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Benchmarking Nuclear Matrix Elements of 0νββ Decay with High-Energy Nuclear Collisions

Yi Li1,2, Xin Zhang3, Giuliano Giacalone4,*, and Jiangming Yao1,2,†

  • 1School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China
  • 2Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-sen University, Zhuhai 519082, China
  • 3Department of Physics, Kyoto University, Kyoto 606-8502, Japan
  • 4Theoretical Physics Department, CERN, CH-1211 Genève 23, Switzerland

  • *Contact author: giuliano.giacalone@cern.ch
  • †Contact author: yaojm8@sysu.edu.cn
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Phys. Rev. Lett. 135, 022301 – Published 8 July, 2025

DOI: https://doi.org/10.1103/zymp-tyjj

Abstract

Reducing uncertainties in the nuclear matrix elements (NMEs) remains a critical challenge in designing and interpreting experiments aimed at discovering neutrinoless double-beta (0νββ) decay. Here, we identify a class of observables, distinct from those employed in low-energy nuclear structure applications, that are strongly correlated with the NMEs: momentum correlations among hadrons produced in high-energy nuclear collisions. Focusing on the Nd150→Sm150 transition, we combine a Bayesian analysis of the structure of Nd150 with simulations of high-energy Nd150+Nd150 collisions. We reveal prominent correlations between the NMEs and features of the quark-gluon plasma formed in these processes, such as spatial gradients and anisotropies, that are accessible via collective flow measurements. Our findings demonstrate collider experiments involving 0νββ decay candidates as a platform for benchmarking theoretical predictions of the NMEs.

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References (94)

  1. Q. R. Ahmad et al. (SNO Collaboration), Measurement of the rate of νe+d→p+p+e− interactions produced by B8 solar neutrinos at the Sudbury Neutrino Observatory, Phys. Rev. Lett. 87, 071301 (2001).
  2. K. Eguchi et al. (KamLAND Collaboration), First results from KamLAND: Evidence for reactor anti-neutrino disappearance, Phys. Rev. Lett. 90, 021802 (2003).
  3. F. P. An et al. (Daya Bay Collaboration), Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108, 171803 (2012).
  4. W. H. Furry, On transition probabilities in double beta-disintegration, Phys. Rev. 56, 1184 (1939).
  5. J. Schechter and J. W. F. Valle, Neutrinoless double beta decay in SU(2)×U(1) theories, Phys. Rev. D 25, 2951 (1982).
  6. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  7. M. Agostini, G. Benato, J. A. Detwiler, J. Menéndez, and F. Vissani, Toward the discovery of matter creation with neutrinoless ββ decay, Rev. Mod. Phys. 95, 025002 (2023).
  8. J. Engel and J. Menéndez, Status and future of nuclear matrix elements for neutrinoless double-beta decay: A review, Rep. Prog. Phys. 80, 046301 (2017).
  9. J. M. Yao, J. Meng, Y. F. Niu, and P. Ring, Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism, Prog. Part. Nucl. Phys. 126, 103965 (2022).
  10. J. M. Yao, B. Bally, J. Engel, R. Wirth, T. R. Rodríguez, and H. Hergert, Ab initio treatment of collective correlations and the neutrinoless double beta decay of Ca48, Phys. Rev. Lett. 124, 232501 (2020).
  11. A. Belley, C. G. Payne, S. R. Stroberg, T. Miyagi, and J. D. Holt, Ab initio neutrinoless double-beta decay matrix elements for Ca48, Ge76, and Se82, Phys. Rev. Lett. 126, 042502 (2021).
  12. S. Novario, P. Gysbers, J. Engel, G. Hagen, G. R. Jansen, T. D. Morris, P. Navrátil, T. Papenbrock, and S. Quaglioni, Coupled-cluster calculations of neutrinoless double-β decay in Ca48, Phys. Rev. Lett. 126, 182502 (2021).
  13. A. Belley, J. Pitcher, T. Miyagi, S. R. Stroberg, and J. D. Holt, Correlation of neutrinoless double-beta decay nuclear matrix elements with nucleon-nucleon phase shifts, arXiv:2408.02169.
  14. A. Belley, J. M. Yao, B. Bally, J. Pitcher, J. Engel, H. Hergert, J. D. Holt, T. Miyagi, T. R. Rodríguez, A. M. Romero, S. R. Stroberg, and X. Zhang, Ab initio uncertainty quantification of neutrinoless double-beta decay in Ge76, Phys. Rev. Lett. 132, 182502 (2024).
  15. N. Shimizu, J. Menéndez, and K. Yako, Double Gamow-Teller transitions and its relation to neutrinoless ββ decay, Phys. Rev. Lett. 120, 142502 (2018).
  16. J. M. Yao, I. Ginnett, A. Belley, T. Miyagi, R. Wirth, S. Bogner, J. Engel, H. Hergert, J. D. Holt, and S. R. Stroberg, Ab initio studies of the double–Gamow-Teller transition and its correlation with neutrinoless double-β decay, Phys. Rev. C 106, 014315 (2022).
  17. L. Jokiniemi and J. Menéndez, Correlations between neutrinoless double-β, double Gamow-Teller, and double-magnetic decays in the proton-neutron quasiparticle random-phase approximation framework, Phys. Rev. C 107, 044316 (2023).
  18. Y. K. Wang, P. W. Zhao, and J. Meng, Correlation between neutrinoless double-β decay and double Gamow-Teller transitions, Phys. Lett. B 855, 138796 (2024).
  19. B. Romeo, J. Menéndez, and C. Peña Garay, γγ decay as a probe of neutrinoless ββ decay nuclear matrix elements, Phys. Lett. B 827, 136965 (2022).
  20. B. Romeo, D. Stramaccioni, J. Menéndez, and J. J. Valiente-Dobón, A pathway to unveiling neutrinoless ββ decay nuclear matrix elements via γγ decay, Phys. Lett. B 860, 139186 (2025).
  21. M. Horoi, A. Neacsu, and S. Stoica, Statistical analysis for the neutrinoless double-β-decay matrix element of Ca48, Phys. Rev. C 106, 054302 (2022).
  22. M. Horoi, A. Neacsu, and S. Stoica, Predicting the neutrinoless double-β-decay matrix element of Xe136 using a statistical approach, Phys. Rev. C 107, 045501 (2023).
  23. A. Belley, T. Miyagi, S. R. Stroberg, and J. D. Holt, Constraining neutrinoless double-beta decay matrix elements from ab initio nuclear theory, AIP Conf. Proc. 3143, 020002 (2025).
  24. X. Zhang, C. C. Wang, C. R. Ding, and J. M. Yao, Subspace-projected multireference covariant density functional theory, arXiv:2408.00691.
  25. X. Zhang, C. C. Wang, C. R. Ding, and J. M. Yao, Global sensitivity analysis and uncertainty quantification of nuclear low-lying states and double-beta decay with a covariant energy density functional, arXiv:2408.13209.
  26. T. R. Rodríguez and G. Martínez-Pinedo, Energy density functional study of nuclear matrix elements for neutrinoless ββ decay, Phys. Rev. Lett. 105, 252503 (2010).
  27. J. M. Yao, L. S. Song, K. Hagino, P. Ring, and J. Meng, Systematic study of nuclear matrix elements in neutrinoless double-β decay with a beyond-mean-field covariant density functional theory, Phys. Rev. C 91, 024316 (2015).
  28. C. Jiao, C. Yuan, and J. Yao, Correlation of neutrinoless double-β decay nuclear matrix element with E2 strength, Symmetry 15, 552 (2023).
  29. L. Adamczyk et al. (STAR Collaboration), Azimuthal anisotropy in U+U and Au+Au collisions at RHIC, Phys. Rev. Lett. 115, 222301 (2015).
  30. S. Acharya et al. (ALICE Collaboration), Anisotropic flow in Xe-Xe collisions at sNN=5.44  TeV, Phys. Lett. B 784, 82 (2018).
  31. A. M. Sirunyan et al. (CMS Collaboration), Charged-particle angular correlations in XeXe collisions at sNN=5.44  TeV, Phys. Rev. C 100, 044902 (2019).
  32. G. Aad et al. (ATLAS Collaboration), Measurement of the azimuthal anisotropy of charged-particle production in Xe+Xe collisions at sNN=5.44  TeV with the ATLAS detector, Phys. Rev. C 101, 024906 (2020).
  33. M. Abdallah et al. (STAR Collaboration), Search for the chiral magnetic effect with isobar collisions at sNN=200  GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 105, 014901 (2022).
  34. S. Acharya et al. (ALICE Collaboration), Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations, Phys. Lett. B 834, 137393 (2022).
  35. G. Aad et al. (ATLAS Collaboration), Correlations between flow and transverse momentum in Xe+Xe and Pb+Pb collisions at the LHC with the ATLAS detector: A probe of the heavy-ion initial state and nuclear deformation, Phys. Rev. C 107, 054910 (2023).
  36. M. I. Abdulhamid et al. (STAR Collaboration), Imaging shapes of atomic nuclei in high-energy nuclear collisions, Nature (London) 635, 67 (2024).
  37. S. Acharya et al. (ALICE Collaboration), Exploring nuclear structure with multiparticle azimuthal correlations at the LHC, arXiv:2409.04343.
  38. G. Giacalone, J. Jia, and V. Somà, Accessing the shape of atomic nuclei with relativistic collisions of isobars, Phys. Rev. C 104, L041903 (2021).
  39. H.-j. Xu, W. Zhao, H. Li, Y. Zhou, L.-W. Chen, and F. Wang, Probing nuclear structure with mean transverse momentum in relativistic isobar collisions, Phys. Rev. C 108, L011902 (2023).
  40. G. Nijs and W. van der Schee, Inferring nuclear structure from heavy isobar collisions using Trajectum, SciPost Phys. 15, 041 (2023).
  41. C. Zhang, S. Bhatta, and J. Jia, Ratios of collective flow observables in high-energy isobar collisions are insensitive to final-state interactions, Phys. Rev. C 106, L031901 (2022).
  42. S. Zhao, H.-j. Xu, Y.-X. Liu, and H. Song, Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs, Phys. Lett. B 839, 137838 (2023).
  43. F. G. Gardim, A. V. Giannini, F. Grassi, K. P. Pala, and W. M. Serenone, Impact of the pre-equilibrium stage for the determination of nuclear geometry in high-energy isobar collisions, Phys. Rev. C 110, 064907 (2024).
  44. G. Giacalone et al., The unexpected uses of a bowling pin: exploiting Ne20 isotopes for precision characterizations of collectivity in small systems, arXiv:2402.05995.
  45. G. Giacalone et al., Anisotropic flow in fixed-target Pb208+Ne20 collisions as a probe of quark-gluon plasma, Phys. Rev. Lett. 134, 082301 (2025).
  46. H.-j. Xu, J. Zhao, and F. Wang, Hexadecapole deformation of U238 from relativistic heavy-ion collisions using a nonlinear response coefficient, Phys. Rev. Lett. 132, 262301 (2024).
  47. H. Mäntysaari, B. Schenke, C. Shen, and W. Zhao, Probing nuclear structure of heavy ions at energies available at the CERN large hadron collider, Phys. Rev. C 110, 054913 (2024).
  48. L. S. Song, J. M. Yao, P. Ring, and J. Meng, Relativistic description of nuclear matrix elements in neutrinoless double-β decay, Phys. Rev. C 90, 054309 (2014).
  49. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zymp-tyjj, which includes Refs. [50–53], for a detailed introduction to the MR-CDFT approach, the expression for the transition operators of neutrinoless double-beta decay, as well as a detailed description of the high-energy collision simulations and observables. Additional results include the correlations between the NME and the quadrupole deformation of the final nucleus Sm150, the correlation of the NME with the difference in the quadrupole deformation between Nd150 and Sm150, as well as the correlation between the NME and high-energy collision observables at higher values of the collision impact parameter.
  50. D. L. Hill and J. A. Wheeler, Nuclear constitution and the interpretation of fission phenomena, Phys. Rev. 89, 1102 (1953).
  51. P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980).
  52. F. Simkovic, G. Pantis, J. D. Vergados, and A. Faessler, Additional nucleon current contributions to neutrinoless double beta decay, Phys. Rev. C 60, 055502 (1999).
  53. J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, and U. Heinz, Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94, 024907 (2016).
  54. V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, E. Mereghetti, S. Pastore, and U. van Kolck, New leading contribution to neutrinoless double-β decay, Phys. Rev. Lett. 120, 202001 (2018).
  55. Y. Yang and P. Zhao, Relativistic model-free prediction for neutrinoless double beta decay at leading order, Phys. Lett. B 855, 138782 (2024).
  56. L.-J. Wang, J. Engel, and J. M. Yao, Quenching of nuclear matrix elements for 0νββ decay by chiral two-body currents, Phys. Rev. C 98, 031301(R) (2018).
  57. T. Burvenich, D. G. Madland, J. A. Maruhn, and P. G. Reinhard, Nuclear ground state observables and QCD scaling in a refined relativistic point coupling model, Phys. Rev. C 65, 044308 (2002).
  58. P. W. Zhao, Z. P. Li, J. M. Yao, and J. Meng, New parametrization for the nuclear covariant energy density functional with point-coupling interaction, Phys. Rev. C 82, 054319 (2010).
  59. J. M. Yao, L. S. Song, K. Hagino, P. Ring, and J. Meng, Systematic study of nuclear matrix elements in neutrinoless double-β decay with a beyond-mean-field covariant density functional theory, Phys. Rev. C 91, 024316 (2015).
  60. S. Raman, C. Nestor, and P. Tikkanen, Transition probability from the ground to the first-excited 2+ state of even–even nuclides, At. Data Nucl. Data Tables 78, 1 (2001).
  61. B. Bally, M. Bender, G. Giacalone, and V. Somà, Evidence of the triaxial structure of Xe129 at the large hadron collider, Phys. Rev. Lett. 128, 082301 (2022).
  62. B. Bally, G. Giacalone, and M. Bender, The shape of gold, Eur. Phys. J. A 59, 58 (2023).
  63. W. Ryssens, G. Giacalone, B. Schenke, and C. Shen, Evidence of hexadecapole deformation in Uranium-238 at the relativistic heavy ion collider, Phys. Rev. Lett. 130, 212302 (2023).
  64. J. S. Moreland, J. E. Bernhard, and S. A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92, 011901(R) (2015).
  65. D. Teaney and L. Yan, Triangularity and dipole asymmetry in heavy ion collisions, Phys. Rev. C 83, 064904 (2011).
  66. G. Giacalone, J. Jia, and C. Zhang, Impact of nuclear deformation on relativistic heavy-ion collisions: Assessing consistency in nuclear physics across energy scales, Phys. Rev. Lett. 127, 242301 (2021).
  67. K. Chaturvedi, R. Chandra, P. K. Rath, P. K. Raina, and J. G. Hirsch, Nuclear deformation and neutrinoless double-beta decay of Zr94,96, Mo98,100, Ru104, Pd110, Te128,130, and Nd150 nuclei within a mechanism involving neutrino mass, Phys. Rev. C 78, 054302 (2008).
  68. D.-L. Fang, A. Faessler, V. Rodin, and F. Simkovic, Neutrinoless double-beta decay of Nd150 accounting for deformation, Phys. Rev. C 82, 051301(R) (2010).
  69. M. T. Mustonen and J. Engel, Large-scale calculations of the double-β decay of Ge76, Te130, Xe136, and Nd150 in the deformed self-consistent Skyrme quasiparticle random-phase approximation, Phys. Rev. C 87, 064302 (2013).
  70. R. Sahu and V. K. B. Kota, Deformed shell model results for neutrinoless double beta decay of nuclei in A=60−90 region, Int. J. Mod. Phys. E 24, 1550022 (2015).
  71. D.-L. Fang, A. Faessler, and F. Simkovic, 0νββ-decay nuclear matrix element for light and heavy neutrino mass mechanisms from deformed quasiparticle random-phase approximation calculations for Ge76, Se82, Te130, Xe136, and Nd150 with isospin restoration, Phys. Rev. C 97, 045503 (2018).
  72. G. Giacalone, Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plasmas to hadron distributions, Eur. Phys. J. A 59, 297 (2023).
  73. J.-Y. Ollitrault, Measures of azimuthal anisotropy in high-energy collisions, Eur. Phys. J. A 59, 236 (2023).
  74. H. Niemi, G. S. Denicol, H. Holopainen, and P. Huovinen, Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions, Phys. Rev. C 87, 054901 (2013).
  75. J. Noronha-Hostler, L. Yan, F. G. Gardim, and J.-Y. Ollitrault, Linear and cubic response to the initial eccentricity in heavy-ion collisions, Phys. Rev. C 93, 014909 (2016).
  76. J. Sousa, J. Noronha, and M. Luzum, Initial energy-momentum to final flow: A general framework for heavy-ion collisions, Phys. Rev. C 110, 044909 (2024).
  77. B. Schenke, C. Shen, and D. Teaney, Transverse momentum fluctuations and their correlation with elliptic flow in nuclear collision, Phys. Rev. C 102, 034905 (2020).
  78. G. Giacalone, F. G. Gardim, J. Noronha-Hostler, and J.-Y. Ollitrault, Correlation between mean transverse momentum and anisotropic flow in heavy-ion collisions, Phys. Rev. C 103, 024909 (2021).
  79. N. M. Fortier, S. Jeon, and C. Gale, Comparisons and predictions for collisions of deformed U238 nuclei at sNN=193  GeV, Phys. Rev. C 111, 014901 (2025).
  80. N. M. Fortier, S. Jeon, and C. Gale, Heavy-ion collisions as probes of nuclear structure, Phys. Rev. C 111, L011901 (2025).
  81. G. Giacalone, Elliptic flow fluctuations in central collisions of spherical and deformed nuclei, Phys. Rev. C 99, 024910 (2019).
  82. H. Mehrabpour and S. M. A. Tabatabaee, Flow distribution analysis as a probe of nuclear deformation, Phys. Rev. C 108, 034902 (2023).
  83. G. Giacalone, Observing the deformation of nuclei with relativistic nuclear collisions, Phys. Rev. Lett. 124, 202301 (2020).
  84. G. Giacalone, Constraining the quadrupole deformation of atomic nuclei with relativistic nuclear collisions, Phys. Rev. C 102, 024901 (2020).
  85. J. Jia, S. Huang, and C. Zhang, Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions, Phys. Rev. C 105, 014906 (2022).
  86. J. Jia, Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions, Phys. Rev. C 105, 044905 (2022).
  87. C. Zhang and J. Jia, Evidence of quadrupole and octupole deformations in Zr96+Zr96 and Ru96+Ru96 collisions at ultrarelativistic energies, Phys. Rev. Lett. 128, 022301 (2022).
  88. E. G. D. Nielsen, F. K. Rømer, K. Gulbrandsen, and Y. Zhou, Generic multi-particle transverse momentum correlations as a new tool for studying nuclear structure at the energy frontier, Eur. Phys. J. A 60, 38 (2024).
  89. Letter of intent for ALICE 3: A next-generation heavy-ion experiment at the LHC, arXiv:2211.02491.
  90. R. Alemany Fernandez, Prospects for light-ion operation at the HL-LHC: Machine developments and physics opportunities, Proc. Sci. LHCP2024 (2025) 335.
  91. R. Álvarez-Rodríguez, P. Sarriguren, E. M. de Guerra, L. Pacearescu, A. Faessler, and F. Šimkovic, Deformed quasiparticle random phase approximation formalism for single- and two-neutrino double β decay, Phys. Rev. C 70, 064309 (2004).
  92. F. Šimkovic, L. Pacearescu, and A. Faessler, Two-neutrino double beta decay of Ge76 within deformed QRPA, Nucl. Phys. A733, 321 (2004).
  93. M. S. Yousef, V. Rodin, A. Faessler, and F. Simkovic, Two-neutrino double beta decay of deformed nuclei within QRPA with realistic interaction, Phys. Rev. C 79, 014314 (2009).
  94. L. Pacearescu, A. Faessler, and F. Simkovic, Nuclear deformation and the double-beta decay, Phys. At. Nucl. 67, 1210 (2004).

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Phys. Rev. Lett. 135, 022301– Published 8 July, 2025
  • Received 5 March 2025
  • Accepted 23 June 2025
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