Searches for the low-energy neutrino signature expected if solar-gravitationally-captured GUT monopoles catalyze proton decay inside the Sun via the Callan-Rubakov process; finds no excess, setting a monopole-flux times catalysis-cross-section limit F(σ0/1mb) < 6.3×10⁻²⁴(βM/10⁻³)² cm⁻²s⁻¹sr⁻¹ at 90% CL, several orders of magnitude tighter than prior cosmic-ray flux limits. relevance_note: the astrophysical/“nature has already run this experiment” analogue for monopole catalysis — bounds ambient monopole flux and catalysis rate directly, independent of collider production questions.
Extracted summary
§1 — scenario under test
H-20 - Solar-captured GUT monopoles catalyze proton decay producing a detectable low-energy neutrino flux
The hypothesis under test. GUT phase transitions generically produce topological monopoles; naive Kibble estimates overproduce them by >14 orders of magnitude (the monopole problem), inflation dilutes them by an uncertain amount, so the surviving flux is essentially unconstrained by theory. Relevant to the main question as the monopole/catalysis analogue of the stable-black-hole disaster mechanism: it is the scenario for which “nature’s own experiment” bounds exist.
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§2-4 — search and null result
O-27 - Super-Kamiokande finds no solar-direction excess of 19-55 MeV neutrinos in 2853 live days
Methodology
Data: SK-I (Apr 1996 - Jul 2001, 1497.4 d), SK-II (Oct 2002 - Oct 2005, 793.7 d), SK-III (Jul 2006 - Aug 2008, 562.0 d); 22,500 t fiducial volume. Detection channels: neutrino-electron elastic scattering (all flavors) and inverse beta decay; MSW oscillation effects in Sun and Earth included. Energy window 19 (20 for SK-II) to 55 MeV chosen to exclude solar neutrinos and spallation below, and the recoil-spectrum endpoint above. Cuts: spallation likelihood, Cherenkov opening angle (38-50 deg), gamma-ray distance-to-wall, pion-like pattern, multi-ring, decay-electron pairs — leaving 317 candidates (from 2108 after the basic cuts). Signal extraction: chi-square fit of the cos(theta_Sun) angular distribution against expected elastic-scattering and inverse-beta-decay shapes plus an iteratively-determined isotropic background; systematic errors 5.6-6.4% per phase. Remaining spallation background estimated 4.7 +/- 4.3 (SK-I/III) and 0.2 +/- 1.7 (SK-II) events; ~1 solar-neutrino event.
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§4 — conversion to a monopole-flux bound
A-42 - Solar capture and catalysis kinematics convert the Super-K neutrino limit into a monopole-flux bound
Reasoning. (1) Catalysis rate: f_p = Integral n_M v_rel sigma rho_p N_A d^3x with sigma = sigma_0/beta_rel^2; assuming monopoles settle at the solar center (rho_p = 50 g/cm^3, beta_rel = thermal = 1.7 x 10^-3) gives f_p = 1.7 x 10^6 (sigma_0/1mb) N_M decays/s. (2) Neutrino budget: each decay yields
3 neutrinos through pi+ → mu+ nu_mu, mu+ → e+ nu_e nu_mu-bar, with nu_e fraction f_nu_e = f_pi+ (1 - a_pi+), f_pi+ ~ 0.5 (GUT-model branching to pi+ + anything), a_pi+ = 0.2 pion absorption at the solar center; so f_p = 4 pi d^2 I0 / 3 / f_nu_e at Earth-Sun distance d = 1.5 x 10^13 cm. (3) Capture: N_M = pi R_sun^2 (1 + (beta_esc/beta_M)^2) epsilon(M_M, beta_M) 4 pi F_M t_sun, with beta_esc = 2 x 10^-3, t_sun = 4.6 x 10^9 yr, and capture efficiency epsilon from monopole energy-loss calculations — epsilon falls below 1 for M_M >10^17 GeV, which bounds the limit’s mass validity. Model dependences carried explicitly: sigma_0 and f_pi+ appear as scaling factors in the quoted bound; assumed central accumulation; monopole-antimonopole annihilation neglected. The nontrivial content is that a null counting experiment on Earth bounds the product (ambient monopole flux) x (catalysis cross section) — the same “nature’s own long-exposure experiment” logic as the compact-star bounds on stable black holes.Step 6 — validity verdict
approved / checked. Reconstruction — the chain: captured monopoles N_M proportional to ambient flux F_M times 4.6-Gyr solar exposure (with capture efficiency epsilon(M_M, beta_M)); catalyzed proton decay f_p proportional to N_M sigma_0; solar low-energy nu_e flux at Earth proportional to f_p times branching/absorption factors. Load-bearing step: every link is monotone increasing in the product F_M sigma_0, so Super-K’s null flux limit I90 inverts to an upper bound on that product — a valid inversion, and the bound is correctly reported as a bound on the product with (sigma_0/1mb) and (f_pi+/0.5) carried as explicit scaling factors rather than hidden assumptions, with the mass-validity edge (epsilon < 1 above ~1e17 GeV) stated. I traced the algebraic structure and dimensional consistency of the three links as recorded; the numerical coefficients (central-settling density, beta_rel, pion absorption) enter as premises whose truth step 8 prices. The “nature’s long-exposure experiment” framing adds nothing beyond the chain and smuggles nothing. Checked.
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O-28 - Super-K bound on GUT-monopole flux times catalysis cross section from solar non-observation
The bound is stated as an explicit function of the catalysis cross section sigma_0 and monopole velocity beta_M, so its model dependence is transparent. It assumes monopole accumulation at the solar center, a proton-decay pi+ branching fraction f_pi+ ~ 0.5 (typical of GUT models), negligible monopole-antimonopole annihilation, and a capture efficiency computed from monopole energy loss in the Sun (which degrades above ~10^17 GeV monopole mass). Also tighter than the old-neutron-star X-ray limit F_M (sigma_0/1mb) < 3r x 10^-23 cm^-2 s^-1 sr^-1 even at its most stringent (r=1).
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