Current Matrix Elements Research Articles

Flavor twisted boundary conditions and the nucleon vector current

Using flavor twisted boundary conditions, we study nucleon matrix elements of the vector current. We twist only the active quarks that couple to the current. Finite volume corrections due to twisted boundary conditions are determined using partially twisted, partially quenched, heavy baryon chiral perturbation theory, which we develop for the graded group $SU(7|5)$. Asymptotically these corrections are exponentially small in the volume, but can become pronounced for small twist angles. Utilizing the Breit frame does not mitigate volume corrections to nucleon vector current matrix elements. The derived expressions will allow for better controlled extractions of the isovector magnetic moment and the electromagnetic radii from simulations at zero lattice momentum. Our formalism, moreover, can be applied to any nucleon matrix elements.

Light-front dynamics and AdS/QCD correspondence: Gravitational form factors of composite hadrons

Light-front holography is a remarkable feature of the AdS/CFT correspondence between gravity in AdS space and conformal field theories in physical space-time; it allows string modes $\ensuremath{\Phi}(z)$ in the anti-de Sitter (AdS) fifth dimension to be precisely mapped to the light-front wave functions of hadrons in physical space-time in terms of a specific light-front impact variable $\ensuremath{\zeta}$ which measures the separation of the quark and gluonic constituents within the hadron. This mapping was originally obtained by matching the exact expression for electromagnetic current matrix elements in AdS space with the corresponding exact expression for the current matrix element using light-front theory in physical space-time. In this paper we show that one obtains the identical holographic mapping using matrix elements of the energy-momentum tensor. To prove this, we show that there exists a correspondence between the matrix elements of the energy-momentum tensor of the fundamental hadronic constituents in QCD with the transition amplitudes describing the interaction of string modes in AdS space with an external graviton field which propagates in the AdS interior. The agreement of the results for electromagnetic and gravitational hadronic transition amplitudes provides an important consistency test and verification of holographic mapping from AdS to physical observables defined on the light front.

Zero-mode contribution in nucleon-delta transition

We investigate the transition form factors between nucleon and $\ensuremath{\Delta}(1232)$ particles by using a covariant quark-spectator-diquark field theory model in $(3+1)$ dimensions. Performing a light-front calculation in parallel with the manifestly covariant calculation in the light-front helicity basis, we examine the light-front zero-mode contribution to the helicity components of light-front good (``$+$'') current matrix elements. Choosing the light-front gauge (${ϵ}_{h=\ifmmode\pm\else\textpm\fi{}}^{+}=0$) with circular polarization in the Drell-Yan-West frame, we find that only the helicity components $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},\ensuremath{-}\frac{1}{2})$ of the good current receive the zero-mode contribution. Taking into account the zero mode, we find the prescription independence in obtaining the light-front solution of form factors from any three helicity matrix elements with smeared light-front wave functions. The angular condition, which guarantees the full covariance of different schemes, is recovered.

GAUSSIAN CONFINEMENT IN A JKJ DECAY MODEL

In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.

Axial current matrix elements and pentaquark decay widths in chiral soliton models

Here I explain why in chiral soliton models the hadronic transition operator of the pentaquark decay cannot be identified from the axial current.

Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula

Exact numerical results for the full counting statistics (FCS) for a one-dimensional tight-binding model of noninteracting electrons are presented without using an idealized measuring device. The two initially separate subsystems are connected at t=0 and the exact time evolution for the large but finite combined system is obtained numerically. At zero temperature the trace formula derived by Klich is used to to calculate the FCS via a finite dimensional determinant. Even for surprisingly short times the approximate description of the time evolution with the help of scattering states agrees well with the exact result for the local current matrix elements. An additional approximation has to be made to recover the Levitov-Lesovik formula in the limit where the system size becomes infinite and afterwards the long time limit is addressed. The new derivation of the Levitov-Lesovik formula is generalized to more general geometries like a Y-junction enclosing a magnetic flux.

Collective resonances in the soliton model approach to meson-baryon scattering

The proper description of hadronic decays of baryon resonances has been a long-standing problem in soliton modeis for baryons. In this paper I present a solution to this problem in the three-flavor Skyrme model that is consistent with large-N C consistency conditions. As an application I discuss hadronic pentaquark decays and show that predictions based on axial current matrix elements are erroneous.

Charm quark contribution toK+→π+νbar nuat next-to-next-to-leading order

We calculate the complete NNLO QCD corrections to the charm contribution of the rare decay K+ -> pi+ nu nu-bar. We encounter several new features, which were absent in lower orders. We discuss them in detail and present the results for the 2-loop matching conditions of the Wilson coefficients, the 3-loop anomalous dimensions, and the 2-loop matrix elements of the relevant operators that enter the NNLO renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the NNLO QCD corrections leads to a significant reduction of the theoretical uncertainty from 9.8% down to 2.4% in the relevant parameter Pc, implying the leftover scale uncertainties in BR(K+ -> pi+ nu nu-bar) and in the determination of |V_td|, sin(2 beta), and gamma from the K -> pi nu nu system to be 1.3%, 1.0%, 0.006, and 1.2 degrees, respectively. For the charm quark MSbar mass mc=(1.30+-0.05) GeV and |V_us|= 0.2248 the NLO value Pc=0.37+-0.06 is modified to Pc=0.38+-0.04 at the NNLO level with the latter error fully dominated by the uncertainty in mc. We present tables for Pc as a function of mc and alphas(MZ) and a very accurate analytic formula that summarizes these two dependences as well as the dominant theoretical uncertainties. Adding the recently calculated long-distance contributions we find BR(K+ -> pi+ nu nu-bar)=(8.0+-1.1)*10^-11 with the present uncertainties in mc and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. We also emphasize that improved calculations of the long-distance contributions to K+ -> pi+ nu nu-bar and of the isospin breaking corrections in the evaluation of the weak current matrix elements from K+ -> pi0 e+ nu would be valuable in order to increase the potential of the two golden K -> pi nu nu decays in the search for new physics.

Advances in light-front quantization and new perspectives for QCD from AdS/CFT

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a Fock space built on a trivial vacuum. The AdS/CFT correspondence has led to important insights into the properties of quantum chromodynamics even though QCD is a broken conformal theory. We have recently shown how a model based on a truncated AdS space can be used to obtain the hadronic spectrum of q q ¯ , qqq and gg bound states, as well as their respective light-front wavefunctions. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state, including orbital angular momentum excitations. The predicted mass spectrum is linear M ∝ L at high orbital angular momentum, in contrast to the quadratic dependence M 2 ∝ L found in the description of spinning strings. Since only one parameter, the QCD scale Λ Q C D , is introduced, the agreement with the pattern of physical states is remarkable. In particular, the ratio of Δ to nucleon trajectories is determined by the ratio of zeros of Bessel functions. As a specific application of QCD dynamics from AdS/CFT duality, we describe a computation of the proton magnetic form factor in both the space-like and time-like regions. The extended AdS/CFT space-time theory also provides an analytic model for hadronic light-front wavefunctions, thus providing a relativistic description of hadrons in QCD at the amplitude level. The model wavefunctions display confinement at large inter-quark separation and conformal symmetry at short distances. In particular, the scaling and conformal properties of the LFWFs at high relative momenta agree with perturbative QCD. These AdS/CFT model wavefunctions could be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian.

Theoretical investigation of the dependence of double beta decay tracks in a Ge detector on particle and nuclear physics parameters and separation from gamma ray events

The sizes of tracks of events of neutrinoless double-beta decay in a Germanium detector depend on particle physics and nuclear physics parameters such as neutrino mass, right-handed current parameters, etc., and nuclear matrix elements. In this paper for the first time Monte Carlo simulations of neutrino-accompanied ($2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) and neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) events, and of various kinds of background processes such as multiple and other $\ensuremath{\gamma}$ interactions are reported for a Ge detector. The time history of the evolution of the individual events is followed and the sizes of the events (partial volumes in the detector inside which the energy of the event is released) are investigated. Effects of the angular correlations of the two electrons in $\ensuremath{\beta}\ensuremath{\beta}$ decay, which again depend on the above nuclear and (for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay) on particle physics parameters, are taken into account and have been calculated for this purpose for the first time on basis of the experimental half-life of $^{76}\mathrm{G}\mathrm{e}$ and of realistic nuclear matrix elements. The sizes determine, together with the location of the events in the detector, the pulse shapes to be observed. It is shown for $\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{76}\mathrm{G}\mathrm{e}$, that $\ensuremath{\beta}\ensuremath{\beta}$ events should be selectable with high efficiency by rejecting large size (high multiplicity) $\ensuremath{\gamma}$ events. Double-escape peaks of similar energy of $\ensuremath{\gamma}$ lines show concerning their sizes similar behavior as $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ events, and in that sense can be of some use for corresponding 'calibration' of pulse shapes of the detector. The possibility to distinguish $\ensuremath{\beta}\ensuremath{\beta}$ events from $\ensuremath{\gamma}$ events is found to be essentially independent of the particle physics parameters of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ process. A brief outlook is given on the potential of future experiments with respect to determination of the particle physics parameters $⟨{m}_{\ensuremath{\nu}}⟩,⟨\ensuremath{\lambda}⟩,⟨\ensuremath{\eta}⟩$.

Exotic baryons in two-dimensional QCD

Two-dimensional QCD has often been used as a laboratory for studying the full four-dimensional theory, providing, for example, an explicit realization of baryons as solitons. We review aspects of conventional baryons in two-dimensional QCD, including the classical and quantum contributions to their masses. We then discuss the spectrum of exotic baryons in two-dimensional QCD, commenting on the solitonic radius inferred from the excitation spectrum as well as the two-dimensional version of the Goldberger-Treiman relation relating meson couplings to current matrix elements. Two-dimensional QCD provides strong overall support to the chiral-soliton picture for the structure of normal and exotic baryons in four dimensions.

Light-front zero-mode contribution to the good current in weak transitions

We examine the light-front zero-mode contribution to the good(+) current matrix elements between pseudoscalar and vector mesons. In particular, we discuss the transition form factor $f(q^2)$ which has been suspected to have the light-front zero-mode contribution. While the zero-mode contribution in principle depends on the form of the vector meson vertex $\Gamma^\mu=\gamma^\mu - (P_V -2k)^\mu/D$, the form factor $f(q^2)$ is found to be free from the zero-mode contribution if the denominator $D$ contains the term proportional to the light-front energy $(k^-)^{n}$ with the power $n>0$. The lack of zero-mode contribution benefits the light-front quark model phenomenology. We present our numerical calculations for the $B\to\rho$ transition.

New Results in Light-Front Phenomenology

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-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. I also briefly review recent analyses which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.

Non-perturbative tests of HQET in small-volume quenched QCD

We quantitatively investigate the quark mass dependence of current matrix elements and energies, calculated over a wide range of quark masses in the continuum limit of small-volume quenched lattice QCD. By a precise comparison of these observables as functions of the heavy quark mass with the predictions of HQET we are able to verify that their large quark mass behaviour is described by the effective theory.

Construction of form factors of composite systems by a generalized Wigner-Eckart theorem for the Poincaré group

The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A special mathematical technique is used for the parametrization of matrix elements of electroweak current operators in terms of form factors. The parametrization is a realization of the generalized Wigner--Eckart theorem on the Poincar\'e group, form factors are corresponding reduced matrix elements and they have the sense of distributions (generalized functions). The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of electromagnetic current it also automatically satisfies the conservation law.

Non-perturbative tests of Heavy Quark Effective Theory

We consider QCD with one massless quark and one heavy quark in a finite volume of linear extent L 0 ? 0.2 fm. In this situation, HQET represents an expansion in terms of 1/z = 1/(mL 0), which we test by a non-perturbative computation of quenched current matrix elements and energies, taking the continuum limit of lattice results. These are seen to approach the corresponding renormalization group invariant matrix elements of the static effective theory as the quark mass becomes large. We are able to obtain estimates of the size of the 1/m -corrections to the static theory, which are also of practical relevance in our recent strategy to implement HQET non-perturbatively by matching to QCD in a finite volume.

Baryon axial charge in a finite volume

We compute finite-volume corrections to nucleon matrix elements of the axial-vector current. We show that knowledge of this finite-volume dependence --as well as that of the nucleon mass-- obtained using lattice QCD will allow a clean determination of the chiral-limit values of the nucleon and Delta-resonance axial-vector couplings.

B−→φφK−decay rate withφφinvariant mass below the charm threshold

We investigate the decay mechanism in the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\varphi}{K}^{\ensuremath{-}}$ decay with the $\ensuremath{\varphi}\ensuremath{\varphi}$ invariant mass below the charm threshold and in the neighborhood of the ${\ensuremath{\eta}}_{c}$ invariant mass region. Our approach is based on the use of the factorization model and the knowledge of matrix elements of the weak currents. For the B meson weak transition we apply the form factor formalism, while for the light mesons we use effective weak and strong Lagrangians. We find that the dominant contributions to the branching ratio come from the $\ensuremath{\eta},$ ${\ensuremath{\eta}}^{\ensuremath{'}}$ and $\ensuremath{\eta}(1490)$ pole terms of the penguin operators in the decay chains ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}},\ensuremath{\eta}(1490)){K}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\varphi}{K}^{\ensuremath{-}}.$ Our prediction for the branching ratio is in agreement with the Belle Collaboration's result.

Gauge theories on the light-front

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitary, and a trivial vacuum. The light-front Hamiltonian form of QCD provides an alternative to lattice gauge theory for the computation of nonperturbative quantities such as the hadronic spectrum and the corresponding eigenfunctions. In the case of the electroweak theory, spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field. Light-front quantization then leads to an elegant ghost-free theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions, as well as the Goldstone boson equivalence theorem.

Nucleon properties at finite lattice spacing in chiral perturbation theory

Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.