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Polarization in $\Lambda\to p\mu^-\bar\nu_\mu$ as a probe of CP-violating new physics

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Qazi Maaz Us Salam, Ishtiaq Ahmed

High Energy Physics - Phenomenology · Submitted 2 Nov 2026 · 64 references

Pith's verdict: Solid, incremental hyperon CP study with one genuinely interesting blind-direction result; check the FSI benchmark from the authors' own unpublished preprint before trusting the SM comparisons.

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arXiv ID2611.03375 (version 1)
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CitationIshtiaq Ahmed, Qazi Maaz Us Salam. "Polarization in $\Lambda\to p\mu^-\bar\nu_\mu$ as a probe of CP-violating new physics." arXiv:2611.03375 (2026). https://pith.science/paper/44CF5MTX
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The paper

The paper claims

The normal muon polarization in $\Lambda\to p\mu^-\bar\nu_\mu$ vanishes in the Standard Model; this paper shows it is a linear probe of CP-violating couplings, reaching 4.5 times the SM background where kaon decays cannot constrain the…

The reading

The aim is to show that the normal, out-of-plane muon polarization in the hyperon decay $\Lambda\to p\mu^-\bar\nu_\mu$ is a viable low-energy probe of CP-violating new physics, since it vanishes at tree level in the Standard Model and responds linearly to the imaginary parts of the scalar, pseudoscalar and tensor couplings of the effective $s\to u$ Lagrangian. A nonzero value can come from the calculable electromagnetic final-state interaction or from such complex couplings, and the paper shows the new-physics piece is not suppressed by the muon mass while the right-handed coupling contributes nothing. Combining the computed sensitivities with current bounds from kaon decays and the LHC, one coupling at a time, the largest allowed effects lie between $0.49\times10^{-3}$ and $0.85\times10^{-3}$, below the Standard Model background of $1.06\times10^{-3}$\u2014except along the circle in the complex pseudoscalar plane on which the $K\to\mu\nu$ rate is unchanged, where the polarization can reach $4.78\times10^{-3}$, about 4.5 times the Standard Model value. Because the final-state interaction contributes the same amount to $\Lambda$ and $\bar\Lambda$ decays while the new-physics contribution flips sign, the difference between the two channels would isolate the new-physics effect without any subtraction, and the distinct $q^2$ shapes of the two contributions give a second, independent separation handle.

What carries the argument

The central object is the normal polarization $P_N$, the asymmetry between muons whose spin points along and opposite to the normal of the decay plane, $\vec s_\ell\cdot(\vec p_\ell\times\vec p_\Lambda)$. Because the hadronic form factors are real, this T-odd asymmetry vanishes at tree level in the Standard Model and for real couplings, and for small couplings it is linear in $\mathrm{Im}\,\epsilon_S$, $\mathrm{Im}\,\epsilon_P$ and $\mathrm{Im}\,\epsilon_T$\u2014that linearity, unsuppressed by the lepton mass, is what carries the whole argument. The machinery consists of an effective Lagrangian for $s\to u$ transitions with complex scalar, pseudoscalar, tensor and right-handed couplings; lattice QCD form factors for the vector, axial-vector, scalar and tensor currents; and the pseudoscalar form factor $g_P$ obtained from the axial Ward identity $g_P(q^2) = ((m_\Lambda+m_p)g_1(q^2) - q^2 g_3(q^2)/m_\Lambda)/(m_s+m_u)$. The analytic sensitivities of Appendix A are the workhorse; combined with the $K\to\mu\nu$ rate formula $R_K = R_K^{SM}|1-\kappa\epsilon_P|^2$ with $\kappa = 24.3$, they expose the flat direction on which the polarization is the only low-energy handle.

Extended reading notes

Core claim

On the paper's own terms, the discovery is a pair of quantitative relations: the phase-space-averaged normal muon polarization in $\Lambda\to p\mu^-\bar\nu_\mu$ is $\langle P_N^\mu\rangle = -0.694(39)\,\mathrm{Im}\,\epsilon_S + 0.332(13)\,\mathrm{Im}\,\epsilon_P + 0.400(13)\,\mathrm{Im}\,\epsilon_T$, with yet larger coefficients in the electron channel, and a purely pseudoscalar coupling obeys the closed forms $\Gamma/\Gamma_{SM} = 1 - 0.172\,\mathrm{Re}\,\epsilon_P + 0.178|\epsilon_P|^2$ and $\langle P_N^\mu\rangle = 0.332\,\mathrm{Im}\,\epsilon_P\,\Gamma/\Gamma_{SM}$. Taking one coupling at a time, the KEK-E246, $R_K$ and LHC bounds leave scalar and tensor effects between $0.49\times10^{-3}$ and $0.85\times10^{-3}$, below the Standard Model final-state-interaction value of $1.06\times10^{-3}$. The exception is the complex-pseudoscalar direction $\epsilon_P = (1-e^{-i\varphi})/\kappa$ on which the $K\to\mu\nu$ rate is unchanged: there the polarization reaches $4.78\times10^{-3}$, about 4.5 times the SM value, while the hyperon decay rate shifts by less than 0.05%. The claim is that this observable is therefore the one place where CP-violating new physics in the muon channel is not yet blinded by the Standard Model background, and that the $\Lambda$\u2013$\bar\Lambda$ difference removes that background entirely.

Load-bearing premise

The load-bearing input is the quoted Standard Model benchmark $\langle P_N^\mu\rangle_{SM} = -(1.06\pm0.15)\times10^{-3}$, taken from the authors' own companion preprint rather than recomputed in this paper, and every ratio in Table 2 and Fig. 3, including the 4.5-times claim along the pseudoscalar circle, inherits this number.

Editorial extensions

If this is right

  • One coupling at a time, present bounds leave the normal muon polarization below the Standard Model background for scalar, tensor and generic-phase pseudoscalar couplings, with the largest allowed values between about half and four-fifths of the SM contribution.
  • Along the circle $\epsilon_P = (1-e^{-i\varphi})/\kappa$ fixed by $K\to\mu\nu$, the polarization can reach $4.78\times10^{-3}$, or 4.5 times the SM value, while the $\Lambda\to p\mu^-\bar\nu_\mu$ rate changes by less than 0.05%.
  • Binning in $q^2$ separates new physics from the final-state interaction: the NP contribution differs by less than 6% between $q^2 = 0.015$ and $0.027$ GeV$^2$, whereas the FSI contribution is 2.5 times smaller in the lower bin.
  • The difference between the normal polarizations in $\Lambda$ and $\bar\Lambda$ decays isolates the new-physics effect without subtracting the SM value, because the FSI contributes equally to both while the NP term flips sign.
  • Reaching a sensitivity of $10^{-3}$ requires on the order of $3\times10^7$ analyzed decays, about 36 times more for stopping negative muons that largely depolarize, so the observable becomes practical only with the larger samples expected at future high-intensity hyperon facilities.

Reading between the lines

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

  • If the pseudoscalar flat direction is realized in nature, hyperon semileptonic decays would become the only current low-energy window onto that CP-violating phase, and the same polarization machinery would transfer to other hyperon modes such as $\Xi\to\Lambda\ell\nu$ and $\Xi\to\Sigma\ell\nu$ once comparable form factors become available.
  • Because the polarization is linear in $\mathrm{Im}\,\epsilon_P$, a single measurement of the $\Lambda$\u2013$\bar\Lambda$ difference would determine the sign of the CP-violating phase, not just bound its magnitude, something kaon rate ratios that depend on the phase quadratically cannot do.
  • The statistics estimate assumes the muon spin is read out from the decay-electron asymmetry, with stopping negative muons depolarizing strongly; a detector that analyzes the muon spin in flight, for instance through spin precession in a magnetic field, would shrink the required sample by the quoted factor of about 36.
  • Because every ratio in Table 2 is a comparison against the quoted $(1.06\pm0.15)\times10^{-3}$ benchmark, an independent recalculation of the final-state-interaction contribution would shift all the ratios roughly proportionally, even if the qualitative ordering, scalar and tensor below the SM and the flat direction above it, would likely survive.
Original abstract

We investigate the normal $\mu$ polarization in the hyperon decay $\Lambda\to p\mu^-\bar\nu_\mu$ as a probe of new physics that violates CP, since this polarization vanishes at tree level in the Standard Model. Using an effective Lagrangian and lattice QCD form factors, we compute its sensitivity to the imaginary parts of the couplings. With the present bounds from kaon decays and the Large Hadron Collider, one coupling at a time, this sensitivity gives an effect below the Standard Model contribution from the electromagnetic final-state interaction. Only a pseudoscalar coupling with a particular phase can exceed this contribution, by several times. The final-state interaction gives the same polarization in $\Lambda$ and $\bar\Lambda$ decays, so the difference between the two decays isolates the new physics effect.

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.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-04: 1 request, 4,347 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.89 · human participants 0.02 · controlled comparison 0.54 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We investigate the normal $\mu$ polarization in the hyperon decay $\Lambda\to p\mu^-\bar\nu_\mu$ as a probe of new physics that violates CP, since this polarization vanishes at tree level in the Standard Model. Using an effective Lagrangian and lattice QCD form factors, we compute its sensitivity to the imaginary parts of the couplings. With the present bounds from kaon decays and the Large Hadron Collider, one coupling at a time, this sensitivity gives an effect below the Standard Model contribution from the electromagnetic final-state interaction. Only a pseudoscalar coupling with a particular phase can exceed this contribution, by several times. The final-state interaction gives the same polarization in $\Lambda$ and $\bar\Lambda$ decays, so the difference between the two decays isolates the new physics effect.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate the normal $\mu$ polarization in the hyperon decay $\Lambda\to p\mu^-\bar\nu_\mu$ as a probe of new physics that violates CP, since this polarization vanishes at tree level in the Standard Model. contribution 0.80 0.40 0.11 asserted 0.99
s1 Using an effective Lagrangian and lattice QCD form factors, we compute its sensitivity to the imaginary parts of the couplings. method 0.97 0.94 0.04 asserted 1.00
s2 With the present bounds from kaon decays and the Large Hadron Collider, one coupling at a time, this sensitivity gives an effect below the Standard Model contribution from the electromagnetic final-state interaction. result 0.96 0.61 0.16 asserted 0.99
s3 Only a pseudoscalar coupling with a particular phase can exceed this contribution, by several times. result 0.98 0.82 0.41 asserted 0.98
s4 The final-state interaction gives the same polarization in $\Lambda$ and $\bar\Lambda$ decays, so the difference between the two decays isolates the new physics effect. method 0.45 0.54 0.17 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from simulation or computation 0.93.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Sensitivity of P µ N to the imaginary parts of the couplings. 4. Present bounds and maximal effects In this section, we discuss the present bounds on the imaginary parts of the muonic couplings and the largest normal polarization they allow, taking one coupling at a time. Scalar coupling. The KEK-E246 experiment measured the T-odd polar￾ization of the muon perpendicular to the decay plane in K+ → π 0µ +νµ, Im ξ = −0.0053 ± 0.0071 ± 0.0036, i.e., |Im ξ| < 0.016 at 90% confidence level (CL) [34, 35]. Here ξ = f−/f+ is the ratio of the K → π form fac￾tors, and a scalar coupling acts a
Figure 2. Complex plane of ϵP with the present bounds and the contours of ⟨P µ N ⟩. |⟨P µ N ⟩| can reach 4.78 × 10−3 , which is 4.5 times the SM contribution. The radiative decay K+ → µ +νµγ is sensitive to this phase, because its inner-bremsstrahlung and structure-dependent amplitudes interfere [58]. We find PT = C κ Im ϵP , with C between 0.02 and 0.075 in the KEK-E246 selection, depending on the form factors [59] and the cuts, assuming uniform acceptance. At the edge of the LHC bound this gives |PT | between 0.7×10−2 and 2.6×10−2 , within the 95% range of the measured (−0.64±1.85±0.10)×…
Figure 3. Largest |P µ N | allowed by the present bounds and the SM contribution. only through the small change of the rate, Eq. (7). Near the origin, the RK band lies between the two SM lines, while along the circle it crosses them and reaches the largest values of

Figures reproduced from arXiv:2611.03375 by the authors.

References

Discussion

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