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DOE OSTI2022

What Hath Weinberg Wrought? Reflections on What Weinberg’s Papers on ‘Nuclear Forces from Chiral Lagrangians’ did and did not Accomplish

Here, I discuss selected legacies of Weinberg's application of chiral Lagrangians to nuclear physics: (1) the use of the chiral expansion to organize the interaction of pions and photons with a nucleus; (2) the much-debated question of why and how the potential derived from a chiral Lagrangian should be inserted in the Schrodinger equation; (3) the emergence of "pionless EFT" as a tool for diagnosing universal correlations that are present in quantum few-body systems of very different sizes, and, perhaps most important of all, (4) an epistemological shift in what is expected of a nuclear-physics calculation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Relativistic Hartree–Fock chiral Lagrangians with confinement, nucleon finite size and short-range effects

A relativistic Hartree–Fock Lagrangian including a chiral potential and nucleon polarisation is investigated in hopes of providing a better description of dense nuclear matter. Here, we fully consider the contribution of the exchange Fock term to the energy and the self-energies, and in addition we investigate the nucleon’s compositeness and finite size effects (confinement and form factors) and short range correlations modeled by a Jastrow ansatz. These effects are added step by step, such that their impact on the dense matter properties can be analysed in details. The parameters of the model are adjusted to reproduce fundamental properties related to the QCD theory at low energy, such as the chiral symmetry breaking, nucleon’s quark substructure and Lattice-QCD predictions, as well as two empirical properties at saturation: the binding energy and the density. All other empirical parameters, e.g., symmetry energy and its slope, incompressibility modulus, effective mass, as well as spin–isospin Landau–Midgal parameter are predictions of the models and can be used to evaluate the gain of the different approximation schemes in describing nuclear properties. Bayesian statistics is employed in order to propagate parameter uncertainties into predictions for the nuclear matter properties. We show that the splitting of the effective Landau mass is largely influenced by the value of the ρ T coupling, and we show that the fit to the symmetry energy, which induces an increase of the coupling constant g ρ by about 20–25% compared to the case where it is fixed by the quark model, provides a very good EoS compatible with the present nuclear physics knowledge.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Chiral Effective Field Theory’s Impact on Advancing Quantum Monte Carlo Methods

Thirty years ago, Steven Weinberg published his seminal paper on “Nuclear Forces from chiral Lagrangians” which has revolutionized the field of theoretical nuclear physics. Nowadays, interactions derived from chiral effective field theory are routinely used to describe nuclear systems ranging from atomic nuclei to the dense matter explored in the core of neutron stars with theoretical uncertainty estimates. Here, in our contribution to the special issue “Celebrating 30 years of Steven Weinberg’s paper Nuclear Forces from Chiral Lagrangians”, we focus on the impact that chiral effective field theory interactions have played in advancing microscopic studies of atomic nuclei and the nuclear-matter equation of state using quantum Monte Carlo methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A Brief Account of Steven Weinberg’s Legacy in ab initio Many-Body Theory

In this contribution to the special issue “Celebrating 30 years of Steven Weinberg’s papers on Nuclear Forces from Chiral Lagrangians,” we emphasize the important role chiral effective field theory has played in leading nuclear physics into a precision era. To this end, we share our perspective on a few of the recent advances made in ab initio calculations of nuclear structure and nuclear matter observables, as well as Bayesian uncertainty quantification of effective field theory truncation errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Constructing chiral effective field theory around unnatural leading-order interactions

A momentum-dependent formulation based on a stationary spin-0 and isospin-1 dibaryon field is proposed to improve convergence of chiral effective field theory in the 1 S 0 channel of NN scattering. Although the two-parameter leading-order interaction appears to be unnatural, it nevertheless has the necessary features of an effective field theory. A rapid order-by-order convergence is found in 1 S 0 . As an application beyond the two-body level, the triton binding energy is studied and compared to standard chiral effective field theory with partly perturbative pions. Here, the consistency of the chiral Lagrangian for the new formulation is examined by working out the pionic radiative corrections, and consequences of nontrivial chiral-connection terms are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Nucleon form factors and parton distributions in nonlocal chiral effective theory

In this work, we present a review of recent applications of nonlocal chiral effective theory to hadron structure studies. Starting from a nonlocal meson-baryon effective chiral Lagrangian, we show how the introduction of a correlation function representing the finite extent of hadrons regularizes the meson loop integrals and introduces momentum dependence in vertex form factors in a gauge invariant manner. We apply the framework to the calculation of nucleon electromagnetic form factors, unpolarized and polarized parton distributions, as well as transverse momentum dependent distributions and generalized parton distributions. Assuming that the nonlocal behavior is a general property of all interactions, we also discuss the application to the lepton anomalous magnetic moment in nonlocal QED.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Nonlinear Sigma model amplitudes to all loop orders are contained in the Tr ( Φ 3 ) theory

Scattering amplitudes for the simplest theory of colored scalar particles—the Tr ( Φ 3 ) theory—have recently been the subject of active investigations. In this work we describe an unanticipated wider implication of this work: the Tr ( Φ 3 ) theory secretly contains nonlinear sigma model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr ( Φ 3 ) amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in the potential, with extrema spontaneously breaking U ( N ) → U ( N − k ) × U ( k ) . The Goldstone amplitudes for this theory coincide with those of pions in the U ( N ) × U ( N ) → U ( N ) chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing that integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr ( Φ 3 ) scalars, most of which are not interpretable from the Lagrangian description. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Emergence of the polydeterminant in QCD

A generalization of the determinant appears in particle physics in effective Lagrangian interaction terms that model the chiral anomaly in quantum chromodynamics (Giacosa et al. in Phys Rev D 97(9):091901, 2018, Phys Rev D 109(7):L071502, 2024), in particular in connection to mesons. This polydeterminant function, known in the mathematical literature as a mixed discriminant, associates N distinct N x N complex matrices into a complex number and reduces to the usual determinant when all matrices are taken as equal. Here, we explore the main properties of the polydeterminant applied to (quantum) fields by using a formalism and a language close to high-energy physics approaches. We discuss its use as a tool to write down novel chiral anomalous Lagrangian terms and present an explicit illustrative model for mesons. Finally, the extension of the polydeterminant as a function of tensors is shown.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A theory of dark pions

We present a complete model of a dark QCD sector with light dark pions, broadly motivated by hidden naturalness arguments. The dark quarks couple to the Standard Model via irrelevant Z- and Higgs-portal operators, which encode the low-energy effects of TeV-scale fermions interacting through Yukawa couplings with the Higgs field. The dark pions, depending on their CP properties, behave as either composite axion-like particles (ALPs) mixing with the Z or scalars mixing with the Higgs. The dark pion lifetimes fall naturally in the most interesting region for present and proposed searches for long-lived particles, at the LHC and beyond. This is demonstrated by studying in detail three benchmark scenarios for the symmetries and structure of the theory. Within a coherent framework, we analyze and compare the GeV-scale signatures of flavor-changing meson decays to dark pions, the weak-scale decays of Z and Higgs bosons to hidden hadrons, and the TeV-scale signals of the ultraviolet theory. New constraints are derived from B decays at CMS and from Z-initiated dark showers at LHCb, focusing on the displaced dimuon signature. We also emphasize the strong potential sensitivity of ATLAS and CMS to dark shower signals with large multiplicities and long lifetimes of the dark pions. As a key part of our phenomenological study, we perform a new data-driven calculation of the decays of a light ALP to exclusive hadronic Standard Model final states. The results are provided in a general form, applicable to any model with arbitrary flavor-diagonal couplings of the ALP to fermions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Amplitude/operator basis in chiral perturbation theory

We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in D = 4 spacetime dimensions and with an arbitrary number of flavors N f . For kinematic factors, we employ spinor-helicity variables to construct the soft blocks, which are local amplitudes satisfying the Adler’s zero condition, as well as to take into account the reduction in the kinematic basis due to the Gram determinant, which arises at O(p 10 ) when the number of multiplicity N in an amplitude becomes large: N > D. For flavor factors, we include group-theoretic relations at small N f , N f ≤ N, which decreases the flavor basis. The result is obtained by adapting the Young tensor method of constructing the operator basis for generic effective field theories to the case of non-linearly realized symmetries. Working in the massless quark limit, we present purely mesonic operators for both even- and odd-parity at O(p 6 ) and O(p 8 ) for N = 6 and arbitrary N f , and establish a direct correspondence between the amplitude basis and the operator basis. Furthermore, the redundancy due to the Gram determinant is studied at O(p 10 ) for N = 6, 8 and 10.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Chiral limit of 2d QCD revisited with lightcone conformal truncation

We study the chiral limit of 2d QCD with a single quark flavor at finite Nc using LCT. By modifying the LCT basis according to the quark mass in a manner motivated by ’t Hooft’s analysis, we are able to restore convergence for quark masses much smaller than the QCD strong coupling scale. For such small quark masses, the IR of the theory is expected to be well described by the Sine-Gordon model. We verify that LCT numerics are able to capture in detail the spectrum and correlation functions of the Sine-Gordon model. This opens up the possibility for studying deformations of various integrable CFTs using LCT by considering the chiral limit of QCD like theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Alpha-alpha scattering in the Multiverse

We investigate the phase shifts of low-energy α-α scattering under variations of the fundamental parameters of the Standard Model, namely the light quark mass, the electromagnetic fine-structure constant as well as the QCD θ-angle. As a first step, we recalculate α-α scattering in our Universe utilizing various improvements in the adiabatic projection method, which leads to an improved, parameter-free prediction of the S- and D-wave phase shifts for laboratory energies below 10 MeV. We find that positive shifts in the pion mass have a small effect on the S-wave phase shift, whereas lowering the pion mass adds some repulsion in the two-alpha system. The effect on the D-wave phase shift turns out to be more pronounced as signaled by the D-wave resonance parameters. Variations of the fine-structure constant have almost no effect on the low-energy α-α phase shifts. We further show that up-to-and-including next-to-leading order in the chiral expansion, variations of these phase shifts with respect to the QCD θ-angle can be expressed in terms of the θ-dependent pion mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Radiative semileptonic $ \overline{B} $ decays

We consider the form factors for the radiative semileptonic decays $ \overline{B} $(v) → D(*)(v')ℓν¯ ℓγ in the kinematic region where the photon momentum, k, is small enough that heavy quark symmetry (HQS) can be applied without the radiated photon changing the heavy quark velocity (i.e., v(') ∙ k < m (b,c) ). We find that HQS is remarkably powerful, leaving only four new undetermined form factors at leading order in 1/m (b,c) . In addition, one of them is fixed in terms of the leading order Isgur-Wise function in the kinematic region, v(') ∙ k < Λ QCD .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Gauged soft recursion: on-shell construction of Goldstone-gauge amplitudes

We present a new on-shell recursion relation for scattering amplitudes involving Nambu-Goldstone bosons with a gauged unbroken symmetry. A central challenge is that gauge interactions break Adler’s zero condition for charged scalars, invalidating the standard soft recursion. To overcome this, we introduce a “gauged soft recursion” that leverages the soft theorems of the gauge bosons themselves, combined with a novel decomposition of amplitudes into gauge-invariant components where Adler’s zero is partially restored. The formalism, which also incorporates internal gauge bosons via angular momentum constraints, enables the systematic construction of tree-level amplitudes with arbitrary numbers of Goldstone bosons and gauge bosons in both Abelian and non-Abelian theories, as we demonstrate with explicit examples.

Chiral Lagrangian↗
DOE OSTI2024

The three-pion K -matrix at NLO in ChPT

The three-particle K-matrix, Κ df,3 , is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

The isospin-3 three-particle K -matrix at NLO in ChPT

The three-particle K-matrix, K df,3 , is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of K df,3 is significantly improved with respect to leading order once NLO effects are incorporated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A lattice study of ππ scattering at large N c

We present the first lattice study of pion-pion scattering with varying number of colors, N c . We use lattice simulations with four degenerate quark flavors, N f = 4, and N c = 3 – 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for N f ≥ 4. A representative state is (|D$^{+}_{s}$π + > – | D + K + >)/√2. Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large N c . For this, we compute the analytical U(N f ) ChPT prediction for two-pion scattering, and use the lattice results to constrain the N c scaling of the relevant low-energy couplings.

1/N Expansion↗