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Xiaonu Xiong

Publications and source records attributed to Xiaonu Xiong.

35 records · Page 2Linked to original sources
arXiv2018

Gauge-invariant decomposition of meson energy in two-dimensional QCD

This work is driven by our curiosity towards some basic questions in QCD: how is the energy of a moving hadron partitioned among different gauge-invariant sectors in QCD Hamiltonian? How is the energy of an massless pion separated between quark and gluon sectors, particularly in the soft pion limit? Is it possible to decompose the celebrated Gell-Mann-Oakes-Renner (GOR) relation? To what extent can we justify the quark potential model from the field-theoretical mass decomposition for heavy quarkonium? Due to limitation of contemporary nonperturbative tools, we do not yet know answers to these questions in realistic QCD. In this work, we take the 't Hooft model (two-dimensional QCD in large-$N$ limit) as a prototype model that mimics some essential aspects of the true QCD. We investigate the gauge-invariant energy decomposition of a flavor-neutral meson that can carry an arbitrary momentum (including stationary case), with meson species ranging from massless pion to bottomonium. All the aforementioned questions can be addressed satisfactorily within this model, in particular some unexpected patterns related to pion are discovered for the first time in two-dimensional QCD. We hope that our study can offer some useful clues and stimulation for future investigations on hadron energy decomposition in realistic QCD.

hep-ph↗
arXiv2018

Partonic quasidistributions in two-dimensional QCD

As a sequel of our preceding work [1] we carry out a comprehensive comparative study between the quasi parton distribution functions (PDFs), distribution amplitudes (DAs) and their light-cone counterparts for various flavor-neutral mesons, in the context of the 't Hooft model, that is, the two-dimensional QCD in the large $N$ limit. In contrast to the original derivation via diagrammatic techniques exemplified by Dyson-Schwinger and Bethe-Salpeter equations, here we employ the Hamiltonian operator approach to reconstruct the celebrated 't Hooft equation in light-front quantization, and Bars-Green equations in equal-time quantization. The novelty of our derivation is to employ the soft momentum cutoff as the IR regulator. As a virtue of this operator approach, the functional form of the quasi distributions can be transparently built out of the Bars-Green wave functions and the Bogoliubov angle with the aid of bosonization technique. Equipped with various bound-state wave functions numerically inferred in [1], we then investigate how rapidly the quasi distributions approach their light-cone counterparts with the increasing meson momentum. We observe that, light mesons' quasi distributions approach the light-cone distributions in a slower pace than the heavy quarkonia. Curiously, lattice simulations of quasi distributions in four-dimensional QCD also discover this feature. Furthermore, we also compute the partonic light-cone PDF and quasi-PDF to one-loop order in perturbation theory, again employing the momentum cutoff as the IR regulator. We explicitly verify one of the backbones underlying the large momentum effective field theory (LaMET), namely, both quasi-PDFs and light-cone PDFs in ${\rm QCD}_2$ indeed possess the same IR behavior at leading order in $1/P^z$

hep-th↗
arXiv2018

Quasi-Parton Distribution Function in Lattice Perturbation Theory

Large momentum effective field theory provides a new direction for lattice QCD calculations of hadronic structure functions, such as parton distribution functions (PDFs), meson distribution amplitudes, and so on, directly with $x$-dependence. In the framework of Lattice Perturbation Theory (LPT), we compute the one-loop quark-in-quark quasi-PDF with the naïve fermion action ($\tilde{q}^{\mathrm{nv}}$) and quasi-PDF with Wilson-Clover action ($\tilde{q}^{\mathrm{WC}}$) and show that $\tilde{q}^{\mathrm{nv}}$ reduces to the continuum quasi-PDF in the continuum limit. We point out, however, that the continuum limit and massless quark limit do not commute. We find that the condition to recover the same collinear divergence that the quasi-PDF has in continuum QCD is $aP_3^2\approx m$ and $m\ll P_3$, while the condition to fully recover the continuum quasi-PDF is $aP_{3}^{2}\ll m\ll P_{3}$, where $P_3$ is the momentum in the direction of the quark's motion (longitudinal direction). These two conditions are based on perturbation calculations and should not be applied to non-perturbative calculations because the non-perturbative effects cure the collinear divergence. The correction to the quasi-PDF using the naïve fermion action is due to the Wilson term and can be viewed as an $\mathcal{O}\left(a^{1}\right)$ correction. For nonzero $r$, the $\mathcal{O}\left(a^{1}\right)$ corrections are subsequently mixed with the quasi-PDF using the naïve fermion action.

hep-ph↗
arXiv2017

Solving the Bars-Green equation for moving mesons in two-dimensional QCD

The two-dimensional QCD in the large $N$ limit, generally referred to as the 't Hooft model, is numerically investigated in the axial gauge in a comprehensive manner. The corresponding Bethe-Salpeter equation for a bound $q\bar{q}$ pair, originally derived by Bars and Green in 1978, was first numerically tackled by Li and collaborators in late 1980s, yet only for the {\it stationary} mesons. In this paper, we make further progress by numerically solving the Bars-Green equation for {\it moving} mesons, ranging from the chiral pion to charmonium. By choosing several different quark masses, we computed the corresponding quark condensates, meson spectra and their decay constants for a variety of meson momenta, and found satisfactory agreement with their counterparts obtained using light-cone gauge, thus numerically verified the gauge and Poincaré invariance of the 't Hooft model. Moreover, we have explicitly confirmed that, as the meson gets more and more boosted, the large component of the Bars-Green wave function indeed approaches the corresponding 't Hooft light-cone wave function, while the small component of the wave function rapidly fades away.

hep-ph↗
arXiv2016

Revisiting the equivalence of light-front and covariant QED in the light-cone gauge

We discuss the equivalence between light-front time-ordered-perturbation theory and covariant quantum field theory in light-front quantization, in the case of quantum electrodynamics at one-loop level. In particular, we review the one-loop calculation of the vertex correction, fermion self-energy and vacuum polarization. We apply the procedure of integration by residue over the light-front energy in the loop to show how the perturbative expansion in covariant terms can be reduced to a sum of propagating and instantaneous diagrams of light-front time-ordered perturbation theory. The detailed proof of equivalence between the two formulations of the theory resolves the controversial question on which form should be used for the gauge-field propagator in the light-cone gauge in the covariant approach.

hep-ph↗
arXiv2016

Reconstructing parton densities at large fractional momenta

Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpolarized and helicity PDFs. In the future, the method can be used to produce PDFs entirely based on lattice QCD results.

hep-ph↗
arXiv2016

Relativistic correction to gluon fragmentation function into pseudoscalar quarkonium

Inspired by the recent measurements of the $η_c$ meson production at LHC, we investigate the relativistic correction effect for the fragmentation function of the gluon into $η_c$, which constitutes the crucial nonperturbative elements to understand $η_c$ production at high $p_T$. Employing three distinct methods, we calculate the leading relativistic correction to the $g\toη_c$ fragmentation function in the NRQCD factorization framework, as well as verify the existing NLO result for the $c\to η_c$ fragmentation function. We also study the evolution behavior of these fragmentation functions with the aid of DGLAP equation.

hep-ph↗
arXiv2015

Quasi Distribution Amplitude of Heavy Quarkonia

The recently-proposed quasi distributions point out a promising direction for lattice QCD to investigate the light-cone correlators, such as parton distribution functions (PDF) and distribution amplitudes (DA), directly in the $x$-space. Owing to its excessive simplicity, the heavy quarkonium can serve as an ideal theoretical laboratory to ascertain certain features of quasi-DA. In the framework of non-relativistic QCD (NRQCD) factorization, we compute the order-$α_s$ correction to both light-cone distribution amplitudes (LCDA) and quasi-DA associated with the lowest-lying quarkonia, with the transverse momentum UV cutoff interpreted as the renormalization scale. We confirm analytically that the quasi-DA of a quarkonium does reduce to the respective LCDA in the infinite-momentum limit. We also observe that, provided that the momentum of a charmonium reaches about 2-3 times its mass, the quasi-DAs already converge to the LCDAs to a decent level. These results might provide some useful guidance for the future lattice study of the quasi distributions.

hep-ph↗
arXiv2015

One-loop matching for transversity generalized parton distribution

Recent developments showed that light cone parton distributions can be studied by investigating the large momentum limit of the so-called quasiparton distributions, which are defined in terms of spacelike correlators, and therefore can be readily computed on the lattice. These two distributions can be connected to each other by a perturbative factorization formula or matching condition that allows one to convert the latter into the former. Here we present the one-loop matching condition for the transversity generalized quark distribution in the nonsinglet case

hep-ph↗
arXiv2015

One-Loop Matching for Generalized Parton Distributions

We present the one-loop matching condition for the unpolarized and polarized generalized quark distributions in the non-singlet case. The matching condition links the quasi distributions defined in terms of spacelike correlators at finite nucleon momentum to the light-cone distributions, and is useful for extracting the latter from the former in a lattice QCD calculation. Our results show that at one-loop and leading power accuracy the matching for the light-cone generalized quark distribution $H$ ($\tilde H$) is non-trivial, whereas no matching is required for $E$ ($\tilde E$). Therefore, $E$ ($\tilde E$) can be smoothly approached by its quasi counterpart in the large momentum limit. We also present the matching for the distribution amplitude of the pion.

hep-ph↗
arXiv2014

Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice

We study the transverse momentum dependent (TMD) parton distributions in the newly proposed quasi-parton distribution function framework in Euclidean space. A soft factor subtraction is found to be essential to make the TMDs calculable on lattice. We show that the quasi-TMDs with the associated soft factor subtraction can be applied in hard QCD scattering processes such as Drell-Yan lepton pair production in hadronic collisions. This allows future lattice calculations to provide information on the non-perturbative inputs and energy evolutions for the TMDs. Extension to the generalized parton distributions and quantum phase space Wigner distributions will lead to a complete nucleon tomography on lattice.

hep-ph↗
arXiv2013

One-Loop Matching for Parton Distributions: Non-Singlet Case

We derive one-loop matching condition for non-singlet quark distributions in transverse-momentum cut-off scheme, including unpolarized, helicity and transversity distributions. The matching is between the quasi-distribution defined by static correlation at finite nucleon momentum and the light-cone distribution measurable in experiments. The result is useful for extracting the latter from the former in a lattice QCD calculation.

hep-ph↗
arXiv2013

Scintillation Efficiency for Low-Energy Nuclear Recoils in Liquid-Xenon Dark Matter Detectors

We perform a theoretical study of the scintillation efficiency in the low-energy region crucial for liquid-xenon dark-matter detectors. We develop a computer program to simulate the cascading process of the recoiling xenon nucleus in liquid xenon and calculate the nuclear quenching effect due to atomic collisions. We use the electronic stopping power extrapolated from the experimental data to the low-energy region, and take into account the effects of electrons escaping from the electron-ion pair recombination using the generalized Thomas-Imel model fitted to scintillation data. Our result agrees well with the experiments from neutron scattering and vanishes rapidly as the recoiling energy drops below 3 keV.

physics.ins-det↗
arXiv2012

Proton Spin Structure from Measurable Parton Distributions

We present a systematic study of the proton spin structure in terms of measurable parton distributions. For a transversely-polarizedproton, we derive a polarization sum rule from the leading generalized parton distributions appearing in hard exclusive processes. For a longitudinally-polarized proton, we obtain a helicity decomposition from well-known quark and gluon helicity distributions and orbital angular-momentum contributions. The latter is shown to be related to measurable subleading generalized parton distributions and quantum-phase space Wigner distributions.

hep-ph↗
arXiv2012

Transverse Polarization of the Nucleon in Parton Picture

The proton's transverse polarization structure is examined in terms of the Lorentz-covariant Pauli-Lubanski vector in QCD. We find that there are contributions from leading, subleading, and next-to-subleading partonic contributions in the light-front system of coordinates. The subleading and next-to-subleading contributions are related to the leading one through Lorentz symmetry. And the leading contribution obeys a simple partonic angular momentum sum rule that gives a clear physical interpretation to a relation known previously.

hep-ph↗
arXiv2012

Probing Parton Orbital Angular Momentum in Longitudinally Polarized Nucleon

While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured through twist-three GPDs. The second is the much-debated canonical OAM distribution natural in free-field theory and light-cone gauge. We show the latter in light-cone gauge can also be related to twist-three GPDs as well as quantum phase-space Wigner distributions, both being measurable in high-energy experiments.

hep-ph↗