Invariant Amplitudes Research Articles

Form factors in [formula omitted] from QCD light-cone sum rules

The form factors of the semileptonic B→ππℓν¯ decay are calculated from QCD light-cone sum rules with the distribution amplitudes of dipion states. This method is valid in the kinematical region, where the hadronic dipion state has a small invariant mass and simultaneously a large recoil. The derivation of the sum rules is complicated by the presence of an additional variable related to the angle between the two pions. In particular, we realize that not all invariant amplitudes in the underlying correlation function can be used, some of them generating kinematical singularities in the dispersion relation. The two sum rules that are free from these ambiguities are obtained in the leading twist-2 approximation, predicting the B¯0→π+π0 form factors F⊥ and F∥ of the vector and axial b→u current, respectively. We calculate these form factors at the momentum transfers 0<q2≲12 GeV2 and at the dipion mass close to the threshold 4mπ2. The sum rule results indicate that the contributions of the higher partial waves to the form factors are suppressed with respect to the lowest P-wave contribution and that the latter is not completely saturated by the ρ-meson term.

Test of T-invariance in pd scattering with double polarization

A formalism of the invariant spin amplitudes of the pd-scattering process in the Madison frame of reference is developed. The condition for T invariance with conservation of P-parity is formulated in terms of these amplitudes, and the relationships between differential spin observables that follow from this condition, are derived. The relative efficiency of the method for testing T-invariance on the basis of these relationships is compared to the method based on recording a null-test signal in an experiment with a polarized proton beam and the deuteron target.

Lattice QCD study of the Boer-Mulders effect in a pion

The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentum-dependent parton distribution functions (TMDs). This work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. Particular emphasis is placed on the behavior as a function of a Collins-Soper evolution parameter quantifying the relative rapidity of the struck quark and the initial hadron, e.g., in a semi-inclusive deep inelastic scattering (SIDIS) process. The lattice calculation, performed at the pion mass m_pi = 518 MeV, utilizes a definition of TMDs via hadronic matrix elements of a quark bilocal operator with a staple-shaped gauge connection; in this context, the evolution parameter is related to the staple direction. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. In contrast to an earlier nucleon study, due to the lower mass of the pion, the calculated data enable quantitative statements about the physically interesting limit of large relative rapidity. In passing, the similarity between the Boer-Mulders effects extracted in the pion and the nucleon is noted.

Lattice QCD calculations of transverse momentum-dependent parton distributions (TMDs)

An ongoing program of evaluating TMD observables within Lattice QCD is reviewed, summarizing recent progress with respect to several challenges faced by such calculations. These lattice calculations are based on a definition of TMDs through hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections. A parametrization of the matrix elements in terms of invariant amplitudes serves to cast them in the Lorentz frame preferred for a lattice calculation. Data on the naively T-odd Sivers and Boer-Mulders effects as well as the transversity TMD are presented.

Bottom baryon decays to pseudoscalar meson and pentaquark

Based on SU(3) flavor symmetry, we decompose the decay amplitudes of bottom baryon decays to a pseudoscalar meson and an octet (a decuplet) pentaquark in terms of three (two) invariant amplitudes $T_1$ and $T_{2,3}$ ($\tilde T_1$ and $\tilde T_2$) corresponding to external $W$-emission and internal $W$-emission diagrams, respectively. For antitriplet bottom baryons $\Lambda_b^0,\Xi_b^0$ and $\Xi_b^-$, their decays to a decuplet pentaquark proceed only through the internal $W$-emission diagram. Assuming the dominance from the external $W$-emission amplitudes, we present an estimate of the decay rates relative to $\Lambda_b^0\to P_p^+K^-$, where $P_p^+$ is the hidden-charm pentaquark with the same light quark content as the proton. Hence, our numerical results will provide a very useful guideline to the experimental search for pentaquarks in bottom baryon decays. For example, $\Xi_b^0\to P_{\Sigma^+}K^-$, $\Xi_b^-\to P_{\Sigma^-}\bar K^0$, $\Omega_b^-\to P_{\Xi^-}\bar K^0$ and $\Omega_b^-\to P_{\Xi^0}K^-$ may have rates comparable to that of $\Lambda_b^0\to P_p^+K^-$ and these modes should be given the higher priority in the experimental searches for pentaquarks.

Gauge invariant formulation of3γdecay of particle-antiparticle bound states

We construct the gauge invariant three-photon decay amplitude of particle-antiparticle bound states modeled by the Dyson-Schwinger and Bethe-Salpeter equations. Application to the quark-antiquark ($q\overline{q}$) bound states is emphasized. An essential aspect of our formulation is that it applies to any underlying quantum field theoretic model of the $q\overline{q}$ system, and not just to models, like exact QCD, where the quark self-energy $\mathrm{\ensuremath{\Sigma}}$ couples to the electromagnetic field solely via dressed quark propagators. In this way, applications to effective field theories and other QCD motivated models are envisioned. The three-photon decay amplitude is constructed by attaching currents to all possible places in the Feynman diagrams contributing to the dressed quark propagator. The gauge invariance of our construction is thus a direct consequence of respecting the underlying structure of the quantum field theory determining the dynamics. In the resultant expression for the three-photon decay amplitude, all the basic ingredients consisting of the bound-state wave function, the final-state interaction $q\overline{q}$ $t$ matrix, the dressed quark propagator, and dressed quark currents, are determined by a universal Bethe-Salpeter kernel.

Some new insights into a known Chen‐like system

In the paper entitled ‘A novel chaotic system and its topological horseshoe’ in [Nonlinear Analysis: Modelling and Control 18 (1) (2013) 66–77], proposed the 3D chaotic system, , and discussed some of its dynamics according to theoretical and numerical analysis of its parameters . The present work is devoted to giving some new insights into the system for b≥0. Combining theoretical analysis and numerical simulations, some new results are formulated. On the one hand, after some known errors, mainly the distribution of its equilibrium point which is pointed out, correct results are formulated. On the other hand, some of its more rich dynamical properties hiding and not found previously, such as the stability, fold bifurcation, pitchfork bifurcation, degenerated pitchfork bifurcation, and Hopf bifurcation of its isolated equilibria, the dynamics of non‐isolated equilibria, the singularly degenerate heteroclinic cycle, the heteroclinic orbit, and the dynamics at infinity are clearly revealed. Using these results, one can easily explain those interesting phenomena for invariant Lyapunov exponent spectrum and amplitude control that are presented in the known literature. What is more important, we probably demonstrate a new route to chaos. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Lattice QCD Studies of Transverse Momentum-Dependent Parton Distribution Functions

Transverse momentum-dependent parton distributions (TMDs) relevant for semi-inclusive deep inelastic scattering and the Drell–Yan process can be defined in terms of matrix elements of a quark bilocal operator containing a staple-shaped gauge link. Such a definition opens the possibility of evaluating TMDs within lattice QCD. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. Results for selected TMD observables are presented, including a particular focus on their dependence on a Collins–Soper-type evolution parameter, which quantifies proximity of the staple-shaped gauge links to the light cone.

Determination of the First Stress Tensor Invariant of a Complex Steel Sheet Structure from Thermoelastic Stress Analysis

The determination of welded steel sheet assemblies high cycle fatigue properties is a prior concern of the automotive industry. Such assemblies are designed as high-safety parts, for which any fatigue failure is supposed to be prevented. Thus, the determination of complex structures stress field is necessary to design them. Even though finite element models are more and more accurate, experimental methods for the stress field tensors measurement under cyclic loadings are useful to validate those models. The purpose of this work is the experimental determination of the first stress tensor invariant amplitude at the surface of a complex structure under cyclic loading, a car wishbone, with a method based on thermal measurements, the Thermoelastic Stress Analysis (TSA). Parameters which have an influence on the measured temperature at the surface of the structure are studied, including the non-adiabatic behaviour of specimens due to a heterogeneous stress field and the influence of the paint used to measure the temperature with an infra-red camera. All these parameters are taken into account to determine successfully the wishbone stress tensor amplitude during a cyclic test.

Heavy-to-light semileptonic decays ofΛbandΛcbaryons in the covariant confined quark model

We present a detailed analysis of the heavy-to-light semileptonic decays of the Lambda_b and Lambda_c baryons Lambda_b -> p l- bar(nu)_l and Lambda_c -> n l+ nu_l in the covariant confined quark model. We calculate the invariant and helicity amplitudes of the two processes which are then used to analyze their angular decay distributions, their rates and asymmetry parameters.

Magnetic moments ofJP=32−baryons in QCD

The magnetic moments of the low lying, negative parity, spin-3/2 baryons are calculated within the light cone QCD sum rules method. The contributions coming from the positive parity, spin-3/2 baryons, as well as from the positive and negative parity spin-1/2 baryons are eliminated by constructing combinations of various invariant amplitudes corresponding to the coefficients of the different Lorentz structures.

CFT4 as [formula omitted]-invariant TFT2

We show that correlators of local operators in four-dimensional free scalar field theory can be expressed in terms of amplitudes in a two-dimensional topological field theory (TFT2). We describe the state space of the TFT2, which has SO(4,2) as a global symmetry, and includes both positive and negative energy representations. Invariant amplitudes in the TFT2 correspond to surfaces interpolating from multiple circles to the vacuum. They are constructed from SO(4,2) invariant linear maps from the tensor product of the state spaces to complex numbers. When appropriate states labeled by 4D-spacetime coordinates are inserted at the circles, the TFT2 amplitudes become correlators of the four-dimensional CFT4. The TFT2 structure includes an associative algebra, related to crossing in the 4D-CFT, with a non-degenerate pairing related to the CFT inner product in the CFT4. In the free-field case, the TFT2/CFT4 correspondence can largely be understood as realization of free quantum field theory as a categorified form of classical invariant theory for appropriate SO(4,2) representations. We discuss the prospects of going beyond free fields in this framework.

Wilson lines and gauge invariant off-shell amplitudes

We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned “polarization vectors” which (in the Feynman gauge) are transverse to their off-shell momenta and define the direction of the corresponding Wilson line operators. The infinite Wilson lines are first regularized to prove the correctness of the method. We have implemented the method in a computer FORM program that can calculate gluonic matrix elements of Wilson line operators automatically. In addition we formulate the Feynman rules that are convenient in certain applications, e.g. proving the Ward identities. Using both the program and the Feynman rules we calculate a few examples, in particular the matrix elements corresponding to gauge invariant g * g * g * g and g * g * g * g * g processes. An immediate application of the approach is in the high energy scattering, as in a special kinematic setup our results reduce to the form directly related to Lipatov’s vertices. Thus the results we present can be directly transformed into Lipatov’s vertices, in particular into RRRP and RRRRP vertices with arbitrary “orientation” of reggeized gluons. Since the formulation itself is not restricted to high-energy scattering, we also apply the method to a decomposition of an ordinary on-shell amplitude into a set of gauge invariant objects.

Energy-dependent analysis of eta-meson photoproduction on protons and neutrons without background in the energy region up to 3.4 GeV

Observed for the processes gamma+p arrow eta+p, gamma+n arrow eta+n are calculated throughout the resonance energy region using the single isobar model without a background. The connection between invariant photoexcitation amplitudes of the resonances on neutrons and protons are calculated. The results are discussed in terms of a comparison with experimental data and calculations performed by other authors.

Discrepancy between the interactions of nucleons in nuclear matter due to different projection choices of invariant amplitudes

Dependence of self-energy components and cross sections of nucleons in-medium on the relative momentum of nucleons in nuclear matter from different projections choices of invariant amplitudes is studied within the framework of Dirac-Brueckner-Hartree-Fock model. Special attention is paid to the discrepancy between the self-energies and cross sections for different choices in various separate chances. Our results indicate that the self-energy of nucleons in the states with spin S = 1 and isospin triplets T = 1 is larger than those with S = 0 and T = 0 at a specified relative momentum. The dependence of the self-energies of nucleons in various reaction channels on the pseudo-scalar (PS) choice are more pronounced than that on the complete pseudo vector (CPV) choice, which is mainly due to the states with smaller total momentum quantum numbers J. Results of the in-medium differential cross sections show that the difference between d/d for the neutron-proton and neutron-neutron (or proton-proton) in various choices is larger for smaller relative momentum of nucleons and smaller scattering angles in mass center reference frame However, the total cross section total in the CPV choice is always larger than that in the PS choice. All these discrepancies will disappear with increasing incident energy.

Polarization effects in the cascade decayΛb→Λ(→pπ−)+J/ψ(→ℓ+ℓ−)in the covariant confined quark model

We calculate the invariant and helicity amplitudes for the nonleptonic decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}+J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)$ in the covariant confined quark model. We discuss joint angular decay distributions in the cascade decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}})+J/\ensuremath{\psi}$, $\ensuremath{\psi}(2S)(\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}})$ and calculate some of the asymmetry parameters that characterize the joint angular decay distribution. We confirm expectations from the naive quark model that the transitions into the ${\ensuremath{\lambda}}_{\ensuremath{\Lambda}}=1/2$ helicity states of the daughter baryon $\ensuremath{\Lambda}$ are strongly suppressed leading to a near maximal negative polarization of the $\ensuremath{\Lambda}$. For the same reason the azimuthal correlation between the two decay planes spanned by ($p{\ensuremath{\pi}}^{\ensuremath{-}}$) and (${\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$) is negligibly small. We provide form factor results for the whole accessible ${q}^{2}$ range. Our results are close to lattice results at minimum recoil and light-cone sum rule results at maximum recoil. A new feature of our analysis is that we include lepton mass effects in the calculation, which allows us to also describe the cascade decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}(\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}})+\ensuremath{\psi}(2S)(\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}})$.

Fragmentation of Heavy Quarks Using Wave Function at the Origin

In this paper we investigate the fragmentation function for heavy quarkanium using a global potential model. We employ the invariant vertex factor under parity, Lorentz transverse and invariant amplitude scattering for the fragmentation function. In the heavy quark limit we have obtained the S-wave analytical fragmentation functions for the heavy mesons at leading order perturbative QCD. The wave function of the bound state for mesons was set at origin of the framework. The fragmentation function is calculated with respect to the Z and Pt variables for m1+m2 and Mexperimental scales. In order to examine the accuracy of our calculations, the obtained results compared to the BFGW method.

Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons

We study the reactions γγ→π 0 π 0, π + π −, $K^{0}\bar{K}^{0}$ , K + K −, ηη and π 0 η based on a chiral Lagrangian with dynamical light vector mesons as formulated within the hadrogenesis conjecture. At present our chiral Lagrangian contains five unknown parameters that are relevant for the photon-fusion reactions. They parameterize the strength of interaction terms involving two vector meson fields. These parameters are fitted to photon-fusion data γγ→π 0 π 0, π + π −,π 0 η and to the decay η→π 0 γγ. In order to derive gauge invariant reaction amplitudes in the resonance region constraints from maximal analyticity and exact coupled-channel unitarity are used. Our results are in good agreement with the existing experimental data from threshold up to about 0.9 GeV for the two-pion final states. The a 0 meson in the π 0 η channel is dynamically generated and an accurate reproduction of the γγ→π 0 η data is achieved up to 1.2 GeV. Based on our parameter sets we predict the γγ→ $K^{0}\bar{K}^{0}$ , K + K −, ηη cross sections.

Temperature Behavior and Compensation of Diode-Based Pre-Distortion Linearizer

This letter presents temperature behavior and compensation technique of Schottky diode and p-i-n diode based pre-distortion linearizer operating at microwave frequency. We have theoretically analyzed and experimentally demonstrated the temperature behavior of the linearizer and proposed a simple but effective temperature compensation technique. The proposed temperature compensation technique provides temperature dependent control bias to the diodes to achieve temperature invariant amplitude and phase expansion of the linearizer. Here design, simulation and test results of a temperature compensated linearizer is presented that compensates amplitude and phase variation from 6 dB and 50° to less than 0.7 dB and 4.5°, respectively, over a temperature range of -20 °C to +80 °C.

Helicity amplitudes for high-energy scattering

Abstract We present a prescription to calculate manifestly gauge invariant tree-level helicity amplitudes for arbitrary scattering processes with off-shell initial-state gluons within the kinematics of high-energy scattering. We show that it is equivalent to Lipatov’s effective action approach, and show its computational potential through numerical calculations for scattering processes with several particles in the final state.