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Quark-level analogue of nuclear fusion with doubly heavy baryons

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The essence of nuclear fusion is that energy can be released by the rearrangement of nucleons between the initial- and final-state nuclei. The recent discovery1 of the first doubly charmed baryon , which contains two charm quarks (c) and one up quark (u) and has a mass of about 3,621 megaelectronvolts (MeV) (the mass of the proton is 938 MeV) also revealed a large binding energy of about 130 MeV between the two charm quarks. Here we report that this strong binding enables a quark-rearrangement, exothermic reaction in which two heavy baryons (Λc) undergo fusion to produce the doubly charmed baryon and a neutron n (), resulting in an energy release of 12 MeV. This reaction is a quark-level analogue of the deuterium–tritium nuclear fusion reaction (DT → 4He n). The much larger binding energy (approximately 280 MeV) between two bottom quarks (b) causes the analogous reaction with bottom quarks () to have a much larger energy release of about 138 MeV. We suggest some experimental setups in which the highly exothermic nature of the fusion of two heavy-quark baryons might manifest itself. At present, however, the very short lifetimes of the heavy bottom and charm quarks preclude any practical applications of such reactions.

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Figure 1: Schematic depiction of quark-level exothermic fusion reactions ΛQΛQΞQQN, where Q, Q {b, c}.
Figure 2: The energy release ΔE in the quark-level fusion reactions ΛQΛQΞQQN, where Q, Q {s, c, b}, plotted against the reduced masses of the doubly heavy diquarks, μred(QQ′).

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  • 30 November 2017

    Please see accompanying Erratum ( In this Letter, on the right-hand side of the fifth line of equation (2), ‘3He p’ should read ‘4He p’. This error has been corrected online.


  1. The LHCb Collaboration. Observation of the doubly charmed baryon . Phys. Rev. Lett. 119, 112011 (2017)

  2. Karliner, M. & Rosner, J. L. Baryons with two heavy quarks: masses, production, decays, and detection. Phys. Rev. D 90, 094007 (2014)

    ADS  Article  Google Scholar 

  3. Karliner, M . & Rosner, J. L. Discovery of doubly-charmed baryon implies a stable tetraquark. Phys. Rev. Lett. (in the press); preprint at (2017)

  4. Atzeni, S . & Meyer-ter-Vehn, J. The Physics of Inertial Fusion Table 1.1, Ch. 1 (Oxford Univ. Press, 2004)

  5. Gell-Mann, M. The Eightfold Way: A Theory of strong interaction symmetry. Report No. TID-12608; CTSL-20, (California Institute of Technology, 1961)

  6. Okubo, S. Note on unitary symmetry in strong interactions. Prog. Theor. Phys. 27, 949–966 (1962)

    ADS  Article  Google Scholar 

  7. Gal, A., Hungerford, E. V. & Millener, D. J. Strangeness in nuclear physics. Rev. Mod. Phys. 88, 035004 (2016)

    ADS  Article  Google Scholar 

  8. Harada, T., Hirabayashi, Y. & Umeya, A. Production of doubly strange hypernuclei via Ξ doorways in the 16O(K, K+) reaction at 1.8 GeV/c. Phys. Lett. B 690, 363–368 (2010)

    ADS  CAS  Article  Google Scholar 

  9. Dover, C. B. & Gal, A. Ξ hypernuclei. Ann. Phys. 146, 309–348 (1983)

    ADS  CAS  Article  Google Scholar 

  10. Wang, M. et al. The AME2016 atomic mass evaluation (II). Tables, graphs and references. Chinese Phys C. 41, 030003 (2017); data available at

    ADS  Article  Google Scholar 

  11. The LHCb Collaboration. RICH Technical Design Report. Report No. LHCC 2000-037, (CERN, 2000)

  12. The LHCb Collaboration. Measurement of the B± production cross-section in pp collisions at = 7 TeV. J. High Energy Phys. 4, 93 (2012)

  13. The LHCb Collaboration. Measurement of B meson production cross-sections in proton-proton collisions at = 7 TeV. J. High Energy Phys. 8, 117 (2013)

  14. The LHCb Collaboration. Study of the production of and hadrons in pp collisions and first measurement of the branching fraction. Chinese Phys. C 40, 011001 (2016)

  15. Dainese, A. Heavy-quark production in heavy-ion collisions. J. Phys. Conf. Ser. 446, 012034 (2013)

    Article  Google Scholar 

  16. Grelli, A. Experimental overview on heavy-flavor production. J. Phys. Conf. Ser. 832, 012020 (2017)

    Article  Google Scholar 

  17. Schaffner, J., Dover, C. B., Gal, A., Greiner, C. & Stoecker, H. Strange hadronic matter. Phys. Rev. Lett. 71, 1328–1331 (1993)

    ADS  CAS  Article  Google Scholar 

  18. Schaffner, J. et al. Multiply strange nuclear systems. Ann. Phys. 235, 35–76 (1994)

    ADS  CAS  Article  Google Scholar 

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We thank A. Gal for calling our attention to refs 17 and 18. We thank V. Belyaev, S. Brodsky, A. Gal and T. Skwarnicki for comments.

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Both authors contributed equally to this work.

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Correspondence to Marek Karliner.

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Reviewer Information Nature thanks G. Miller and S. Stone for their contribution to the peer review of this work.

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Karliner, M., Rosner, J. Quark-level analogue of nuclear fusion with doubly heavy baryons. Nature 551, 89–91 (2017).

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