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We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark T⁺_(cc)(3875) from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the effect of the one-pion exchange diagram in DDπ and DD∗ scattering, making it applicable at energies coinciding with the left-hand cut in the partial-wave projected DD∗ amplitude. We present an example application of this framework to existing lattice QCD data at mπ = 280 MeV. We solve the integral equations describing the DDπ reaction, use LSZ reduction to determine the corresponding DD∗ amplitude, and find the values of the infinite-volume two- and three-body K matrices that lead to agreement with lattice DD∗ phase shifts within their uncertainties. Using these K matrices in the three-particle quantization condition, we describe the finite- volume DD∗ spectrum and find good agreement with the lattice QCD energies. Our results suggest that, at this pion mass, the tetraquark appears as a pair of subthreshold complex poles whose precise location strongly depends on the value of the DDπ three-particle K matrix.

We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method first relates the finite-volume spectrum to an infinite-volume short-range quantity, denoted 𝓜₀, and then relates the latter to the physical scattering amplitudes via known integral equations. The derivation of both relations is performed using all-orders perturbation theory and is exact up to neglected exponentially suppressed volume dependence. The relations hold for arbitrary two-particle systems with any number of coupled channels, non-identical and non-degenerate particles, and any intrinsic spin.

In this work, we report a lattice calculation of x-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on an Nf = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t.

In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD), $\\overset{\\sim }{H}\\left(x,\\xi, t\\right)$ , at zero skewness, ξ, with multiple values of the momentum transfer, t. Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on an Nf = 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing of a = 0.093 fm, and a pion mass of mπ = 260 MeV. We consider both the iso-vector and iso-scalar cases, utilizing next-to-leading-order perturbative matching while omitting the disconnected contributions and gluon mixing in the iso-scalar case. For the first time, we determine the Mellin moments of $\\overset{\\sim }{H}$ up to the fifth order. From these moments, we discuss the quark helicity and orbital angular momentum contributions to the nucleon spin, as well as the spin-orbit correlations of the quarks. Additionally, we perform a Fourier transform over the momentum transfer, which allows us to explore the spin structure in the impact-parameter space.

Abstract 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$$ \\left(\\left.\\left|{D}_s^{+}{\\pi}^{+}\\right.\\right\\rangle -\\left.\\left|{D}^{+}{K}^{+}\\right.\\right\\rangle \\right)/\\sqrt{2} $$. 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.

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

Abstract By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark statesP_(ψ)ᴺ\\left{(}{444}{0}\\right)⁺andP_(ψ)ᴺ\\left{(}{4457}{\\right)}⁺reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation ofP_(ψ)ᴺ\\left{(}{444}{0}\\right)⁺andP_(ψ)ᴺ\\left{(}{4457}{\\right)}⁺as the isospin-½\\left{[}{D̅ }{^(*)}Σ_(c)\\right{]}{}{}molecular states with J P configuration\\left{(}{(3/2)}{\\right)}⁻and\\left{(}{½}{\\right)}⁻, respectively. We first calculate the one-boson-exchange interaction kernel of\\left{[}{D̅ }{^(*)}Σ_(c)\\right{]}{}{}in the isospin-½configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a½baryon withJᴾ=½⁻and(3/2)⁻. The obtained mass results for the\\left{(}{(3/2)}{\\right)}⁻and\\left{(}{½}{\\right)}⁻are 4.442 and 4.457 GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channelsD̅ ^((*)0)Λ_(c)⁺, J/ψ(η c )p, andD̅Σ _(c)^((*))for the twoP_(ψ)ᴺstates. In the favored(3/2)⁻and½⁻configuration, the obtained total widths are 21.8 MeV and 13.0 MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest thatD̅ ⁰Λ_(c)⁺andD̅ ^((*)0)Λ_(c)⁺are the dominant decay channels to detectP_(ψ)ᴺ\\left{(}{444}{0}\\right)⁺andP_(ψ)ᴺ\\left{(}{4457}{\\right)}⁺, respectively.

We perform a detailed comparison between three formalisms used in recent studies of DD* scattering at heavier-than-physical pion masses, which aim to understand the properties of the doubly-charmed tetraquark, T_(cc)⁺(3875). These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baião Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

We perform a detailed comparison between three formalisms used in recent studies of DD* scattering at heavier-than-physical pion masses, which aim to understand the properties of the doubly-charmed tetraquark, T_(cc)⁺ (3875). These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baião Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

A bstract We present our lattice QCD result for the long-distance part of the hadronic vacuum polarization contribution, ( a μ hvp ) LD , to the muon g − 2 in the time-momentum representation. This is the numerically dominant, and at the same time the most challenging part regarding statistical precision. Our calculation is based on ensembles with dynamical up, down and strange quarks, employing the O( a )-improved Wilson fermion action with lattice spacings ranging from 0 . 035–0 . 099 fm. In order to reduce statistical noise in the long-distance part of the correlator to the per-mille level, we apply low-mode averaging and combine it with an explicit spectral reconstruction. Our result is ( a μ hvp ) LD = 423 . 2(4 . 2) stat (3 . 4) syst × 10 −10 in isospin-symmetric QCD, where the pion decay constant is used to set the energy scale. When combined with our previous results for the short- and intermediate-distance window observables and after including all sub-dominant contributions as well as isospin-breaking corrections, we obtain the total leading-order hadronic vacuum polarization contribution as a μ hvp = 724 . 5(4 . 9) stat (5 . 2) syst × 10 −10 . Our result displays a tension of 3.9 standard deviations with the data-driven estimate published in the 2020 White Paper, but leads to a SM prediction for the total muon anomalous magnetic moment that agrees with the current experimental average.