The covariant parton model is generalized to describe quark correlators in a systematic way. Previous results are reproduced for the T-even leading-twist transverse momentum dependent parton distribution functions (TMDs), and for the first time all T-even twist-3 TMDs are evaluated in this model. We apply the approach to evaluate the fully unintegrated quark correlator which allows us to understand the model-specific relations between different TMDs. We verify the consistency of the approach, present numerical results and compare to available TMD parametrizations.
We extend the analysis of two-hadron fragmentation functions to the subleading twist, discussing also the issue of color gauge invariance. Our results can be used anywhere two unpolarized hadrons are semi-inclusively produced in the same fragmentation region, also at moderate values of the hard scale Q. Here, we consider the example of polarized deep-inelastic production of two hadrons and we give a complete list of cross sections and spin asymmetries up to subleading twist. Among the results, we highlight the possibility of extracting the transversity distribution with longitudinally polarize…
We consider the azimuthal distribution of the final observed hadron in semi-inclusive deep-inelastic scattering and the lepton pair in the Drell-Yan process. In particular, we focus on the $\cos ϕ$ modulation of the unpolarized cross section and on its dependence upon transverse momentum. At low transverse momentum, for these observables we propose a factorized expression based on tree-level approach and conjecture that the same formula is valid in transverse-momentum dependent (TMD) factorization when written in terms of subtracted TMD parton distributions. Our formula correctly matches with …
We construct the higher twist structure functions that describe inclusive b hadron decays in regions of phase space where the hadronic decay products carry high energy but have low invariant mass. We show that, for B meson decays, there are four new non-vanishing matrix elements of non-local operators. We show that to subleading twist these decays are parametrized in terms of four functions. We compute the tree-level matching for a general heavy-to-light current and apply it to B -> X_s gamma. Using a simple model for these functions we estimate the subleading twist contributions to this decay…
We calculate the subleading twist contributions to the endpoint of the inclusive lepton energy spectrum in B -> X_u l ν. We show that the same two subleading twist functions that appear in the decay B -> X_s γgovern the subleading effects in this decay. Using these results we find large O(Lambda/mB) corrections to the determination of |Vub| from the endpoint of the charged lepton spectrum. Using a simple model for the relevant subleading shape functions, we estimate the uncertainty in |Vub| from Lambda/mb corrections to be at the ~ 15% level for a lower lepton energy cut of 2.2 GeV.
In this paper we investigate the subleading twist corrections to the photon energy spectrum in the decay Lambda_b -> X_s γand to the lepton energy spectrum in Lambda_b -> X_u l \barν. As a first step we rederive the matching coefficients of the subleading twist using a much simpler method. Parametrizing the matrix elements for Lambda_b and using reparametrization invariance, we show that the energy spectra close to the endpoints are given in terms of only a single universal function.
We discuss the most general form of the leading power suppressed collinear operators in the soft-collinear effective theory. Such operators appear in the description of power corrections to exclusive heavy flavor decays into energetic light hadrons. Reparametrization invariance in the SCET provides powerful constraints on the Wilson coefficients of the subleading collinear operators. We present explicit results for the matrix elements of these operators on pseudoscalar and vector mesons, which are expressed in terms of twist-2 and twist-3 light-cone wave functions. We consistently include the …
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.
We reconsider the QCD predictions for the radiative decay $B\to γ\ell ν_\ell$ with an energetic photon in the final state by taking into account the $1/E_γ, 1/m_b$ power-suppressed hard-collinear and soft corrections from higher-twist $B$-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA $ϕ_+(ω)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to cons…
We discuss the light-front zero-mode issue in the light-front quark model prediction of the twist-3 distribution amplitude of a pseudoscalar meson from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD.
Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B \to γ\ell ν$ decay, at next-to-leading order in QCD for the twist-two contribution and at leading order in $α_s$ for the higher-twist contributions, induced by the hadronic component of the collinear photon. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two $B \to γ$ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking…
We study the single-spin asymmetries with the $\sinϕ_S$ and $\sin(2ϕ_h -ϕ_S)$ angular dependences for charged and neutral pions produced in semi-inclusive deep inelastic scattering on the transversely polarized proton target. The theoretical interpretations of the two asymmetries are presented in terms of the convolution of the twist-3 quark transverse momentum dependent distributions and twist-2 fragmentation functions. Specifically, we investigate the role of the distributions $f_T$, $h_T$ and $h_T^\perp$ in the $\sinϕ_S$ asymmetry, as well as the role of the distributions $f_T^\perp$, $h_T$…
We investigate the nucleon's transverse spin-dependent structure function g_2(x, Q^2) in the framework of the operator product expansion and the renormalization group. We construct the complete set of the twist-3 operators for the flavor singlet channel, and give the relations among them. We develop an efficient, covariant approach to derive the anomalous dimension matrix of the twist-3 singlet operators by computing the off-shell Green's functions. As an application, we investigate the Q^2-evolution of g_2(x, Q^{2}) for the lowest moment case, and discuss its experimental implication.
Although the meson decay amplitude described by a two-point function may be regarded as one of the simplest possible physical observable, it is interesting that this apparently simple amplitude bears abundant fundamental informations on QCD vacuum dynamics and chiral symmetry. The light-front zero-mode issue of the vector meson decay constant $f_V$ is in this respect highly non-trivial and deserves careful analyses. We discuss the zero-mode issue in the light-front quark model (LFQM) prediction of $f_V$ from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. …
Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\ll |v\cdot v'|\ll m_Q/Λ$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\cdot v'|\gg m_Q/Λ$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum o…
Recently a concise expression for the subleading infrared singularity of dimensional-regularized gauge theories has been proposed. For conformal theories, such relation involves a universal eikonal contribution plus a non-eikonal contribution, related to the subleading term in the anomalous dimension of twist two operators with large spin. In this note we make use of the AdS/CFT correspondence in order to check such conjecture at strong coupling for the case of N=4 SYM.
I discuss several corrections to leading twist calculations of nucleon structure functions which are needed to include experimental data at large parton fractional momentum x and at low scales Q^2 in global fits of parton distribution functions. In particular I discuss the results of the CTEQ6X global fit, and some work in progress. Topics covered include the interplay of target mass and higher-twist corrections, the importance of nuclear corrections for deuterium target data, and applications to the study of quark-hadron duality. Implications for collider physics are highlighted.
We present an improved calculation of the strong coupling constants $g_{D^*Dρ}$ and $g_{B^*Bρ}$ in light-cone sum rules including the one-loop QCD corrections of leading power with $ρ$ meson distribution amplitudes. We further compute the subleading-power corrections from two-particle and three-particle higher-twist contributions at leading order up to twist-4 accuracy. The next-to leading order corrections to leading power contribution offset the subleading-power corrections to some extend numerically, and our numerical results are consistent with previous works from sum rules. The comparison…
I discuss the two-particle subleading power corrections in radiative leptonic $B \to γ\ell ν$ decay at next-to-leading order in $α_s$ with the dispersion approach. Employing the method of regions, factorization of the $B \to γ^{\ast}$ form factors is demonstrated explicitly, at one loop, for a space-like hard-collinear photon. The two-particle soft (end-point) contribution is shown to be suppressed by one power of $Λ/m_b$, in the heavy quark limit, compared with the leading power contribution computed from QCD factorization. I further report the recent calculation on the three-particle sublead…
We revisit QCD calculations of radiative heavy meson decay form factors by including the subleading power corrections from the twist-two photon distribution amplitude at next-to-leading-order in $α_s$ with the method of the light-cone sum rules (LCSR). The desired hard-collinear factorization formula for the vacuum-to-photon correlation function with the interpolating currents for two heavy mesons is constructed with the operator-product-expansion technique in the presence of evanescent operators. Applying the background field approach, the higher twist corrections from both the two-particle a…
We derive a generalized Ward identity for color-superconducting quark matter via the functional integral approach. The identity implies the gauge independence of the color-superconducting gap parameter on the quasi-particle mass shell to subleading order in covariant gauge.
We prove that the twist-3 chiral-odd parton distributions obey simple Gribov-Lipatov-Altarelli-Parisi evolution equations in the limit $N_c\to\infty$ and give analytic results for the corresponding anomalous dimensions. To this end we introduce an evolution equation for the corresponding three-particle twist-3 parton correlation functions and find an exact analytic solution. For large values of n (operator dimension) we are further able to collect all corrections subleading in N_c, so our final results are valid to $O(1/N_c^2\cdot \ln(n)/n)$ accuracy.
We investigate the subleading-power corrections to the exclusive $B\to D \ell ν_\ell$ form factors at ${\cal O} (α_s^0)$ in the light-cone sum rules (LCSR) framework by including the two- and three-particle higher-twist contributions from the $B$-meson light-cone distribution amplitudes up to the twist-six accuracy, by taking into account the subleading terms in expanding the hard-collinear charm-quark propagator, and by evaluating the hadronic matrix element of the subleading effective current $\bar q \, γ_μ \, i \not\!\!{D}_\perp / (2 \, m_b) \, h_v$. Employing further the available leading-…
The unpolarized twist-2 (leading) and twist-3 (subleading), T-even, transverse-momentum dependent quark distributions in the pion are evaluated for the first time by using the actual solution of a dynamical equation in Minkowski space. The adopted theoretical framework is based on the homogeneous Bethe-Salpeter integral equation with an interaction kernel given by a one-gluon exchange, featuring an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice-QCD calculations, and calibrated to reproduce both…
We present {\tt SKMHS22}, a new set of diffractive parton distribution functions (PDFs) and their uncertainties at next-to-leading-order accuracy in perturbative QCD within the {\tt xFitter} framework. We describe all available diffractive DIS data sets from HERA and the most recent high-precision H1/ZEUS combined measurements considering three different scenarios. First, we extract the diffractive PDFs considering the standard twist-2 contribution. Then, we include the twist-4 correction from the longitudinal virtual photons. Finally, the contribution of subleading Reggeon exchange to the str…
Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading corrections suppressed by powers of the Lorentz spin. We argue that this structure is a manifestation of the `self-tuning' property of the multi-loop anomalous dimensions - in a conformal gauge theory, the anomalous dimension of Wilson operators is a function of their conformal spin which is modified in higher loops by an amount proportional to the anomalous di…
The isoscalar twist-two generalized parton distributions (GPDs) of the pion and the kaon are calculated in a Poincare covariant Bethe-Salpeter constituent quark model. Results are presented for several values of the parameters xi and t. The results satisfy the form factor constraints and the polynomiality condition. For the pion GPD, also the isospin symmetry constraint is fulfilled. The influence of kinematical variables and model parameters on the support of the GPDs is investigated. To this end, the strength parameters and quark masses of the constituent quark model are artificially varied.
The twist--2 contributions to the polarized structure functions in deep inelastic lepton--hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A new relation between two structure functions leading to a sequence of new sum rules is found. The light quark mass corrections to the structure functions are derived in lowest order QCD.
The recent measurements of azimuthal single spin asymmetries by the HERMES collaboration has opened up new possibility to measure chiral-odd distribution functions through semi-inclusive deep-inelastic scatterings. Here, predictions are given for the twist-2 and twist-3 chiral-odd distribution functions of the nucleon within the framework of the chiral quark soliton model, with full inclusion of the vacuum polarization effects as well as the subleading $1/N_c$ corrections. The importance of the vacuum polarization effects is demonstrated by showing that the so-called Soffer inequality holds no…
We provide the all-loop structure of gauge-variant operators required for the renormalisation of Green's functions with insertions of twist-two operators in Yang-Mills theory. Using this structure we work out an explicit basis valid up to 4-loop order for an arbitrary compact simple gauge group. To achieve this we employ a generalised gauge symmetry, originally proposed by Dixon and Taylor, which arises after adding to the Yang-Mills Lagrangian also operators proportional to its equation of motion. Promoting this symmetry to a generalised BRST symmetry allows to generate the ghost operator fro…
We reconsider QCD factorization for the leading power contribution to the $γ^{\ast} γ\to π^0$ form factor $F_{γ^{\ast} γ\to π^0} (Q^2)$ at one loop using the evanescent operator approach, and demonstrate the equivalence of the resulting factorization formulae derived with distinct prescriptions of $γ_5$ in dimensional regularization. Applying the light-cone QCD sum rules (LCSRs) with photon distribution amplitudes (DAs) we further compute the subleading power contribution to the pion-photon form factor induced by the "hadronic" component of the real photon at the next-to-leading-order in ${\ca…
The twist-2 contributions to the polarized structure functions in deep inelastic lepton--hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A new relation between two structure functions leading to a sequence of new sum rules is found. The light quark mass corrections to the structure functions are derived in lowest order QCD.
Within the framework of a generalized collinear factorization for multiple parton scattering in nuclear medium, twist-4 contributions to DIS off a large nucleus can be factorized as a convolution of hard parts and two-parton correlation functions. The hard parts for the quark scattering in the light-cone gauge correspond to interaction with a transverse (physical) gluon in the target, while they are given by the second derivative of the cross section with a longitudinal gluon in the covariant gauge. We provide a general proof of the equivalence of the hard parts in the light-cone and covariant…
We set up a framework for the study of the power-suppressed three-parton contribution to the pion electromagnetic form factor in the $k_T$ factorization theorem. It is first shown that the gauge dependence proportional to parton transverse momenta from the two-parton Fock state and the gauge dependence associated with the three-parton Fock state cancel each other. After verifying the gauge invariance, we derive the three-parton-to-three-parton $k_T$-dependent hard kernel at leading order of the coupling constant, and find that it leads to about 5% correction to the pion electromagnetic form fa…
We develop a general theoretical framework for the description of higher-twist baryon operators which makes maximal use of the conformal symmetry of the QCD Lagrangian. The conformal operator basis is constructed for all twists. The complete analysis of the one-loop renormalization of twist-4 operators is given. The evolution equation for three-quark operators of the same chirality turns out to be completely integrable. The spectrum of anomalous dimensions coincides in this case with the energy spectrum of the twist-4 subsector of the SU(2,2) Heisenberg spin chain. The results are applied to g…
We derive relations between transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDFs f_1(x) and g_1(x) as input we predict the x- and pT-dependence of all twist-2 T-even TMDs.
The decay $B\to f_0(980)K is studied within the framework of QCD factorization and the two-quark scenario for $f_0(980)$. There are two distinct penguin contributions and their interference depends on the unknown mixing angle $θ$ of strange and nonstrange quark contents of $f_0(980)$: destructive for $0<θ<π/2$ and constructive for $π/2<θ<π$. The QCD sum rule method is applied to evaluate the leading-twist light-cone distribution amplitudes and the scalar decay constant of $f_0$. We conclude that the short-distance approach is not adequate to explain the observed large rates of $f_0K^-$ and $f_…
We derive relations between polarized transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDF $g_{1}^{q}(x)$ as input we predict the $x$- and $\mathbf{p}_{T}$-dependence of all polarized twist-2 naively time-reversal even (T-even) TMDs.
Dynamical gluon effects in twist-3 generalized parton distributions of the proton
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large $N_c$ limit and can be solved exactly. The lowest anomalous dimension is separated from the remaining, continuous, spectrum by a finite gap. The corresponding eigenfunction coincides with the contribution of quark-gluon states to the two-particle DA $ϕ_-(ω)$ so that the evolution equation for the latter is the same as for the leading-twist DA $ϕ_+(ω)$ up to a constant shift in the anomalous dimension. Thus, ``genuine'' t…
We calculate the nonperturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the nonperturbative resummation affects the $NN$ phase shifts for partial waves with $J \geq 3$ and $L \leq 6$. No significant differences are observed between the nonperturbative phase shifts and perturbative ones for most partial waves except for $^3D_3$, for which the nonperturbative resummation greatly improves the description of the phase shifts. However, a significant cutoff dependence is found for this partial wave and a reasonable d…
We analyze the longitudinal-transverse double-spin asymmetry in lepton-nucleon collisions where a single hadron is detected in the final state, i.e., $\vec{\ell}\,N^\uparrow \rightarrow h\,X$. This is a subleading-twist observable in collinear factorization, and we look at twist-3 effects in both the transversely polarized nucleon and the unpolarized outgoing hadron. Results are anticipated for this asymmetry from both HERMES and Jefferson Lab Hall A, and it could be measured as well at COMPASS and a future Electron-Ion Collider. We also perform a numerical study of the distribution term, whic…
We update QCD calculations of $B \to π, K$ form factors at large hadronic recoil by including the subleading-power corrections from the higher-twist $B$-meson light-cone distribution amplitudes (LCDAs) up to the twist-six accuracy and the strange-quark mass effects at leading-power in $Λ/m_b$ from the twist-two $B$-meson LCDA $ϕ_B^{+}(ω, μ)$. The higher-twist corrections from both the two-particle and three-particle $B$-meson LCDAs are computed from the light-cone QCD sum rules (LCSR) at tree level. In particular, we construct the local duality model for the twist-five and -six $B$-meson LCDAs…
Higher-twist transverse momentum dependent parton distribution functions (TMDs) are a valuable probe of the quark-gluon dynamics in the nucleon, and play a vital role for the explanation of sizable azimuthal asymmetries in hadron production from unpolarized and polarized deep-inelastic lepton-nucleon scattering observed in experiments at CERN, DESY and Jefferson Lab. The associated observables are challenging to interpret, and still await a complete theoretical explanation, which makes guidance from models valuable. In this work we establish the formalism to describe unpolarized higher-twist T…
