Nucleon Distribution Amplitudes Research Articles

Experimental access to Transition Distribution Amplitudes with the P̄ANDA experiment at FAIR

Baryon-to-meson Transition Distribution Amplitudes (TDAs) encoding valuable new information on hadron structure appear as building blocks in the collinear factorized description for several types of hard exclusive reactions. In this paper, we address the possibility of accessing nucleon-to-pion (pi N) TDAs from (p) over barp -> e(+)e(-)pi(0) reaction with the future PANDA detector at the FAIR facility. At high center-of-mass energy and high invariant mass squared of the lepton pair q(2), the amplitude of the signal channel (p) over barp -> e(+)e(-)pi(0) admits a QCD factorized description in terms of pi N TDAs and nucleon Distribution Amplitudes (DAs) in the forward aid backward kinematic regimes. Assuming the validity of this factorized description, we perform feasibility studies for measuring (p) over barp -> e(+)e(-)pi(0) with the PANDA detector. Detailed simulations on signal reconstruction efficiency as well as on rejection of the most severe background channel, i.e. (p) over barp -> pi(+)pi(-)pi(0) were performed for the center-of-mass energy squared s = 5 GeV2 and s = 10 GeV2, in the kinematic regions 3.0 0.5 in the proton-antiproton center-of-mass frame. Results of the simulation show that the particle identification capabilities of the PANDA detector will allow to achieve a background rejection factor of 5 . 10(7) (1 . 10(7)) at low (high) q(2) for s = 5 GeV2, and of 1 . 10(8) (6 . 10(6)) at low (high) q(2) for s = 10 GeV2, while keeping the signal reconstruction efficiency at around 40%. At both energies, a clean lepton signal can be reconstructed with the expected statistics corresponding to 2 of integrated luminosity. The cross sections obtained from the simulations are used to show that a test of QCD collinear factorization can be done at the lowest order by measuring scaling laws and angular distributions. The future measurement of the signal channel cross section with PANDA will provide a new test of the perturbative QCD description of a novel class of hard exclusive reactions and will open the possibility of experimentally accessing pi N TDAs.

QCD radiative corrections to the soft spectator contribution in the wide angle Compton scattering

We derive the complete factorization formula for the leading power contribution in wide angle Compton scattering. It consists of the soft- and hard-spectator contributions. The hard-spectator contribution is well known and defined in the form of the convolution of a hard kernel with the nucleon distribution amplitudes. The soft-spectator contribution describes the scattering which involves the soft modes. We use the soft collinear effective theory in order to define this term in a field theoretical approach. Using the SCET framework we provide the proof of the factorization formula. We also compute the next-to-leading QCD corrections to the hard coefficient function of the soft spectator contribution and perform a phenomenological analysis of existing experimental data within the developed formalism.

Higher twist nucleon distribution amplitudes in Wandzura-Wilczek approximation

We derive the higher twist (four and five) nucleon distribution amplitudes in the Wandzura-Wilczek approximation. Our method is based on an analysis of the conformal expansion of nonlocal operators in the spinor formalism.

Nucleon form factors and distribution amplitudes in QCD

We derive light-cone sum rules for the electromagnetic nucleon form factors including the next-to-leading-order corrections for the contribution of twist-three and twist-four operators and a consistent treatment of the nucleon mass corrections. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations. A selfconsistent picture emerges, with the three valence quarks carrying 40%:30%:30% of the proton momentum.

QCD description of charmonium plus light meson production in [formula omitted] annihilation

The associated production of a J/ψ and a π meson in antiproton–nucleon annihilation is studied in the framework of QCD collinear factorization. In this approach, a hard subprocess responsible for the production of the heavy quark–antiquark pair factorizes from soft hadronic matrix elements, such as the antiproton (nucleon) distribution amplitude and the nucleon-to-pion (antiproton-to-pion) transition distribution amplitude. This reaction mechanism should dominate the forward and backward kinematical regions, where the cross sections are expected to be measurable in the set-up of the P̄ANDA experiment at the GSI-FAIR facility.

Accessing baryon to meson transition distribution amplitudes in meson production in association with a high invariant mass lepton pair at GSI-FAIR withP¯ANDA

Nucleon antinucleon annihilation into a near backward (or forward) produced meson and a high invariant mass lepton pair admits a factorized description in terms of antinucleon (or nucleon) distribution amplitudes and nucleon to meson (or antinucleon to meson) transition distribution amplitudes. We estimate the cross section of backward (and forward) pion and eta meson production in association with a high invariant mass lepton pair for the kinematical conditions of GSI-FAIR. The cross sections are found to be large enough to be measured with the PANDA detector. Interesting phenomenological applications of the approach are thus expected.

Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F1 at large Q2

We investigate the soft spectator scattering contribution for the FF $F_{1}$. We focus our attention on factorization of the hard-collinear scale $\sim Q\Lambda$ corresponding to transition from SCET-I to SCET-II. We compute the leading order jet functions and find that the convolution integrals over the soft fractions are logarithmically divergent. This divergency is the consequence of the boost invariance and does not depend on the model of the soft correlation function describing the soft spectator quarks. Using as example a two-loop diagram we demonstrated that such a divergency corresponds to the overlap of the soft and collinear regions. As a result one obtains large rapidity logarithm which must be included in the correct factorization formalism. We conclude that a consistent description of the factorization for $F_{1}$ implies the end-point collinear divergencies in the hard and soft spectator contributions, i.e. convolution integrals with respect to collinear fractions are not well-defined. Such scenario can only be realized when the twist-3 nucleon distribution amplitude has specific end-point behavior which differs from one expected from the evolution of the nucleon distribution amplitude. Such behavior leads to the violation of the collinear factorization for the hard spectator scattering contribution. We suggest that the soft spectator scattering and chiral symmetry breaking provide the mechanism responsible for the violation of collinear factorization in case of form factor $F_{1}$.

Heavy-to-light baryonic form factors at large recoil

We analyze heavy-to-light baryonic form factors at large recoil and derive the scaling behavior of these form factors in the heavy quark limit. It is shown that only one universal form factor is needed to parameterize Lambda_b to p and Lambda_b to Lambda matrix elements in the large recoil limit of light baryons, while hadronic matrix elements of Lambda_b to Sigma transition vanish in the large energy limit of Sigma baryon due to the space-time parity symmetry. The scaling law of the soft form factor eta(P^{\prime} \cdot v), P^{\prime} and v being the momentum of nucleon and the velocity of Lambda_b baryon, responsible for Lambda_b to p transitions is also derived using the nucleon distribution amplitudes in leading conformal spin. In particular, we verify that this scaling behavior is in full agreement with that from light-cone sum rule approach in the heavy-quark limit. With these form factors, we further investigate the Lambda baryon polarization asymmetry alpha in Lambda_b to Lambda gamma and the forward-backward asymmetry A_{FB} in Lambda_b to Lambda l^{+} l^{-}. Both two observables (alpha and A_{FB}) are independent of hadronic form factors in leading power of 1/m_b and in leading order of alpha_s. We also extend the analysis of hadronic matrix elements for Omega_b to Omega transitions to rare Omega_b to Omega gamma and Omega_b to Omega l^{+} l^{-} decays and find that radiative Omega_b to Omega gamma decay is probably the most promising FCNC b to s radiative baryonic decay channel. In addition, it is interesting to notice that the zero-point of forward-backward asymmetry of Omega_b to Omega l^{+} l^{-} is the same as the one for Lambda_b to Lambda l^{+} l^{-} to leading order accuracy provided that the form factors \bar{\zeta}_i (i=3, 4, 5) are numerically as small as indicated from the quark model.

Form factors and strong couplings of heavy baryons from QCD light-cone sum rules

We derive QCD light-cone sum rules for the hadronic matrix elements of the heavy baryon transitions to nucleon. In the correlation functions the $\Lambda_c,\Sigma_c$ and $\Lambda_b$ -baryons are interpolated by three-quark currents and the nucleon distribution amplitudes are used. To eliminate the contributions of negative parity heavy baryons, we combine the sum rules obtained from different kinematical structures. The results are then less sensitive to the choice of the interpolating current. We predict the $\Lambda_{b}\to p$ form factor and calculate the widths of the $\Lambda_{b}\to p\ell\nu_l$ and $\Lambda_{b}\to p \pi$ decays. Furthermore, we consider double dispersion relations for the same correlation functions and derive the light-cone sum rules for the $\Lambda_cND^{(*)}$ and $\Sigma_cND^{(*)}$ strong couplings. Their predicted values can be used in the models of charm production in $p\bar{p}$ collisions.

Study of two-photon corrections in thepp¯→e+e−process: Hard rescattering mechanism

We investigate the two-photon corrections to the process $p\overline{p}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ at large momentum transfer, aimed to access the timelike nucleon form factors. We estimate the two-photon corrections using a hard rescattering mechanism, which has already been used to calculate the corresponding corrections to elastic electron-proton scattering. Using different nucleon distribution amplitudes, we find that the two-photon corrections to the $p\overline{p}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ cross sections in the momentum transfer range $5--30\text{ }\text{ }{\mathrm{GeV}}^{2}$ is below the 1% level.

FCNC transitions of Λb, c to nucleon in SM

We provide a comprehensive study of semileptonic flavor-changing neutral current transitions for Λb → nℓ+ℓ− and Λc → pℓ+ℓ− in the context of light cone QCD sum rules. Using the most general form of the interpolating current for Λb, c, as well as nucleon distribution amplitudes, we calculate all 12 form factors entering the calculations in full theory. We obtain the order of heavy quark effective theory violation and argue that the Λb → nℓ+ℓ− case can be studied at LHC, but the other one has a very small branching ratio.

Flavor-changing neutral currents transition of the ΣQ to nucleon in full QCD and heavy quark effective theory

The loop-level flavor-changing neutral currents transitions of the Σb → nl+l− and Σc → pl+l− are investigated in full QCD and heavy quark effective theory in the light cone QCD sum rules approach. Using the most general form of the interpolating current for ΣQ, Q = b or c, as members of the recently discovered sextet heavy baryons with spin 1/2 and containing one heavy quark, the transition form factors are calculated using two sets of input parameters entering the nucleon distribution amplitudes. The obtained results are used to estimate the decay rates of the corresponding transitions. Since such a type of transitions occurrs at the loop level in the standard model (SM), they can be considered as good candidates to search for the new physics effects beyond the SM.

SemileptonicΛb,cto nucleon transitions in full QCD at light cone

The tree level semileptonic $\Lambda_{b}\to pl\nu$ and $\Lambda_{c}\to nl\nu$ transitions are investigated using the light cone QCD sum rules approach in full theory. The spin--1/2, $\Lambda_{Q}$ baryon with $Q=b$ or $c$, is considered by the most general form of its interpolating current. The time ordering product of the initial and transition currents is expanded in terms of the nucleon distribution amplitudes with different twists. Considering two sets of independent input parameters entering to the nucleon wave functions, namely, QCD sum rules and Lattice QCD parameters, the related form factors and their heavy quark effective theory limits are calculated and compared with the existing predictions of other approaches. It is shown that our results satisfy the heavy quark symmetry relations for lattice input parameters and b case exactly and the maximum violation is for charm case and QCD sum rules input parameters. The obtained form factors are used to compute the transition rates both in full theory and heavy quark effective theory. A comparison of the results on decay rate of $\Lambda_{b}\to pl\nu$ with those predicted by other phenomenological methods or the same method in heavy quark effective theory with different interpolating current and distribution amplitudes of the $\Lambda_{b}$ is also presented.

Two-Photon Exchange in Elastic Electron-Proton Scattering: A QCD Factorization Approach

We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer Q(2). It is shown that the leading two-photon exchange amplitude behaves as 1/Q(4), and can be expressed in a model independent way in terms of the leading twist nucleon distribution amplitudes. Using several models for the nucleon distribution amplitudes, we provide estimates for existing data and for ongoing experiments.

Parton content of the nucleon from distribution amplitudes and transition distribution amplitudes

The nucleon distribution amplitudes and the nucleon-to-pion transition distribution amplitudes are investigated at leading twist within the frame of a light-cone quark model. The distribution amplitudes probe the three-quark component of the nucleon light-cone wave function, while higher order components in the Fock-space expansion of the nucleon state are essential to describe the nucleon-to-pion transition distribution amplitudes. Adopting a meson-cloud model of the nucleon the nucleon-to-pion transition distribution amplitudes are calculated for the first time.

Nucleon distribution amplitudes and their application to nucleon form factors and theN→Δtransition at intermediate values ofQ2

We compare a recent lattice determination of the nucleon distribution amplitudes with other approaches and models. We study the nucleon distribution amplitudes up to twist 6 in next-to-leading conformal spin and we also investigate conformal $d$-wave contributions to the leading-twist distribution amplitude. With the help of light-cone sum rules one can relate the distribution amplitudes to the form factors of the nucleon or the $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transition at intermediate values of the momentum transfer. We compare our results with experimental data in the range $1\text{ }\text{ }{\mathrm{GeV}}^{2}\ensuremath{\le}{Q}^{2}\ensuremath{\le}10\text{ }\text{ }{\mathrm{GeV}}^{2}$. Keeping in mind that we are working only in leading order QCD and next-to-leading order QCD corrections might be sizeable, we already obtain a surprisingly good agreement for the nucleon form factors ${G}_{M}^{n}$, ${G}_{M}^{p}$, ${G}_{A}^{p}$, and ${G}_{T}^{p}$ and for the $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transition form factor ratios ${R}_{\mathrm{EM}}$ and ${R}_{\mathrm{SM}}$.

Nucleon distribution amplitudes and proton decay matrix elements on the lattice

Baryon distribution amplitudes (DAs) are crucial for the theory of hard exclusive reactions. We present a calculation of the first few moments of the leading-twist nucleon DA within lattice QCD. In addition we deal with the normalization of the next-to-leading (twist-four) DAs. The matrix elements determining the latter quantities are also responsible for proton decay in Grand Unified Theories. Our lattice evaluation makes use of gauge field configurations generated with two flavors of clover fermions. The relevant operators are renormalized nonperturbatively with the final results given in the MSbar scheme. We find that the deviation of the leading-twist nucleon DA from its asymptotic form is less pronounced than sometimes claimed in the literature.

Non-perturbative renormalization of three-quark operators

High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wave function and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS ¯ scheme at μ = 2 GeV .

Nucleon Distribution Amplitudes from Lattice QCD

We calculate low moments of the leading-twist and next-to-leading-twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MS[over ] scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.

Baryon operators of higher twist in QCD and nucleon distribution amplitudes

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 give a general classification and calculate the scale dependence of subleading twist-4 nucleon distribution amplitudes that are relevant for hard exclusive reactions involving a helicity flip. In particular we find an all-order expression (in conformal spin) for the contributions of geometric twist-3 operators to the (light-cone) twist-4 nucleon distribution amplitudes, which are usually referred to as Wandzura–Wilczek terms.