The OPE of the B-meson light-cone wavefunction for exclusive B decays: radiative corrections and higher-dimensional operators
Hiroyuki Kawamura, Jiro Kodaira, Kazuhiro Tanaka
备注：
6 pages, to appear in the proceedings of 8th International Symposium on Radiative Corrections (RADCOR 2007), Florence, Italy, October 1-5; corrected typos
We discuss the B-meson light-cone wavefunction relevant for QCD factorization approach for exclusive B-meson decays. We derive the operator product expansion for the B-meson light-cone wavefunction, taking into account the local composite operators of dimension less than 6 and calculating the radiative corrections at order α_s for the corresponding Wilson coefficients. The result embodies peculiar UV and IR behaviors of the B-meson light-cone wavefunction, the Sudakov-type double logarithmic effects and the mixing of the multiparticle states with additional gluons inside the B meson. The former effects are induced from the cusp singularity in the radiative corrections, while the latter is manifested by the participation of the higher-dimensional operators associated with the nonperturbative structure of the B meson.
Exclusive B decays can be factorized as convolutions of hard scattering amplitudes involving the weak interaction with universal hadron distribution amplitudes, thus providing a new QCD-based phenomenology. In addition, semi-leptonic decay amplitudes can be computed exactly in terms of the diagonal and off-diagonal overlap of hadronic light-cone wavefunctions. I review these formalisms and the essential QCD ingredients. canonical form of the light-cone wavefunctions, valid at low values of the transverse momenta, is presented. The existence of intrinsic charm Fock states in the B meson wavefun…
The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon's electromagnetic form-factor at high $Q^2$ is proportional to the bare nucleon probability $Z$ and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to $Z^2$. Our present knowledge of the pion-nucleon system is consistent with $Z = 0.7 \pm 0.2$. If we…
The matrix elements of electroweak currents which occur in exclusive decays of heavy hadrons are evaluated in the nonperturbative light-cone Fock representration. In general, each semileptonic exclusive decay amplitude receives two contributions, a diagonal $Δn = 0$ parton-number-conserving amplitude and a $Δn = -2$ contribution in which a quark and an antiquark from the initial hadron Fock state annihilate to the leptonic current. The general formalism can be used as a basis for systematic approximations to heavy hadron decay amplitudes such as hard perturbative QCD contributions. We illustra…
In the last years, the need of the colour octet state in inclusive P-wave charmonium decay has been firmly established. However, the implications of this in the corresponding exclusive reactions have not been fully recognized. We argue for the necessity of the colour octet in P- and higher-wave quarkonium decay. Using a set of phenomenologically constructed baryon wavefunctions, we consider the Chi_J decay into octet and decuplet baryon-antibaryon pair. By doing so, we subject the wavefunctions to a test of applicability. We show that the colour singlet component alone is insufficient to accou…
We consider the transitions between electromagnetic bound states, such as the exclusive weak decay of a muonic atom into an electronic atom: $(μ^- Z) \to (e^- Z) {\bar ν_e }ν_μ. $ We show that relativistic effects in the atomic wavefunctions are crucial for determining the rate. In the case of heavy atoms, the exclusive channel branching ratios exceed $10^{-6},$ possibly bringing the study of these rare decays within experimental reach. Such processes thus provide a detailed laboratory for studying the high momentum tail of wavefunctions in atomic physics; in addition, they provide a simple to…
A fundamental goal in QCD is to understand the non-perturbative structure of hadrons at the amplitude level--not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quant…
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.
The light-cone Fock representation encodes the bound-state quark and gluon properties of hadrons, including their helicity and flavor correlations, in terms of universal process-independent and frame-independent wavefunctions. It also provides a physical factorization scheme for separating hard and soft contributions in both exclusive and inclusive hard processes. A new type of jet production reaction, ''self-resolving diffractive interactions'' can provide direct information on the light-cone wavefunctions of hadrons in terms of their QCD degrees of freedom as well as the composition of nucle…
A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A numbe…
Light-cone Fock-state wavefunctions encode the properties of a hadron in terms of its fundamental quark and gluon degrees of freedom. A recent experiment at Fermilab, E791, demonstrates that the color coherence and shape of light-cone wavefunctions in longitudinal momentum fraction can be directly measured by the high energy diffractive jet dissociation of hadrons on nuclei. Given the proton's light-cone wavefunctions, one can compute not only the quark and gluon distributions measured in deep inelastic lepton-proton scattering, but also the multi-parton correlations which control the distribu…
It is argued that colour octet contribution in exclusive charmonium decays is very important even though the same infrared divergence found in P-wave colour singlet inclusive decay is absent. This comes about because of the suppression at the level of the wavefunction of P-wave quarkonia. Using the modified hard scattering approach of Brodsky, Lepage, Botts, Li and Sterman, we use charmonium decay into baryon-antibaryon pair as an example and show that the colour singlet contribution alone is clearly insufficient to explain the experimental decay widths.
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…
The diffractive dissociation of a hadron at high energies, by either Coulomb or Pomeron exchange, has a natural description in QCD as the materialization of the projectile's light-cone wavefunctions; in particular, the diffractive dissociation of a meson, baryon, or photon into high transverse momentum jets measures the shape and other features of the projectile's distribution amplitude. Diffractive dissociation can thus test fundamental properties of QCD, including color transparency and intrinsic charm. All of these effects have an impact on exclusive decays of $B$ mesons and the study of $C…
The light-cone Fock-state representation of QCD encodes the properties of a hadrons in terms of frame-independent wavefunctions, providing a systematic framework for evaluating structure functions, exclusive hadronic matrix elements, including time-like heavy hadron decay amplitudes, form factors, and deeply virtual Compton scattering. A new type of jet production reaction, "self-resolving diffractive interactions" can provide direct information on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their…
The light-front representation of quantum chromodynamics provides a frame-independent, quantum-mechanical representation of hadrons at the amplitude level, capable of encoding their multi-quark, hidden-color and gluon momentum, helicity, and flavor correlations in the form of universal process-independent hadron wavefunctions. The universality and frame-independence of the LCWF's thus allow a profound connection between diffractive dissociation, hard scattering exclusive processes such as elastic form factors, two-photon reactions, and heavy hadron decays. In this concluding talk of the ECT* I…
We improve the pNRQCD approach to annihilation processes of heavy quarkonium and make first pNRQCD predictions for exclusive electromagnetic production of heavy quarkonium. We consider strongly coupled quarkonia, i.e., quarkonia that are not Coulombic bound states. Possible strongly coupled quarkonia include excited charmonium and bottomonium states. For these, pNRQCD provides expressions for the decay and exclusive electromagnetic production NRQCD matrix elements that depend on the wavefunctions at the origin and few universal gluon field correlators. We compute electromagnetic decay widths a…
The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. One can use holography to map the amplitude describing the hadronic state in the fifth dimension of Anti-de Sitter space to the light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons in QCD at the amplitude level. In particular, we show that ther…
We argue that the proton multiplicities measured in Roman pot detectors at an electron ion collider can be used to determine centrality classes in incoherent diffractive scattering. Incoherent diffraction probes the fluctuations in the interaction strengths of multi-parton Fock states in the nuclear wavefunctions. In particular, the saturation scale that characterizes this multi-parton dynamics is significantly larger in central events relative to minimum bias events. As an application, we study the centrality dependence of incoherent diffractive vector meson production. We identify an observa…
We report on recent progress on perturbative QCD calculations of certain exclusive rare weak $B$ meson decays involving hard photons. In the limit of a photon energy $E_γ$ much larger than $Λ_{QCD}$, the amplitudes for such processes can be analyzed in a twist expansion in powers of $Λ/E_γ$. The leading twist amplitude is given by the convolution of a hard scattering amplitude with the $B$ meson light-cone wavefunction. This approach is applied to a calculation of the leptonic radiative $B\to γ\ell ν_\ell$ formfactors and to an estimate of the weak annihilation contribution to the penguin deca…
The ensemble of light-cone Fock wavefunctions $\{ψ_{n/H}(x_i,\vec k_{\perp i},λ_i)\}$ provides a conceptual basis for representing physical hadrons and nuclei in terms of their fundamental quark and gluon degrees of freedom. A number of applications of the light-cone formalism to QCD phenomenology are briefly reviewed, such as the origin of Regge behavior of polarized structure functions, the high momentum transfer behavior of exclusive reactions, the color transparency properties of diffractive vector meson photoproduction, and the behavior of quark distributions at large $x_{bj}$. The light-…
We elucidate the role of time scales that determine heavy quark dynamics in the QGP. Quark-antiquark potentials extracted from the lattice are used to demonstrate the existence of open heavy flavor bound-state solutions in the vicinity of the critical temperature, and their light cone wavefunctions are obtained. We use these wavefunctions to calculate the in-medium modification of the heavy quark distribution and decay probabilities. For the case of high transverse momentum D or B mesons traversing the QGP, we combine the new meson formation and dissociation mechanism with the traditional part…
Light-front Fock state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conform…
In these lectures, I survey a number of applications of light-front methods to hadron and nuclear physics phenomenology and dynamics, Light-front Fock-state wavefunctions provide a frame-independent representation of hadrons in terms of their fundamental quark and gluon degrees of freedom. Nonperturbative methods for computing LFWFs in QCD are discussed, including string/gauge duality which predicts the power-law fall-off at high momentum transfer of light-front Fock-state hadronic wavefunctions with an arbitrary number of constituents and orbital angular momentum. The AdS/CFT correspondence h…
The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and to define a kinematical definition of angular momentum. The AdS/CFT correspondence of large $N_C$ supergravity theory in higher-d…
In this paper, we study the $0^{+}$ nonet mesons as tetraquark states with interpolating currents induced from the color-magnetic wavefunction. This wavefunction is the eigenfunction of effective color-magnetic Hamiltonian with the lowest eigenvalue, meaning that the state depicted by this wavefunction is the most stable one and is most probable to be observed in experiments. Our approach can be recognized as determining interpolating currents dynamically. We perform an OPE calculation up to dimension eight condensates and find that the best QCD sum rule is achived when the current induced fro…
We prove a factorization theorem for heavy-to-light form factors. Our result differs in several important ways from previous proposals. A proper separation of scales gives hard kernels that are free of endpoint singularities. A general procedure is described for including soft effects usually associated with the tail of wavefunctions in hard exclusive processes. We give an operator formulation of these soft effects using the soft-collinear effective theory, and show that they appear at the same order in the power counting as the hard spectator contribution.
I discuss several theoretical tools which are useful for analyzing perturbative and non-perturbative problems in quantum chromodynamics, including (a) the light-cone Fock expansion, (b) the effective charge $α_V$, (c) conformal symmetry, and (d) commensurate scale relations. Light-cone Fock-state wavefunctions encode the properties of a hadron in terms of its fundamental quark and gluon degrees of freedom. Given the proton's light-cone wavefunctions, one can compute not only the quark and gluon distributions measured in deep inelastic lepton-proton scattering, but also the multi-parton correla…
Several topics in QCD are reviewed, including: the light-cone Fock state representation, which encodes the flavor, spin and other quark and gluon correlations of hadrons in the form of universal process-independent amplitudes; the light-cone factorization scheme for inclusive and exclusive processes; the application of the light-cone formalism to semi-leptonic B decay amplitudes; self-resolving diffractive interactions as a tool for measuring light-cone wavefunctions; and the use of conformal symmetry as a template for QCD predictions, such as commensurate scale relations, which relate observa…
A fundamental understanding of quantum chromodynamics, particularly at the amplitude level, is essential for progress in high energy physics. For example, the measurement and interpretation of the basic parameters of the electroweak theory and CP violation depends on an understanding of the dynamics and phase structure of exclusive B-meson decay amplitudes. In this review, I discuss a number of ways in which the required hadron wavefunctions can be measured (such as two-photon reactions and diffractive dissociation) or calculated from first principles. An important tool for describing relativi…
The B-meson wavefunction has been studied with the help of the vacuum-to-meson matrix element of the nonlocal operators in the heavy quark effective theory. In order to obtain the Wandzura-Wilczek-type B-meson wavefunction, we solve the equations which are derived from the equation of motion of the light spectator quark in the B meson by using two different assumptions. Under the condition that $ω_0=2\barΛ$, the solutions for the B-meson wavefunction in this paper agree well with the one obtained by directly taking the heavy quark limit $m_b\to\infty$. Our results show that the equation of mot…
We discuss a number of novel applications of Quantum Chromodynamics to nuclear structure and dynamics, such as the reduced amplitude formalism for exclusive nuclear amplitudes. We particularly emphasize the importance of light-cone Hamiltonian and Fock State methods as a tool for describing the wavefunctions of composite relativistic many-body systems and their interactions. We also show that the use of covariant kinematics leads to nontrivial corrections to the standard formulae for the axial, magnetic, and quadrupole moments of nucleons and nuclei.
We discuss the results of exclusive $p p \to p p K^{+} K^{-}$ reaction at high energies which constitutes an irreducible background to three-body processes $p p \to p p M$, where $M=ϕ$, $f_{2}(1275)$, $f_{0}(1500)$, $f_{2}'(1525)$, $χ_{c0}$. We consider central diffractive contribution mediated by Pomeron and Reggeon exchanges including absorption effects due to proton-proton interaction and kaon-kaon rescattering. We make predictions for future experiments at RHIC, Tevatron and LHC. Differential distributions in invariant two-kaon mass, kaon rapidities and transverse momenta of kaons are pres…
We consider the effective Hamiltonian of four quark operators in the Standard Model in the exclusive and quasi-inclusive decays of the type $B\to K^{(*)} η^{\prime}$, $B\to η' X_s$, where $X_s$ contains a single Kaon. Working in the factorization assumption we find that the four quark operators can account for the recently measured exclusive decays $B\to η^{\prime}(η) K$ and $B\to K π$ for appropriate choice of form factors but cannot explain the large quasi-inclusive rate.
The decays $B^+\to D_{s,d}^+e^+e^-$ and $B^+\to D_{s,d}^{*+}e^+e^-$ proceed through a weak and an electromagnetic interaction. This is a typical ``long distance'' process, usually difficult to compute systematically. We propose that over a large fraction of phase space a combination of an operator product and heavy quark expansions effectively turns this process into one in which the weak and electromagnetic interactions occur through a local operator. Moreover, we use heavy quark spin symmetry to relate all the local operators that appear in leading order of the operator expansion to two basi…
B decay sum rules relate exclusive B semileptonic decay matrix elements to forward B-meson matrix elements of operators in HQET. At leading order the operators that occur are the b-quark kinetic energy $λ_1$ and chromomagnetic energy $λ_2$. The latter is determined by the measured $B^*-B$ mass splitting. The derivation of these sum rules is reviewed and perturbative QCD corrections are discussed. A determination of $λ_1$ and the energy of the light degrees of freedom in a B-meson, $\barΛ$, from semileptonic B decay data is presented. Future prospects for improving these sum rules are discussed…
There exist an infinite number of exact small momentum fraction-$x$ boundary conditions on light-cone wavefunctions of bound states in gauge theory. They are necessary for finite expectation values of the invariant mass operator and relate components of the wavefunction from different Fock sectors. We illustrate their consequences by analyzing the small-$x$ quark Regge behavior of a heavy large-$N$ meson, finding power-law rise of unpolarized distributions. The polarized distribution changes sign and then vanishes with minus the unpolarized Regge intercept.
We calculate the lowest order charm and beauty parton distribution functions in and fragmentation functions into D and B mesons using the operator definitions of factorized perturbative QCD. In the vacuum, we find the leading corrections that arise from the structure of the final-state hadrons. Quark-antiquark potentials extracted from the lattice are employed to demonstrate the existence of open heavy flavor bound-state solutions in the QGP in the vicinity of the critical temperature. We provide first results for the in-medium modification of the heavy quark distribution and decay probabiliti…
The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semi-classical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. Although QCD is not conformally invariant, one can nevertheless use the mathematical representation of the conformal group in five-dimensional anti-de Sitter space to construct a first approximation to the theory. The AdS/CFT correspondence also provides insights into the inherently non-perturbative aspe…
We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. This process offers one of the best ways to obtain information about gluon distributions at small $x$, in ultraperipheral heavy ion collisions and in deep inelastic scattering. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. In this paper, we discuss the compatibility of the dipole appr…
Wavefunction-based operator optimization for two-hadron systems in lattice QCD
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论与科学数学中心）；Fundamental Quantum Science Program (FQSP), TRIP Headquarters, RIKEN（理化学研究所基础量子科学计划总部）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息研究中心）；Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo（东京大学宇宙物理数学研究所）；Department of Physics, Institute of Science Tokyo（东京科学大学物理学部）；Faculty of Data Science, Rissho University（立正大学数据科学学部）
Decoding Two-Particle States in QCD with Spatial Wavefunctions
RIKEN（理化学研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo（东京大学 Kavli宇宙物理数学研究所 (WPI)）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Faculty of Data Science, Rissho University（立教大学数据科学学院）
