High Energy exclusive Leptoproduction of the rho-meson: Theory and Phenomenology
I. V. Anikin, A. Besse, D. Yu. Ivanov, B. Pire, L. Szymanowski, S. Wallon
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4 pages, 3 figures, to appear in the proceedings of 20th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2012), Bonn, Germany, 26-30 March 2012
We describe the hard leptoproduction of transversally polarized rho-meson, up to twist 3 accuracy, including 2- and 3- particles Fock-states, in the HERA kinematics of high center-of-mass energy. We first build a model based on a simple approach to the unintegrated gluon density (the parton impact factor) that we compare with H1 and ZEUS data for the ratios of helicity amplitudes T(gamma*T -> rhoT)/T(gamma*L -> rhoL) and T(gamma*T -> rhoL)/T(gamma*L -> rhoL) and get a good description of the data. We also show how saturation effects can be included in this model by extending the dipole representation of the scattering amplitude in coordinate space up to twist 3.
We apply a previously developed scheme to consistently include the twist-3 distribution amplitudes for transversely polarized rho meson in order to evaluate, in the framework of kT factorization, the helicity amplitudes for exclusive leptoproduction of a light vector meson, at leading order in alphaS. We compare our results with high energy experimental data for the ratios of helicity amplitudes T11/T00 and T01/T00 and get a good description of the data.
The amplitude of diffractive $ρ$ (and open quark) leptoproduction on a polarized target is calculated in the leading log approximation of pQCD using the hadron-parton duality hypothesis. The spin-spin asymmetry is expressed in terms of the spin dependent gluon and quark structure functions in the small $x$ region. Therefore the $γ^*+p\to ρ+p$ reaction provides a promising tool to study the spin dependent gluon distribution $ΔG(x,q^2)$.
We discuss the elastic photo- and leptoproduction of rho^0-mesons from nucleons at Q^2 < 1 GeV^2 as studied in recent experiments at HERA and FNAL. We find that the mass distribution of the measured π^+π^- pairs is determined to a large extent by the two-pion contribution to the photon spectral function as given by the pion form factor. With rising Q^2 the rate of diffractive events decreases and the π^+π^- mass distribution approaches a symmetric shape.
We investigate the longitudinal and transverse polarized cross-sections of the leptoproduction of the rho meson in the high energy limit. Our model is based on the computation of the impact factor gamma*(lambda_gamma) -> rho(lambda_rho) using the twist expansion in the forward limit and expressed in the impact parameter space. This treatment involves in the final stage the twist 2 and twist 3 distribution amplitudes (DAs) of the rho meson and the dipole scattering amplitude. Taking models that exist for the DAs and for the dipole cross-section, we get a phenomenological model for the helicity …
We review here two approaches to describe hard leptoproduction of transversally polarized rho-meson, based on recent calculation of the gamma*T -> rhoT impact factor up to twist 3 accuracy in the collinear factorization frame, including 2- and 3- particles Fock-states. The first approach uses a model of the unintegrated gluon density (the proton impact factor) which allows a comparison of our predictions with H1 and ZEUS data for the ratios of helicity amplitudes T(gamma*T -> rhoT)/T(gamma*L -> rhoL) and T(gamma*T -> rhoL)/T(gamma*L -> rhoL). In the second approach, we transform the gamma*T ->…
Hard exclusive leptoproductions of real photons, lepton pairs and mesons are the most promising tools to unravel the three-dimensional picture of the nucleon, which cannot be deduced from conventional inclusive processes like deeply inelastic scattering.
We present a phenomenological model for the helicity amplitudes T11 and T00 of the rho meson exclusive diffractive leptoproduction in the forward limit. This model leads to a very good description of the polarized cross-sections sigmaT and sigmaL when compared to HERA data. This model is based on the impact factor representation of the helicity amplitudes. The gamma* -> rho impact factor is computed within the light-cone collinear factorization scheme, the impact parameter space representation allowing to factorize out the dipole-target amplitude. Finally our description combines a model for t…
HEPGEN is a generator of Monte Carlo events, which is dedicated to studies of hard exclusive single photon or meson production processes at the COMPASS experiment kinematic domain. In addition HEPGEN allows to generate also single photon or meson production accompanied by the diffractive dissociation of the nucleon, which is one of the main sources of background in analyses of exclusive processes.
We present a model for the polarized cross-sections of the hard diffractive leptoproduction of rho meson in the high energy limit. Our model is based on the light-cone collinear factorization of the virtual photon to rho meson impact factor when using the impact factor representation of the helicity amplitudes of the rho meson leptoproduction. This gauge invariant treatment when expressed in impact parameter space, leads to the factorization on one hand of the color dipole scattering amplitude and on the other hand of the distribution amplitudes of the rho meson up to twist 2 and 3. We show th…
The Regge inspired k_T-factorization scheme expresses the scattering amplitude for exclusive leptoproduction of a light vector meson rho in terms of two impact factors, one for the gamma* - rho transition and the other one for the nucleon to nucleon transition, with, at leading order, a two "reggeized" gluon exchange in the t-channel. We report here on a recent phenomenological study where we apply a previously developped scheme which consistently takes into account the twist 3 distribution amplitudes for transversely polarized rho meson. The computation of the gamma* to rho impact factor are …
We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of charged vector mesons. These processes are determined by nonforward parton distribution functions which are nondiagonal in quark flavor. We derive relations between flavor diagonal and nondiagonal distribution functions based on isospin symmetry. Furthermore, we discuss general features of rho^+ and rho^- production cross sections, and present estimates based on a simple model for nonforward distribution functions.
The semi-analytical approach to the model independent leptonic QED corrections to exclusive $ρ^0$ meson leptoproduction (i.e. electron and muon scattering experiments) is presented. The corrections to $ρ^0$ production at large $Q^2$ as well as to $ρ^0$ photoproduction are studied in details. The numerical results are calculated for two different experimental analyses: NMC (muoproduction at large $Q^2$) and ZEUS at HERA (photoproduction). It is shown that the corrections are 2-5 \% for NMC and below 2 \% for the ZEUS measurement. The application of the presented approach to other vector mesons …
We consider the exclusive production of $J/ψ$ mesons in polarized virtual-photon--proton collisions. We derive helicity amplitudes for the dominant subprocess $γ^* g \to J/ψg$ and show that polarization asymmetries vanish in the case of collinear scattering. Thus, contrary to what has been suggested earlier, this process is not a good probe of the polarized gluon distribution $Δg(x,Q^2)$ of the proton.
The physics of diffractive vector meson production in virtual photon nucleon scattering at NMC energies is reviewed. A particular attention is paid to the physical aspects of the reaction and how they influence the observables. The reaction is a good probe to investigate both soft exchange mechanisms and hadronic wave functions. Extension to either HERA or ELFE kinematics is sketched out.
The role of transversity or helicity-flip generalized parton distributions (GPDs) in leptoproduction of vector mesons is investigated within the framework of the handbag approach. The transversity GPDs in combination with twist-3 meson wave functions, occur in the amplitudes for transitions from a transversely polarized virtual photon to a longitudinal polarized vector meson. The importance of the transversity GPDs can be examined in some of the spin density matrix elements and in transverse target spin asymmetries. Using suitable parametrizations of both helicity-flip and non-flip GPDs, which…
We investigate exclusive electroproduction of vector and pseudoscalar mesons at large photon virtuality $Q^2$. These reactions were analyzed within the handbag approach where amplitudes factorize into hard subprocesses and generalized parton distributions (GPDs). The essential role of transversity effects were found in pseudoscalar and light vector meson leptoproduction. These contributions are important at low $Q^2$ and determined by twist-3 effects accompanied by transversity GPDs. The transversity contributions lead to large transverse cross sections for most reactions of pseudoscalar meson…
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…
The contribution of exclusive radiative tail to the cross section of semi-inclusive hadron leptoproduction has been calculated exactly for the first time. Although the experience of inclusive data analyses suggests us that the contribution of radiative tail from the elastic peak is of particular importance, similar effects in the semi-inclusive process were only recently estimated in the peaking approximation. The explicit expressions for the lepton part of the lowest order QED contribution of exclusive radiative tail to the five-fold differential cross section are obtained and discussed. Nume…
We present a status report on a study of vector meson leptoproduction for the HERA energy range on the basis of the generalized handbag approach. In contrast to the leading twist approach transverse degrees of freedom as well as Sudakov suppressions are taken into account in the subprocess. First results for the cross section for photoproduction of longitudinally polarized rho-mesons are found to be in fair agreement with experiment.
Generalized parton distributions (GPDs) extracted from exclusive meson leptoproduction within the handbag approach are briefly reviewed. Only the GPD E is discussed in some detail. Applications of these GPDs to virtual Compton scattering (DVCS) and to Ji's sum rule are also presented.
We investigate exclusive leptoproduction of $ρ^0$ meson. These reactions were analyzed within the factorizing handbag approach. In our model good agreement of observables for light meson production with experimental data in a wide energy range was found. Using the model results we calculate the ratio of different helicity amplitudes for a transversely polarized proton target to the leading twist longitudinal amplitude. Our results are close to the amplitude ratios measured by HERMES.
We evaluate perturbative next-to-leading order corrections to the hard exclusive leptoproduction of pi+ mesons on a transversely polarized proton target. A model dependent study shows that these corrections can be large. We analyze the scale dependence and explore the Brodsky-Lepage-Mackenzie scale setting procedure. Although the predictions for the cross section suffer from theoretical uncertainties, the transverse nucleon single spin asymmetry turns out to be a rather stable observable since higher order effects approximately cancel there.
Using the renormalon technique, we estimate higher-twist contributions in deeply virtual Compton scattering and in hard exclusive $π^0$ leptoproduction.
We re-examine the issue of the pQCD factorization scale in the exclusive rho production in diffractive DIS from the k_t-factorization point of view. We find that this scale differs significantly from, and possesses much flatter Q^2 behavior than widely used value (Q^2 + m_ρ^2)/4. With these results in mind, we discuss the Q^2 shape of the rho meson production cross section. We introduce rescaled cross sections, which might provide further insight into the dynamics of rho production. We also comment on the recent ZEUS observation of energy-independent ratio sigma(gamma* p --> rho p) / sigma_{to…
We fitted the pi-pi mass distribution in the range 0.5 < mpipi < 1.1 GeV measured in hard exclusive positron-proton reactions at HERA by the form dictated by QCD at leading twist level. Extracted parameters are related to valence quark distribution in the pion, and to the pion and rho meson distribution amplitudes. We obtain, for the first time, a measurement of the second Gegenbauer coefficient of the rho meson distribution amplitude: $a_2^{(ρ)}= -0.10\pm 0.20 $ for a photon virtuality of <Q^2>=21.2 GeV^2.
Exclusive rho0 electroproduction at HERA has been studied with the ZEUS detector, using 120 pb{-1} integrated luminosity, in the kinematic range of photon virtuality of 2 < Q2 < 160 GeV2, and gamma* p center-of-mass energy of 32 < W < 180 GeV. The results include the Q2 and W dependence of the gamma* p --> rho0 p cross section and the distribution of the squared-four-momentum transfer to the proton, t. Also included is the ratio of longitudinal to transverse gamma* p cross section as a function of Q2, W and t. Finally, the effective Pomeron trajectory was extracted. The results are compared to…
We use recent results for the gamma*L -> rhoL and gamma*T -> rhoT impact factors, computed in the impact parameter representation within the collinear factorization scheme, to get predictions for the polarized cross-sections sigmaT and sigmaL of the diffractive leptoproduction of the rho meson at high energy. In this approach the helicity amplitude is a convolution of the scattering amplitude of a color dipole with a target, together with the virtual gamma wave function and with the first moments of the rho meson wave function (in the transverse momentum space), given by the distribution ampli…
The exclusive process e+ e- -> e+ e- rho^0_L rho^0_L allows to study various dynamics and factorization properties of perturbative QCD. At moderate energy, we demonstrate how collinear QCD factorization emerges, involving generalized distribution amplitudes (GDA) and transition distribution amplitudes (TDA). At higher energies, in the Regge limit of QCD, we show that it offers a promising probe of the BFKL resummation effects to be studied at the International Linear Collider (ILC).
The exclusive process e+ e- -> e+ e-rho0_L rho0_L allows to study various dynamics and factorization properties of perturbative QCD. At moderate energy, we demonstrate how collinear QCD factorization emerges, involving either generalized distribution amplitudes (GDA) or transition distribution amplitudes (TDA). At higher energies, in the Regge limit of QCD, we show that it offers a promising probe of the BFKL resummation effects to be studied at ILC.
We compare the contributions from quark and from gluon exchange to the exclusive process gamma* p -> rho0 p. We present evidence that the gluon contribution is substantial for values of the Bjorken variable xB around 0.1.
Exclusive and semi-exclusive processes, the diffractive dissociation of hadrons into jets, and hard diffractive processes such as vector meson leptoproduction provide new testing grounds for QCD and essential information on the structure of light-cone wavefunctions of hadrons, particularly the pion distribution amplitude. I review the basic features of the leading-twist QCD predictions and the problems and challenges of studying QCD at the amplitude level. The application of the light-cone formalism to the exclusive semi-leptonic decay of heavy hadrons is also discussed.
We describe hard exclusive processes involving a transversally polarized rho meson in the twist 3 approximation, in a framework based on the Taylor expansion of the amplitude around the dominant light-cone direction.
We discuss the interpretation of the $ep\to epρ^0$ process in terms of, on the one hand, Generalized Parton Distributions and, on the other hand, an effective hadronic model based on Regge theory.
We calculate the Born order cross-section for the exclusive production of rho meson pairs in e+e- scattering in the Regge limit of QCD and we show the feasibility of the measurement of this process at the ILC. We also investigate the leading and next-to-leading order BFKL evolution, making this process a very clean test of the BFKL resummation effects.
We use Omnes representations of the form factors V, A_1 and A_2 for exclusive semileptonic B--> rho decays, and apply them to combine experimental partial branching fraction information with theoretical calculations of the three form factors to extract |Vub|. We find a slightly lower result, |Vub|=(2.8 +- 0.2)x 10^{-3}, than the values extracted from exclusive semileptonic B-->pi decays and using all other inputs in CKM fits. The disagreement is greater when we compare to the result extracted from inclusive B -> X_u l nu decays.
The double-lepton polarization asymmetries in (B -> rho l^+ l^-) decay is analyzed in a model independent framework. The general expressions for nine double-polarization asymmetries are calculated. It is shown that the study of the double-lepton polarization asymmetries proves to be very useful tool in looking for new physics beyond the standard model.
We provide Standard Model expectations for the rare radiative decays B->K^* gamma, B->rho gamma and B-> omega gamma, and the electroweak penguin decays B->K^* l^+ l^- and B->rho l^+ l^- at the next-to-leading order (NLO), extending our previous results to b->d transitions. We consider branching fractions, isospin asymmetries and direct CP asymmetries. For the electroweak penguin decays, the lepton-invariant mass spectrum and forward-backward asymmetry is also included. Radiative and electroweak penguin transitions in b->d are mainly interesting in the search for new flavour-changing neutral cu…
We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive pi^0, eta, and neutral vector meson production am…
The polarized lepton pair forward-backward asymmetries in (B -> rho l^+ l^-) decay using a general, model independent form of the effective Hamiltonian is studied. The general expression for nine double-polarization forward-backward asymmetries are calculated. The study of the forward-backward asymmetries of the doubly-polarized lepton pair proves to be very useful tool in looking for new physics beyond the standard model.
Exclusive processes in hard electroproduction is one of the best place for understanding the factorization properties of QCD. The HERA experiment recently provided precise data for rho electroproduction, including all spin density matrix elements. From QCD, it is expected that such a process should factorize between a hard (calculable) coefficient function, and hadronic (p and rho) matrix elements. Such a factorization is up to now only proven for a longitudinaly polarized rho. Within the kt-factorization approach (valid at large s_{gamma* p}), we evaluate the impact factor of the transition g…
The process of exclusive vector meson production (gamma gamma to J/psi rho^0) is studied for almost real photons. This process may be reduced to photoproduction of J/psi off the rho^0 meson. We discuss the possibility of extracting the gluon distribution of rho^0 and of the photon from such measurement. Predictions are also given for the reaction (e+e- to e+ e- J/psi rho^0) for various e+e- cms energies typical for LEP and for the future linear colliders.
We calculate cross sections for the exclusive diffractive leptoproduction of $ρ$-mesons, $γ^*~p~\to~ρ~p$, within the framework of high-energy factorization. Cross sections for longitudinally and transversally polarized mesons are shown. We employ a wide variety of unintegrated gluon distributions available in the literature and compare to HERA data. The resulting cross sections strongly depend on the choice of unintegrated gluon distribution. We also present predictions for the proton target in the kinematics of the Brookhaven EIC.
We investigate the exclusive B -> pi e^+ e^- and B -> rho e^+ e^- decays in framework of the general two Higgs doublet model (model III), in which an extra phase angle in the charged--Higgs fermion coupling, i.e., a new source for CP violation exists. The CP violation for both decays are calculated and it is observed that the CP violating asymmetry in model III differs significantly than the one predicted by the standard model and model II which is a special case of model III. Furthermore, it is shown that the zero value of forward backward asymmetry A_{FB} is shifted when compared with the SM…
Exclusive processes in hard electroproduction are one of the best place for understanding QCD in view of its factorization properties. In particular, in the limit of asymptotic gamma* p center of mass energy, they give an access to the perturbative Regge properties of QCD. The HERA experiment recently provided precise data for rho electroproduction, including all spin density matrix elements. From QCD, it is expected that such a process should factorize between a hard (calculable) coefficient function, and hadronic (p and rho) matrix elements. Such a factorization is up to now only proven for …
A Pomeron-exchange model of exclusive electroproduction of $ρ$-mesons is examined using a dressed-quark propagator. It is shown that by representing the photon-$ρ$-meson-Pomeron coupling by a nonperturbative, confined-quark loop, one obtains predictions for $ρ$-meson electroproduction that are in good agreement with experiment.
We discuss exclusive electromagnetic production of two neutral $ρ$ mesons in coherent photon-photon processes in ultrarelativistic heavy-ion collisions. The cross section is calculated in the equivalent photon approximation (EPA). Both uncertainties of the flux factors and photon-photon cross sections are discussed in details. We show that inclusion of precise charge densities in nuclei is essential for realistic evaluations of the nuclear photon-photon cross sections. We find that the cross section, especially with realistic flux factors, is sensitive to low energy in the subsystem $γγ\to ρ^0…
Exclusive electroproduction of vector mesons is a crucial way to probe QCD factorization properties. Such a factorization is up to now only proven, at the twist 2 level, for a longitudinaly polarized meson. It is crucial to extend our understanding to the case of transversely polarized vector mesons. As a first step in this direction, we evaluate the impact factor of the transition gamma* -> rhoT, which is the relevant part of the amplitude within the kt-factorization approach valid at large energies, taking into account the twist 3 contributions, coming both from quark antiquark and from quar…
Exclusive emissions of vector mesons in forward directions of rapidity offer us a faultless chance to probe the proton structure at small-$x$. A high-energy factorization formula is established within BFKL, given as the convolution of an impact factor depicting the forward-meson emission and of an unintegrated gluon distribution (UGD) driving the gluon evolution at small-$x$. As a nonperturbative quantity, the UGD is not well known and several models for it exist. We present recent progresses on the study of the exclusive forward $ρ$-meson leptoproduction at HERA and EIC energies, showing how …
As a sequel to the calculation of the CP-violating asymmetry in the decay rates of b -> d l^+l^- and \bar{b} -> \bar{d} l^+l^-, we address in this paper the asymmetry in exclusive channels \bar{B} -> pi e^+e^- and \bar{B} -> rho e^+e^-, using form factors from two different models. In the invariant mass region 1GeV < \sqrt{s} < M_{J/psi}, the partial width asymmetry in the channel \bar{B} -> pi is -6% (-2%), and that in the channel \bar{B} -> rho, for one choice of form factors, is -5% (-2%), assuming CKM parameters eta = 0.34, rho = 0.3 (-0.3). We also calculate the forward-backward asymmetry…
We describe a consistent approach to factorization of scattering amplitudes for exclusive processes beyond the leading twist approximation. The method involves the Taylor expansion of the scattering amplitude in the momentum space around the dominant light-cone direction and thus naturally introduces an appropriate set of non-perturbative correlators which encode effects not only of the lowest but also of the higher Fock states of the produced particle. The reduction of original set of correlators to a set of independent ones is achieved with the help of equations of motion and invariance of t…
The Cabibbo-Kobayashi-Maskawa matrix element |V_ub| is not well determined yet. It can be extracted from both inclusive or exclusive decays, like B --> pi (rho) l nu-bar_l. However, the exclusive determination from B --> rho l nu-bar_l, in particular, suffers from a large model dependence. In this paper, we propose to extract |V_ub| from the four-body semileptonic decay B --> pi pi l nu-bar_l, where the form factors for the pion-pion system are treated in dispersion theory. This is a model-independent approach that takes into account the pi-pi rescattering effects, as well as the effect of the…
Recent small-t ZEUS data for exclusive rho photoproduction are in excellent agreement with exchange of the classical soft pomeron with slope alpha'=0.25 GeV^{-2}. Adding in a flavour-blind hard-pomeron contribution, whose magnitude is calculated from the data for exclusive J/psi photoproduction, gives a good fit also to the ZEUS data for rho photoproduction at larger values of t, and to phi photoproduction.
We investigate the radiative B_c -> rho^+ gamma and B_c -> K^{*+} gamma decays in the standard model. The transition form factors are calculated in the framework of the light cone QCD sum rules method. We estimate the branching ratios of the B_c -> rho^+ gamma and B_c -> K^{*+} gamma decays.
We calculate the exclusive process gamma* gamma* ->rho rho at high energy. The Born order estimate and the leading (LLA) and next to leading order (NLLA) BFKL resummation effects show the feasibility of experimental detection in a quite large range of Q2 values at future high energy e+e- linear colliders.
Ongoing experiments at JLAB investigate the nuclear transparency in exclusive rho0(770) electroproduction off nuclei. In this work we present transport model predictions for the attenuation of rho0s in nuclei and for color transparency (CT) effects as observable at CLAS with a 5 GeV electron beam energy. A full event simulation presented here permits to study the impact of actual experimental acceptance conditions and kinematical cuts. The exclusive (e,e'rho0) cross section off nucleons is described by diffractive and color string breaking mechanisms extended toward the onset of the deep inela…
