Light-cone Distribution Functions Research Articles

Light-cone and quasigeneralized parton distributions in the ’t Hooft model

We present a comprehensive study of the light-cone generalized parton distribution (GPD) and quasi-GPD of a flavor-neutral meson in the ’t Hooft model, i.e., two-dimensional QCD (QCD2) in the Nc→∞ limit. With the aid of the Hamiltonian approach, we construct the light-cone GPD in terms of the meson’s light-cone wave function in the framework of light-front quantization and express the quasi-GPD in terms of the meson’s Bars-Green wave functions and the chiral angle in the framework of equal-time quantization. We show that, both analytically and numerically, the quasi-GPD does approach the light-cone GPD when the meson is boosted to the infinite momentum frame, which justifies the tenet underlying the large momentum effective theory for the off-forward parton distribution. Upon taking the forward limit, the light-cone and quasi-GPDs reduce to the light-cone and quasi parton distribution functions (quasi-PDFs). As a bonus, we take this chance to correct the incomplete expression of the quasi-PDFs in the ’t Hooft model reported in our preceding work [Y. Jia , ]. Published by the American Physical Society 2024

Theoretical predictions for inclusive B→Xuτν¯ decay

With the expected large increase in datasets, previously not measured decays will be studied at Belle II. We derive standard model predictions for the $B\ensuremath{\rightarrow}{X}_{u}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ decay rate and distributions. The region in the lepton energy spectrum where higher-dimension operators in the local operator product expansion need to be resummed into the $b$-quark light-cone distribution function is a significantly greater fraction of the phase space than for massless leptons. The finite $\ensuremath{\tau}$ mass has the novel effect of shifting and squeezing how the distribution function enters the lepton energy spectrum. We also derive new predictions for the $\ensuremath{\tau}$ polarization.

Recent highlights with baryons from lattice QCD

Highlights from recent computations in lattice QCD involving baryons are presented. Calcula tions of the proton mass and spin decompositions are discussed, a percent level determination of the nucleon axial coupling is described, and determinations of the proton and neutron electromagnetic form factors and light-cone parton distribution functions are outlined. Recent results applying the so-called Luscher method to meson-baryon systems are presented. Key points emphasized are that much better precision with disconnected diagrams is being achieved, incorporating multi-hadron operators is now feasible, and more and more studies are being done with physical quark masses.

Light-Cone Parton Distribution Functions from Lattice QCD.

We extract parton distribution functions (PDFs) of the nucleon from lattice QCD using an ensemble of gauge field configurations simulated with light quark masses fixed to their physical values. Theoretical and algorithmic improvements that allow such a calculation include momentum smearing to reach large nucleon boosts with reduced statistical errors, nonperturbative renormalization, target mass corrections, and a novel modified matching of lattice QCD results to connect to what is extracted from experimental measurements. We give results on the unpolarized and helicity PDFs in the modified minimal subtraction scheme at a scale of 2GeV and reproduce the main features of the experimentally determined quantities, showing an overlap for a range of Bjorken-x values. This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an abinitio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.

Factorization theorem relating Euclidean and light-cone parton distributions

In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization theorem with a non-trivial matching coefficient. Using the operator product expansion we prove the large-momentum factorization of the quasi-parton distribution function in LaMET, and show that the more recently discussed Ioffe-time distribution approach also obeys an equivalent factorization theorem. Explicit results for the coefficients are obtained and compared at one-loop. Our proof clearly demonstrates that the matching coefficients in the $\overline{\rm MS}$ scheme depend on the large partonic momentum rather than the nucleon momentum.

Nondipolar Wilson links for quasiparton distribution functions

We propose a modified definition for a quasi-parton distribution function (QPDF) with an equal-time correlator in the large momentum limit, whose two pieces of space-like Wilson links are oriented in orthogonal directions. It is explicitly shown at one-loop level that the linear divergence in the original QPDF with dipolar Wilson links, which complicates its matching to the standard light-cone parton distribution function (LPDF), is removed. The LPDF can then be extracted reliably from Euclidean lattice data for the QPDF with the non-dipolar Wilson links.

Reconciling the light-cone and nonrelativistic QCD approaches to calculatinge+e−→J/ψ+ηc

It has been suggested in Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] that the disagreement between theoretical calculations and experimental observations for the rate for the process e{sup +}e{sup -}{yields}J/{psi}+{eta}{sub c} at the B factories might be resolved by using the light-cone method to take into account the relative momentum of the heavy-quark and antiquark in the quarkonia. The light-cone result for the production cross section in Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] is almost an order-of-magnitude larger than existing NRQCD factorization results. We investigate this apparent theoretical discrepancy. We compute light-cone distribution functions by making use of quarkonium wave functions from the Cornell potential model. Our light-cone distribution functions are similar in shape to those of Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] and yield a similar cross section. However, when we subtract parts of the light-cone distribution functions that correspond to corrections of relative-order {alpha}{sub s} in the NRQCD approach, we find that the cross section decreases by about a factor of three. When we set certain renormalization factors Z{sub i} in the light-cone calculation equalmore » to unity, we find a further reduction in the cross section of about a factor of two. The resulting light-cone cross section is similar in magnitude to the NRQCD factorization cross sections and shows only a modest enhancement over the light-cone cross section in which the relative momentum of the heavy-quark and antiquark is neglected.« less

Model-independent results for SU(3) violation in twist-3 light-cone distribution functions

Using chiral symmetry we investigate the leading SU(3) violation in the complete set of quark twist-3 light-cone distribution functions of the pion, kaon, and eta, including the two-parton distributions ${\ensuremath{\phi}}_{M}^{p}$, ${\ensuremath{\phi}}_{M}^{\ensuremath{\sigma}}$, and the three-parton distribution ${\ensuremath{\phi}}_{M}^{3}$. It is shown that terms nonanalytic in the quark masses do not affect the shape, and only appear in the normalization constants. Predictive power is retained including the leading analytic ${m}_{q}$ operators. With the symmetry violating corrections we derive useful model-independent relations between ${\ensuremath{\phi}}_{\ensuremath{\pi}}^{p,\ensuremath{\sigma},3}$, ${\ensuremath{\phi}}_{\ensuremath{\eta}}^{p,\ensuremath{\sigma},3}$, ${\ensuremath{\phi}}_{{K}^{+},{K}^{0}}^{p,\ensuremath{\sigma},3}$, and ${\ensuremath{\phi}}_{{\overline{K}}^{0},{K}^{\ensuremath{-}}}^{p,\ensuremath{\sigma},3}$. We also comment on the calculations of the moments of these distributions using lattice QCD and light-cone sum rules.

On the photon energy moments and their ‘bias’ corrections in [formula omitted

Photon energy moments in B → X s + γ and the impact of experimental cuts are analyzed, including the biases exponential in the effective hardness missed in the conventional OPE. We incorporate the perturbative corrections fully implementing the Wilsonian momentum separation ab initio. This renders perturbative effects numerically suppressed while leaving heavy quark parameters and the corresponding light-cone distribution function well defined and preserving their physical properties. The moments of the distribution function are given by the heavy quark expectation values of which many have been extracted from the B → X c ℓ ν decays. The quantitative estimates for the biases in the heavy quark parameters determined from the photon moments show they cannot be neglected for E cut ≳ 1.85 GeV , and grow out of theory control for E cut above 2.1 GeV. Implications for the moments in the B → X c ℓ ν decays at high cuts are briefly addressed.

Model-independent results for SU(3) violation in light-cone distribution functions.

Using chiral symmetry we investigate the leading SU(3) violation in light-cone distribution functions phi(M)(x) of the pion, kaon, and eta. It is shown that terms nonanalytic in the quark masses do not affect the shape, and only appear in the decay constants. Predictive power is retained including the leading analytic m(q) operators. With the symmetry violating corrections we derive useful model-independent relations between phi(pi),phi(eta),phiK+(,K0), and phiK(0)(,K-). Using the soft-collinear effective theory we discuss how factorization generates the subleading chiral coefficients.

Problems of QCD factorization in exclusive decays of B meson to charmonium

We study the exclusive decays of B meson into P-wave charmonium states χcJ (J=0,1) in the QCD factorization approach with light-cone distribution functions describing the mesons in the processes. For B→χc1K decay, we find that there are logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order and the decay rate is too small to accommodate the experimental data. For B→χc0K decay, we find that aside from the logarithmic divergences arising from spectator interactions at leading-twist order, more importantly, the factorization will break down due to the infrared divergence arising from nonfactorizable vertex corrections, which is independent of the specific form of the light-cone distribution functions. Our results may indicate that QCD factorization in the present form may not be safely applied to B-meson exclusive decays to charmonium states.

Precision determination of|Vub|from inclusive decays

We propose determining |V_{ub}| from inclusive semileptonic B decay using combined cuts on the leptonic and hadronic invariant masses to eliminate the b->c background. Compared to a pure dilepton invariant mass cut, the uncertainty from unknown order (\Lambda_{QCD}/m_b)^3 terms in the OPE is significantly reduced and the fraction of b->u events is roughly doubled. Compared to a pure hadronic invariant mass cut, the uncertainty from the unknown light-cone distribution function of the b quark is significantly reduced. We find that |V_{ub}| can be determined with theoretical uncertainty at the 5-10% level.

Evolution of the light-cone distribution function for a heavy quark

We compute the one-loop anomalous dimension for the light-cone distribution function of a heavy quark and solve the corresponding evolution equation analytically. Some implications of the results for inclusive B decays are discussed.

Quark model description of the N-N system: Momentum distributions, structure functions, and the EMC effect.

We employ a relativistic quark bag picture, the chromo-dielectric soliton model, to discuss the quarks' symmetry structure and momentum distribution in the $N$-$N$ system. Six-quark clusters are constructed in a constrained mean-field calculation. The corresponding Hamiltonian contains not only an effective interaction between the quarks and a scalar field, which is assumed to parameterize all non-perturbative effects due to the non-linearity of QCD, but also quark-quark interactions mediated through one-gluon-exchange. We also evaluate the quark light-cone distribution functions, characterizing inclusive deep-inelastic lepton scattering, for the nucleon as well as for the six-quark structures. We find a competition between a softening of the quarks' momenta through the increase of the confinement volume, and a hardening via the admixture of higher symmetry configurations due to the color-electrostatic one-gluon-exchange. These findings suggest an unexpected absence of many-nucleon, multi-quark effects, even though six-quark structures should represent a non-negligible part of the nuclear ground state.

Chiral symmetry breaking and the quark model: Unification of baryon and meson constraints

We review the subject of chiral symmetry breaking and its connection with the quark model. When the light plane SU(3) charges and quark field density matrix elements are transformed back to the usual static basis it becomes clear that expectation values of chiral breaking operators, such as qλ iq , do not necessarily have simple SU(3) transformation properties. Starting with the standard current quark chiral Hamiltonian H′ = m u uu + m d dd + m s ss , we then use current quark light-cone distribution function concepts in combination with constraints from (i) Compton amplitude fixed poles, (ii) baryon octet and decuplet mass differences, (iii) πN and KN σ terms, (iv) G A/ G V, (v) low-energy π photoproduction multipoles, (vi) Goldberger-Treiman discrepancies, (vii) meson mass ratios in PCAC and, (viii) meson mass differences to determine m ̂ = 1 2 (m u + m d) and m s in more than four independent ways. Our results are all mutually consistent and yield the values m ̂ ≈ m π and m s/ m ̂ ≈ 5 . In particular the independent baryon and meson sectors of the theory are completely compatible.