Two-Loop Radiative Jet Function for Exclusive $B$-Meson and Higgs Decays
Ze Long Liu, Matthias Neubert
备注：
1 figure, 19 pages plus appendices; v2: significantly extended version containing new results for the 2-loop anomalous dimensions of the jet function and the B-meson light-cone distribution amplitude in momentum space (section 2.4), and analytic solutions of the RG equations at 2-loop order (section 2.5), references added; v3: extended discussion in Sections 2.1 and 4, version published in JHEP
The rare radiative $B$-meson decay $B^-\toγ\ell^-\barν$ and the radiative Higgs-boson decay $h\toγγ$ mediated by light-quark loops both receive large logarithmic corrections in QCD, which can be resummed using factorization theorems derived in soft-collinear effective theory. In these factorization theorems the same radiative jet function appears, which is a central object in the study of factorization beyond the leading order in scale ratios. We calculate this function at two-loop order both in momentum space and in a dual space, where its renormalization-group evolution takes on a simpler form. We also derive the two-loop anomalous dimension of the jet function and present the exact solution to its evolution equation at two-loop order. Another important outcome of our analysis is the explicit form of the two-loop anomalous dimension of the $B$-meson light-cone distribution amplitude in momentum space.
I review recent theory developments for hard exclusive and semi-exclusive production of mesons, emphasising the variety of physics issues that can be studied in these processes.
We present a detailed analysis of exclusive semileptonic decays of Bc meson involving pseudoscalar and vector mesons in the BSW framework, by investigating the effects of the flavor dependence on the average transverse quark momentum inside a meson. Branching ratios of exclusive semileptonic decays of Bc meson are predicted.
The perturbative QCD formalism for exclusive heavy meson decays, especially the three-scale factorization theorem for nonleptonic modes is reviewed and compared to the conventional Bauer-Stech-Wirbel model.
I discuss mechanisms of exclusive production of mesons at high energies. Some illustrative examples for the FNAL Tevatron and CERN LHC as well as for lower energies are shown.
We report on numerical studies of the NLO corrections to exclusive meson electroproduction, both in collider and fixed-target kinematics. Corrections are found to be huge at small xB and sizeable at intermediate or large xB.
The spin and flavor symmetries of the heavy quark effective theory are employed to discuss the exclusive cross sections for pair production of heavy mesons in photon-photon collision. The ratios of the exclusive cross sections for heavy mesons are obtained explicitly and the validity of results is discussed.
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 $B\to ϕK_S$.
We present the results of recent work on the central exclusive production of meson pairs. We concentrate on the case of flavour-singlet pseudoscalar mesons eta, eta' and show that the central exclusive process, as modelled using a recent novel application of the 'hard exclusive' perturbative formalism, is potentially highly sensitive to the size of the gluon content of these states. We also discuss the exclusive production of meson pairs in the lower mass region, and present the first results of the new Dime Monte Carlo.
Exclusive vector meson production from real and virtual photons is, for the most part, described well by soft pomeron exchange. However, there are some unsolved normalisation problems, and just a hint that an additional contribution from hard pomeron exchange may be needed.
We point out that hard exclusive production of tensor mesons $f_2(1270)$ with helicity $λ=\pm 2$ is dominated by the gluon component in the meson wave function and can be used to determine gluon admixture in tensor mesons in a theoretically clean manner. We present a detailed analysis of the tensor meson distribution amplitudes and calculate the transition form factor $γ+γ^*\to f_2(1270)$ for one real and one virtual photon.
The paper is devoted to investigation of $K$ mesons production in exclusive $B_{c}$ decays $B_{c} \to ψ^{(')}K^{+}K^{-}π^{+}$ and $B_{c} \to ψ^{(')}K^{+}π^{+}π^{-}$. In the framework of resonance approximation we obtain theoretical predictions for branching fractions of these decays and present distributions over different kinematical variables.
Exclusive semileptonic B meson decays to orbitally excited D mesons are investigated in the infinitely heavy quark limit in the framework of the relativistic quark model based on the quasipotential approach. The B\to D^{**}eνIsgur-Wise functions τ_{3/2}(w) and τ_{1/2}(w) are determined. It is found that the relativistic transformation of the meson wave functions (Wigner rotation of the light quark spin) contribute already at the leading order of the heavy quark expansion.
We give a theoretical description of the L3 Collaboration data on the cross-section of the exclusive two $ρ$-mesons production in $γγ^*$ collision with large photon virtuality. These data prove the scaling behaviour of the leading twist generalized distribution amplitude of vector mesons. They thus prove the relevance of a partonic description of the exclusive process $γγ^*\toρ^0ρ^0$ at $Q^2\geq 1.2 {\rm GeV^2}$ and $W\leq 3.0 {\rm GeV}.$
The paper is devoted to vector or pseudoscalar heavy quarkonia production J/ψ, ψ(2S), B_{s} or B_s^* in association with five charged π-mesons in exclusive B_c-meson decays. Using available formfactors parameterizations and spectral functions of $W \to 5 π$ transition we obtain branching fractions of these decays and distributions over invariant mass of (5π)-system.
We investigate the exclusive production of the pseudoscalar mesons pi0, eta, eta', K+ and of the vector mesons omega, phi in a microscopic gluon-exchange or instanton model. We describe the baryons as covariant quark - scalar diquark systems with harmonic confinement, thus taking into account center-of-mass corrections and Lorentz contraction in different frames. The excitation of intermediate baryon resonances is accounted by colorless 2-gluon (soft Pomeron) exchange. We find that our model accounts for the systematics of the high precision data on exclusive meson production from various mode…
We discuss the possibility of measuring generalized parton distributions in exclusive electroproduction of mesons off the nucleon and estimate the uncertainty from perturbatively induced higher-twist corrections. We find that, while the magnitude of the cross section changes significantly taking into account twist-four contributions modeled via renormalons, the transverse spin asymmetry is weakly sensitive to them and displays the precocious scaling.
The energetic exclusive two-body nonleptonic decays of B mesons are investigated in the framework of the relativistic quark model within the factorization approximation. The heavy quark expansion is used for the calculation of form factors. The obtained results are in agrement with available experimental data.
QED radiative effects are considered in the case of measurement of spin-density matrix elements of diffractive $ρ$-meson electroproduction. Large radiative correction for $r^5_{00}$ is found in the kinematics of collider experiments at HERA.
We present a study of the central exclusive production (CEP) of meson pairs, MMbar, at sufficiently high invariant mass that a perturbative QCD formalism is applicable. Within this framework, MMbar production proceeds via the gg --> MMbar hard scattering sub-process, which can be calculated within the hard exclusive formalism. We present explicit calculations for the gg --> MMbar helicity amplitudes for different meson states and, using these, show results for meson pair CEP in the perturbative regime.
I review recent progress on understanding QCD dynamics involved in exclusive $B$ meson decays. Different frameworks, including light-cone sum rules, QCD factorization, perturbative QCD, soft-collinear effective theory, light-front QCD, are discussed. Results from lattice QCD are quoted for comparison. I point out the important issues in the above QCD methods, which require further investigation.
The process of exclusive elastic vector meson production in deep inelastic scattering is investigated within the dipole model framework supplemented by the small $x$ evolution. The dipole-proton amplitude is obtained from the nonlinear Balitsky-Kovchegov evolution equation with impact parameter dependence. This dipole amplitude is used to compute the differential cross section for exclusive production of J/Ψ, ϕ, and ρ, vector mesons. These numerical calculations are compared with the wide range of experimental data from HERA. Good agreement between the experimental data and the calculations is…
We calculate distributions of different vector mesons in purely exclusive ($p p \to p p V$) and semi-exclusive ($p p \to p X V$) processes with electromagnetic dissociation of a proton. The cross section for the electromagnetic dissociation is expressed through electromagnetic structure functions of the proton. We include the transverse momentum distribution of initial photons in the associated flux. Contributions of the exclusive and semi-exclusive processes are compared for different vector mesons ($V = ϕ, J/ψ, Υ$). We discuss how the relative contribution of the semi-exclusive processes dep…
We explore the feasibility to study exclusive meson production (EMP) in hard muon-proton scattering at the COMPASS experiment. These measurements constrain the off-forward parton distributions (OFPD's) of the proton, which are related to the quark orbital contribution to the proton spin.
Exclusive vector meson production and deeply virtual Compton scattering are ideally suited reactions for studying the structure of the proton and the transition from soft to hard processes. The main experimental data obtained at HERA are summarised and presented in the light of QCD approaches.
Radiative effects in the electroproduction of photons in polarized ep-scattering are calculated in the leading log approximation and analyzed numerically for kinematical conditions of current measurement at Jefferson Lab. Radiative corrections to the cross sections, their azimuthal distributions and Fourier coefficients are in particular focus. Kinematical regions where the radiative corrections are considerable are identified.
Recent results obtained at HERA on deeply virtual Compton scattering and exclusive vector meson production are reviewed, with the emphasis on the transition from soft to hard diffraction and on spin dynamics.
Relying on the collinear factorization approach, we demonstrate that H1 and ZEUS measurements of exclusive light vector meson and photon electroproduction cross sections can be simultaneously described for photon virtualities of $Q >2 GeV$. Our findings reveal that quark exchanges are important in this small $x_{Bj}$ region and that in leading order approximation the gluonic skewness ratio is much smaller than one.
We discuss the salient features of exclusive vector meson production in heavy ion collisions at LHC energies. Special attention is paid to the space-time picture of the process. We account for both coherent and incoherent contributions. The explicit quantitative predictions are given for the $ρ$-meson differential cross section in lead-lead collisions in different kinematical configurations relevant for the LHCb and ALICE experiments.
We show that the leading twist contribution to exclusive electroproduction of transversely polarized vector mesons vanishes at all orders in perturbation theory. Therefore one cannot extract information on the quark transversity distribution of the nucleon from this reaction. In turn one has that the produced vector meson is purely longitudinal in the large-Q^2 limit, which provides a new test of the dominance of leading twist at finite Q^2.
We present the results of a recent novel application of the `hard exclusive' perturbative formalism to the process gg --> MMbar at large angles, where M (Mbar) is a light meson (anti-meson). As well as discussing the important theoretical features of the relevant leading-order gg --> qqbar(gg) qqbar(gg) 6-parton amplitudes, we also comment on their phenomenological implications. In particular, we consider the central exclusive production of meson pairs at comparatively large transverse momentum k_t, which is expected to proceed via this mechanism. We show that this leads to various non-trivial…
In this paper, the semileptonic decays of heavy mesons are treated fully relativistically. By means of an effective vertex, the effect of Fermi momentum are included both at the inclusive and at the exclusive levels, and the spin of both parent and daughter particles are taken into account. The differential decay rates with respect to the lepton energy and momentum transfer are compared with data from ARGUS and CLEO.
The exclusive photon-photon production of the $K$-meson pairs has been analyzed within the partonic model of QCD for the kinematical conditions of BELLE experiment. The cross section dependences on partonic masses, charges, and a shape of $K$-meson wave function have been studied for the process under discussion.
We present within the Standard Model the exclusive radiative decays B -> K*/rho gamma and B_(s/d) -> gamma gamma in QCD factorization based on the heavy-quark limit m_b >> Lambda_QCD. For the decays with a vector meson in the final state we give results complete to next-to-leading order in QCD.
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.
A nonperturbative calculation of elastic electroproduction of the J/psi meson is presented and compared to the experimental data. Our model describes well the observed dependences of the cross sections on the photon virtuality Q2 and on the energy, and the measured ratio R of longitudinal to transverse cross sections.
A brief report on the QCD factorization approach to exclusive B decays and its applications is presented. In an appendix a subtle issue concerning partial integration in the parameterization of infrared-sensitive power corrections is clarified.
We calculate the nuclear cross section for coherent and incoherent vector meson production within the QCD color dipole picture, including saturation effects. Theoretical estimates for scattering on both light and heavy nuclei are given over a wide range of energy.
An earlier developed model for vector meson photoproduction, based on a dipole Pomeron exchange, is extended to electroproduction. Universality of the non linear Pomeron trajectory is tested by fitting the model to ZEUS and H1 data as well as to CDF data on $\bar pp$ elastic scattering.
{We investigate the photoproduction process $ p γ\rightarrow Λ_{c}^{+} \overline{D^{0}}$ within the handbag approach, which we assume to be the dominant mechanism at energies well above the production threshold and in the forward scattering hemisphere.
Data for the differential cross sections for $γ^* p\toρ^0 p$, $γ^* p \to ϕp$ and $γ^* p\to J/ψp$, at all available values of $Q^2$, fit very well to a combination of soft pomeron, hard pomeron and $f_2$ exchange.
Exclusive vector meson production is an excellent probe for describing the structure of proton. In this paper, based on dipole model, the differential cross sections, total cross sections and the ratios of the longitudinal to transverse cross sections of $J/ψ$ and $ρ^0$ productions are calculated with the analytical solution of Balitsky-Kovchegov (BK) equation. In addition, we also consider the influences of two meson wave function models on the results. Our predictions, which are little sensitive to meson wave functions, agree with the experimental data. The analytical solution of BK equation…
The structure of the nonperturbative vector meson vertex function complicates the proof of the factorisation theorem for the reaction $γ^*p\to Vp$. It leads to additional contributions but, in a simple model for the vertex function, gauge invariance ensures that they cancel and factorisation is preserved.
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…
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.
In this paper we compute, within in the context of a relativistic quark model, the Isgur-Wise functions for exclusive semileptonic $\bar B \to X_c$ decays, where $X_c$ is any charmed mesons with total spin $J=0,1,2$ or one of their first excited states. The relevant matrix elements are computed by a direct numerical integration, in coordinate space, of the convolution of the wave function of the $B$ meson at rest and the wave function of the $X_c$ meson, boosted according with its recoil factor. Our results are compared with other predictions found in the existing literature.
The central exclusive production (CEP) of heavy resonance states that subsequently decay into meson pairs, MMbar, is an important signature for such processes at hadron colliders. However there is a potentially important background from the direct QCD production of meson pairs, as mediated for example by the exclusive gg --> MMbar hard scattering subprocess. This is in fact an interesting process in its own right, testing novel aspects of perturbative QCD technology. We explicitly calculate the gg --> MMbar helicity amplitudes for different meson states within the hard exclusive formalism, and…
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.
We study exclusive nonleptonic and semileptonic decays of the Bc-meson within a relativistic constituent quark model previously developed by us. For the nonleptonic decays we use the factorizing approximation. We update our model parameters by using new experimental data for the mass and the lifetime of the Bc meson and the leptonic decay constants of the D-meson. We calculate the branching ratios for a large set of exclusive nonleptonic and semileptonic decays of the $B_c$ meson and compare our results with the results of other studies. As a guide for further experimental exploration we provi…
A semi-classical picture is given for the production of exclusive meson pairs in γγ^* scattering using elements of the Lund string fragmentation model, spin and C-parity conservation. The model can be generalized to the production of any few meson states in scattering reactions at intermediate momentum transfers. As an example we show that we get a consistent description for the time-like pion form factor. For the reaction γγ^*\to π^+π^- we find a seizable cross section at LEP2 energies.
We present predictions for differential cross sections for the reaction $γp \to Φp$ and give an outlook to which extent our calculations may be generalized to the photoproduction of $J/Ψ$ mesons. Our results are obtained within perturbative QCD treating the proton as a quark-diquark system.
We analyze in detail the size of next-to-leading order corrections to hard exclusive meson production within the collinear factorization approach. Corrections to the cross section are found to be huge at small xB and substantial in typical fixed-target kinematics. With the models we take for nucleon helicity-flip distributions, the transverse target polarization asymmetry in vector meson production is strongly affected by radiative corrections, except at large xB. Its overall size is very small for rho production but can be large in the omega channel.
We review the perturbative QCD formalism for exclusive heavy meson decays, concentrating on the three-scale factorization theorem for nonleptonic processes. The formalism is then extended to the radiative decay $B\to K^*γ$, which occurs through penguin diagrams. It is observed that the contributions from the operators other than the penguin one $b\to sγ$ are not negligible. From the best fit to the experimental data of the branching ratio ${\cal B}(B\to K^*γ)$, we extract the $B$ meson wave function, which possesses a sharp peak in the region with a small momentum fraction.
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.
Exclusive production of the $π$ mesons in neutrino--photon interactions at low momentum transfer is studied within the standard model. The corresponding cross sections are calculated analytically. Potential astrophysical implications and the significance for testing the standard model are discussed. The presented formalism applies to other pseudoscalar mesons as well.
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.
