Distribution Functions Of Pion Research Articles

Pion distribution functions from low-order Mellin moments

Exploiting an evolution scheme for parton distribution functions (DFs) that is all-orders exact, contemporary lattice-QCD (lQCD) results for low-order Mellin moments of the pion valence quark DF are shown to be mutually consistent. The analysis introduces a means by which key odd moments can be obtained from the even moments in circumstances where only the latter are available. Combining these elements, one arrives at parameter-free lQCD-based predictions for the pointwise behaviour of pion valence, glue, and sea DFs, with sound uncertainty estimates. The behaviour of the pion DFs at large light-front momentum fraction, x≳0.85, is found to be consistent with QCD expectations and continuum analyses of pion structure functions, i.e., damping like (1−x)βparton, with βvalence≈2.4, βglue≈3.6, βsea≈4.6. It may be possible to test these predictions using data from forthcoming experiments.

The unpolarized TMD valence quark distributions of light mesons in the statistical covariant parton model approach

We investigate the unpolarized transverse momentum dependent (TMD) structure of light mesons at low Q^2 scales in nonperturbative region of quantum chromodynamics (QCD). To this end, we calculate the unpolarized TMD valence quark distribution functions of pion and kaon based on the covariant parton model in which the flavour dependent covariant momentum distribution of quarks is needed. We apply the statistical model for this momentum distribution, for the first time, and also consider the quarks to be massive. The results of TMD valence distributions of light mesons show convenient general properties. We also obtain the integrated valence quark distributions of pion and kaon and compare our results with those of other models.

Proton and pion distribution functions in counterpoint

Working with proton and pion valence distribution functions (DFs) determined consistently at the same, unique hadron scale and exploiting the possibility that there is an effective charge which defines an evolution scheme for DFs that is all-orders exact, we obtain a unified body of predictions for all proton and pion DFs – valence, glue, and four-flavour-separated sea. Whilst the hadron light-front momentum fractions carried by identifiable parton classes are the same for the proton and pion at any scale, the pointwise behaviour of the DFs is strongly hadron-dependent. All calculated distributions comply with quantum chromodynamics constraints on low- and high-x scaling behaviour and, owing to emergent hadron mass, pion DFs are the most dilated. These results aid in elucidating the sources of similarities and differences between proton and pion structure.

Parton distributions of light quarks and antiquarks in the proton

An algebraic Ansatz for the proton's Poincaré-covariant wave function, which includes both scalar and pseudovector diquark correlations, is used to calculate proton valence, sea, and glue distribution functions (DFs). Regarding contemporary data, a material pseudovector diquark component in the proton is necessary for an explanation of the neutron-proton structure function ratio; and a modest Pauli blocking effect in the gluon splitting function is sufficient to explain the proton's light-quark antimatter asymmetry. In comparison with pion DFs, the light-front momentum fractions carried by all identifiable parton classes are the same; on the other hand, the higher moments are different. Understanding these features may provide insights that explain distinctions between Nambu-Goldstone bosons and seemingly less complex hadrons.

Nonequilibrium Pion Distribution within the Zubarev Approach

We discuss how the non-equilibrium process of pion production within the Zubarev approach of the non-equilibrium statistical operator leads to a theoretical foundation for the appearance of a non-equilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC.

Symmetry, symmetry breaking, and pion parton distributions

Pion valence, glue and sea distributions are calculated using a continuum approach to the two valence-body bound-state problem. Since the framework is symmetry preserving, physical features of the distributions are properly expressed. The analysis reveals that the emergent phenomenon of dynamical chiral symmetry breaking causes a hardening of the valence-quark distribution function, ${q}^\pi(x)$. Nevertheless, this distribution exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). At the scale $\zeta_2:=2\,$GeV, the following momentum fractions are predicted: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$. Evolving to $\zeta=5.2\,$GeV, the result for ${q}^\pi(x)$ agrees with that computed using lattice QCD. These outcomes should both spur improved analyses of existing experiments and stimulate efforts to obtain new data on the pion distribution functions using available and envisioned facilities.

Drawing insights from pion parton distributions * * Supported by the Chinese Government's Thousand Talents Plan for Young Professionals; Jiangsu Province Hundred Talents Plan for Professionals; and Forschungszentrum Jülich GmbH

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale , , ; and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, , exhibits the behaviour predicted by quantum chromodynamics (QCD). After evolution to , the prediction for matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

Boer-Mulders effect in the unpolarized pion induced Drell\u2013Yan process at COMPASS within TMD factorization

We investigate the theoretical framework of the cos 2phi azimuthal asymmetry contributed by the coupling of two Boer-Mulders functions in the dilepton production unpolarized pi p Drell–Yan process by applying the transverse momentum dependent factorization at leading order. We adopt the model calculation results of the unpolarized distribution function f_1 and Boer-Mulders function h_1^perp of pion meson from the light-cone wave functions. We take into account the transverse momentum dependent evolution effects for both the distribution functions of pion and proton by adopting the existed extraction of the nonperturbative Sudakov form factor for the pion and proton distribution functions. An approximate kernel is included to deal with the energy dependence of the Boer-Mulders function related twist-3 correlation function T_{q,F}^{(sigma )}(x,x) needed in the calculation. We numerically estimate the Boer-Mulders asymmetry nu _{BM} as the functions of x_p, x_pi , x_F and q_T considering the kinematics at COMPASS Collaboration.

Valence quark distribution functions of pion and kaon in the modified chiral quark model

We investigate the structure of pion and kaon based on the modified chiral quark model (χQM). To this end, we calculate the valence quark distribution functions of pion and kaon using the modified χQM in which the bare quarks inside these mesons are dressed by the clouds of Goldstone (GS) bosons and gluons. In order to compute the valence distributions of the light mesons using the modified χQM, the bare quark distribution functions of these mesons are needed. We apply the bare distributions which have been obtained via a phenomenological approach. We compare the results of our theoretical model for the valence distributions of the light mesons with those of some parametrization models and also the available experimental data.

Nucleon and pion distribution functions in the valence region

An experimental and theoretical perspective is provided on the behavior of unpolarized distribution functions for the nucleon and pion on the valence-quark domain, namely, Bjorken $x\ensuremath{\gtrsim}0.4$. This domain is a key to much of hadron physics; e.g., a hadron is defined by its flavor content and that is a valence-quark property. Furthermore, its accurate parametrization is crucial to the provision of reliable input for large collider experiments. The focus is on experimental extractions of distribution functions via electron and muon inelastic scattering, and from Drell-Yan interactions; and on theoretical treatments that emphasize an explanation of the distribution functions, providing an overview of major contemporary approaches and issues. Valence-quark physics is a compelling subject, which probes at the heart of our understanding of the standard model. There are numerous outstanding and unresolved challenges, which experiment and theory must confront. In connection with experiment, an explanation that an upgraded Jefferson Laboratory facility is well suited to provide new data on the nucleon is provided, while a future electron-ion collider could provide essential new data for the mesons. There is also great potential in using Drell-Yan interactions, at FNAL, CERN, J-PARC, and GSI, to push into the large-$x$ domain for both mesons and nucleons. Furthermore, it is argued that explanation, in contrast to modeling and parametrization, requires a widespread acceptance of the need to adapt theory: to the lessons learnt already from the methods of nonperturbative quantum-field theory and a fuller exploitation of those methods.

Pion production in nonequilibrium chiral perturbation theory

We apply the formalism of chiral perturbation theory out of thermal equilibrium to describe explosive production of pions via the parametric resonance mechanism. To lowest order the Lagrangian is that of the nonlinear sigma model where the pion decay constant becomes a time-dependent function. This model allows for a consistent nonequilibrium formulation within the framework of the closed time path method, where one-loop effects can be systematically accounted for and renormalized. We work in the narrow resonance regime where there is only one resonant band. The pion distribution function is peaked around the resonant band where the number of pions grow exponentially in time. The present approach is limited to remain below the back-reaction time, although it accounts for nearly all the pion production during the typical plasma lifetime. Our results agree with the analysis performed in the $O(4)$ model. The space and time components ${f}_{\ensuremath{\pi}}^{s,t}(t)$ are also analyzed. To one loop ${f}_{\ensuremath{\pi}}^{s}\ensuremath{\ne}{f}_{\ensuremath{\pi}}^{t}$ unlike the equilibrium case and their final central values are lower than the initial ones. This effect can be interpreted in terms of a reheating of the plasma.

Relativistic quantum transport theory of hadronic matter: The coupled nucleon,Δ, and pion system

We derive the relativistic quantum transport equation for the pion distribution function based on an effective Lagrangian of the QHD-II model. The closed time-path Green's function technique, the semi-classical, quasi-particle and Born approximation are employed in the derivation. Both the mean field and collision term are derived from the same Lagrangian and presented analytically. The dynamical equation for the pions is consistent with that for the nucleons and deltas which we developed before. Thus, we obtain a relativistic transport model which describes the hadronic matter with $N$, $\Delta$ and $\pi$ degrees of freedom simultaneously. Within this approach, we investigate the medium effects on the pion dispersion relation as well as the pion absorption and pion production channels in cold nuclear matter. In contrast to the results of the non-relativistic model, the pion dispersion relation becomes harder at low momenta and softer at high momenta as compared to the free one, which is mainly caused by the relativistic kinetics. The theoretically predicted free $\pi N \to \Delta$ cross section is in agreement with the experimental data. Medium effects on the $\pi N \to \Delta$ cross section and momentum-dependent $\Delta$-decay width are shown to be substantial.

Model independent constraints on the nuclear pion distribution function in the EMC effect

Abstract A series of constraints on the nuclear pion momentum distribution function is obtained from the moment analysis of structure functions, using the standard convolution formalism together with nonrelativistic dynamics of nucleons.

Deep-inelastic scattering on nuclei: Impulse approximation and mesonic corrections

We present a unified relativistic covariant description of nucleon binding and mesonic corrections to nuclear structure functions in terms of a Feynman diagram approach. The connection between considerations in the infinite momentum frame, where the parton model can be applied, and in the nucleus rest frame is discussed. A new method to estimate mesonic corrections in terms of a nuclear model based on effective meson-nucleon theory is proposed. We apply this method to evaluate the mean mesonic excess in nuclei n mes , the mean mesonic momentum squared k mes 2 , and to derive the bounds on pion distribution function in nuclei. We find that the bulk of the EMC effect at x > 0.1 is reproduced within the impulse approximation with mesonic corrections, while this approximation fails to explain new EMC data at x < 0.1.

Analysis of pion electroproduction data in terms of a pion distribution function of the proton

Experimental data on the longitudinal π + electroproduction on hydrogen have been analyzed in terms of a pion distribution function of the proton. This interpretation is based on the assumption that the pion can be considered as a parton in the nucleon for low momentum transfer Q 2. For the kinematical conditions photon mass Q 2 < 1 GeV 2 and electron energy loss ν > 2.2 GeV the pion electroproduction in the direction of the virtual photon can be viewed upon as quasielastic e π + → e′ π + scattering. Using the impulse approximation the pion distribution function of the proton can be deduced. According to the distribution function evaluated from pion electroproduction in the infinite momentum frame, the physical proton has a 3% admixture of the n π + state and the π + in the n π + state carries 0.6% of the proton momentum.

Q2-dependent parametrizations of pion parton distribution functions

Pion distribution functions have been obtained by performing fits to data on $\frac{J}{\ensuremath{\psi}}$ and dimuon production. Simple ${Q}^{2}$-dependent parametrizations of the results are presented. Some of the implications for high-${p}_{T}$ phenomenology are discussed.

Contribution of Pion Production by Primary Cosmic-Ray Nucleons to the Interstellar Electron-Positron Flux

The secondary electron-positron component of high-energy cosmic radiation is calculated. Using the Feynman scaling law for the inclusive pion distribution function, it is shown that the secondary positron-electron component will have the same power law as the primary electron component if the proton and electron injection spectra are the same. Numerical estimates are made using an appropriate fit of the pion single-particle distribution function to accelerator data. The ${\ensuremath{\pi}}^{0}\ensuremath{-}\ensuremath{\gamma}$-ray component is also discussed.

Role of Diffractive Excitation Mechanism in Multiple Production of Hadrons

The role of diffractive excitation mechanism is examined; the rate of total diffractive cross section is estimated to be about 1/3, at most, of the total inelastic rrN cross section at 16 Ge V /c. A large non-diffractive production mechanism is needed. Behavior of the average multi­ plicity and its dispersion are discussed in the case that the diffractive and non-diffractive me­ chanism coexist. A simple model with a pomeron as a fixed pole is given, which is nor­ malized absolutely so that it reproduces experimental low mass spectra approximately. A single pion distribution function is also discussed.