ} is performed via a fit to angular observables generated from tau decay matrix elements and polarization transfer in simulation. No data-driven constraint or closure test on the accuracy of this modeling (e.g., acoplanarity or decay-plane angle distributions) is reported at a level comparable to the 16° combined uncertainty, which is the dominant systematic risk for the central claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. Below we provide a point-by-point response to the major comment.

read point-by-point responses

  1. Referee: [Analysis and fit procedure (as described in the body)] The extraction of α^{Hττ} is performed via a fit to angular observables generated from tau decay matrix elements and polarization transfer in simulation. No data-driven constraint or closure test on the accuracy of this modeling (e.g., acoplanarity or decay-plane angle distributions) is reported at a level comparable to the 16° combined uncertainty, which is the dominant systematic risk for the central claim.

    Authors: The tau decay matrix elements and polarization transfer are modeled using the standard TAUOLA and PYTHIA implementations, which have been validated against data in multiple prior CMS publications on Z→ττ and Higgs boson analyses. We agree that an explicit data-driven closure test at the level of the reported precision would strengthen the presentation of the result. In the revised manuscript we will add a dedicated subsection (with associated figures) describing validation studies of the acoplanarity and decay-plane angle distributions in both simulation and data control regions, including quantitative comparisons. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the data-driven extraction of α^{Hττ}

full rationale

The paper extracts the CP mixing angle from a fit to observed angular distributions in H→ττ events using new 13.6 TeV collision data. This is a direct statistical inference from experimental observables under modeling assumptions for decays and backgrounds; the central result does not reduce by the paper's equations or self-citations to a quantity defined by construction from prior inputs. The combination with the earlier 13 TeV CMS result incorporates independent data and does not render the new measurement circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard experimental assumptions about simulation fidelity and background modeling that are not independently verified from the abstract.

free parameters (1)
  • α^{Hττ} = 7 ± 16°
    Effective CP mixing angle extracted from the fit to angular correlations in the data.
axioms (1)
  • domain assumption Tau decay angular distributions and detector response are correctly modeled in simulation.
    Required to interpret observed correlations as a constraint on the Yukawa CP structure.

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discussion (0)

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Reference graph

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