Light-cone distribution amplitudes of the nucleon and ∆ baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

A Novel Feature of Valence Quark Distributions in Hadrons

Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)≡xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2.

An analysis of parton distribution functions of the pion and the kaon with the maximum entropy input

We present pion and kaon parton distribution functions from a global QCD analysis of the experimental data within the framework of dynamical parton model. We use the DGLAP equations with parton–parton recombination corrections and the valence input of uniform distribution which maximizes the information entropy. At our input scale $$Q_0^2$$ Q 0 2 , there are no sea quark and gluon distributions. All the sea quarks and gluons of the pion and the kaon are completely generated from the parton splitting processes. The mass-dependent parton splitting kernel is applied for the strange quark distribution in the kaon. The obtained valence quark and sea quark distributions at high $$Q^{2}$$ Q 2 ($$Q^2>5$$ Q 2 > 5 GeV$$^2$$ 2 ) are compatible with the existed experimental measurements. Furthermore, the asymptotic behaviours of parton distribution functions at small and large x have been studied for both the pion and the kaon. Lastly, the first three moments of parton distributions at high $$Q^{2}$$ Q 2 scale are calculated, which are consistent with other theoretical predictions.

Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs

We present the new MSHT20 set of parton distribution functions (PDFs) of the proton, determined from global analyses of the available hard scattering data. The PDFs are made available at NNLO, NLO, and LO, and supersede the MMHT14 sets. They are obtained using the same basic framework, but the parameterisation is now adapted and extended, and there are 32 pairs of eigenvector PDFs. We also include a large number of new data sets: from the final HERA combined data on total and heavy flavour structure functions, to final Tevatron data, and in particular a significant number of new LHC 7 and 8 TeV data sets on vector boson production, inclusive jets and top quark distributions. We include up to NNLO QCD corrections for all data sets that play a major role in the fit, and NLO EW corrections where relevant. We find that these updates have an important impact on the PDFs, and for the first time the NNLO fit is strongly favoured over the NLO, reflecting the wider range and in particular increased precision of data included in the fit. There are some changes to central values and a significant reduction in the uncertainties of the PDFs in many, though not all, cases. Nonetheless, the PDFs and the resulting predictions are generally within one standard deviation of the MMHT14 results. The major changes are the $$u-d$$ u - d valence quark difference at small x, due to the improved parameterisation and new precise data, the $${\bar{d}}, {\bar{u}}$$ d ¯ , u ¯ difference at small x, due to a much improved parameterisation, and the strange quark PDF due to the effect of LHC W, Z data and inclusion of new NNLO corrections for dimuon production in neutrino DIS. We discuss the phenomenological impact of our results, and in general find reduced uncertainties in predictions for processes such as Higgs, top quark pair and W, Z production at post LHC Run-II energies.

Contact interaction analysis of pion GTMDs

A contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction’s simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions, it is found that the pion’s mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion’s core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions, their magnitude and domain of material support decrease with increasing twist. The simplest Wigner distribution associated with the pion’s twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.

Kaon and pion parton distributions

Beginning with results for the leading-twist two-particle distribution amplitudes of $$\pi $$ π - and K-mesons, each of which exhibits dilation driven by the mechanism responsible for the emergence of hadronic mass, we develop parameter-free predictions for the pointwise behaviour of all $$\pi $$ π and K distribution functions (DFs), including glue and sea. The large-x behaviour of each DF meets expectations based on quantum chromodynamics; the valence-quark distributions match extractions from available data, including the pion case when threshold resummation effects are included; and at $$\zeta _5=5.2\,$$ ζ 5 = 5.2 GeV, the scale of existing measurements, the light-front momentum of these hadrons is shared as follows: $$\langle x_{\mathrm{valence}} \rangle ^\pi = 0.41(4)$$ ⟨ x valence ⟩ π = 0.41 ( 4 ) , $$\langle x_{\mathrm{glue}} \rangle ^\pi = 0.45(2)$$ ⟨ x glue ⟩ π = 0.45 ( 2 ) , $$\langle x_{\mathrm{sea}} \rangle ^\pi = 0.14(2)$$ ⟨ x sea ⟩ π = 0.14 ( 2 ) ; and $$\langle x_{\mathrm{valence}} \rangle ^K = 0.42(3)$$ ⟨ x valence ⟩ K = 0.42 ( 3 ) , $$\langle x_{\mathrm{glue}} \rangle ^K = 0.44(2)$$ ⟨ x glue ⟩ K = 0.44 ( 2 ) , $$\langle x_{\mathrm{sea}} \rangle ^K = 0.14(2)$$ ⟨ x sea ⟩ K = 0.14 ( 2 ) . The kaon’s glue and sea distributions are similar to those in the pion, although the inclusion of mass-dependent splitting functions introduces some differences on the valence-quark domain. This study should stimulate improved analyses of existing data and motivate new experiments sensitive to all $$\pi $$ π and K DFs. With little known empirically about the structure of the Standard Model’s (pseudo-) Nambu-Goldstone modes and analyses of existing, limited data being controversial, it is likely that new generation experiments at upgraded and anticipated facilities will provide the information needed to resolve the puzzles and complete the picture of these complex bound states.

Improved pion mean fields and masses of singly heavy baryons

A singly heavy baryon can be viewed as $N_c-1$ ($N_c$ being the number of colors) light valence quarks bound by the pion mean fields that are created by the presence of the $N_c-1$ valence quarks self-consistently, while the heavy quark inside a singly heavy baryon is regarded as a static color source. We investigate how the pion mean fields are created by the presence of $N_c$, $N_c-1$, and $N_c-2$ light valence quarks, which correspond to the systems of light baryons, singly heavy baryons, and doubly heavy baryons. As the number of colors decreases from $N_c$ to $N_c-1$, the pion mean fields undergo changes. As a result, the valence quark contributions to the moments of inertia of the soliton become larger than for $N_c$ valence quarks, whereas the sea quark contributions decrease systematically. On the other hand, the presence of the $N_c-2$ valence quarks is not enough to produce the strong pion mean fields, which leads to the classical soliton not being formed. This indicates that the pion mean-field approach is not suitable to describe doubly heavy baryons. We show that the mass spectra of the singly heavy baryons are better described by the improved pion mean fields, compared with the previous work in which the pion mean fields are assumed to be intact with $N_c$ varied.

Theory and applications of parton pseudodistributions

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator [Formula: see text] of the parton fields is a function [Formula: see text] of Lorentz invariants [Formula: see text], the Ioffe time, and the invariant interval [Formula: see text]. This observation allows to extract the Ioffe-time distribution [Formula: see text] from Euclidean separations [Formula: see text] accessible on the lattice. Another basic feature is the use of the ratio [Formula: see text], that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining [Formula: see text]-dependence of the reduced Ioffe-time distribution [Formula: see text] corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions [Formula: see text] using matching relations. The [Formula: see text]-dependence of [Formula: see text] governs the [Formula: see text]-dependence of parton densities [Formula: see text]. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.