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This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program., Perspective pieces of the virtual INT program 21-1b "Nuclear Forces for Precision Nuclear Physics", 107 pages

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.

The axial charge of the triton is investigated using lattice quantum chromodynamics (QCD). Extending previous work at heavier quark masses, calculations are performed using three ensembles of gauge field configurations generated with quark masses corresponding to a pion mass of 450 MeV and a single value of the lattice spacing. Finite-volume energy levels for the triton, as well as for the deuteron and diproton systems, are extracted from analysis of correlation functions computed on these ensembles, and the corresponding energies are extrapolated to infinite volume using finite-volume pionless effective field theory (FVEFT). It is found with high likelihood that there is a compact bound state with the quantum numbers of the triton at these quark masses. The axial current matrix elements are computed using background field techniques on one of the ensembles and FVEFT is again used to determine the axial charge of the proton and triton. A simple quark mass extrapolation of these results and earlier calculations at heavier quark masses leads to a value of the ratio of the triton to proton axial charges at the physical quark masses of gAH3/gAp=0.91−0.09+0.07. This result is consistent with the ratio determined from experiment and prefers values less than unity (in which case the triton axial charge would be unmodified from that of the proton), thereby demonstrating that QCD can explain the modification of the axial charge of the triton.

Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear reactions in astrophysics, dark matter direct detection experiments, and experimental searches for violations of the symmetries of the Standard Model, including searches for additional CP violation in the hadronic and leptonic sectors, baryon-number violation, and lepton-number or flavor violation. Similarly, important inputs to neutrino experiments seeking to determine the neutrino-mass hierarchy and oscillation parameters, as well as other electroweak and beyond-Standard-Model processes can be determined. The phenomenological implications of existing studies of electroweak and beyond-Standard-Model matrix elements in light nuclear systems are discussed, and future prospects for the field toward precision studies of these matrix elements are outlined.

The nonmesonic weak decay of the doubly strange hypernucleus $_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{\phantom{\rule{1em}{0ex}}6}\mathrm{He}$ is studied within a model that considers the exchange of pseudoscalar and vector mesons. Special attention is paid to quantifying the strong interaction effects, focusing on the interaction among the two $\mathrm{\ensuremath{\Lambda}}$ hyperons that induces novel weak transitions, whereby $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Xi}}N$, and $\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}$ states decay into a hyperon-nucleon pair. The initial strangeness $\ensuremath{-}2$ wave function is obtained from the solution of a $G$-matrix equation with the input of realistic strong baryon-baryon potentials, while the final hyperon-nucleon wave functions are derived analogously from a microscopic $T$-matrix calculation. The new $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}YN$ decay rate studied in this work, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\Lambda}}n}+{\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Sigma}}}^{0}n}+{\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}p}$, represents 3--4% of the total one-baryon-induced nonmesonic decay and is remarkably affected by strong interaction effects. In particular, the relative importance of the partial decay rates encoded in the ratio ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\Lambda}}n}/({\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Sigma}}}^{0}n}+{\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}p})$ gets inverted when the mixing to $\mathrm{\ensuremath{\Xi}}N$ states is incorporated in the initial correlated $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ wave function. This sensitivity can be used experimentally to learn about the strong interaction in the strangeness $\ensuremath{-}2$ sector.

Magnetic moments of the octet baryons are computed using lattice QCD in background magnetic fields, including the first treatment of the magnetically coupled Sigma-Lambda system. Although the computations are performed for relatively large values of the up and down quark masses, we gain new insight into the symmetries and relations between magnetic moments by working at a three-flavor mass-symmetric point. While the spin-flavor symmetry in the large Nc limit of QCD is shared by the naive constituent quark model, we find instances where quark model predictions are considerably favored over those emerging in the large Nc limit. We suggest further calculations that would shed light on the curious patterns of baryon magnetic moments., 8 pages, 5 figures, talk given at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June 2017

Lattice QCD calculations with background magnetic fields are used to determine the magnetic moments of the octet baryons. Computations are performed at the physical value of the strange quark mass, and two values of the light quark mass, one corresponding to the three-flavor symmetric point, where the pion mass is 800 MeV, and the other corresponding to a pion mass of 450 MeV. The moments are found to exhibit only mild pion-mass dependence when expressed in terms of appropriately chosen magneton units- the natural baryon magneton. A curious pattern is revealed among the anomalous baryon magnetic moments which is linked to the constituent quark model, however, careful scrutiny exposes additional features. Relations expected to hold in the large-Nc limit of QCD are studied; and, in one case, a clear preference for the quark model over the large-Nc prediction is found. The magnetically coupled Lambda-Sigma system is treated in detail at the three-flavor symmetric point, with the lattice QCD results comparing favorably with predictions based on SU(3)F symmetry. This analysis enables the first extraction of the isovector transition magnetic polarizability. The possibility that large magnetic fields stabilize strange matter is explored, but such a scenario is found to be unlikely., Comment: 30 pages, 18 figures, v2 revision corresponds to published version

An effective field theory for the Λ N → N N weak decay is developed beyond O ( q ) , where q is the transferred momentum. A leading order fit for the low energy constants is presented. Explicit expressions for the loop contributions are provided.

The potential in coordinate space for the Λ N → N N weak transition, which drives the weak decay of most hypernuclei, is derived within the effective field theory formalism up to next-to-leading order. This coordinate space potential allows us to discuss how the different contributions to the potential add up at the different scales. Explicit expressions are given for each two-pion-exchange diagram contributing to the interaction. The potential is also reorganized into spin and isospin operators, and the coefficient for each operator is given in analytical form and represented in coordinate space. The relevance of explicitly including the mass differences among the baryons appearing in the two-pion-exchange diagrams is also discussed in detail.

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 extraction, from scattering experiments, of precise information on the strong baryon–baryon interaction in the strange sector is hindered by the instability of hyperons against weak decay modes. The consequent large uncertainties in the hyperon–nucleon and hyperon–hyperon scattering amplitudes propagate through the potentials used as input in hypernuclear and astrophysical investigations. Lattice QCD simulations of baryon–baryon interactions point out as a reliable way to obtain complementary information to what can be obtained from low-energy experiments. In the present paper I will outline the Lattice QCD methodology used to extract one- and two-particle ground state energies, and present the most recent results obtained by the Nuclear Physics with Lattice QCD Collaboration regarding the identification of two-body bound states.

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

One of the main motivations for investing human and economic effort in Lattice QCD calculations of nuclear physics quantities is to explore sectors that cannot be accessed experimentally, or which can be measured with only limited precision. Two lines of research where such kind of calculations may have a clear impact are the study of the evolution of supernova and of the structure and decay of conventional and strange nuclei. Key ingredients for both investigations are the low energy interactions among baryons. Unfortunately, due to the short lifetime of hyperons, the interactions among baryons in the strange sector are only approximately known. The unsatisfactory amount of data coming from scattering experiments produces large uncertainties in the scattering amplitudes. Lattice QCD simulations of baryon-baryon interactions can play a crucial role, and points out as a reliable way to obtain complementary information to what can be obtained from experiments involving baryons in the low energy region.

The physics of the weak decay of hypernuclei is briefly reviewed from a theoretical point of view. Special regard is devoted to the recent progress concerning the determination of the non-mesonic decay widths and the asymmetry parameters. Convincing evidence has been achieved for a solution of the long-standing puzzle on the ratio Γ n / Γ p . Very recently, it has been shown that the exchange of a ππ pair in the weak mechanism plays a crucial role in explaining the discrepancies between theory and experiment on the decay asymmetries.

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

We perform a direct finite nucleus calculation of the partial width of a bound Δ isobar decaying through the non-mesonic decay mode, Δ N → N N . This transition is modeled by the exchange of the long ranged π meson and the shorter ranged ρ meson. The contribution of this decay channel is found to be approximately 60% of the decay width of the Δ particle in free space. Considering the additional pionic decay mode, we conclude that the total decay width of a bound Δ resonance in nuclei is of the order of 100 MeV and, consequently, no narrow Δ nuclear states exist, contrary to recent claims in the literature. Our results are in complete agreement with microscopic many-body calculations and phenomenological approaches performed in nuclear matter.

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

Theoretical descriptions of the non-mesonic weak decay of Λ-hypernuclei are unable to reproduce the experimental values of the ratio Γ n / Γ p ≡ Γ ( Λ n → n n ) / Γ ( Λ p → n p ) . In this contribution we discuss a new approach to this problem. We have incorporated a one-meson-exchange model for the Λ N → n N transition in finite nuclei in an intranuclear cascade code for the calculation of double-coincidence nucleon distributions corresponding to the non-mesonic decay of 5ΛHe and 12ΛC. The two-nucleon induced decay mechanism, Λ n p → n n p , has been taken into account within a local density approximation scheme using a one-pion-exchange model supplemented by short range correlations. A weak decay model independent analysis of preliminary KEK coincidence data for 5ΛHe allows us to extract Γ n / Γ p = 0.39 ± 0.11 when the two-nucleon induced channel is neglected (i.e., Γ 2 = 0 ) and Γ n / Γ p = 0.26 ± 0.11 when Γ 2 / Γ 1 = 0.2 .

The nonleptonic weak | Δ S | = 1 ΛN interaction, responsible for the dominant, nonmesonic decay of all but the lightest hypernuclei, is studied in the framework of an effective field theory. The long-range physics is described through tree-level exchange of the SU(3) Goldstone bosons (π and K), while the short-range potential is parametrized in terms of lowest-order contact terms obtained from the most general non-derivative local four-fermion interaction. Fitting to available weak hypernuclear decay rates for 5ΛHe, 11ΛB and 12ΛC yields reasonable values for the low-energy constants.

We present the results of the Meson-Exchange model of Refs. [1,2] for the nonmesonic weak decay of single- and double-Λ hypernuclei. The results shown here include the total nonmesonic ( π NM ) decay rate, partial decay rates ( i. e. decays induced separately by neutrons, π Λn , protons, π Λp , and Λs, π ΛΛ ), the kinetic energy correlation of np coincidence pairs emitted in the decay of Λ 5 He, and A , the longitudinal asymmetry in the distribution of final protons coming from the decay of polarized hypernuclei.

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

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 weak production of Lambdas in nucleon-nucleon scattering is studied in a meson-exchange framework. The weak transition operator for the $NN \to N \Lambda$ reaction is identical to a previously developed weak strangeness-changing transition potential $\Lambda N \to NN$ that describes the nonmesonic decay of hypernuclei. The initial $NN$ and final $YN$ state interaction has been included by using realistic baryon-baryon forces that describe the available elastic scattering data. The total and differential cross sections as well as the parity-violating asymmetry are studied for the reaction $pn \to p\Lambda$. These observables are found to be sensitive to the choice of the strong interaction potential and the structure of the weak transition potential.

The nonmesonic decay of the hypertriton is calculated based on a hypertriton wavefunction and 3N scattering states, which are rigorous solutions of 3-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion-exchange together with heavier meson exchanges for the $\Lambda N \to N N $ transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free $\Lambda$ decay rate. Integrated as well as differential decay rates are given. The p- and n- induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually., Comment: 27 pages, 20 figures, revtex, submitted to Phys. Rev. C

I present some recent results regarding the use of numerical Lattice QCD techniques to describe light nuclear systems from the underlying theory of the strong interaction, QCD.

We consider the $\Lambda N\to NN$ weak transition, responsible for a large fraction of the non-mesonic weak decay of hypernuclei. We follow on the previously derived effective field theory and compute the next-to-leading one-loop corrections. Explicit expressions for all diagrams are provided, which result in contributions to all relevant partial waves.

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

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.

The nonmesonic weak decay of polarized Λ hypernuclei is studied with a microscopic diagrammatic formalism in which one- and two-nucleon-induced decay mechanisms, Λ→N → NN and Λ→NN → NNN, are considered together with (and on the same ground of) nucleon final state interactions. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation. Our approach adopts different one-meson-exchange weak transition potentials, while the strong interaction effects are accounted for by a Bonn nucleon-nucleon interaction. We also consider the two-pion-exchange effect in the weak transition potential. Both the twonucleon-induced decay mechanism and the final state interactions reduce the magnitude of the asymmetry. The quantum interference terms considered in the present microscopic approach give rise to an opposite behavior of the asymmetry with increasing energy cuts to that observed in models describing the nucleon final state interactions semiclassically via the intranuclear cascade code. Our results for the asymmetry parameter in Λ¹²C obtained with different potential models are consistent with the asymmetry measured at KEK., Facultad de Ciencias Exactas, Instituto de Física La Plata

The relation between the low-energy constants appearing in the effective field theory description of the �N → NN transition potential and the parameters of the one-meson-exchange model previously developed is obtained. We extract the relative importance of the different exchange mechanisms included in the meson picture by means of a comparison to the corresponding operational structures appearing in the effective approach. The ability of this procedure to obtain the weak baryon-baryon-meson couplings for a possible scalar exchange is also discussed.

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

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

We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292, 500 sets of measurements are made using 1194 gauge configurations of size 20{sup 3}x128 with an anisotropy parameter {xi}=b{sub s}/b{sub t}=3.5, a spatial lattice spacing of b{sub s}=0.1227{+-}0.0008 fm, and pion mass of M{sub {pi}}{approx}390 MeV. Ground state baryon masses are extracted with fully quantified uncertainties that are at or below the {approx}0.2%-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the N{pi} threshold and, therefore, the isospin-(1/2) {pi}N s-wave scattering phase-shift can be extracted using Luescher's method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time slices. This is due to backward propagating states arising from the antiperiodic boundary conditions imposed onmore » the quark propagators in the time direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables.« less

The $I=2$ $\ensuremath{\pi}\ensuremath{\pi}$ scattering length is calculated in fully dynamical lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations (with fourth-rooted staggered sea quarks) at four light-quark masses. Two- and three-flavor mixed-action chiral perturbation theory at next-to-leading order is used to perform the chiral and continuum extrapolations. At the physical charged pion mass, we find ${m}_{\ensuremath{\pi}}{a}_{\ensuremath{\pi}\ensuremath{\pi}}^{I=2}=\ensuremath{-}0.043\text{ }30\ifmmode\pm\else\textpm\fi{}0.000\text{ }42$, where the error bar combines the statistical and systematic uncertainties in quadrature.

I present the main theoretical attempts carried out during the last few years to understand the weak hyperon-nucleon interaction through the comparison with hypernuclear decay observables, as well as the present perspectives and research avenues in the field.

The non-mesonic weak decay of $\Lambda$--hypernuclei is studied within a one-meson-exchange potential supplemented by a chirally motivated two-pion-exchange mechanism. The effects of final state interactions on the outgoing nucleons are also taken into account. In view of the severe discrepancies between theoretical expectations and experimental data, particular attention is payed to the asymmetry of the protons emitted by polarized hypernuclei. The one-meson-exchange model describes the non-mesonic rates and the neutron-to-proton ratio satisfactorily but predicts a too large and negative asymmetry parameter. The uncorrelated and correlated two-pion mechanisms change the rates moderately, thus maintaining the agreement with experiment. The modification in the strength and sign of some decay amplitudes becomes crucial and produces asymmetry parameters which lie well within the experimental observations., Comment: 20 pages, 3 figures Uses elsart.cls

We calculate the pi+ K+ scattering length in fully-dynamical lattice QCD with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b=0.125 fm, lattice spatial size of L =2.5 fm and at pion masses of m_pi=290, 350, 490 and 600 MeV. The lattice data, analyzed at next-to-leading order in chiral perturbation theory, allows an extraction of the full pi K scattering amplitude at threshold. Extrapolating to the physical point gives m_pi a_3/2 = -0.0574 (+- 0.0016)(+0.0024 -0.0058) and m_pi a_1/2 = 0.1725 (+- 0.0017)(+0.0023 -0.0156) for the I=3/2 and I=1/2 scattering lengths, respectively, where the first error is statistical and the second error is an estimate of the systematic due to truncation of the chiral expansion., 14 pages, 9 figures

The nonmesonic weak decay of L hypernuclei is studied in a shell model framework. A complete strangeness-changing weak LN!NN transition potential, based on one boson exchange, is constructed by including the exchange of the pseudoscalar mesons p, K, h as well as the vector mesons r,v, and K*, whose weak-coupling constants are obtained from soft meson theorems and SU~6! w . General expressions for nucleons in arbitrary shells are obtained. The transition matrix elements include realistic LN short-range correlations and NN final state interactions based on the Nijmegen baryon-baryon potential. The decay rates are found to be especially sensitive to the inclusion of the strange mesons K and K* even though the role of kaon exchange is found to be reduced with recent couplings obtained from one-loop corrections to the leading order in chiral perturbation theory. With the weak couplings used in this study the rates remain dominated by the pion-exchange mechanism since the contributions of heavier mesons either cancel each other or are suppressed by form factors and short-range correlations. The total decay rate therefore remains in agreement with present measurements. However, the partial rates which are even more sensitive to the inclusion of heavier mesons cannot be reconciled with the data. The proton asymmetry changes by 50% once heavier mesons are included and agrees with the available data. @S0556-2813~97!05807-X#