### Conveners

#### Hadron Structure: Hadron Structure I

- Martha Constantinou (Temple University)

#### Hadron Structure: Hadron Structure II

- Giannis Koutsou (The Cyprus Institute)

#### Hadron Structure: Hadron Structure III

- Jeremy Green (Trinity College Dublin)

#### Hadron Structure: Hadron Structure IV

- Michael Engelhardt (New Mexico State University)

#### Hadron Structure: Hadron Structure V

- Fernanda Steffens (Helmholtz-Institut für Strahlen- und Kernphysik)

#### Hadron Structure: Hadron Structure VI

- Raza Sufian (William & Mary / Jefferson Lab)

#### Hadron Structure: Hadron Structure VII

- Konstantin Ottnad (University of Mainz)

We present results for the electromagnetic form factors of the proton and neutron computed on the Coordinated Lattice Simulations (CLS) ensembles with $N_\mathrm{f} = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the...

We present results for the nucleon electromagnetic form factors using $N_f$=2+1+1 twisted mass lattice QCD with clover improvement and with quarks with masses tuned to their physical values. Our preliminary analysis includes three ensembles at similar physical volume and lattice spacings $a\sim$0.08 fm, $\sim$0.07 fm, and $\sim$0.06 fm allowing us to take the continuum limit directly at the...

We present the results of a complete lattice calculation of the gravitational form factors (GFFs) of the proton and pion, including glue as well as connected and disconnected quark contributions, on an ensemble with 2+1 flavors of Wilson fermions with close-to-physical pion mass of 170 MeV. We use these results to predict full, physical densities of energy, pressure, and shear forces inside...

Nucleon isovector form factors calculated on a 2+1-flavor domain-wall-fermions ensemble with strange and degenerate up and down quarks at physical mass and lattice cut off, $a^{-1}$, of about 1.730(4) GeV, will be presented. The ensemble was generated jointly by RBC and UKQCD collaborations with a spatial extent of $48a$ or about 5.5 fm. The form factors are calculated in collaboration with...

I will discuss progress on computing nucleon elastic form factors with the stochastic LapH method.

OR, if results these results are not yet ready,

I will discuss preliminary results on the nucleon-pion sigma term determined with O(30) HISQ ensembles with MDWF valence fermions. The nucleon spectrum results are determined at 7 pion masses in the range 130 < Mpi < 400 MeV, four lattice...

We present results for the isovector axial form factor of the nucleon computed on a set of $N_f = 2 + 1$ CLS ensembles with $\mathcal{O}(a)$-improved Wilson fermions and the Lüscher-Weisz gauge action. The set of ensembles covers a range of pion masses from 353 MeV down to the physical pion mass, and lattice spacings between 0.05 fm and 0.09 fm.

We use the summed operator insertion method...

We present the current status of our analyis of nucleon structure observables including isovector charges and twist-2 matrix elements as well as the nucleon mass. Results are computed on a large set of CLS $N_f=2+1$ gauge ensembles with $M_\pi\approx 0.130\mathrm{MeV} \ldots 350\mathrm{MeV}$, four values of the lattice spacing $a\approx0.05\mathrm{fm}\ldots0.09\mathrm{fm}$ and covering a large...

The study of resonance form factors in lattice QCD is a challenging endeavor. Namely, the infinite-volume limit, $L \rightarrow \infty$, is not well defined in the matrix element (here, $L $ is the spacial extension of a rectangular lattice). This irregular behavior persists even after multiplying each external leg with the pertinent Lellouch-Lüscher factor and stems from the so-called...

We present results of nucleon structure studies measured in 2+1 flavor QCD with the physical light quarks ($m_\pi$ = 135 MeV) in a large spatial extent of about 10 fm. Our calculations are carried out with the PACS10 gauge configurations generated by the PACS Collaboration with the stout-smeared $O(a)$ improved Wilson fermions and Iwasaki gauge action at $\beta$=1.82 and 2.00 corresponding to...

We report on the recent progress of our analysis into nucleon sigma terms, as well as the singlet axial and tensor nucleon charges.

These are extracted from the CLS gauge configurations, which utilise the Lüscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_{f} = 2 + 1$ fermions, with pion masses ranging from the physical value up to 410 MeV, and lattice spacings...

We present an analysis of the pion-nucleon sigma term on the CLS ensembles with $N_f = 2 + 1$ flavors of ${\cal O}(a)$-improved Wilson fermions. We perform a chiral interpolation based on ensembles with pion masses ranging from 130 MeV to roughly 350 MeV. The analysis covers four lattice spacings between $a\approx 0.05\mathrm{fm}\ldots0.09\mathrm{fm}$, allowing for an estimate of systematics...

A lot of progress has been made in the direct determination of nucleon sigma terms. Using similar methods we consider the sigma terms of the other octet baryons as well. These are determined on CLS gauge field ensembles employing the Lüscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_\mathrm{f} = 2 + 1$. The ensembles have pion masses ranging from...

Previous Lattice QCD calculations of nucleon transverse

momentum-dependent parton distributions (TMDs) focused

on the case of transversely polarized nucleons, and thus

did not encompass two leading-twist TMDs associated with

longitudinal polarization, namely, the helicity TMD and

the worm-gear TMD corresponding to transversely polarized

quarks in a longitudinally polarized nucleon....

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings $a=0.04$ fm and $0.06$ fm and valence pion mass $m_\pi=300$ MeV, at boost momentum as large as $2.42$ GeV. As a crucial step to control the systematics, we renormalize the pion valence quasi...

We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical limit using large-momentum effective theory. The calculation is done at three lattice spacings $a \approx$ {0.085, 0.064, 0.049} fm and various pion masses $m_{\pi} \approx$ {350, 280, 220} MeV, with the proton momenta up to 2.8 GeV. The result is...

We present an exploratory study of the quasi-beam function on a $N_f = 2 + 1 + 1$ twisted mass lattice of size $24^3 \times 48$, with a pion mass of $350$ MeV and of lattice spacing $0.093$ fm. We show preliminary results for longitudinal momentum of up to $1.7$ GeV and transverse separation of up to $0.28$ fm. We also discuss the possible renormalization of the bare matrix element using...

In this talk I will show our calculations of Collins-Soper kernel and soft function on a newly generated 2+1 flavor clover fermion CLS ensemble of size $48^4$ with $a=0.098$ fm. The light sea quark mass corresponds to a pion mass of 333 MeV for this ensemble and the valence quark mass to 662 MeV. We measure the large-momentum-transfer meson form factors and its transverse-momentum-depdent wave...

We present results for the parton distribution functions (PDFs) of the nucleon at the physical point from lattice QCD utilizing a next-to-next-to-leading order (NNLO) matching. We consider two different strategies in our calculation. The first makes use of the short-distance factorization formalism to extract the first few Mellin moments in a model-independent way. In the second approach, we...

We present results of the x-dependence of the unpolarized gluon PDF for the proton. We use an $N_f = 2+1+1$ ensemble of maximally twisted mass fermions with clover improvement and the Iwasaki improved gluon action. The quark masses are tuned so that the pion mass is $260$ MeV. We use a $32^3 \times 64$ lattice size with a lattice spacing $a=0.093$ fm giving a spatial extent of $3$ fm. We...

Precise exploration of the partonic structure of the nucleon is one of

the most important aims of high-energy physics. In recent years, it has

become possible to address this topic with first-principle Lattice QCD

investigations. In this talk, we focus on the so-called

pseudo-distribution approach to determine the isovector unpolarized

PDFs. In particular, we employ three lattice spacings...

"We present results on the chiral-even twist-3 quark GPDs for the proton using one ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover term, corresponding to a pion mass of 260 MeV. We employ the quasi-distribution method which relates lattice matrix elements of non-local operators defined in coordinate space to the...

The Parton Distribution Functions (PDFs) encode the non-perturbative collinear dynamics of a hadron probed in inclusive and semi-inclusive scattering processes, and hence provide an avenue to address a number of key questions surrounding the structure of hadrons. This talk will summarize recent efforts of the HadStruc Collaboration to map out the leading-twist quark PDFs of the nucleon using...

We present a lattice QCD calculation towards determining gluon helicity distribution and how much of the proton’s spin budget is contributed by gluons. We consider matrix elements of bilocal operators composed of two gluon fields that can be used to determine the polarized gluon Ioffe-time distribution and the corresponding parton distribution function. We employ a high-statistics computation...

A major focus of the new Electron-Ion Collider will be the experimental determination of generalised parton distributions (GPDs). I will give an outline of the CSSM/QCDSF collaboration's determination of GPD properties from a lattice calculation of the off-forward Compton amplitude (OFCA). By determining the OFCA, we can access phenomenologically important properties such as scaling and...

The nucleon transverse quark spin densities are presented. The densities are extracted from the unpolarized and transversity generalized form factors using three Nf = 2 + 1 + 1 twisted mass fermion ensembles simulated with physical quark masses. The results obtained for three lattice spacings are extrapolated to the continuum limit directly at the physical pion mass. The isovector tensor...

It is often taken for granted that Generalized Parton Distributions (GPDs) are defined in the "symmetric" frame, where the transferred momentum is symmetrically distributed between the incoming/outgoing hadrons. However, such frames pose more computational challenges for the lattice QCD practitioners. In this talk, we lay the foundation for lattice QCD calculations of GPDs in non-symmetric...

We present a numerical investigation of a novel Lorentz covariant parametrization to extract x-dependent GPDs using off-forward matrix elements of momentum-boosted hadrons coupled to non-local operators. The novelty of the method is the implementation of a non-symmetric frame for the momentum transfer between the initial and final hadron state and the parametrization of the matrix elements...

Distribution amplitudes (DAs) describe the momentum of a meson’s constituent partons and are of great importance in quantum chromodynamics (QCD) experiments and phenomenology. The advent of large-momentum effective theory (LaMET) in 2013 made the determination of DAs amenable to lattice calculations. Parton physics is described in the limit of infinite momentum and corrections to LaMET...

Information about double parton distributions (DPDs) can be obtained by calculating four-point functions on the lattice. We continue our study on the first DPD Mellin moment of the unpolarized proton by considering interference effects w.r.t. the quark flavor. In our simulation we employ an $n_{f} = 2+1$ ensemble with inverse coupling $\beta = 3.4$, and pseudoscalar masses of $m_{\pi} =...

We study the dependence of hadronic resonances on the mass of quarks through the analysis of data from QCD lattice simulations form various collaborations. Using Machine Learning techniques as the LASSO algorithm we fit lattice data in order to extrapolate them to the physical point and extract the results for the quark mass dependence for exotic resonances like Ds0 and Ds1.

Calculations of nucleon charges and form factors have reached a level

of precision requiring a more precise accounting of the contribution

of excited states in both the two and three point functions. Recently,

it was suggested that the excited states that are suppressed in two-point

function maybe enhanced in certain three point functions. Such an enhancement increases when using...

We present preliminary results of the renormalization functions (RFs) for a number of quark and gluon operators studied in lattice QCD using a gauge-invariant renormalization scheme (GIRS). GIRS is a variant of the coordinate-space renormalization prescription, in which Green's functions of gauge-invariant operators are calculated in position space. A novel aspect is that summations over...

We study the electric polarizability of a charged pion from four-point functions in lattice QCD as an alternative to the background field method. We show how to evaluate the correlation functions under special kinematics to access the polarizability. The elastic form factor (charge radius) is needed in the method which can be obtained from the same four-point functions at large current...

We investigate an improved analysis method of the recently-proposed model-independent method to obtain the pion charge radius from the electromagnetic pion three-point function. We discuss a systematic error of the original method in small volume, and propose an improvement to reduce it. Using the $N_f = 2+1$ lattice QCD data at $m_\pi = 0.51$ GeV, we compare the result of the pion charge...

I will give a status report on our calculations of matrix elements of quark bilinear operators between nucleon states. Summary of results for isovector charges, moments, and axial, electric and magnetic form factors will be presented.

Excited state contamination is one of the most challenging sources of systematics to tackle in the determination of nucleon matrix elements and form factors. The signal-to-noise problem prevents one from considering large source-sink time separations. Instead, state-of-the-art analyses consider multi-state fits. Excited state contributions to the correlation functions are particularly...

Determining the quark and gluon contributions to the momentum of a hadron is a difficult and computationally expensive problem. This difficulty mainly arises from the calculation of the gluon matrix element which involves a quark-line disconnected gluon operator, which suffers from noisy ultra-violet fluctuations. Furthermore, a complete calculation also requires a determination of the...

The light-cone distribution amplitude (LCDA) of the pion carries information about the parton momentum distribution and is an important theoretical input into various predictions of exclusive measurements at high energy, including the pion electromagnetic form factor. We present progress towards a lattice calculation of the fourth Mellin moment of the LCDA using the heavy quark operator...

We present an update on the calculation of flavor diagonal nucleon axial, scalar and tensor charges on eight 2+1+1-flavor MILC HISQ ensembles using Wilson-clover fermions. We discuss the excited state contributions (ESC) in the connected and disconnected diagrams, nonperturbative calculation of the renormalization constants and flavor mixing in the RI-sMOM scheme. These data are extrapolated...

The determination of a function from a finite set of points is notoriously an ill-defined problem, which clearly affects the determination of PDFs. As high-energy physics moves into the era of precision, it is mandatory to find a robust way of quantifying the uncertainties affecting the determination of PDFs, which play a central role in the analysis of experimental data at hadronic colliders....