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Nuclear Physics from Lattice QCD

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Lattice QCD for Nuclear Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 889))

Abstract

I present a pedagogical overview of the application of lattice QCD to the physics of multi-hadron systems. This is a relatively new area of research in which progress has been significant in the last few years and the aim of these lectures is to provide a perspective on the current and future scope of this emerging frontier. After reviewing the recent developments that are beginning to enable nuclear physics to be studied from the underlying theory of the Standard Model, I discuss the recent results that have been obtained in the study of two-hadron and multi-hadron systems. I also explore the difficulties particular to lattice QCD calculations of such systems and emphasise the issues that remain to be resolved.

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Notes

  1. 1.

    This is very loose terminology as the ground state should not be thought of as a bare object to which pions are added to get an excited state.

  2. 2.

    At a minimum, stable under the strong interaction.

  3. 3.

    See also the original derivation [125, 227] or [123] for a particularly clear alternate derivation.

  4. 4.

    Working with relativistic particles does not modify the resulting expressions. In the non-relativistic context, the relativistic corrections can be accounted for by changes in higher-derivative operators.

  5. 5.

    With flavour independent boundary conditions, quarks and anti-quarks receive equal and opposite twists so mesonic systems are unaffected. One can introduce flavour-twisted boundary conditions [266–270] to modify flavour non-singlet mesonic quantisation conditions, but this introduces difficulties in importance sampling and can only be easily implemented for valence quarks.

  6. 6.

    Only states that are the lightest state with a given set of quantum numbers are asymptotically stable: for hadrons composed of light and strange quarks, only the pion, kaon, proton and Λ, Ξ and Ω baryons are stable under the strong interaction. Interestingly, at unphysically heavy quark masses and finite volume, a number of other states such as the ρ and Δ become stable because the pion mass increases more rapidly than that of other hadrons as the quark masses increase.

  7. 7.

    In the strict definition of a hadron as a localised colourless asymptotic state, what we refer to as a multi-hadron bound state is itself a hadron.

  8. 8.

    In the limit that the masses of both hadrons become infinite, only the first term in Eq. (5.28) survives and an energy-independent local potential can be defined [287–292]. In this limit, r also becomes a well-defined quantum number.

  9. 9.

    In a finite volume, it is not obvious that any state can be purely an elastic state, a concept that requires asymptotic separations. Nevertheless, for large volumes, it is perhaps enough to invoke the cluster decomposition property.

  10. 10.

    We note that all of the calculations discussed here are performed at essentially one lattice spacing, a ∼ 0. 1—0.12 fm in the isospin symmetric limit. It is expected that lattice artifacts, which are typically \(\mathcal{O}(a^{2})\) in these calculations, and isospin-breaking effects produce sub-leading modifications to dibaryon energies.

  11. 11.

    It is an interesting and subtle question as to whether a nucleus is indeed more complex than a proton; from the QCD point of view, both are complicated systems made of many quarks, anti-quarks and gluons.

  12. 12.

    The methods of [374, 375] differ in the way in which the lists of weights are constructed. Reference [374] iterates over the full, factorially-large set of possible index values, whereas [375] constructs the index lists recursively by building a multi-baryon system up one baryon at a time. In [376], the recursive approach is further developed with a clever definition of the antisymmetrisation operation.

  13. 13.

    For kaons there is a minor problem with the growth of noise.

  14. 14.

    As discussed above, in [381], a first numerical investigation of matrix elements of multi-pion systems has been presented. Even in this simplest case, theoretical difficulties remain to be resolved.

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Acknowledgements

I warmly thank Stefan Meinel, Zhifeng Shi, Brian Tiburzi and my colleagues in the NPLQCD collaboration for many interesting discussions on the topics of these lectures and Zhifeng Shi for producing Fig. 5.7. I also thank Huey-Wen Lin, Harvey Meyer and David Richards for their hard work in organising this very successful summer school. Finally, I thank the students, in particular Raul Briceno and Zoreh Davoudi, for making the lectures enjoyable. This work was supported by the U.S. Department of Energy through Outstanding Junior Investigator Award DE-SC0001784 and Early Career Award DE-SC0010495 and by the Solomon Buchsbaum Fund at MIT.

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  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    William Detmold

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  1. William Detmold
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Correspondence to William Detmold .

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  1. Department of Physics, University of Washington, Seattle, Washington, USA

    Huey-Wen Lin

  2. Institute of Nuclear Physics, Johannes Gutenberg-Universität Mainz, Mainz, Germany

    Harvey B. Meyer

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Detmold, W. (2015). Nuclear Physics from Lattice QCD. In: Lin, HW., Meyer, H. (eds) Lattice QCD for Nuclear Physics. Lecture Notes in Physics, vol 889. Springer, Cham. https://doi.org/10.1007/978-3-319-08022-2_5

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