In the framework of the k_T-factorization approach, the production and polarization of Upsilon mesons at the Fermilab Tevatron is considered, and a comparision of the calculated double differential distributions and spin alignment parameter $α$ with the D0 experimental data is shown. We argue that measuring the double differential cross section and the polarization of upsilonium states can serve as a crucial test discriminating two competing theoretical approaches to the parton dynamics in QCD.
The calculation of the partial width of the rare t-quark decay into Upsilon-meson, W-boson and b-quark (t -> ΥW b) is presented. The branching ratio equals Br(t -> Upsilon W b) = 1.3 * 10^{-5} that make possible searches for this rare $t$-quark decay at LHC.
Applying the effective amplitude, which is evidently consistent with general constraints from chiral symmetry, the pipi spectra in the relevant processes are analyzed, leading to a strong evidence for existence of the light sigma meson. It is also pointed out that the pipi scattering process, which had been one of the main sources for PDG table for these many years, is, in principle, exceptionally difficult to investigate the property of sigma-meson.
We present the complete next-to-next-to-next-to-leading order short-distance and bound-state QCD correction to the leptonic decay rate Gamma(Upsilon(1S)->l+l-) of the lowest-lying spin-1 bottomonium state. The perturbative QCD prediction is compared to the measurement Gamma(Upsilon(1S)->e+e-)=1.340(18) keV.
We analyze the pi pi production amplitudes in the excited Upsilon decay processes, Upsilon(2S)-->Upsilon(1S)pi+pi-, Upsilon(3S)-->Upsilon(1S)pi+pi- and Upsilon(3S)-->Upsilon(2S)pi+pi-, and the pi pi and KKbar production amplitudes in the charmonium decay processes, psi(2S)-->J psi pi+pi- and J psi-->phi pi+pi-, phi K+K-. The amplitudes are parametrized by the sum of Breit-Wigner amplitudes for the sigma and the other relevant particles and of the direct 2pi-production amplitude, following the VMW method. All the pi pi (and KKbar) invariant mass spectra are reproduced well with the sigma Breit-…
It is shown that the ratio of the production rates of the pairs (B+ B-) and (B0 anti-B0) should experience a substantial and rapid variation with energy within the width of the Upsilon(4S) resonance, crossing the value of one near the center of the resonance. This behavior is due to an interference of the rapidly changing with energy Breit-Wigner phase with the phase introduced in the wave function of charged mesons by their Coulomb interaction.
Bottomonium-like resonances Zb(10610) and Zb'(10650) are good candidates of hadronic molecules composed of BBbar* (or B*Bbar) and B*Bbar*, respectively. Considering Zb (Zb') as heavy meson molecules, we investigate the decays of Zb(')^+ -> Upsilon (nS) pi^+$ in terms of the heavy meson effective theory. We find that the intermediate B (B*) and Bbar (Bbar*) meson loops and the form factors play a significant role to reproduce the experimental values of the decay widths. We also predict the decay widths of Zc^+ -> J/ψpi^+ and psi(2S) pi^+ for a charmonium-like resonance Zc which has been reporte…
We analyze the pipi production amplitudes in the excited Upsilon decay processes, Upsilon (2S) to Upsilon (1S)pi^+pi^-, Upsilon (3S) to Upsilon (1S)pi^+pi^- and Upsilon (3S) to Upsilon (2S)pi^+pi^-, and the pipi and KKbar production amplitudes in the charmonium decay processes, psi (2S) to Jpsi pi^+pi^- and Jpsi to phi pi^+pi^-, phi K^+K^-, including the possible effect of light sigma production. The amplitudes are parametrized by the sum of Breit-Wigner amplitudes for the sigma and the other relevant particles and of the direct 2pi-production amplitude, following the VMW method. All the pipi …
The results of analyses obtained in Part I are examined from the viewpoint of chiral symmetry. The mass spectra of pi pi system are widely believed to be suppressed generally near the threshold, because of the derivative coupling property of Nambu-Goldstone pi meson. However, this suppression does not hold in the processes with large energy release, and the steep increase from the pi pi threshold observed in the transition Upsilon (3S-->1S) is shown to be consistent with general constraints from chiral symmetry.
If the recently-discovered charmonium state X(3870) is a loosely-bound molecule of the charm mesons D^0 and \bar D^{*0} or \bar D^0 and D^{*0}, it can be produced in e^+ e^- annihilation at the Υ(4S) resonance by the coalescence of charm mesons produced in the decays of B^+ and B^- mesons. Remarkably, in the case of 2-body decays of the B mesons, the leading contribution to the coalescence probability depends only on hadron masses and on the width and branching fractions of the B meson. As the binding energy E_b of the molecule goes to zero, the coalescence probability scales as E_b^{1/2} log(…
The effect of isoscalar S-wave multichannel pi pi -> pi pi, K antiK, eta eta scattering is considered in the analysis of decay data of the Upsilon-mesons. We show that when allowing for the final state interaction contribution to the decays Upsilon(mS) -> Upsilon(nS) pi pi (m>n, m=2,3, n=1,2) in our model-independent approach, we can explain the two-pion energetic spectra of these Upsilon transitions including the two-humped shape of the di-pion mass distribution in Upsilon(3S) -> Upsilon(1S) pi pi as the coupled-channel effect. It is shown also that the considered bottomia decay data do not o…
We review predictions, based on the nonrelativistic QCD factorization framework, for the polarizations of prompt J/psi's and Upsilon(nS)'s produced at the Fermilab Tevatron. We also discuss the effect of relativistic corrections on the theoretical prediction for the polarization of prompt J/psi's at the Tevatron.
The polarization of inclusive Upsilon(nS) at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. We use a recent determination of the NRQCD matrix elements from fitting the CDF data on bottomonium production from Run IB of the Tevatron. The result for the polarization of Upsilon(1S) integrated over the transverse momentum bin 8 < p_T < 20 GeV is consistent with a recent measurement by the CDF Collaboration. The transverse polarization of Upsilon(1S) is predicted to increase steadily for p_T greater than about 10 GeV. The Upsilon(2S) and Upsilon(3S) are p…
The forward photoproduction amplitude for gamma p to Upsilon p is calculated in a pQCD k_t-factorization approach with an unintegrated gluon distribution constrained by inclusive deep-inelastic structure functions. The total cross section for diffractive Upsilons is compared with a recent HERA data. We also discuss the 2S/1S ratio in diffractive Upsilon-production. The amplitude is used to predict the cross section for exclusive Upsilon production in hadronic reactions. Differential distributions for the exclusive p pbar to p Upsilon pbar process are calculated for Tevatron energies. We also s…
I consider the dissociation of the upsilon meson due to absorption of a thermal gluon. I discuss the dissociation rate in terms of the energy density, the number density, and the temperature of the quark-gluon plasma. I compare this to the effect due to screening.
In the framework of the $k_T$-factorization approach, the production of Upsilon mesons at the Fermilab Tevatron is considered, and the comparisions of calculated $p_T$-distributions and spin alignment parameter $α$ with the D0 experimental data are shown. We argue that measuring the double cross section and the polarization of upsilonium states can serve as a crucial test discriminating two competing theoretical approaches to parton dynamics in QCD.
We study pp and p\bar p collisions which lead to the exclusive production of J/psi or Upsilon from the pomeron-odderon and the pomeron-photon fusion. We calculate scattering amplitudes of these processes in the lowest order approximation and in the framework of k_T factorization. We present estimates of cross sections for the kinematic conditions of the Tevatron and of the LHC.
We discuss in detail the photon spectrum of radiative Upsilon 1S decays taking into account a number of results that have recently appeared in the literature. In particular, we show how to consistently combine expressions which are valid in the upper end-point region, where NRQCD factorization breaks down, with those of the central region, where NRQCD factorization holds. An excellent description of data is achieved, but theoretical errors are large.
In the framework of the k_t-factorization approach, the production of $Υmesons at the Fermilab Tevatron and CERN LHC is considered, and the predictions on the spin alignment parameter $α$ are presented. We argue that measuring the polarization of quarkonium states can serve as a crucial test discriminating two competing theoretical approaches to parton dynamics in QCD.
We study the exclusive production of J/psi or Upsilon in pp and bar pp collisions, where the meson emerges from the pomeron--odderon and the pomeron--photon fusion. We estimate the cross sections for these processes for the kinematical conditions of the Tevatron and of the LHC.
The effects of the finite charm quark mass on bottom quark mass determinations from $Υ$ sum rules are examined in detail. The charm quark mass effects are calculated at next-to-next-to-leading order in the non-relativistic power counting for the $Υ$ sum rules and at order $α_s^3$ for the determination of the bottom MSbar mass. For the bottom 1S mass, which is extracted from the $Υ$ sum rules directly, we obtain $M_b^{1S}=4.69\pm 0.03$ GeV with negligible correlation to the value of the strong coupling. For the bottom MSbar mass we obtain $\bar M_b(\bar M_b) = 4.17\pm 0.05$ GeV taking $α_s^{(n_…
Data on e+e- -> piplus-piminus-Upsilon(1S,2S,3S) show a large increase in branching fractions near Upsilon(10860). A suggestion of Ali et al. is to interpret this as evidence for a tetraquark, Yb(10890) = b-bbar. However, it may also be interpreted in terms of Upsilon(10860) -> B-B*, B*B* and BsB*s above the open-b threshold, followed by de-excitation processes such as $BB* -> Upsilon (1S,2S,3S). In the charm sector, a hypothesis open to experimental test is that X,Y and Z peaks in the mass range 3872 to 3945 MeV may all be due to regular 3P1 and 3P2 c-cbar states (and perhaps 3P0) mixed with …
The masses of open bottom mesons ($B$($B^+$,$B^0$), $\bar{B}$($B^-$,$\bar{B^0}$), $B_s$(${B_{s}}^0$, $\bar{{B_s}^0}$)) and upsilon states ($Υ(1S)$, $Υ(2S)$, $Υ(3S)$, $Υ(4S)$, and $Υ(1D)$) are investigated in the isospin asymmetric strange hadronic medium at finite temperature in the presence of strong magnetic fields using a chiral effective Lagrangian approach. For charged baryons, the magnetic field introduces contribution from Landau energy levels. The masses of the open bottom mesons get modified through their interactions with the baryons and the scalar mesons, which undergo modifications…
We compute the rate for diffractive upsilon meson production at the Tevatron and the LHC. The upsilon is produced diffractively via the subprocess gamma + p -> upsilon + p where the initial photon is radiated off an incoming proton (or antiproton). We consider the possibility to use low angle proton detectors to make a measurement of the gamma p cross-section and conclude that a measurement of the cross-section at a centre of mass energy in excess of 1 TeV is possible at the LHC. This is in the region where saturation effects are likely to reveal themselves.
A systematic gauge-invariant method is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v^2) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.
High-accuracy $Υ$-meson photoproduction data from EIC and EicC experiments will allow the measurement of the near-threshold total cross section of the reaction $γp\toΥp$, from which the absolute value of the $Υp$ scattering length, $|α_{Υp}|$, can be extracted using a Vector-Meson Dominance model. For this evaluation, we used $Υ$-meson photoproduction quasi-data from the QCD approach (the production amplitude can be factorized in terms of gluonic generalized parton distributions and the quarkonium distribution amplitude). A comparative analysis of $|α_{Υp}|$ with the recently determined scatte…
Exclusive diffractive photoproduction of heavy vector mesons (V=phi, J/psi and Upsilon) at HERA is studied in a model employing a dipole Pomeron exchange (P) with an inelastic gamma-P-V vertex. The model is fitted to the data on dsigma/dt, B and elastic sigma for Q^2=0 and beyond the threshold region. The elastic cross sections for both phi and J/psi photoproduction show a moderate increase within the HERA energy region. The flattening of the slope B(s) (little or no shrinkage) for J/psi is not correlated with the slope of the Pomeron trajectory. Estimates for Upsilon photoproduction at HERA a…
Within the NRQCD factorization approach the production of heavy quarkonia can be calculated in perturbative QCD in terms of a few production-process-independent NRQCD matrix elements. We test the universality of these long-distance matrix elements by comparing their values as determined from charmonium production at p pbar, e p, and e+ e- colliders, and in Z^0, Upsilon, and B decays.
We discuss the potential to constrain the small-$x$ PDFs using the exclusive production of heavy vector mesons. The calculation of $J/ψ$ and $Υ$ photoproduction at NLO in collinear factorisation is described. The different behaviour of the NLO corrections for $J/ψ$ and $Υ$ is highlighted and we outline what might be expected from the inclusion of these processes in a PDF fit.
Several works analyzing the new physics contributions from the Left-Right Symmetric Model to the CP violation phenomena in the neutral B mesons can be found in the literature. These works exhibit interesting and experimentally sensible deviations from the Standard Model predictions but at the expense of considering a low right scale \upsilon_R around 1 TeV. However, when we stick to the more conservative estimates for \upsilon_R which say that it must be at least 10^7 GeV, no experimentally sensible deviations from the Standard Model appear for indirect CP violation. This estimate for \upsilon…
We study prompt Upsilon(nS) hadroproduction (n=1,2,3) invoking the hypothesis of gluon Reggeization in t-channel exchanges at high energy and the factorization formalism of nonrelativistic quantum chromodynamics at leading order in the strong-coupling constant alpha_s and the relative velocity v of the bound quarks. The transverse-momentum distributions of prompt Upsilon(nS)-meson production measured by the ATLAS Collaboration at the CERN LHC are fitted to obtain the color-octet nonperturbative long-distance matrix elements, which are used to predict prompt Upsilon(nS) production spectra measu…
We compare the theoretical frameworks and the phenomenological applications of the factorization approaches to exclusive $B$ meson decays, which include QCD-improved factorization, perturbative QCD, and soft-collinear effective theory. Recent progress on two-body nonleptonic $B$ meson decays made in these approaches are reviewed.
I explain how various aspects of factorization in exclusive b decays can be studied with mesons having a small decay constant or spin greater than one.
We propose a QCD-based model for calculation of the non-perturbative corrections to the factorization approximation in the decays of heavy mesons. In the framework of the model, factorization in pseudoscalar transitions holds exactly at the leading order leaving the opportunity to calculate non-leading corrections consistently.
I review recent progress on exclusive $B$ meson decays made in the perturbative QCD approach, concentrating on the evolution of the $B$ meson wave function in $k_T$ factorization, radiative decays, polarizations in $VV$ modes, and new physics effect in $B\to ϕK_S$.
Recent data from the CDF collaboration on the production of spin-triplet bottomonium states at the Tevatron p \bar p collider are analyzed within the NRQCD factorization formalism. The color-singlet matrix elements are determined from electromagnetic decays and from potential models. The color-octet matrix elements are determined by fitting the CDF data on the cross sections for Upsilon(1S), Upsilon(2S), and Upsilon(3S) at large p_T and the fractions of Upsilon(1S) coming from chi_b(1P) and chi_b(2P). We use the resulting matrix elements to predict the cross sections at the Tevatron for the sp…
A brief review of checking the factorization hypothesis for matrix element of $B^0 - \bar B^0$ mixing within operator product expansion and QCD sum rules is given. Both perturbative and power corrections are considered.
The angular distributions of the decay products in the successive decays chi_c (chi_b) to J/psi (Upsilon) gamma and J/psi (Upsilon) to l+l- are calculated as a function of the angular momentum composition of the decaying chi meson and of the multipole structure of the photon radiation, using a formalism independent of production mechanisms and polarization frames. The polarizations of the chi states produced in high energy collisions can be derived from the dilepton decay distributions of the daughter J/psi or Upsilon mesons, with a reduced dependence on the details of the photon reconstructio…
In the following, we will present a generalization of the proof of factorization for electroproduction of vector mesons to the production of several mesons such as $π^+π^-$ and a proof of factorization for exclusive $γ^* γ$ production of several hadrons for example $p \bar p$ or $π^+π^-$ to all orders in perturbation theory up to power suppressed terms.
Exclusive nonleptonic bottom meson decays are studied in the covariant osillator quark model using the factorization assumption. The main feature of this model is that it can simultaniously be applied to both heavy to heavy and heavy to light transitions, satisfying the constraints of the heavy quark effective theory (HQET) in the appropriate limit. The results obtained are in overall agreement with the present experimental data for various B decays.
Based on nonrelativistic QCD factorization scheme, we present the first complete next-to-leading order study on the yield and polarization of Upsilon(1S,2S,3S) hadroproduction. By using the color-octet long-distance matrix elements obtained from fits of the experimental measurements on Upsilon yield and polarization at the Tevatron and LHC, our results can explain the measurements on the yield very well, and for the polarizations of Upsilon(1S,2S,3S), they are in (good, good, bad) agreement with recent CMS measurement, but still have some distance from the CDF measurement.
Based on the NRQCD factorization formalism, we calculate the inclusive charm production rate in Upsilon(nS) decay at leading order in the strong coupling constant alpha_s and the relative velocity v of the b quark in the quarkonium rest frame. The branching fractions for Upsilon(nS) to charm for n=1, 2, and 3 are all around 7-9%. About 60% of the branching fraction into charm is from annihilation of the color-singlet bb-bar pair into gamma^* -> cc-bar. Most of the remaining branching fraction is from annihilation of the color-singlet bb-bar pair decaying into cc-bar gg. We also compute the mom…
We describe the current status of the diffractive vector meson production calculations within the k_t-factorization approach. Since the amplitude of the vector meson production off a proton is expressed via the differential gluon structure function (DGSF), we take a closer look at the latter and present results of our new improved determination of the DGSF from the structure function F_2p. Having determined the differential glue, we proceed to the k_t-factorization results for the production of various vector mesons. We argue that the properties of the vector meson production can reveal the in…
In the framework of the kT-factorization approach we have calculated in the fragmentation model the pT-spectra of B(c) mesons at the energies of the Tevatron and the LHC Colliders and at the large pT domain. We compare the obtained results with the existing experimental data and with the predictions obtained in the collinear parton model.
We summerize the status of factorization hypothesis in the color-suppressed B meson decays : $B \to J/ψK^{(*)}$. We present the general formalism for decay rates and polarization fractions with considering all possible non-factorizable contributions which also include the color-octet contributions, and a new factorization scheme comes appear when the universality is exist : $χ_{F1} = χ_{A1} = χ_{A2} = χ_{V} = χ$. We consider various phenomenological models to compare their theoretical predictions with the recent CLEO II experimental measurements.
Some recent progress in China in the study of charmless B decays with QCD factorization is reviewed. Chirally enhanced power corrections and infrared divergence problem are stressed.
In the framework of the $κ$-factorization approach and on the basis of recently determined DGSF, we calculated the production rates of ground and excited (2S and D wave) states of vector mesons and investigated their various kinematical and spin dependencies. We also addressed the issue of S/D wave mixing in quarkonia.
With a consistent definition of transverse-momentum-dependent(TMD) light-cone wave function of $B$-meson, we show that the amplitude of the radiative leptonic B-decay can be factorized at one-loop level as a convolution with the wave function and a perturbative coefficient function, combined with a soft factor. In this TMD factorization, the transverse momenta of partons in the $B$-meson are taken into account and all soft divergences are contained in the wave function and the soft factor. The coefficient function is infrared-safe. The factorization works on a diagram-by-diagram basis and is p…
The k_T-factorization has been widely used for exclusive decays of B-mesons. In this factorization the pertubative coefficients are extracted from scattering of off-shell partons. Because the off-shellness of partons the extracted pertubative coefficients in general are not gauge-invariant. We show that these perturbative coefficients contain gauge-dependent singularities beyond tree-level. This leads to that the k_T-factorization is gauge-dependent and violated in the general covariant gauge. This is not consistent with expectations of physics. In the factorization there exist two different w…
Results on elastic vector meson production at HERA are presented in the framework of perturbative QCD. The energy dependence of the cross section for J/Psi photoproduction and for rho electroproduction is studied. A full polarisation analysis, including the measurement of the 15 elements of the spin density matrix and of R=sigma_L/sigma_T, is presented for rho electroproduction. Finally heavier vector mesons (Psi' and Upsilon) production is discussed.
We provide a rigorous basis for factorization for a large class of non-leptonic two-body $B$-meson decays in the heavy-quark limit. The factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as $B\to Dπ$ and $B\to ππ$. We discuss the factorization formula for a general final state from a general point of view. We then consider factorization for decays into heavy-light final states (such as $B\to Dπ$) in more detai…
We apply the QCD factorization approach to exclusive, radiative B meson decays in the region of small invariant photon mass. We calculate factorizable and non-factorizable corrections to leading order in the heavy quark mass expansion and next-to-leading order in the strong coupling constant. Phenomenological consequences for the B -> K* gamma decay rate and the B -> K* ell+ ell- forward-backward asymmetry are discussed.
The two newly observed hidden-bottom mesons Zb(10610) and Zb'(10650) with quantum numbers J(P) = 1(+) are considered as hadronic molecules composed of BB(*) and B(*)B(*), respectively. We give predictions for the widths of the strong two-body decays Zb(+) to Upsilon(nS) + pi(+) and Zb'(+) to Upsilon(nS) + pi(+) in a phenomenological Lagrangian approach.
A number of charmonium- and bottomonium-like meson states have been observed that have properties that do not match well to expectations for the simple quark-antiquark substructure suggested by the constituent quark model. Some of them are electrically charged and decay to final states containing hidden charmonum or bottomonium mesons and, thus, must contain at least four quarks. Common properties of these so-called XYZ mesons are partial widths for decays to hidden quarkonium states plus light hadrons that are much larger than corresponding partial widths for established quarkonium mesons. I …
We study the asymptotic behavior of the $B$ meson wave function in the framework of $k_T$ factorization theorem. We first construct a definition of the $k_T$-dependent $B$ meson wave function, which is free of light-cone divergences. Next-to-leading-order corrections are then calculated based on this definition. The treatment of different types of logarithms in the above corrections, including the Sudakov logarithms, and those depending on a renormalization scale and on an infrared regulator, is summarized. The criticism raised in the literature on our resummation formalism and Sudakov effect …
The in-medium partial decay widths of $Υ(4S) \rightarrow B\bar B$ in magnetized asymmetric nuclear matter are studied using a field theoretic model for composite hadrons with quark (and antiquark) constituents. The medium modifications of the decay widths of $Υ(4S)$ to $B\bar B$ pair in magnetized matter arise due to the mass modifications of the decaying $Υ(4S)$ as well as of the produced $B$ and $\bar B$ mesons. The in-medium masses of the open bottom meson in magnetized nuclear matter are computed from their interactions with the nucleons and the scalar mesons within a chiral effective mode…
We investigate whether the Balitsky-Fadin-Kuraev-Lipatov (BFKL) low x evolution equation is capable to describe the energy dependence of the exclusive photo-production cross-section of vector mesons J/Psi and Upsilon on protons. Such cross-sections have been measured by both HERA experiments H1 and ZEUS in electron-proton collisions and by LHC experiments ALICE, CMS and LHCb in ultra-peripheral proton-proton and ultra-peripheral proton-lead collisions. Our approach provides a perturbative description of the rise with energy and relies only on a fit of the initial transverse momentum profile of…
We formulate and prove a QCD factorization theorem for hard exclusive electroproduction of mesons in QCD. The proof is valid for the leading power in Q and all logarithms. This generalizes previous work on vector meson production in the diffractive region of small x. The amplitude is expressed in terms of off-diagonal generalizations of the usual parton densities. The full theorem applies to all kinds of meson and not just to vector mesons. The parton densities used include not only the ordinary parton density, but also the helicity density (g_1 or $Δq$) and the transversity density ($h_1$ or …
The end-point contributions in the quark longitudinal momentum fraction of the virtual photon ($γ^*$) to vector meson ($V$) impact factor to the diffractive electroproduction amplitude can be factorized in terms of a generalized parton evolution of the target parton distribution. The result is used to model the helicity amplitudes $γ^* p \to V p$ in terms of small $x$ generalized parton distributions.
In this work, we study the factorization of the radiative leptonic decays of $B^-$ and $D^-$ mesons, the contributions of the order $O(Λ_{\rm QCD}\left/m_Q\right.)$ are taken into account. The factorization is proved to be valid explicitly at the order $O(α_sΛ_{\rm QCD}\left/m_Q\right.)$. The hard kernel is obtained. The numerical results are calculated using the wave-function obtained in relativistic potential model. The $O(Λ_{\rm QCD}\left/m_Q\right.)$ contribution is found to be very important, the correction to the decay amplitudes of $B^-\to γe\barν$ is about $20\% - 30\%$. For $D$ mesons…
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.
