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Register a new userContraction Diagram Analysis in Pion-Kaon Scattering
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We study the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude within the framework of SU$(4|1)$ partially-quenched chiral perturbation theory. Combining this with a finite-volume analysis, we demonstrate that a lattice calculation of the easier computable connected correlation functions is able to provide valuable information of the noisier disconnected correlation functions, and may serve as a theory guidance for the future refinement of the corresponding lattice techniques.
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Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the low-energy constant $L_0^r$ in SU$(4|1)$ Partially-Quenched Chiral Perturbation Theory from data of the Extended Twisted Mass Collaboration, $L_0^r = 0.51(26)cdot 10^{-3}$ at $mu=1$ GeV.
We present a lattice-QCD calculation of the pion, kaon and $eta_s$ distribution amplitudes using large-momentum effective theory (LaMET). Our calculation is carried out using three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC collaboration, at 310 MeV pion mass with 0.06, 0.09 and 0.12 fm lattice spacings. We use clover fermion action for the valence quarks and tune the quark mass to match the lightest light and strange masses in the sea. The resulting lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and extrapolated to the continuum. We use two approaches to extract the $x$-dependence of the meson distribution amplitudes: 1) we fit the renormalized matrix elements in coordinate space to an assumed distribution form through a one-loop matching kernel; 2) we use a machine-learning algorithm trained on pseudo lattice-QCD data to make predictions on the lattice data. We found the results are consistent between these methods with the latter method giving a less smooth shape. Both approaches suggest that as the quark mass increases, the distribution amplitude becomes narrower. Our pion distribution amplitude has broader distribution than predicted by light-front constituent-quark model, and the moments of our pion distributions agree with previous lattice-QCD results using the operator production expansion.
We present the first lattice-QCD calculation of the kaon valence-quark distribution functions using the large-momentum effective theory (LaMET) approach. The calculation is performed with multiple pion masses with the lightest one around 220 MeV, 2 lattice spacings $a=0.06$ and 0.12 fm, $(M_pi)_text{min} L approx 5.5$, and high statistics ranging from 11,600 to 61,312 measurements. We also calculate the valence-quark distribution of pion and find it to be consistent with the FNAL E615 experimental results, and our ratio of the $u$ quark PDF in the kaon to that in the pion agrees with the CERN NA3 experiment. We also make predictions of the strange-quark distribution of the kaon.
We study the coupled pion-nucleon system (negative parity, isospin 1/2) based on a lattice QCD simulation for nf=2 mass degenerate light quarks. Both, standard 3-quarks baryon operators as well as meson-baryon (4+1)-quark operators are included. This is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic s-wave scattering and can derive values of the phase shift.
We determine the $Delta(1232)$ resonance parameters using lattice QCD and the Luscher method. The resonance occurs in elastic pion-nucleon scattering with $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is performed with $N_f=2+1$ flavors of clover fermions on a lattice with $Lapprox 2.8$ fm. The pion and nucleon masses are $m_pi =255.4(1.6)$ MeV and $m_N=1073(5)$ MeV, and the strong decay channel $Delta rightarrow pi N$ is found to be above the threshold. To thoroughly map out the energy-dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to $vec{P}=frac{2pi}{L}(1,1,1)$, including irreps that mix $S$ and $P$ waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the $P$-wave phase shift and the effective-range expansion for the $S$-wave phase shift. From the location of the pole in the $P$-wave scattering amplitude, we obtain the resonance mass $m_Delta=1378(7)(9)$ MeV and the coupling $g_{Deltatext{-}pi N}=23.8(2.7)(0.9)$.
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