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Influence of the Dirac-Hartree-Fock starting potential on the parity-nonconserving electric-dipole-transition amplitudes in cesium and thallium
The parity-nonconserving electric-dipole-transition amplitudes for the 6s1/2-7s1/2 transition in cesium and the 6p1/2-7p1/2 transition in thallium have been calculated by the Dirac-Hartree-Fock method. The effects of using different Dirac-Hartree-Fock atomic core potentials are examined and the transition amplitudes for both the length and velocity gauges are given. It is found that the parity-nonconserving transition amplitudes exhibit a greater dependence on the starting potential for thallium than for cesium.
Non-gauge phase transformations in quantum transition amplitudes
The prescription for introducing a gauge transformation into a quantum transition amplitude, nominally well known, contains an ambiguous feature. It is presumed by some authors that an appropriate transformation of the phase of a wave function will generate the associated gauge transformation. It is shown that this is a necessary but not sufficient step. Examples from the literature are cited to show the consequences of the failure of this procedure. One must distinguish between true gauge transformations and unitary transformations within a fixed gauge.
Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume
We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $\rho$-meson form factor, in which the unstable nature of the $\rho$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.
Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume
We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volume $\textbf{0}\rightarrow\textbf{2}$ and $\textbf{1}\rightarrow\textbf{2}$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $N+\mathcal{J}~\rightarrow~(N\pi,N\eta,N\eta',\Sigma K,\Lambda K)$ transitions, where $\mathcal{J}$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.
Development of One and Two Current Transition Amplitudes with Two Body Final States
One of the biggest challenges facing modern day nuclear physics is understanding the structure of states within the hadronic spectrum of Quantum Chromodynamics (QCD). We have shown this spectrum to be quite rich with hundreds of allowed states; however, if we wish to better grasp the dynamics of QCD, then it is necessary that we start investigating the internal structure of these states. This may be done by probing these states with external currents, but this requires a description of the intersection of QCD with the electroweak sector. This work acts as a stepping stone in this direction. Working to all orders in the strong interaction and to leading order in electroweak effects we present novel formalisms for transition amplitudes with one and two currents with two hadrons in the final state, namely the 2 + J ? 2 and 1 + J ? 2 + J amplitudes. Our results are valid for spinless hadrons with any number of open channels between two- and three-particle threshold, place no restrictions on the Lorentz structure or quantum numbers of the current, and are independent of any underlying model. We also show how this formalism may be used to rigorously access elastic form factors of resonances which has proven challenging to do experimentally. Finally, we present a toy calculation of elastic resonance form factors using the 2 + J ? 2 formalism in which we stress the importance of treating resonances rigorously as poles in the complex plane.
One-loop transition amplitudes in the D1D5 CFT
We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed of the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coeffcients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.
A second look at transition amplitudes in (2 + 1)-dimensional causal dynamical triangulations
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On-shell representations of two-body transition amplitudes: Single external current
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Two-current transition amplitudes with two-body final states
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γvNN^* Transition Amplitudes and Excited Baryon Structure from CLAS
Studying excited nucleon structure through exclusive-meson electroproduction reactions is key for understanding the nature of the strong interaction in the non-perturbative regime. With its nearly complete coverage of the final-state phase space, the CLAS detector at JLab has provided the lion's share of the world's meson-electroproduction data for differential cross sections and the asymmetries arising from single- and double-polarization observables. Electrocouplings for most of the excited nucleon states (N*) in mass range of up to 1.8~GeV have been determined from several analyses of the CLAS data for photon virtualities (Q2) up to 5.0 GeV2 for the pi+n, pi0p, and eta p channels [1,3] as well as for the pi+pi-p reaction for Q2<1.5~GeV2 [2,3]. Physics analyses of these N* electrocouplings [2,3] have revealed that the structure of excited nucleon is formed of an internal core of dressed quarks with an external meson-baryon cloud. Our N*-electrocoupling results afford access to the non-perturbative strong interaction responsible for generating the different N* states and will also provide testing ground for the inspired by QCD quark model predictions. A dedicated experiment will run after the 12 GeV upgrade to JLab on the extraction of the N* electrocouplings in the yet unexplored region of high photon virtualities ranging from 5.0 to 12 GeV2. The anticipated results are of particular importance in providing a understanding of the nature of confinement and dynamical chiral symmetry breaking in baryons based upon the QCD [3].\\[4pt] [1] I.G. Aznauryan and V.D. Burkert, Prog. Part. Nucl. Phys. \textbf{67}, 1 (2012).\\[0pt] [2] V.I. Mokeev \textit{et~al.} (CLAS Collaboration), Phys. Rev. \textbf{C86}, 035203 (2012).\\[0pt] [3] I.G. Aznauryan \textit{et~al.}, ``Studies of Nucleon Resonance Structure in Exclusive Meson Electroproduction,'' arXiv:1212.4891[nucl-th].
Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations
The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.
Multi-channel 1-to-2 transition amplitudes in a finite volume
We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar out-state. Our result, which is valid for energies below higher-particle inelastic thresholds, generalizes the Lellouch-Luscher formula in two ways: we allow the external current to inject arbitrary momentum into the system and we allow for the final state to be composed an arbitrary number of strongly coupled two-particle states with arbitrary partial waves (including partial-wave mixing induced by the volume). We also illustrate how our general result can be applied to some key examples, such as heavy meson decays and meson photo production. Finally, we point out complications that arise involving unstable resonance states, such as B to K*+l+l when staggered or mixed-action/partially-quenched calculations are performed.
Off-Shell Extension of the Partial Wave Transition Amplitude
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TRANSITION AMPLITUDES IN THE N BODY FADDEEV TYPE THEORY
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Helicity Formalism for Transition Amplitudes
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{pi}N transition distribution amplitudes: Their symmetries and constraints from chiral dynamics
Baryon to meson transition distribution amplitudes (TDAs) extend the concept of generalized parton distributions. Baryon to meson TDAs appear as building blocks in the collinear factorized description of amplitudes for a class of hard exclusive reactions, prominent examples of which being hard exclusive meson electroproduction off a nucleon in the backward region and baryon-antibaryon annihilation into a meson and a lepton pair. We study the general properties of these objects following the underlying symmetries of QCD. In particular, the Lorentz symmetry results in the polynomiality property of the Mellin moments in longitudinal momentum fractions. We present a detailed account of the isotopic and permutation symmetry properties of nucleon to pion ({pi}N) TDAs. This restricts the number of independent leading twist {pi}N TDAs to eight functions, providing description of all isotopic channels. Using chiral symmetry and the crossing relation between {pi}N TDAs and {pi}N generalized distribution amplitudes, we establish soft pion theorems for {pi}N TDAs, which determine the magnitude of {pi}N TDAs. Finally, we build a simple resonance exchange model for {pi}N TDAs considering N and {Delta}(1232) exchange contributions into the isospin-(1/2) and isospin-(3/2) {pi}N TDAs.
Baryon to meson transition distribution amplitudes and their spectral representation
We consider the problem of construction of a spectral representation for nucleon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of nonlocal three quark operators between a nucleon and a meson states. We introduce the notion of quadruple distributions and generalize Radyshkin's factorized Ansatz for this issue. Modelling of baryon to meson TDAs in the complete domain of their definition opens the way to quantitative estimates of cross-sections for various hard exclusive reactions.