The Gallium Anomaly

Matteo Cadeddu INFN Cagliari matteo.c[email protected] The Gallium Anomaly Based on Cadeddu et al. arXiv:2507.13103 “Reassessing the gallium anomaly using exact electron wave functions” In collaboration with Nicola Cargioli, Giovanni Carotenuto, Francesca Dordei, Carlo Giunti and Luca Ferro. Neutrinos: tiny, ubiquitous, surprising 2 Matteo Cadeddu Neutrinos are elusive particles —nearly massless, neutral, and weakly interacting— constantly challenging our understanding and revealing unexpected phenomena. Why anomalies matter In neutrino physics, persistent discrepancies between data and prediction, so called “anomalies”, have repeatedly led to breakthroughs rather than dead ends. The solar neutrino deficit ultimately revealed flavor oscillations and non-zero neutrino masses. Other tensions (reactor, short-baseline) have pushed the community to refine fluxes, cross sections, and detection systematics, and to explore new-physics hypotheses such as sterile neutrinos. Today’s focus Based on Cadeddu et al. arXiv:2507.13103 The solar neutrino problem led to the discovery of neutrino oscillations. The Nobel Prize in Physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald ”for the discovery of neutrino oscillations, which shows that neutrinos have mass”. What makes neutrinos special I will revisit one notable case: the Gallium Anomaly. Using updated theory for νₑ capture on ⁷¹Ga - built on improved electron wave functions and improved nuclear inputs - I’ll show how the predicted rates shift, what this means for the long-standing deficit, and how it interfaces with oscillation and sterile-neutrino interpretation. How “anomalies” drive discoveries "An anomaly is not just a deviation — it is a clue that reality may be richer than our current understanding." Short-baseline anomalies Anomaly Channel Status Explanation Reactor 𝜈𝑒→ 𝜈𝜇Disappearing (<2𝜎) systematics/nuclear physics LSND 𝜈𝜇→ 𝜈𝑒Significant (4.8𝜎) “old anomaly” Unknown MiniBooNE 𝜈𝜇→ 𝜈𝑒Very significant (4.8𝜎) Unknown But sterile-neutrino hypothesis recently disfavored by MicroBooNE (Phys. Rev. Lett. 135, 081802) Gallium 𝜈𝑒→ 𝜈𝑒Very significant (>5𝜎) Unknown [C. Giunti et al. 2110.06820] Matteo Cadeddu This talk! 3 See also Concha’s talk See Miquel and Fao’s talks The Gallium Anomaly (formal, but approachable) Matteo Cadeddu From https://www.explainxkcd.com/wiki/index.php/3115:_Unsolved_Physics_Problems Among the “unsolved physics problems”, we chose one that seems manageable for a paper and a 15-minute talk: a clear and simple deficit in a clean experimental setup (Inspired by xkcd’s recent “Unsolved Physics Problems”). 4 Using Bahcall cross-section The experimental deficit Matteo Cadeddu No clear model-independent anomaly from different path lengths. A constant suppression can fit all data. The anomaly persists, motivating more theory work and BSM interpretations. Electron-capture sources (⁵¹Cr, ³⁷Ar) placed in gallium targets produce monoenergetic νₑ that are captured via inverse beta decay (IBD) process νₑ + ⁷¹Ga → e⁻ + ⁷¹Ge. Define the data/prediction ratio Across multiple calibrations (GALLEX, SAGE) and recently the two-zone BEST experiment, R < 1 consistently. 𝑅 ≡ 𝑁meas /𝑁pred, with 𝑁pred = ∫ Φ(E) · Pₑₑ(L,E) · σ(E) · ε · dE (× exposure). BEST reaffirmed the deficit with two baselines and higher statistics; no clear baseline dependence was seen! After BEST: >5𝜎deficit BEST: 2109.11482, 2109.14654, 2201.07364; Barinov and Gorbunov: 2109.14654; Huber et al: 2111.12530, 2209.02885; Brdar et al: 2303.05528; Banks et al: 2311.06352; Schwetz et al: 2303.15524, 306.09422; Elliott et al: 2303.13623, 2306.03299; Giunti et al: 2209.00916, 2212.09722, 2312.00565, 2507.13103 σ(E): the theoretical cross section. Bahcall pioneered the calculation of the charged-current νₑ capture on ⁷¹Ga [PRC 56, 3391 (1997),arXiv:hep-ph/9710491.]. Later works by Haxton and others [Elliott et al, PRC 108, 035502 (2023), 2303.13623] refined the cross section and its uncertainties. 5 𝑬𝐭𝐡 ≅0.233 MeV The ingredients of the Gallium Anomaly 1 Matteo Cadeddu 2 3 The νₑ flux νₑ +⁷¹Ga → e⁻ + ⁷¹Ge. The neutrino flux is evaluated by calorimetric measurements of the activity of the sources. e⁻ + 51Cr→ + 51V + νₑ E ≃ 0.75 MeV and E ≃ 0.43 MeV [SAGE, hep-ph/9803418] e⁻ + 37Ar→ + 37Cl + νₑ E ≃ 0.81 MeV [SAGE, nucl-ex/051204] The νₑ propagation probability The νₑ +⁷¹Ga → e⁻ + ⁷¹Ge detection cross section The radiochemical ⁷¹Ga extraction efficiency [Brdar, Gehrlein, Kopp, arXiv:2303.05528] This talk! Neutrino propagation can involve oscillations: electron-flavor neutrinos may convert into sterile states, lowering the effective survival probability below unity and potentially accounting for the ~20% deficit. 6 The detection cross section (Bahcall prescription revisited) 7 Matteo Cadeddu The deficit could be due to an overestimation of the IBD cross section 𝜎(νₑ + ⁷¹Ga → e⁻ + ⁷¹Ge). An early theoretical work by Bahcall [J. N. Bahcall, PRCC 56, 3391 (1997), arXiv:hep-ph/9710491] established the foundation for this prediction. Bahcall’ approach: capture cross section from first principles, then anchor it to data. Start from Fermi’s Golden Rule for an allowed Gamow-Teller (GT) transition: The term ℋIBD represents the matrix element of the transition and incorporates the involved lepton, 𝝍, and nuclear, 𝜳, wave functions, and the GT Hamiltonian Bypass ab-initio via the inverse process: νₑ + ⁷¹Ga ⟷e⁻ + ⁷¹Ge Detailed balance principle IBD EC By detailed balance we can bypass an ab-initio calculation: the GT strength for ⁷¹Ga → ⁷¹Ge inferred from the inverse electron-capture (EC) rate ⁷¹Ge → ⁷¹Ga, via the measured 𝒇𝒕 value. νₑ ⁷¹Ga ⁷¹Ge e⁻ EC IBD Underlying Assumption: factorizing nuclear and leptonic matrix elements, and use of leading-order (LO) approximations for the lepton wave functions [Cadeddu et al. arXiv:2507.13103] ⁷¹Ga ⁷¹Ge Τ 3 2− Τ 1 2− 232 keV gs The detection cross section (Bahcall prescription revisited) cont’d 8 Matteo Cadeddu The electron capture rate is defined as: Factorizing out the leptonic wave functions the EC matrix element becomes ft-value Phase space factor for allowed EC. EC happens mainly with the 1s shell electrons: 1s electron density at the nucleus g1s(r) and f1s(r) exact solution of the DiracHartree-Fock-Slater (DHFS) equations Well-known EC ⁷¹Ge half-life EC probabilities Experimentally measured EC prob. for L, M and K shells. [Hampel, Remsberg (1985)] [Collar and Yoon, 2023] [Norman et al. (LLNL), 2024] [A. Derbin et al 2025] The GA could be explained through an increase of the ⁷¹Ge half life. [ W. Bambynek et al. Rev. Mod. Phys. 49, 77 (1977) ] ℳnuc EC can be extracted from the ⁷¹Ge EC ft-value! 𝜎gs ∝1 𝑡1/2(71Ge) ✓However recent measurements of t1/2 confirm the Hampel and Remsberg one! The ground state cross section & the role of the Fermi function 9 Matteo Cadeddu Following the detailed balance (db) principle, the ground-state neutrino induced IBD cross section reduces to The Fermi function corrects for the distortion of the electron wave function due to the Coulomb potential of the daughter nucleus. ⁷¹Ge in the nuclear and atomic coulomb field We use a generalised Fermi function where the electron wave functions fκ(r) and gκ(r) are the exact radial solutions of the DHFS equations for the outgoing electron of the IBD process for the eigenvalue κ, which assumes values κ = ±1 for allowed decays, obtained with the RADIAL package [F. Salvat and J. M. Fernndez-Varea, Computer Physics Communications 240, 165 (2019)]. The generalized Fermi function should be compared to the standard literature definition, given as a product of multiple factors and corrections 𝐹 𝐸𝑒, 𝑍 = 𝐹0𝐸𝑒, 𝑍 ×𝐿0𝐸𝑒, 𝑍 ×𝑈 𝐸𝑒, 𝑍 ×𝑆(𝐸𝑒, 𝑍) Point-like nucleus Atomic-screening correction Finite-size correction From box to 2pF density [Cadeddu et al. arXiv:2507.13103] Standard VS Generalized MC, Nicola Cargioli, Giovanni Carotenuto, Francesca Dordei, Carlo Giunti and Luca Ferro, Reassessing the gallium anomaly using exact electron wavefunctions arXiv:2507.13103 Matteo Cadeddu All results are available online at this new website: https://levs-fit.ca.infn.it/ Thanks for your attention!