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The s-wave nucleon-nucleon (NN) scattering matrix ($S$-matrix) exhibits UV/IR symmetries which are hidden in the effective field theory (EFT) action and scattering amplitudes, and which explain some generic features of the phase shifts. These symmetries offer clarifying interpretations of existing pionless EFT expansions, and suggest starting points for novel expansions. The leading-order (LO) $S$-matrix obtained in the pionless EFT with scattering lengths treated exactly is shown to have a UV/IR symmetry which leaves the sum of s-wave phase shifts invariant. A new scheme, which treats effective range corrections exactly, and which possesses a distinct UV/IR symmetry at LO, is developed up to NLO (next-to-LO) and compared with data., 20 pages, 4 figures. Contribution to Special Issue of Few-Body Systems: Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians. References and clarifications added in v2

The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an effective field theory framework. It has long been observed that universal corrections to the energy density to two orders in the interaction strength do not agree with Monte Carlo simulations in the weak-coupling regime. Here, universal corrections to three orders in the interaction strength are obtained for the first time, and are shown to provide agreement between theory and simulation. Special consideration is given to the scale ambiguity associated with the non-trivial renormalization of the singular contact interactions. The isotropic superfluid gap is obtained to next-to-leading order, and nonuniversal contributions to the energy density due to effective range effects, p-wave interactions and three-body forces are computed. Results are compared with precise Monte Carlo simulations of the energy density and the contact in the weakly-coupled attractive and repulsive Fermi liquid regimes. In addition, the known all-orders sum of ladder and ring diagrams is compared with Monte Carlo simulations at weak coupling and beyond., Comment: 35 pages, 18 figures. Clarifications and references added in v2

Recent work arXiv:1812.03138 [nucl-th] conjectured that entanglement is minimized in low-energy hadronic scattering processes. It was shown that the minimization of the entanglement power (EP) of the low-energy baryon-baryon $S$-matrix implies novel spin-flavor symmetries that are distinct from large-$N_c$ QCD predictions and are confirmed by high-precision lattice QCD simulations. Here the conjecture of minimal entanglement is investigated for scattering processes involving pions and nucleons. The EP of the $S$-matrix is constructed for the $\pi\pi$ and $\pi N$ systems, and the consequences of minimization of entanglement are discussed and compared with large-$N_c$ QCD expectations., Comment: 18 pages, 2 figures. References and clarifications added in v2

The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_{\pi}\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $\Sigma N$ ($I=3/2$), and $\Xi\Xi$ states, the spin-singlet $\Sigma\Sigma$ ($I=2$) and $\Xi\Sigma$ ($I=3/2$) states, and the spin-triplet $\Xi N$ ($I=0$) state. The $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using L\"uscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $\Sigma N$ and $\Xi\Xi$ channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.

A formulation of nucleon-nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix -- that appears at leading-order in the EFT description -- possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code., Comment: 44 pages, 18 figures. References and clarifications added in v2

Entanglement suppression in the strong interaction $S$-matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner $SU(4)$ symmetry for two flavors and an $SU(16)$ symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints on the nature of nuclear and hypernuclear forces in dense matter., Comment: 6 pages, 5 pages supplemental, 4 figures

Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial-vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial-vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler-Weisberger, Gerasimov-Drell-Hearn, Cabbibo-Radicatti and Fubini-Furlan-Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S-matrix elements in the Regge limit., Comment: 38 pages, 2 figures

I review various aspects of chiral symmetry and its spontaneous breaking on null planes, including the interesting manner in which Goldstone's theorem is realized and the constraints that chiral symmetry imposes on the null-plane Hamiltonians. Specializing to QCD with N massless flavors, I show that there is an interesting limit in which the chiral constraints on the null-plane Hamiltonians can be solved to give the spin-flavor algebra SU(2N), recovering a result originally found by Weinberg using different methods., 6 pages, written version of talk presented at the Light Cone 2014 Conference held at North Carolina State Univ. May 26-30

The nucleon is naturally viewed as a bipartite system of valence spin -- defined by its non-vanishing chiral charge -- and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the resulting entanglement entropy acts as an order parameter of chiral symmetry breaking in the nucleon. In the large-$N_c$ limit, the entanglement entropy vanishes and the valence spin accounts for all of the nucleon spin, while in the limit of maximal entanglement entropy, the nucleon loses memory of the valence spin and consequently has spin dominated by the sea. The nucleon state vector in the chiral basis, fit to low-energy data, gives a valence spin content consistent with experiment and lattice QCD determinations, and has large entanglement entropy., Comment: 6 pages, 3 figures

The Adler-Weisberger sum rule for the nucleon axial-vector charge, $g_A$, offers a unique signature of chiral symmetry and its breaking in QCD. Its derivation relies on both algebraic aspects of chiral symmetry, which guarantee the convergence of the sum rule, and dynamical aspects of chiral symmetry breaking---as exploited using chiral perturbation theory---which allow the rigorous inclusion of explicit chiral symmetry breaking effects due to light-quark masses. The original derivations obtained the sum rule in the chiral limit and, without the benefit of chiral perturbation theory, made various attempts at extrapolating to non-vanishing pion masses. In this paper, the leading, universal, chiral corrections to the chiral-limit sum rule are obtained. Using PDG data, a recent parametrization of the pion-nucleon total cross-sections in the resonance region given by the SAID group, as well as recent Roy-Steiner equation determinations of subthreshold amplitudes, threshold parameters, and correlated low-energy constants, the Adler-Weisberger sum rule is confronted with experimental data. With uncertainty estimates associated with the cross-section parameterization, the Goldberger-Treimann discrepancy, and the truncation of the sum rule at $\mathcal{O}(M_\pi^4)$ in the chiral expansion, this work finds $g_A = 1.248 \pm 0.010 \pm \ 0.007 \pm 0.013$., Comment: 19 pages, 5 figures

The nuclear matrix element determining the $pp\to d e^+ \nu$ fusion cross section and the Gamow-Teller matrix element contributing to tritium $\beta$-decay are calculated with lattice Quantum Chromodynamics (QCD) for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3)-flavor-symmetric value of the quark masses, corresponding to a pion mass of $m_\pi$ ~ 806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within $2\sigma$ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated $pp\to d e^+ \nu$ transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be $L_{1,A}=3.9(0.1)(1.0)(0.3)(0.9)\ {\rm fm}^3$ at a renormalization scale set by the physical pion mass, also in agreement with the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics., Comment: Published version with supplementary material

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of $m_\pi\sim 450$ and 806 MeV in uniform, time-independent magnetic fields of strength {\bf B}| \sim 10^{19}$-$10^{20}$ Gauss to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems., Comment: Accepted journal version

The current constraints from lattice QCD on the existence of the H-dibaryon are discussed. With only two significant lattice QCD calculations of the H-dibaryon binding energy at approximately the same lattice spacing, the forms of the chiral and continuum extrapolations to the physical point are not determined. In this brief report, we consider the constraints on the H-dibaryon imposed by two simple chiral extrapolations. In both instances, the extrapolation to the physical pion mass allows for a bound H-dibaryon or a near-threshold scattering state. Further lattice QCD calculations are required to clarify this situation., 8 pages, 2 figures, 1 table; revised for the journal

Isotropic scattering in various spatial dimensions is considered for arbitrary finite-range potentials using non-relativistic effective field theory. With periodic boundary conditions, compactifications from a box to a plane and to a wire, and from a plane to a wire, are considered by matching S-matrix elements. The problem is greatly simplified by regulating the ultraviolet divergences using dimensional regularization with minimal subtraction. General relations among (all) effective-range parameters in the various dimensions are derived, and the dependence of bound states on changing dimensionality are considered. Generally, it is found that compactification binds the two-body system, even if the uncompactified system is unbound. For instance, compactification from a box to a plane gives rise to a bound state with binding momentum given by $\ln \left({\scriptstyle \frac{1}{2}}\left(3+\sqrt{5} \right) \right)$ in units of the inverse compactification length. This binding momentum is universal in the sense that it does not depend on the two-body interaction in the box. When the two-body system in the box is at unitarity, the S-matrices of the compactified two-body system on the plane and on the wire are given exactly as universal functions of the compactification length, Comment: 16 pages, 4 figures

We present results of the first fully-dynamical lattice QCD determination of hyperon-nucleon scattering. One s-wave phase shift was determined for n Lambda scattering in both spin-channels at pion masses of 350, 490, and 590 MeV, and for n Sigma- scattering in both spin channels at pion masses of 490, and 590 MeV. The calculations were performed with domain-wall valence quarks on dynamical, staggered gauge configurations with a lattice spacing of b ~ 0.125 fm., Comment: 10 pages, 15 figures

Nucleon-nucleon systems are studied with lattice quantum chromodynamics at a pion mass of $$m_\pi\sim 450~{\rm MeV}$$ in three spatial volumes using $n_f=2+1$ flavors of light quarks. At the quark masses employed in this work, the deuteron binding energy is calculated to be $$B_d = 14.4^{+3.2}_{-2.6} ~{\rm MeV}$$, while the dineutron is bound by $$B_{nn} = 12.5^{+3.0}_{-5.0}~{\rm MeV}$$. Over the range of energies that are studied, the S-wave scattering phase shifts calculated in the 1S0 and 3S1-3D1 channels are found to be similar to those in nature, and indicate repulsive short-range components of the interactions, consistent with phenomenological nucleon-nucleon interactions. In both channels, the phase shifts are determined at three energies that lie within the radius of convergence of the effective range expansion, allowing for constraints to be placed on the inverse scattering lengths and effective ranges. Thus, the extracted phase shifts allow for matching to nuclear effective field theories, from which low energy counterterms are extracted and issues of convergence are investigated. As part of the analysis, a detailed investigation of the single hadron sector is performed, enabling a precise determination of the violation of the Gell-Mann–Okubo mass relation.

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process np→dγ, and the photo-disintegration processes γ^{(*)}d→np. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m_{π}~450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m_{π}~806 MeV, using only lattice QCD inputs, a cross section σ^{806 MeV}~17 mb is found at an incident neutron speed of v=2,200 m/s. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ^{lqcd}(np→dγ)=334.9(+5.2-5.4) mb is obtained at the same incident neutron speed, consistent with the experimental value of σ^{expt}(np→dγ)=334.2(0.5) mb.

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process np→dγ, and the photo-disintegration processes γ^{(*)}d→np. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m_{π}~450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m_{π}~806 MeV, using only lattice QCD inputs, a cross section σ^{806 MeV}~17 mb is found at an incident neutron speed of v=2,200 m/s. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ^{lqcd}(np→dγ)=334.9(+5.2-5.4) mb is obtained at the same incident neutron speed, consistent with the experimental value of σ^{expt}(np→dγ)=334.2(0.5) mb.

Lattice QCD with background magnetic fields is used to calculate the magnetic moments and magnetic polarizabilities of the nucleons and of light nuclei with $A\le4$, along with the cross-section for the $M1$ transition $np\rightarrow d\gamma$, at the flavor SU(3)-symmetric point where the pion mass is $m_\pi\sim 806$ MeV. These magnetic properties are extracted from nucleon and nuclear energies in six uniform magnetic fields of varying strengths. The magnetic moments are presented in a recent Letter. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter non-trivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with $\beta_p=5.22(+0.66/-0.45)(0.23) \times 10^{-4}$ fm$^3$ and $\beta_n=1.253(+0.056/-0.067)(0.055) \times 10^{-4}$ fm$^3$, exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses and its magnetic polarizability, $\beta_{nn}=1.872(+0.121/-0.113)(0.082) \times 10^{-4}$ fm$^3$ differs significantly from twice that of the neutron. A linear combination of deuteron scalar and tensor polarizabilities is determined by the energies of the $j_z=\pm 1$ deuteron states, and is found to be $\beta_{d,\pm 1}=4.4(+1.6/-1.5)(0.2) \times 10^{-4}$ fm$^3$. The magnetic polarizabilities of the three-nucleon and four-nucleon systems are found to be positive and similar in size to those of the proton, $\beta_{^{3}\rm He}=5.4(+2.2/-2.1)(0.2) \times 10^{-4}$ fm$^3$, $\beta_{^{3}\rm H}=2.6(1.7)(0.1) \times 10^{-4}$ fm$^3$, $\beta_{^{4}\rm He}=3.4(+2.0/-1.9)(0.2) \times 10^{-4}$ fm$^3$. Mixing between the $j_z=0$ deuteron state and the spin-singlet $np$ state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, ${\bar L}_1$, of the pionless effective theory for $NN$ systems (equivalent to the meson-exchange current contribution in nuclear potential models), that dictates the cross-section for the $np\to d\gamma$ process near threshold. Combined with previous determinations of NN scattering parameters, this enables an ab initio determination of the threshold cross-section at these unphysical masses., Comment: 49 pages, 24 figures

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., Comment: 16 pages TeX, uses mtexsis.tex

A critical appraisal is given of a recent analysis of the quark-mass and finite-size dependence of unquenched lattice QCD data for the nucleon mass. We use this forum to estimate the boundary of the chiral regime for nucleon properties., 7 pages, 6 figures

Lattice QCD simulations of the potential between two baryons, each containing a heavy quark and two light quarks, such as the Λ Q Λ Q potential, will provide insight into the nucleon–nucleon interaction. As one-pion exchange does not contribute to the Λ Q Λ 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 Λ Q Λ Q potential in QCD and in partially-quenched QCD in the low-energy 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., 10 pages LaTeX, 4 eps figs

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., 12 pages LaTeX, 6 ps figs, comments added

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., 15 pages LaTeX

Quarkonium-nucleus systems are composed of two interacting hadronic states without common valence quarks, which interact primarily through multi-gluon exchanges, realizing a color van der Waals force. We present lattice QCD calculations of the interactions of strange and charm quarkonia with light nuclei. Both the strangeonium-nucleus and charmonium-nucleus systems are found to be relatively deeply bound when the masses of the three light quarks are set equal to that of the physical strange quark. Extrapolation of these results to the physical light-quark masses suggests that the binding energy of charmonium to nuclear matter is B < 40 MeV., published version

The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. We review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts., A review article. 36 pages, 14 figures

We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton and ${}^3$He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to $m_\pi \sim 800$ MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of ${}^3$He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, $\mu_{{}^3{\rm H}} \sim \mu_p$. The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations., Comment: 5 pages, 4 figures, published version

The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A1+ irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves., 20 pages, 6 figures

We investigate implications of quark-hadron duality for hybrid mesons in the large-Nc limit. A simple formalism is developed which implements duality for QCD two-point functions of currents of quark bilinears, with any number of gluons. We argue that the large-Nc meson masses share a common parameter, which is related to the QCD string tension. This parameter is fixed from correlators of conserved vector and axial-vector currents, and using lattice QCD determinations of the string tension. Our results predict towers of hybrid mesons which, within expected 1/Nc corrections, naturally accommodate the 1^(-+) experimental hybrid candidates., 13 pages TeX, uses mtexsis.tex, 4 eps figures

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., 15 pages LaTeX, 9 eps figures, discussions extended and references added

The low-energy effective theories for the two- and three-flavor color-superconductors arising in the high density limit of QCD are discussed. Using an effective field theory to describe quarks near the fermi surface, we compute the masses of the pseudo-Goldstone bosons that dominate the low-momentum dynamics of these systems., Comment: 13 pages, 3 figures, latex

Compton scattering on the deuteron is studied in the framework of baryon chiral perturbation theory to third order in small momenta, for photon energies of order the pion mass. The scattering amplitude is a sum of one- and two-nucleon mechanisms with no undetermined parameters. Our results are in good agreement with existing experimental data, and a prediction is made for higher-energy data being analyzed at SAL., 39 pages LaTeX, 19 figures (uses epsf)

Sigma models in which the integer coefficient of the Wess-Zumino term vanishes are easy to construct. This is the case if all flavor symmetries are vectorlike. We show that there is a subset of SU(N)XSU(N) vectorlike sigma models in which the Wess-Zumino term vanishes for reasons of symmetry as well. However, there is no chiral sigma model in which the Wess-Zumino term vanishes for reasons of symmetry. This can be understood in the sigma model basis as a consequence of an index theorem for the axialvector coupling matrix. We prove this index theorem directly from the SU(N)XSU(N) algebra., Comment: 11 pages TeX and mtexsis.tex, 1 figure (uses epsf), corrected typos

The results given for the isoscalar combinations of nucleon electromagnetic polarizabilities in [Phys. Lett. B 567 (2003) 200] are incorrect. After correcting errors in our O ( Q 4 ) chiral perturbation theory calculation of elastic γd scattering we obtain a fit to recent experimental data with χ 2 / d.o.f. = 26.6 / 20 . For the isoscalar electric polarizability this fit yields α N = ( 13.0 ± 1.9 ( stat ) ) −1.5 +3.9 ( theory ) , while β N is consistent with zero within sizable error bars. These mistakes in our γd calculation do not affect the results quoted in [Phys. Lett. B 567 (2003) 200] for the proton polarizabilities.

It has been argued that the leading scalar-isoscalar WIMP-nucleus interactions receive parametrically enhanced contributions in the context of nuclear effective field theories. These contributions arise from meson-exchange currents (MECs) and potentially modify the impulse approximation estimates of these interactions by 10--60%. We point out that these MECs also contribute to the quark mass dependence of nuclear binding energies, that is, nuclear \sigma-terms. In this work, we use recent lattice QCD calculations of the binding energies of the deuteron, He-3 and He-4 at pion masses near 500 MeV and 800 MeV, combined with the experimentally determined binding energies at the physical point, to provide approximate determinations of the \sigma-terms for these light nuclei. For each nucleus, we find that the deviation of the corresponding nuclear \sigma-term from the single-nucleon estimate is at the few percent level, in conflict with the conjectured enhancement. As a consequence, lattice QCD calculations currently indicate that the cross sections for scalar-isoscalar WIMP-nucleus interactions arising from fundamental WIMP interactions with quarks do not suffer from significant uncertainties due to enhanced meson-exchange currents., Comment: journal version

The scattering lengths and effective ranges that describe low-energy nucleon-nucleon scattering are calculated in the limit of SU(3)-flavor symmetry at the physical strange-quark mass with Lattice Quantum Chromodynamics. The calculations are performed with an isotropic clover discretization of the quark action in three volumes with spatial extents of L \sim 3.4 fm, 4.5fm and 6.7 fm, and with a lattice spacing of b \sim 0.145 fm. With determinations of the energies of the two-nucleon systems (both of which contain bound states at these up and down quark masses) at rest and moving in the lattice volume, Luscher's method is used to determine the low-energy phase shifts in each channel, from which the scattering length and effective range are obtained. The scattering parameters, in the 1S0 channel are found to be m_pi a^(1S0) = 9.50^{+0.78}_{-0.69}^{+1.10}_{-0.80} and m_pi r^(1S0) = {4.61^{+0.29}_{-0.31}^{+0.24}_{-0.26}, and in the 3S1 channel are m_pi a^(3S1) = 7.45^{+0.57}_{-0.53}^{+0.71}_{-0.49} and m_pi r^(3S1) = 3.71^{+0.28}_{-0.31}^{+0.28}_{-0.35}. These values are consistent with the two-nucleon system exhibiting Wigner's supermultiplet symmetry, which becomes exact in the limit of large-N_c. In both spin channels, the phase shifts change sign at higher momentum, near the start of the t-channel cut, indicating that the nuclear interactions have a repulsive core even at the SU(3)-symmetric point., 17 pages, 29 figures

On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincar\'e generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone's theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann-Oakes-Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model., Comment: 42 pages, 2 figures; several typos and minor errors corrected

Threshold neutral pion photoproduction on light nuclei is studied in the framework of baryon chiral perturbation theory. We obtain a general formula for the electric dipole amplitude in the special case of neutral pion photoproduction on a nucleus. To third order in small momenta, the amplitude is a sum of 2- and 3-body interactions with no undetermined parameters. With reasonable input from the single nucleon sector, our result for neutral pion photoproduction on the deuteron is in agreement with experiment., 24 pages, 4 uuencoded postscript figures, uses LaTex and epsf.tex. Added footnote and references. Minor changes in text and format

An analysis of the pion mass and pion decay constant is performed using mixed-action Lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n_f = 2+1 MILC configurations. Calculations were performed at two lattice spacings of b~0.125 fm and b~0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1

eld theory. The interactions determined from QCD are consistent with those extracted from hyperon-nucleon experimental data within uncertainties, and strengthen theoretical arguments that the strange quark is a crucial component of dense nuclear matter. The interactions between hyperons and nucleons are important for understanding the composition of dense nuclear matter. In high-density baryonic systems, the large values of the Fermi energies may make it energetically advantageous for some of the nucleons to transform into hyperons via the weak interactions, with the increase in rest mass being more than compensated for by the decrease in combined Fermi energy of the baryon-lepton system. This is speculated to occur in the interior of neutron stars, but a quantitative understanding of this phenomenon depends on knowledge of the hyperon-nucleon (YN) interactions in the medium. In this letter we use n scattering phase shifts in the 1 S0 and 3 S1 spinchannels calculated with Lattice QCD (LQCD) to quantify the energy shift of the hyperon in dense neutron matter, as might occur in the interior of a neutron star. Our results strongly suggest an important role for strangeness in such environments. Precise nucleon-nucleon (NN) interactions constrained by experiment and chiral symmetry, together with numerically small but important three-nucleon interactions, have served as input to rened many-body techniques for

The binding energies of a range of nuclei and hypernuclei with atomic number A, 35 pages, 45 figures Increased statistics, enhanced discussion, fixed typos

The π+π+ s-wave scattering phase-shift is determined below the inelastic threshold using Lattice QCD. Calculations were performed at a pion mass of mπ ≈ 390 MeV with an anisotropic nf = 2+1 clover fermion discretization in four lattice volumes, with spatial extent L ≈ 2.0, 2.5, 3.0 and 3.9 fm, and with a lattice spacing of bs ≈ 0.123 fm in the spatial direction and bt bs/3.5 in the time direction. The phase-shift is determined from the energy-eigenvalues of π+π+ systems with both zero and non-zero total momentum in the lattice volume using Luscher's method. Our calculations are precise enough to allow for a determination of the threshold scattering parameters, the scattering length a, the effective range r, and the shape-parameter P, in this channel and to examine the prediction of two-flavor chiral perturbation theory: mπ2 a r = 3+O(mπ2/Λχ2). Chiral perturbation theory is used, with the Lattice QCD results as input, to predict the scattering phase-shift (and threshold parameters) at the physical pion mass. Our results are consistent with determinations from the Roy equations and with the existing experimental phase shift data.

Observable consequences of the hypothesis that the observed universe is a numerical simulation performed on a cubic space-time lattice or grid are explored. The simulation scenario is first motivated by extrapolating current trends in computational resource requirements for lattice QCD into the future. Using the historical development of lattice gauge theory technology as a guide, we assume that our universe is an early numerical simulation with unimproved Wilson fermion discretization and investigate potentially-observable consequences. Among the observables that are considered are the muon g-2 and the current differences between determinations of alpha, but the most stringent bound on the inverse lattice spacing of the universe, b^(-1) >~ 10^(11) GeV, is derived from the high-energy cut off of the cosmic ray spectrum. The numerical simulation scenario could reveal itself in the distributions of the highest energy cosmic rays exhibiting a degree of rotational symmetry breaking that reflects the structure of the underlying lattice., 14 pages, 3 figures

The volume dependence of the octet baryon masses and relations among them are explored with Lattice QCD. Calculations are performed with n_f=2+1 clover fermion discretization in four lattice volumes, with spatial extent L ~ 2.0, 2.5, 3.0 and 3.9 fm, with an anisotropic lattice spacing of b_s ~ 0.123 fm in the spatial direction, and b_t = b_s/3.5 in the time direction, and at a pion mass of m_pi ~ 390 MeV. The typical precision of the ground-state baryon mass determination is ~0.2%, enabling a precise exploration of the volume dependence of the masses, the Gell-Mann--Okubo mass relation, and of other mass combinations. A comparison of the volume dependence with the predictions of heavy baryon chiral perturbation theory is performed in both the SU(2)_L X SU(2)_R and SU(3)_L X SU(3)_R expansions. Predictions of the three-flavor expansion for the hadron masses are found to describe the observed volume dependences reasonably well. Further, the Delta-N-pi axial coupling constant is extracted from the volume dependence of the nucleon mass in the two-flavor expansion, with only small modifications in the three-flavor expansion from the inclusion of kaons and etas. At a given value of m_pi L, the finite-volume contributions to the nucleon mass are predicted to be significantly smaller at m_pi ~ 140 MeV than at m_pi ~ 390 MeV due to a coefficient that scales as ~ m_pi^3. This is relevant for the design of future ensembles of lattice gauge-field configurations. Finally, the volume dependence of the pion and kaon masses are analyzed with two-flavor and three-flavor chiral perturbation theory., Comment: 34 pages, 45 figures

By employing the dictum that axiomatic principles are devoid of predictive power, we find that the the elastic unitarity constraint, applied to strong WLWL scattering, does not alter the assumed spectrum of intermediate states. In other words, if one integrates out the heavy degrees of freedom in an effective theory, then imposing elastic unitarity on the resultant low-energy theory effectively integrates back in the original heavy degrees of freedom, but otherwise leaves the spectrum unchanged. As a case study, we consider intermediate states involving a heavy Higgs and heavy fermions of a hypothetical fourth doublet. In contrast to recent studies, we find no p-wave resonance.

We present evidence for the existence of a bound H-dibaryon, an I=0, J=0, s=-2 state with valence quark structure uuddss, at a pion mass of m_pi ~ 389 MeV. Using the results of Lattice QCD calculations performed on four ensembles of anisotropic clover gauge-field configurations, with spatial extents of L ~ 2.0, 2.5, 3.0 and 3.9 fm at a spatial lattice spacing of b ~ 0.123 fm, we find an H-dibaryon bound by B = 16.6 +- 2.1 +- 4.6 MeV at a pion mass of m_pi ~ 389 MeV., 4 pages and 3 figures. v2 accepted by PRL