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1. Two-Pole Nature of the Lambda(1405) Resonance from Lattice QCD

   https://doi.org/10.1103/PhysRevLett.132.051901  

   Bulava, John; Cid-Mora, Bárbara; Hanlon, Andrew D.; Hörz, Ben; Mohler, Daniel; Morningstar, Colin; Moscoso, Joseph; Nicholson, Amy; Romero-López, Fernando; Skinner, Sarah; et al (January 2024, Physical Review Letters)

   This Letter presents the first lattice QCD computation of the coupled channel πΣ−¯KN scattering amplitudes at energies near 1405 MeV. These amplitudes contain the resonance Λ(1405) with strangeness S=−1 and isospin, spin, and parity quantum numbers I(JP)=0(1/2−). However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to mπ≈200  MeV and mK≈487  MeV, this study finds the amplitudes exhibit a virtual bound state below the πΣ threshold in addition to the established resonance pole just below the ¯KN threshold. Several parametrizations of the two-channel K matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity. 

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2. Lattice QCD study of $\pi \mathrm{\Sigma }-\overline{K}N$ scattering and the $\mathrm{\Lambda }\left(1405\right)$ resonance

   https://doi.org/10.1103/PhysRevD.109.014511  

   Bulava, John; Cid-Mora, Bárbara; Hanlon, Andrew D.; Hörz, Ben; Mohler, Daniel; Morningstar, Colin; Moscoso, Joseph; Nicholson, Amy; Romero-López, Fernando; Skinner, Sarah; et al (January 2024, Physical Review D)

   A lattice QCD computation of the coupled channel πΣ–¯KN scattering amplitudes in the Λ(1405) region is detailed. Results are obtained using a single ensemble of gauge field configurations with Nf=2+1 dynamical quark flavors and mπ≈200  MeV and mK≈487  MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering K-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the πΣ threshold and a resonance pole just below the ¯KN threshold. 

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3. D meson -- pion scattering on CLS 2+1 flavor ensembles

   https://doi.org/10.22323/1.430.0068  

   Mohler, Daniel; Bulava, John; Hoerz, Ben; Johnson, Christopher; Morningstar, Colin; Hudspith, Renwick J. (February 2023, Proceedings of Science)

   We report progress on finite-volume determinations of heavy light-meson – Goldstone boson scattering phase shifts using the Luescher method on CLS 2+1 flavor gauge field ensembles. In a first iteration we will focus on D-meson – pion scattering in the elastic scattering region at various pion masses using ensembles with three lattice spacings. We employ ensembles on the CLS quark-mass trajectory with a fixed trace of the quark-mass matrix as well as ensembles with a strange-quark mass fixed close to its physical value, which will allow us to study both the light and the strange quark-mass dependence of positive parity heavy-light hadrons close to threshold. 

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4. Gluon Parton Distribution of the Pion from Lattice QCD

   Zhouyou Fan, Huey-Wen Lin (January 2021, Physics letters)

   null (Ed.)

   We present the first determination of the x-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, at two lattice spacings a≈0.12 and 0.15~fm and three pion masses Mπ≈220, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our results from the lightest pion mass ensemble with the determination by JAM and xFitter global fits. 

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5. Breakdown of Regularity of Scattering for Mass-Subcritical NLS

   https://doi.org/10.1093/imrn/rnaa072  

   Lee, Gyu Eun (April 2020, International Mathematics Research Notices)

   null (Ed.)

   Abstract We study the scattering problem for the nonlinear Schrödinger equation $$i\partial _t u + \Delta u = |u|^p u$$ on $$\mathbb{R}^d$$, $$d\geq 1$$, with a mass-subcritical nonlinearity above the Strauss exponent. For this equation, it is known that asymptotic completeness in $L^2$ with initial data in $$\Sigma$$ holds and the wave operator is well defined on $$\Sigma$$. We show that there exists $$0<\beta <p$$ such that the wave operator and the data-to-scattering-state map do not admit extensions to maps $$L^2\to L^2$$ of class $$C^{1+\beta }$$ near the origin. This constitutes a mild form of ill-posedness for the scattering problem in the $L^2$ topology. 

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