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Ian C. Cloët

Publications and source records attributed to Ian C. Cloët.

31 records · Page 2Linked to original sources

arXiv2019

Distinguishing Quarks and Gluons in Pion and Kaon PDFs

The leading-twist parton distribution functions of the pion and kaon are calculated for the first time using a rainbow-ladder truncation of QCD's Dyson-Schwinger equations (DSEs) that self-consistently sums all planar diagrams. The non-perturbative gluon dressing of the quarks is thereby correctly accounted for, which in practice means solving the inhomogeneous Bethe-Salpeter equation (BSE) for the quark operator that defines the spin-independent quark distribution functions. An immediate consequence of using this dressed vertex is that gluons carry 35% of the pion's and 30% of the kaon's light-cone momentum, with the remaining momentum carried by the quarks. The scale associated with these DSE results is $μ_0 = 0.78\,$GeV. The gluon effects generated by the inhomogeneous BSE are inherently non-perturbative and cannot be mimicked by the perturbative QCD evolution equations. A key consequence of this gluon dressing is that the valence quarks have reduced support at low-to-intermediate $x$, where the gluons dominate, and increased support at large $x$. As a result, our DSE calculation of the pion's valence quark distribution is in excellent agreement with the Conway et al. pion-induced Drell-Yan data, but nevertheless exhibits the $q_π(x) \simeq (1-x)^2$ behavior as $x\to 1$ predicted by perturbative QCD.

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arXiv2018

Intrinsic Transverse Motion of the Pion's Valence Quarks

Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations (DSEs), we determine the pion's $l_z=0$ and $|l_z|=1$ leading Fock-state light-front wave functions (LFWFs) [labeled by $ψ_{l_z}(x,k_T^2)$]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained from these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction $x$. The LFWFs have a non-trivial $(x,k_T^2)$ dependence and in general do not factorize into separate functions of each variable. The $l_z=0$ LFWF is concave with a maximum at $x=1/2$, whereas orbital angular momentum effects causes the $|l_z|=1$ LFWF to have a slight {\it double-humped} structure for quark transverse momentum in the range $0.5 \lesssim k_T^2 \lesssim 5\,$GeV$^2$. For $k_T^2 \lesssim 1\,$GeV$^2$ the $k_T^2$ dependence of the LFWFs is well described by a Gaussian, however for $k_T^2 \gtrsim 10\,$GeV$^2$ these LFWFs behave as $ψ_0 \propto x(1-x)/k_T^2$ and $ψ_1 \propto x(1-x)/k_T^4$, and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD inherits many features from the LFWFs, where for $k_T^2 \lesssim 1\,$GeV$^2$ the $k_T^2$ dependence is well described by a Gaussian, and for large $k_T^2$ the TMD behaves as $f_π^q \propto x^2(1-x)^2/k_T^4$. At the model scale we find the average transverse momentum, defined by a Bessel-weighted moment with $b_T=0.3\,$fm, to equal $\langle k_T^2\rangle = 0.19\,$GeV$^2$. The TMD evolution of our result is studied using both the $b^*$ and $ζ$ prescriptions which allows a qualitative comparison with existing Drell-Yan data.

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arXiv2018

Charge Symmetry Breaking Effects in Pion and Kaon Structure

Charge symmetry breaking (CSB) effects associated with the $u$ and $d$ quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu--Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed $u$ and $d$ quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiquark governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with a pion mass difference given by $m_{π^+}^2 - m_{π^0}^2 \propto (m_u - m_d)^2$ as demanded by dynamical chiral symmetry breaking. We find significant CSB effects for realistic current quark mass ratios ($m_u/m_d \sim 0.5$) in the quark flavor-sector electromagnetic form factors of both the pion and kaon. For example, the difference between the $u$ and $d$ quark contributions to the $π^+$ electromagnetic form factors is about 8\% at a momentum transfer of $Q^2 \simeq 10\,$GeV$^2$, while the analogous effect for the light quark sector form factors in the $K^+$ and $K^0$ is about twice as large. For the Parton distribution functions, we find CSB effects which are considerably smaller than those found in the electromagnetic form factors.

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arXiv2018

Nucleon Quark Distribution Functions from the Dyson-Schwinger Equations

We present results for the nucleon's leading-twist spin-independent valence parton distribution functions obtained from a theoretical framework based on the Dyson-Schwinger equations (DSEs) of QCD that previously gave an excellent description of nucleon electromagnetic form factors. We employ the rainbow-ladder truncation of the DSEs and utilize nucleon bound state amplitudes from the Poincaré-covariant Faddeev equation, where the dominant scalar and axial-vector quark-quark correlations are included. This DSE framework is used to numerically evaluate the first 20 moments of the valence $u$ and $d$ quark distribution functions, from which the $x$-dependence of the distributions is found to be well constrained. We find good agreement with empirical parameterizations of experimental data and make the prediction that the $d/u$ ratio in the $x\to 1$ limit, invariant under scale evolution, takes the value $d/u \to 0.087 \pm 0.010$. We find that this ratio is rather sensitive to the strength of axial-vector diquark correlations. However, contrary to a naive expectation, our result for the $d/u$ ratio in the $x\to 1$ limit does not vanish when only scalar diquark correlations are present, although it is an order of magnitude smaller than our $d/u$ result that also includes axial-vector diquarks. The valence quark distribution results are set in a broader context via a simple pion cloud model estimate of sea-quark light-cone momenta and gluon light-cone momentum.

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arXiv2017

TMDs of Spin-one Targets: Formalism and Covariant Calculations

We present a covariant formulation and model calculations of transverse momentum-dependent quark distribution functions (TMDs) for spin-one hadrons. Emphasis is placed on a description of these 3-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even $ρ$ meson TMDs in the framework provided by the Nambu--Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cut-off in the proper-time regularization scheme. In particular, the behavior of the 3-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Results of particular interest include the finding that the tensor polarized TMDs -- associated with spin-one hadrons -- are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator $γ^+\boldsymbolγ_Tγ_5$ would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the $ρ$ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. A qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to previous experimental and theoretical results for the two-nucleon (deuteron) bound state.

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arXiv2016

Baryon Octet Electromagnetic Form Factors in a confining NJL model

Electromagnetic form factors of the baryon octet are studied using a Nambu--Jona-Lasinio model which utilizes the proper-time regularization scheme to simulate aspects of colour confinement. In addition, the model also incorporates corrections to the dressed quarks from vector meson correlations in the t-channel and the pion cloud. Comparison with recent chiral extrapolations of lattice QCD results shows a remarkable level of consistency. For the charge radii we find the surprising result $r_{E}^p < r_{E}^{Σ^+}$ and $|r_{E}^n| < |r_{E}^{Ξ^0}|$, whereas the magnetic radii have a pattern largely consistent with a naive expectation based on the dressed quark masses.

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arXiv2015

Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule

In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers $\left|\mathbf{q}\right| \gtrsim 0.5\,$GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.

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arXiv2015

Rho meson form factors in a confining Nambu--Jona-Lasinio model

Elastic electromagnetic form factors for the $ρ^+$ meson are calculated in a Nambu--Jona-Lasinio model which incorporates quark confinement through the use of the proper-time regularization scheme. A comparison is made with recent lattice QCD results and previous quark model calculations for static quantities and the Sachs form factors. The results are qualitatively in good agreement with the lattice QCD calculations, with the exception of the quadrupole moment and corresponding form factor, which may be related to a lack of spherical symmetry on the lattice.

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arXiv2015

SU(3)-flavour breaking in octet baryon masses and axial couplings

The lightest baryon octet is studied within a covariant and confining Nambu--Jona-Lasinio model. By solving the relativistic Faddeev equations including scalar and axialvector diquarks, we determine the masses and axial charges for ΔS = 0 transitions. For the latter the degree of violation of SU(3) symmetry arising because of the strange spectator quark(s) is found to be up to 10%.

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arXiv2014

Role of diquark correlations and the pion cloud in nucleon elastic form factors

Electromagnetic form factors of the nucleon in the space-like region are investigated within the framework of a covariant and confining Nambu-Jona-Lasinio model. The bound state amplitude of the nucleon is obtained as the solution of a relativistic Faddeev equation, where diquark correlations appear naturally as a consequence of the strong coupling in the colour $\bar{3}$ $qq$ channel. Pion degrees of freedom are included as a perturbation to the "quark-core" contribution obtained using the Poincaré covariant Faddeev amplitude. While no model parameters are fit to form factor data, excellent agreement is obtained with the empirical nucleon form factors (including the magnetic moments and radii) where pion loop corrections play a critical role for $Q^2 \lesssim 1\,$GeV$^2$. Using charge symmetry, the nucleon form factors can be expressed as proton quark sector form factors. The latter are studied in detail, leading, for example, to the conclusion that the $d$-quark sector of the Dirac form factor is much softer than the $u$-quark sector, a consequence of the dominance of scalar diquark correlations in the proton wave function. On the other hand, for the proton quark sector Pauli form factors we find that the effect of the pion cloud and axialvector diquark correlations overcomes the effect of scalar diquark dominance, leading to a larger $d$-quark anomalous magnetic moment and a form factor in the $u$-quark sector that is slightly softer than in the $d$-quark sector.

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arXiv2013

Elastic and transition form factors of the Δ(1232)

Predictions obtained with a confining, symmetry-preserving treatment of a vector-vector contact interaction at leading-order in a widely used truncation of QCD's Dyson-Schwinger equations are presented for Δand Ωbaryon elastic form factors and the γN -> Δtransition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest. The Δelastic form factors are very sensitive to m_Δ. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Δ-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Δ(1232). Considering the Δ-baryon's quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the Δ-baryon's deformation in the infinite momentum frame. Results for analogous properties of the Ωbaryon are less contentious. In connection with the N->Δtransition, the Ash-convention magnetic transition form factor falls faster than the neutron's magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Δ; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.

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arXiv2012

Dihadron Fragmentation Functions from the NJL-jet model and their QCD Evolution

We present results for dihadron fragmentation functions from the NJL-jet model evolved from the model scale to a typical experimental scale of $4 \mathrm{GeV}^2$. The numerical method used in this evolution is discussed in detail. The effect of evolution on the shapes of the dihadron fragmentation functions is discussed for a doubly favored process ($u \to π^+π^-$), as well as a singly favored ($u \to π^+K^-$) process involving light quarks. Finally, we explore the production of $K^+ K^-$ pairs from an initial $u$, $d$ or $s$ quark.

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arXiv2012

Transverse Momentum Dependent Fragmentation and Quark Distribution Functions from the NJL-jet Model

Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $ $ has a sizable $z$ dependence, in contrast with the naive Gaussian ansatz for the fragmentation functions. Diquark correlations in the nucleon give rise to a non-trivial flavor dependence in the unpolarized transverse momentum dependent quark distribution functions. The $ $ of the quarks in the nucleon are also found to have a sizable $x$ dependence. Finally, these results are used as input to a Monte Carlo event generator for semi-inclusive deep inelastic scattering (SIDIS), which is used to determine the average transverse momentum squared of the produced hadrons measured in SIDIS, namely $ $. Again we find that the average $P_T^2$ of the produced kaons in SIDIS is significantly larger than that of the pions and in each case $\la P_T^2 \ra$ has a sizable $z$ dependence.

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