Nuclear Physics from QCD
Recent attempts to make direct contact between QCD and simple nuclear systems are reviewed.
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arXiv subjects
Silas R. Beane
Publications and source records attributed to Silas R. Beane.
Nucleons Properties at Finite Lattice Spacing in Chiral Perturbation Theory
Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.
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The Lambda_Q-Lambda_Q Potential
Lattice QCD simulations of the potential between two baryons, each containing a heavy quark and two light quarks, such as the Lambda_Q-Lambda_Q potential, will provide insight into the nucleon-nucleon interaction. As one-pion exchange does not contribute to the Lambda_Q-Lambda_Q potential, the long-distance behavior is dominated by physics that contributes to the intermediate-range attraction between two nucleons. We compute the leading long-distance contributions to the Lambda_Q-Lambda_Q potential in QCD and in partially-quenched QCD in the low-energy effective field theory.
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Exploring Baryon Chiral Multiplets
The full QCD chiral symmetry algebra has predictive consequences at low energies. I discuss the ground-state chiral multiplet involving the light baryons and emphasize the special role of the Roper resonance.
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The Quark-Mass Dependence of Two-Nucleon Systems
We explore the quark-mass dependence of two-nucleon systems. Allowed regions for the scattering lengths in the 1S0 and 3S1 channels as functions of the light-quark masses are determined from the current uncertainty in strong-interaction parameters that appear at next-to-leading order in the effective field theory. Where experimental constraints are absent, as is the case for the quark-mass dependent four-nucleon operators, we use naive dimensional analysis. We find it likely that there is no bound state in the 1S0 channel in the chiral limit. However, given the present uncertainties in strong-interaction parameters it is unclear whether the deuteron is bound or unbound in the chiral limit.
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A Conjecture about Hadrons
We conjecture that in the chiral limit of QCD the spectrum of hadrons is comprised of decoupled, reducible chiral multiplets. A simple rule is developed which identifies the chiral representations filled out by the ground-state hadrons. Our arguments are based on the algebraic structure of superconvergence relations derived by Weinberg from the high-energy behavior of pion-hadron scattering amplitudes.
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The Role of the Roper in QCD
We show that existing data suggest a simple scenario in which the nucleon, and the Delta and Roper resonances act as chiral partners in a reducible representation of the full QCD chiral symmetry group. We discuss the peculiar interpretation of this scenario using spin-flavor symmetries of the naive constituent quark model, as well as the consistency of the scenario with large-Nc expectations.
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Partially-Quenched Nucleon-Nucleon Scattering
Nucleon-nucleon scattering is studied to next-to-leading order in a partially-quenched extension of an effective field theory used to describe multi-nucleon systems in QCD. The partially-quenched nucleon-nucleon amplitudes will play an important role in relating lattice simulations of the two-nucleon sector to nature.
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Variation of Fundamental Couplings and Nuclear Forces
The dependence of the nuclear force on standard model parameters plays an important role in bounding time and space variations of fundamental couplings over cosmological time scales. We discuss the quark-mass dependence of deuteron and di-neutron binding in a systematic chiral expansion. The leading quark-mass dependence of the nuclear force arises from one-pion exchange and from local quark-mass dependent four-nucleon operators with coefficients that are presently unknown. By varying these coefficients while leaving nuclear observables at the physical values of the quark masses invariant, we find scenarios where two-nucleon physics depends both weakly and strongly on the quark masses. While the determination of these coefficients is an exciting future opportunity for lattice QCD, we conclude that, at present, bounds on time and space variations of fundamental parameters from the two-nucleon sector are much weaker than previously claimed. This brings into question the reliability of coupling-constant bounds derived from more complex nuclei and nuclear processes.
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Pions in the Pionless Effective Field Theory
We show that processes involving pions that remain very near their mass-shell can be reliably computed in the pionless effective field theory, with the pion integrated in as a heavy field. As an application, we compute the pion-deuteron scattering amplitude near threshold to next-to-leading order in the momentum expansion. This amplitude is formally dominated by an infrared logarithm of the form log(gamma/mpi), where gamma is the deuteron binding momentum, and mpi is the mass of the pion. The coefficient of this logarithm is determined by the S-wave pion-nucleon scattering lengths.
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Nucleon-Nucleon Scattering in the 1/N Expansion
The nucleon-nucleon 3S1-3D1 coupled-channel problem is solved analytically to leading order in a joint expansion in the quark masses and in 1/N. An approximate expression is derived for the 3S1 scattering length in the large-N limit, and the large-N behavior of the deuteron is discussed.
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Hadronic Parity-Violation on the Lattice
We motivate lattice QCD studies of the parity-violating pion-nucleon coupling constant and extend flavor-conserving hadronic parity-violation from QCD to partially-quenched QCD. The parity-violating pion-nucleon coupling and the anapole form factor (and moment) of the proton are computed to one-loop order in the partially-quenched chiral expansion. For the parity-violating pion-nucleon interaction, we include the contributions from total derivative operators necessary to match the kinematics that will be used in lattice simulations.
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Nucleons in Two-Flavor Partially-Quenched Chiral Perturbation Theory
Properties of the proton and the neutron are explored in partially-quenched chiral perturbation theory with two non-degenerate light flavors. Masses, magnetic moments, matrix elements of isovector twist-2 operators and axial-vector currents are computed at the one-loop level in the chiral expansion.
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Nucleon-Nucleon Interactions on the Lattice
We consider the nucleon-nucleon potential in quenched and partially-quenched QCD. The leading one-meson exchange contribution to the potential is found to fall off exponentially at long-distances, in contrast with the Yukawa-type behaviour found in QCD. This unphysical component of the two-nucleon potential has important implications for the extraction of nuclear properties from lattice simulations.
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Photonic Probes of the Deuteron in Effective Field Theory
I give a taste of recent progress in using chiral perturbation theory to understand nucleon and deuteron structure.
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Rearranging Pionless Effective Field Theory
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
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From Hadrons to Nuclei: Crossing the Border
The study of nuclei predates by many years the theory of quantum chromodynamics. More recently, effective field theories have been used in nuclear physics to ``cross the border'' from QCD to a nuclear theory. We are now entering the second decade of efforts to develop a perturbative theory of nuclear interactions using effective field theory. This work describes the current status of these efforts.
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How to Renormalize the Gap Equation in High Density QCD
We discuss two technical issues related to the gap equation in high-density QCD: i) how to obtain the asymptotic solution with well controlled approximations, and ii) the renormalization of four-quark operators in the high-density effective field theory.
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