Session DL: Hadrons: Pions and Light Mesons

The Valence-Quark Distribution of the Pion and Kaon

We present the first lattice-QCD calculation of the kaon valence-quark distribution functions using the large-momentum effective field theory (LaMET) approach, a method that has been applied to a wide variety of isovector nucleon distributions and valence pion distributions. This is the first such lattice calculation with multiple pion masses with the lightest one around 220~MeV, 2 lattice spacings a=0.06 and 0.12~fm. We find the valence-quark distribution of pion to be consistent with the FNAL E615 experimental results. Our ratio of the up quark PDF in the kaon to that in the pion agrees with the CERN NA3 experiment. We make predictions of the strange quark distribution of the kaon.   

Lattice calculation of $F_K / F_\pi$ from a mixed domain-wall on HISQ action.

I will present a lattice calculation of the ratio of the leptonic decay constants $F_K/F_\pi$. Per Marciano, $F_K/F_\pi$ can be related to the CKM matrix element $|V_{us}|$, therefore allowing us to probe the flavor-changing nature of the weak interaction and more generally providing constraints on the Standard Model. Further, $F_K/F_\pi$ serves as a gold-plated quantity in LQCD, providing a means to benchmark competing lattice techniques and actions. In our work, we employ a mixed-action with twisted-mass fermions in the sea and domain-wall fermions in the valence sector. We include five pion masses, ranging from 130 MeV to 350 MeV; four lattice spacings, ranging from 0.06 fm to 0.15 fm; and multiple lattice volumes. The extrapolation to the physical point is performed using SU(2) $\chi$PT to NNLO at 2-loops, from which we find $F_{K^\pm}/F_{\pi^\pm}=1.1942(45)$ with isospin breaking, consistent with the FLAG average value. Combining this result with experiment, we also determine $|V_{us}|=0.2251(10)$.   

Light mesons within the basis light-front quantization framework

We study the light-unflavored mesons as relativistic bound states in the nonperturbative Hamiltonian formalism of the basis light-front quantization (BLFQ) approach. The dynamics for the valence quarks of these mesons is specified by an effective Hamiltonian containing the one-gluon exchange interaction and the confining potentials both introduced in our previous work on heavy quarkonia, supplemented additionally by a pseudoscalar contact interaction. We diagonalize this Hamiltonian in our basis function representation to obtain the mass spectrum and the light-front wave functions (LFWFs). Based on these LFWFs, we then study the structure of these mesons by computing the electromagnetic form factors, the decay constants, the parton distribution amplitudes (PDAs), and the parton distribution functions (PDFs). In particular, we investigate the QCD evolution of the PDA and the PDF for the ground state of the pion, and compare our results with available experiments and other theoretical models.   

Pion Parton Distributions Using Threshold Resummation

Following our recent Monte Carlo determination of the pion's PDFs from Drell-Yan (DY) and leading neutron electroproduction data, we extend the analysis by including effects from threshold resummation. At higher orders in the strong coupling, $\alpha_S$, large logarithmic corrections due to soft gluon emissions become important in the $q\bar{q}$ channel near threshold, which can be summed over all orders of $\alpha_S$. However, different prescriptions exist for how the threshold resummation is implemented, for instance, using varying levels of approximation in the Minimal Prescription with cosine, expansion, and double Mellin methods. We report the first Monte Carlo results of the first simultaneous fit to the valence, sea, and gluon distributions in the pion taking into account the ambiguities in the resummation calculations.   

The 3-D structure of pions

We present a study of the transverse momentum dependent distribution of the pion (pion TMD) from pion-induced Drell-Yan (DY) scattering. We describe the DY cross section over the entire range of transverse momentum for moderate $Q$ kinematics, using the state-of-the-art Collins Soper Sterman (CSS) transverse momentum dependent factorization formalism. Using the JLAB Angular Momentum Collaboration (JAM) machinery we extract the pion TMD using Bayesian inference. This setup will allow us to perform a simultaneous self-consistent determination of pion and nucleon TMDs from hard processes and map out the 3-D structure of pions.   

The Mellin Moments〈x〉and〈x^2〉for the Pion and Kaon from Lattice QCD

We present a calculation of the pion and kaon second and third Mellin moments, $\langle x \rangle$ and $\langle x^2 \rangle$, within lattice using twisted mass formulations. The ensemble we use corresponds to a pion and kaon mass of 260 MeV and 530 MeV, respectively. Systematic errors due to excited states are investigated and controlled using different methods. We compare with other studies and available experimental and phenomenological data.   

Meson Structure Function through Tagged Deep Inelastic Scattering

The internal structure of the Nucleon has been studied for more than 60 years providing a very good understanding of its dynamics. On the other hand, the internal structure of the pion, which is in principle the simplest QCD bound state, is less explored, and its Parton distribution functions less known. Nevertheless, the presence of a virtual meson-cloud surrounding the Nucleon has been successful to explain the deviation of the Gottfried sum rule and implying the possibility of using the cloud as a virtual target, thus accessing pion structure through the Sullivan process (electron scattering off the nucleon meson cloud). Making use of the tagging technique (measuring one or more of the recoil nucleons in coincidence with the scattered electron) allows to isolate the Sullivan process from competing reactions. The Tagged Deep Inelastic Scattering (TDIS) experiment at Hall A at the Jefferson Laboratory will make use of the Sullivan process to access the pion structure function, tagging the leading nucleon of the reaction with a new state-of-the-art multi time projection chamber in conjunction with the new Super Bigbite Spectrometer for electron detection. This talk will present the motivation and present status of the experiment.   

Heavy-Light Mesons on the Light Front

We study the heavy-light mesons within basis light-front quantization. The resulting mass spectra of $D$, $D_s$, $B$, and $B_s$ agree reasonably well with experiments. We also predict states which could be measured in the near future. In the light-front formalism, we calculate the light-front wave functions and additional experimental observables, such as parton distribution functions, distribution amplitudes, and decay constants by means of integrations over light-front wave functions. We also provide ratios of decay constants for selected pseudoscalar meson decays ($D_s$ to $D$ and $B_s$ to $B$) as they may prove to be theoretically more robust and more reliably determined in experiments.