We present the chiral odd generalized parton distributions (GPDs) for non-zero skewness $ζ$ in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively using overlaps of light-front wave functions (LFWFs) in a simple model. We also present the chiral even GPDs in positon space in a phenomenological model.
T-odd distributions like Sivers and Boer-Mulders functions are normally modeled using few-body models. In the present work I want to follow the completely opposite point of view, and study a high-energy proton-proton Drell-Yan where both the annihilating partons are wee, and one (at least) comes from a high-order Fok state of the parent proton, i.e. a state where a large number N of partons is present. I show that rescattering between active and spectator partons is modified, with suppression of those terms that are needed to build T-odd parton distributions.
Quantum chromodynamics is a fundamental non-abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state, $|θ\rangle$, is a linear superposition of the $n$-vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in th…
We report on a calculation of the chiral odd generalized parton distributions (GPDs) for non-zero skewness $ζ$ in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively using overlaps of light-front wave functions (LFWFs).
We derive the overlap representation of chiral-odd generalized parton distributions using the Fock-state decomposition in the transverse-spin basis. This formalism is applied to the case of light-cone wave functions in a constituent quark model. Numerical results for the four chiral-odd generalized parton distributions at the hadronic scale are shown in different kinematics. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon.
We present a study of the chiral-odd generalized parton distributions for $u$ and $d$ quarks in a proton using the light front wave functions of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We obtain the GPDs in terms of overlaps of the LFWFs. Numerical results for chiral-odd GPDs in momentum as well as transverse position spaces considering both zero and nonzero skewness($ζ$) are presented. For nonzero skewness, the GPDs are also evaluated in longitudinal position space.
We investigate the chiral odd generalized parton distributions (GPDs) for the quantum fluctuations of an electron in QED. The light-front wave function (LFWF) of this system gives a template for the quark spin-one diquark structure of the valence LFWF of the proton. We express the GPDs in terms of overlaps of LFWFs and obtain their representation in impact parameter space when the momentum transfer is purely transverse. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.
Using a physically motivated parameterization based on the reggeized diquark model we perform a flavor separation of the chiral-odd generalized parton distributions obtained from both $π^0$ and $η$ exclusive electroproduction. In our approach we exploit a connection between the chiral-even and chiral-odd reduced helicity amplitudes using Parity transformations that are relevant for a class of models that includes two-component models. We compare our results for $η$ production to the previously obtained $π^0$ results, and we make predictions for the transverse single spin asymmetry components w…
Exclusive $π^o$ electroproduction is suggested for extracting both the tensor charge and the transverse anomalous magnetic moment from experimental data. A connection between partonic degrees of freedom, given in terms of Generalized Parton Distributions, and Regge phenomenology is discussed. Calculations are performed using a physically motivated parametrization that is valid at values of the skewness, $ζ\neq 0$. Our method makes use of information from the nucleon form factor data, from deep inelastuc scattering parton distribution functions, and from lattice results on the Mellin moments of…
In the present work we have studied the chiral odd Generalized Parton Distributions (GPDs) in the impact parameter space by assuming a flexible parametrization in a quark-diquark model. In order to obtain the explicit contributions from the up and down quarks, we have considered both the scalar (spin-0) and the axial-vector (spin-1) configurations for the diquark. We have also studied the spin densities for the up and down quarks in this model for monopole, dipole and quadrupole contributions for unpolarized and polarized quarks in unpolarized and polarized proton.
We present a physically motivated parameterization of the chiral-odd generalized parton distributions. The parametrization is an extension of our previous one in the chiral-even sector which was based on the reggeized diquark model. While for chiral even generalized distributions a quantitative fit with uncertainty estimation can be performed using deep inelastic scattering data, nucleon electromagnetic, axial and pseudoscalar form factors measurements, and all available deeply virtual Compton scattering data, the chiral-odd sector is far less constrained. While awaiting the analysis of measur…
We present the general framework to calculate chiral-odd generalized parton distributions in the overlap representation using the Fock-state decomposition in the transverse spin basis. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon. Numerical results are obtained by applying the formalism to the case of light-cone wavefunctions of constituent quark models.
Within the framework of light-cone quantization we derive the overlap representation of generalized parton distributions for transversely polarized quarks using the Fock-state decomposition in the transverse-spin basis. We apply this formalism to the case of light-cone wave functions in a constituent quark model giving numerical results for the four chiral-odd generalized parton distributions in a region where they describe the emission and reabsorption of a quark by the nucleon. With the transversity distribution obtained in the forward limit of the generalized distribution, we provide some p…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally od…
We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions $h_L(x)$ and $e(x)$, and also the twist-two transversity distribution $δq(x)$. The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the $h_L$ quasi(pseudo)-…
We compute the parton distributions for the chiral quark model. We present a new technique for performing such computations based on Green functions. This approach avoids a discretization of the spectrum. It therefore does not need any smoothing procedures. The results are similar to those of other groups, however the distributions peak at smaller $x$.
The first moment the chirality-odd twist-3 parton distribution $e(x)$ is related to the pion-nucleon $σ$-term which is important for phenomenology. However, the possible existence of a singular contribution proportional to $δ(x)$ in the distribution prevents from the determination of the $σ$-term with $e(x)$ from experiment. There are two approaches to show the existence. The first one is based on an operator identity. The second one is based on a perturbative calculation of a single quark state with finite quark mass. We show that all contributions proportional to $δ(x)$ in the first approach…
Parton distributions for the pion are studied in a chiral quark model characterized by a quark propagator for which a spectral representation is assumed. Electromagnetic and chiral symmetry constraints are imposed through the relevant Ward-Takahashi identities for flavoured vertex functions. Finiteness of the theory, requires the spectral function to be non-positive definite. Straightforward calculation yields the result that the pion structure function becomes one in the chiral limit, regardless of the details of the spectral function. LO and NLO evolution provide a satisfactory description o…
The chirally-odd twist-3 parton distribution function e(x) of the nucleon is studied in the large-Nc limit in the framework of the chiral quark-soliton model. It is demonstrated that in spite of properties not shared by other distribution functions, namely the appearance of a delta(x)-singularity and quadratic divergences in e(x), an equally reliable calculation is possible. Among the most remarkable results obtained in this work is the fact that the coefficient of the delta(x)-singularity can be computed exactly in this model, avoiding involved numerics. Our results complete existing studies …
The small $x$ behaviour of the structure function $h_1(x,Q^2)$ is studied within the leading logarithmic approximation of perturbative QCD. There are two contributions relevant at small $x$. The leading one behaves like $(\frac{1}{x})^0$ i.e. it is just a constant in this limit. The second contribution, suppressed by one power of $x$, includes the terms summed by the GLAP equation. Thus for $h_1(x,Q^2)$ the GLAP asymptotics and Regge asymptotics are completely different, making $h_1(x,Q^2)$ quite an interesting quantity for the study of small $x$ physics.
We evaluate Generalized Parton Distributions of the pion in two chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the alpha representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules and soft pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale…
We revisit the connection between generalized parton distributions in impact parameter space and T-odd effects in single spin asymmetries of the semi-inclusive deep inelastic process. We show that nontrivial relations can be established only under very specific conditions, typically realized only in models that describe hadrons as two-body bound systems and involving a helicity-conserving coupling between the gauge boson and the spectator system. Examples of these models are the the scalar-diquark spectator model or the quark-target model for the nucleon, and relativistic models for the pion a…
We calculate the isosinglet unpolarized quark-- and antiquark distributions at a low normalization point in the large--$N_c$ limit. The nucleon is described as a self-consistent soliton solution of the effective chiral theory. The ultraviolet cutoff is implemented by a Pauli-Villars subtraction. The quark and antiquark distributions satisfy the momentum as well as the baryon number sum rule, corresponding to ``constituent'' quarks whose structure is not yet resolved at the low scale. Already at this level a sizable number of antiquarks is present.
The unpolarized spin-flip isoscalar generalized parton distribution function (E^u+E^d)(x,xi,t) is studied in the large-Nc limit at a low normalization point in the framework of the chiral quark-soliton model. This is the first study of generalized parton distribution functions in this model, which appear only at the subleading order in the large-Nc limit. Particular emphasis is put therefore on the demonstration of the theoretical consistency of the approach. The forward limit of (E^u+E^d)(x,xi,t) of which only the first moment -- the anomalous isoscalar magnetic moment of the nucleon -- is kn…
We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion.
The dynamical breaking of chiral symmetry in QCD is caused by nonperturbative interactions on a scale rho ~ 0.3 fm, much smaller than the hadronic size R ~ 1 fm. These short-distance interactions influence the intrinsic transverse momentum distributions of partons and their correlations at a low normalization point. We study this phenomenon in an effective description of low-energy dynamics based on chiral constituent quark degrees of freedom, which refers to the large-N_c limit of QCD. The nucleon is obtained as a system of constituent quarks and antiquarks moving in a self-consistent classic…
While the chiral-even content of the nucleon is better and better studied, the chiral-odd transversity generalized parton distributions (GPDs) remain almost unknown. These GPDs can be accessed experimentally through the exclusive photoproduction process gamma + N -> pi + rho + N', in the kinematics where the meson pair has a large invariant mass and the final nucleon has a small transverse momentum, provided the vector meson is produced in a transversally polarized state. We calculate perturbatively the scattering amplitude at leading order in alpha_s. We build a simple model for the dominant …
The T-odd quark distrbutions are shown to vanish in the chiral sigma model in contrast to the opposite widespread opinion. This failure of the chiral sigma model is a feature of the model itself and has nothing to do with the recent progress in the clarification of the status of the T-odd distributions in QCD.
Generalized transverse momentum dependent parton distributions (GTMDs), as mother funtions of transverse momentum dependent parton distributions (TMDs) and generalized parton distributions (GPDs), encode the most general parton structure of hadrons. We calculate four twist-two time reversal odd GTMDs of pion in a scalar spectator model. We study the dependence of GTMDs on the longitudinal momentum fraction $x$ carried by the active quark and the transverse momentum $|\vec k_T|$ for different values of skewness $ξ$ defined as the longitudinal momentum transferred to the proton as well as the to…
We evaluate both chirally even and odd generalized parton distributions(GPDs) in the leading twist in a recently proposed quark-diquark model for the proton where the light front wavefunctions are constructed from the soft-wall AdS/QCD prediction. The GPDs in transverse impact parameter space give the spin densities for different quark and proton polarizations. For longitudinally polarized proton only chiral even GPDs contribute but for transversely polarized proton both chiral even and chiral odd GPDs contribute to the spin densities. We present a detail study of the spin densities in this mo…
We define in the framework of light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the $π^0$) up to twist 6. For that, we introduce the relevant matrix elements for 2-parton non-local operators, as well as matrix elements for 3-parton non-local correlators. Their detailed parametrization is fixed based on parity, charge conjugation and time reversal invariance. This leads to the introduction of 28 real GPDs, which are subject to constraints coming from the QCD equations of motion.
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 reexamine the derivation of the leading order QCD evolution equations of twist-3 quark-gluon correlation functions, $T_{q,F}(x,x)$ and $T^{(σ)}_{q,F}(x,x)$, which are the first transverse-momentum-moment of the naive-time-reversal-odd parton distribution functions - the Sivers and Boer-Mulders function, respectively. The evolution equations were derived by several groups with apparent differences. We identify the sources that are responsible for the differences, and are able to reconcile the results from various groups.
We clarify the nonperturbative origin of the $δ$-function singularity at $x = 0$ in the chiral-odd twist-3 distribution function $e(x)$ of the nucleon. We also compare a theoretical prediction for $e(x)$ based on the chiral quark soliton model with the empirical information extracted from the CLAS semi-inclusive DIS measurement.
The chirally-odd twist-3 nucleon distribution e(x) is studied in the large-Nc limit in the framework of the chiral quark-soliton model at a low normalization point of about 0.6 GeV. The remarkable result is that in the model e(x) contains a delta-function-type singularity at x=0. The regular part of e(x) is found to be sizeable at the low scale of the model and in qualitative agreement with bag model calculations.
A formula for the single transverse spin asymmetry in the large-$p_T$ pion production in the nucleon-nucleon collision is derived. We focuss on the chiral-odd contribution where the transversity distribution and the chiral-odd spin-independent twist-3 distribution contributes. This contribution is expected to give rise to a large effect at $x_F\to -1$.
The so-called time-reversal odd distribution functions are known to be non-vanishing in QCD due to the presence of the link operator in the definition of these quantities. I show that T-odd distributions can be non-vanishing also in chiral models, if vector mesons are introduced as dynamical gauge bosons of a hidden local symmetry. Moreover, since the flavor dependence of these distributions is different in chiral models respect to non chiral ones, the phenomenological analysis of experimental data will be able to distinguish between these two classes of models.
Results of the chiral quark models for the soft matrix elements involving pions and photons, relevant for high-energy processes, are reviewed. We discuss quantities related to the generalized parton distributions of the pion: the parton distribution functions, the parton distribution amplitudes, and the generalized form factors. The model predictions are compared to the data or lattice simulations, with good agreement. The QCD evolution from the low quark model scale up to the experimental scales is a crucial ingredient of the approach.
We present an estimate of a chiral-odd contribution to the single transverse-spin asymmetry in the large-$p_T$ pion production in the nucleon-nucleon collision. In this contribution the transversity distribution and the chiral-odd spin-independent twist-3 distribution appear. Because of the smallness of the corresponding hard cross section, this term turned out to be negligible in all kinematic regions compared with the chiral-even contribution.
T-odd parton distribution functions in a Drell-Yan process are here studied by examining the evolution of the internal statistical properties of the interacting hadrons. T-odd functions are shown to be a signature of the irreversible process in which a hadronic state characterized by long range correlation properties (hadronic phase) decays to produce a cloud of independent partons (partonic phase) because of initial/final state interactions. The relevant considered variable is the rate of increase of the entropy of the hadronic system. This quantity is shown to be roughly equal to the decay r…
We discuss the predictions of chiral quark models for basic pion properties entering high-energy processes: generalized parton distributions (GPD's) and unintegrated parton distributions (UPD's). We stress the role of the QCD evolution, necessary to compare the predictions to data.
Like the even chirality correlation functions of, say, the two vector currents, one can also consider odd chirality correlation functions to write thermal QCD sum rules. They contain fewer non-perturbative corrections, at least to the leading order. Here we write such a sum rule for the correlation function of vector and tensor 'currents'. The odd and even chirality sum rules are taken together to evaluate the effective parameters of the $ρ$ meson to second order in temperature. To within errors, the results are consistent and reproduce the absence of shift in the $ρ$ meson mass to this order.
The theoretical predictions are given for the forward limit of the unpolarized spin-flip isovector generalized parton distribution function $(E^u - E^d)(x, ξ, t)$ within the framework of the chiral quark soliton model, with full inclusion of the polarization of Dirac sea quarks. We observe that $[(H^u - H^d) + (E^u - E^d)](x,0,0)$ has a sharp peak around $x=0$, which we interpret as a signal of the importance of the pionic $q \bar{q}$ excitation with large spatial extension in the transverse direction. Another interesting indication given by the predicted distribution in combination with Ji's …
Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GP…
We analyze the moments of the isosinglet generalized parton distributions H, E, H-tilde, E-tilde of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit.
We define in a systematic way, based on the light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the pi0) up to twist 5. For that, we introduce the relevant matrix elements for 2-parton non-local operators, as well as matrix elements for 3-parton non-local correlators. Their detailed parametrization is fixed based on parity, charge conjugation and time reversal invariance. This leads to the introduction of 20 real GPDs, whose symmetry properties are explicitely given. The reduction of these GPDs to a minimal set is …
In this paper we present chiral extrapolation formulas for the generalized form factors connected to the first moments of chiral-even generalized parton distributions. For the description of QCD at low energies we employ the framework of two-flavor covariant baryon chiral perturbation theory at full one-loop accuracy. Our results are well suited for the extrapolation of lattice QCD data to physical quark masses.
The chiral-odd structure function h_{1}^D(x) and the tensor charge of the deuteron are studied within the Bethe-Salpeter formalism for the deuteron amplitude. Utilizing a simple model for the nucleon structure function, h_1^N, h_1^D(x) is calculated and the nuclear effects are analyzed.
We calculate the chiral odd quark distributions and the corresponding structure functions $h_T(x,Q^2)$ and $h_L(x,Q^2)$ within the Nambu-Jona-Lasinio chiral soliton model for the nucleon. The $Q^2$ evolution of the twist-2 contributions is performed according to the standard GLAP formalism while the twist-three piece, $\bar{h}_L(x)$, is evolved according to the large $N_C$ scheme. We carry out a comparison between the chiral odd structure functions of the proton and the neutron. At the low model scale ($Q_0^2$) we find that the leading twist effective quark distributions,$f_1^{(q)}(x,Q_0^2)$, …
We study large-distance contributions to the nucleon's parton densities in the transverse coordinate (impact parameter) representation based on generalized parton distributions (GPDs). Chiral dynamics generates a distinct component of the partonic structure, located at momentum fractions x ~< M_pi/M_N and transverse distances b ~ 1/M_pi. We calculate this component using phenomenological pion exchange with a physical lower limit in b (the transverse "core" radius estimated from the nucleon's axial form factor, R_core = 0.55 fm) and demonstrate its universal character. This formulation preserve…
We study the scale dependence of twist-3 distributions defined with chirality-odd quark-gluon operators. To derive the scale dependence we explicitly calculate these distributions of multi-parton states instead of a hadron. Taking one-loop corrections into account we obtain the leading evolution kernel in the most general case. In some special cases the evolutions are simplified. We observe that the obtained kernel in general does not get simplified in the large-$N_c$ limit in contrast to the case of those twist-3 distributions defined only with chirality-odd quark operators. In the later, the…
We define a number of quark fragmentation functions for spin-0, -1/2 and -1 hadrons, and classify them according to their twist, spin and chirality. As an example of their applications, we use them to analyze semi-inclusive deep-inelastic scattering on a transversely polarized nucleon.
The chiral-odd distribution function $h_1$ is discussed in the framework of the renormalon approach. Using a bag-model calculation for $h_1$, we calculate its intrinsic uncertainty due to renormalon poles. The result is given as a function of Bjorken-$x$ as well as for the first moments separately. We also extract the perturbative corrections to the first moments of $h_1$.
