A 2025–2026 series of methanol (CH3OH) spectroscopic measurements toward the Galactic-center molecular cloud Sgr B2(N)/(M) indicates that the electron-to-proton mass ratio μ = m_e/m_p is lower there than in the laboratory by (−3.4 ± 0.4)×10⁻⁷, while an identical line set toward the Orion-KL cloud near the solar circle shows no significant shift. The authors conjecture that the effect traces a dark-matter-induced modulation of the Higgs vacuum expectation value, since the claimed Δμ/μ profile along the Galactic radius appears to track the ratio of dark-matter to baryonic density. Two coupled questions remain entirely open: (1) is the inner-Galaxy μ depression real — i.e. can it survive independent instrumental confirmation and exclusion of reference-frequency, calibration, blending, and excitation systematics — and what is its radial profile across the Galaxy; and (2) what physical mechanism, if any, quantitatively produces the measured magnitude and spatial dependence, in particular whether a dark-matter–Higgs-sector coupling with plausible particle parameters can do so while satisfying terrestrial clock and equivalence-principle constraints and the existing ≤2×10⁻⁸ limits elsewhere in the Galactic disk.

Background

The electron-to-proton mass ratio μ = m_e/m_p, together with the fine-structure constant, fixes the frequencies of all molecular transitions: torsional and vibrational frequencies scale sensitively with μ because they arise from nuclear motion in the molecule. If μ differed between a distant cloud and the laboratory by Δμ/μ, each transition would shift by Δf/f = Q·Δμ/μ, where the dimensionless sensitivity coefficient Q is computable from molecular structure theory. Methanol (CH3OH) is especially valuable because its hindered-rotor (torsional-rotational) transitions span Q from about −0.1 to +1.8 (and its isotopologues much more), so comparing radial velocities of lines with different Q in the same cloud converts an observed velocity offset ΔV into Δμ/μ ≈ −ΔV/(c·Q). This is a test of local position invariance (LPI), the part of the Einstein equivalence principle stating that measured constants do not depend on where or in what environment the measurement is made. The same program earlier developed the ammonia method (comparing NH3 inversion lines with pure rotational lines of other molecules), which bounds Δμ/μ < 2×10⁻⁸ in nearby dark clouds, and used Class I methanol masers (maser amplification of methanol rotational lines, pumped by collisions rather than by ambient infrared radiation) to bound any smooth μ gradient in the disk to k_μ < 2×10⁻⁹ per kpc over galactocentric radii 4–12 kpc. Because μ is set by particle masses, which arise from the vacuum expectation value (VEV) v ≈ 246 GeV of the Higgs field and the QCD scale, a spatially varying scalar field coupled to the Higgs sector would make μ position-dependent; chameleon-type scalar fields (whose effective properties depend on the ambient baryonic matter density) and gravitational-potential models (Δμ/μ = k_μ·ΔΦ) are the classic such scenarios. In 2025–2026 Vorotyntseva, Levshakov and collaborators published a series of JETP Letters papers claiming a detection: Paper I used three Herschel 542–543 GHz methanol lines toward Sgr B2(N) and Orion-KL (a hot molecular cloud complex about 100 pc from the Galactic center, and a star-forming region in Orion near the solar circle at R_GC ∼ 9 kpc, respectively), finding Δμ/μ = (−4.2 ± 0.7)×10⁻⁷ for Sgr B2(N) versus laboratory and no significant shift for Orion-KL; Paper II added IRAM 30-m 3 mm methanol lines toward Sgr B2(N) and (M), giving (−2.1 ± 0.6)×10⁻⁷; Paper III analyzed thirteen methanol lines in the 490–640 GHz band of HIFI (the Heterodyne Instrument for the Far-Infrared aboard the Herschel space observatory) toward both clouds, verified by non-LTE (non-local-thermodynamic-equilibrium) radiative-transfer modeling with the RADEX code that the A- and E-symmetry species trace the same gas, and combined all data into ⟨Δμ/μ⟩ = (−3.4 ± 0.4)×10⁻⁷ for Sgr B2(N)/(M) versus (−1.1 ± 0.8)×10⁻⁷ for Orion-KL. The authors note that the Δμ/μ values from various clouds appear to change sharply within 0 < R_GC/R_eff ≲ 1 (R_eff being the effective radius of the Galactic stellar disk), where the mean dark-matter-to-baryonic-matter density ratio ρ_DM/ρ_br rises, and disfavor both gravitational-potential and baryon-density (chameleon) explanations because Sgr B2(N) and Orion-KL have comparable gravitational potentials and comparable local baryon densities yet different Δμ/μ. They conjecture instead a dark-matter-induced modulation of the Higgs scalar field. None of the existing disk constraints (≤2×10⁻⁸ at R_GC ≳ 4 kpc) probes the inner Galaxy, where the claimed effect resides, and no laboratory or clock experiment couples directly to a dark-matter-density (as opposed to gravitational-potential) dependence.

Problem Statement

Determine whether the electron-to-proton mass ratio μ varies with position in the Galaxy, and if so, identify and quantitatively model the physical mechanism. Concretely, the problem comprises two coupled open questions: (1) confirming, with observations independent of the combined Herschel/HIFI and IRAM 30-m datasets, or refuting, using any data including those same datasets, whether μ is genuinely depressed by ⟨Δμ/μ⟩ ≈ (−3.4 ± 0.4)×10⁻⁷ in the inner Galaxy (Sgr B2 region) relative to its terrestrial value, with the reference-frequency choice (flabf_{\rm lab} versus calculated fcalf_{\rm cal}), instrument calibration, line blending, and segregation of lines into different physical gas components controlled as systematics, and determining the actual radial profile of Δμ/μ — in particular whether the apparent sharp change within 0<RGC/Reff≲10 < R_{\rm GC}/R_{\rm eff} \lesssim 1 is real and maps quantitatively onto the ratio of dark-matter to baryonic density ρDM/ρbr\rho_{\rm DM}/\rho_{\rm br}; and (2) identifying the mechanism: either constructing a quantitative physical model — for example a dark-matter–Higgs-sector coupling that modulates the Higgs vacuum expectation value — that reproduces the measured magnitude and Galactic-radius profile of Δμ/μ from plausible dark-matter densities and particle properties while remaining consistent with terrestrial atomic-clock limits, equivalence-principle tests, and the existing bounds of |Δμ/μ| ≲ 2×10⁻⁸ at galactocentric radii ≳ 4 kpc, or demonstrating that a specific instrumental or astrophysical systematic, or one of the alternative mechanisms (chameleon-like scalar fields tied to baryonic density or gravitational-potential coupling Δμ/μ=kμ ΔΦ\Delta\mu/\mu = k_\mu\,\Delta\Phi that additionally reproduce the Sgr B2(N)-versus-Orion-KL contrast, or multidimensional/Kaluza–Klein-type effects), accounts for the observations. Both questions serve one objective — establishing whether and why μ varies across the Galaxy. Each question has its own completion boundary. Question (1) is resolved affirmatively, by observations independent of the combined Herschel/HIFI and IRAM 30-m datasets that establish the inner-Galaxy depression as real together with its radial profile Δμ/μ — the quantitative comparison with ρDM/ρbr\rho_{\rm DM}/\rho_{\rm br} being required only in this affirmative case — or negatively, by a demonstration, using any data including the combined Herschel/HIFI and IRAM 30-m datasets, that a specific instrumental or astrophysical systematic accounts for the reported offset. Question (2) is resolved either by a quantitative physical model that reproduces the measured magnitude and Galactic-radius profile while satisfying the stated bounds, or by such a demonstrated systematic. A demonstration that a systematic accounts for the reported offset thus resolves question (1) in the negative and discharges question (2), so the task is completed without a mechanism model.

References

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