Conjugation Invariance Research Articles

Theoretical examination of QED Hamiltonian in relativistic molecular orbital theory.

Theoretical discussions are given on issues in relativistic molecular orbital theory to which the quantum electrodynamics (QED) Hamiltonian is applied. First, several QED Hamiltonians previously proposed are sifted by the orbital rotation invariance, the charge conjugation and time reversal invariance, and the nonrelativistic limit. The discussion on orbital rotation invariance shows that orbitals giving a stationary point of total energy should be adopted for QED Hamiltonians that are not orbital rotation invariant. A new total energy expression is then proposed, in which a counter term corresponding to the energy of the polarized vacuum is subtracted from the total energy. This expression prevents the possibility of total energy divergence due to electron correlations, stemming from the fact that the QED Hamiltonian does not conserve the number of particles. Finally, based on the Hamiltonian and energy expression, the Dirac-Hartree-Fock (DHF) and electron correlation methods are reintroduced. The QED-based DHF equation is shown to give information on positrons from negative-energy orbitals while having the same form as the conventional DHF equation. Three electron correlation methods are derived: the QED-based configuration interactions and single- and multireference perturbation methods. Numerical calculations show that the total energy of the QED Hamiltonian indeed diverged and that the counter term is effective in avoiding the divergence. The relativistic molecular orbital theory presented in this article also provides a methodology for dealing with systems containing positrons based on the QED Hamiltonian.

Precision measurement of the matrix elements for η→π+π−π0 and η→π0π0π0 decays

A precision measurement of the matrix elements for $\eta\to\pi^+\pi^-\pi^0$ and $\eta\to\pi^0\pi^0\pi^0$ decays is performed using a sample of $(10087\pm44)\times10^6$ $J/\psi$ decays collected with the BESIII detector. The decay $J/\psi \to \gamma \eta$ is used to select clean samples of 631,686 $\eta\to\pi^+\pi^-\pi^0$ decays and 272,322 $\eta\to\pi^0\pi^0\pi^0$ decays. The matrix elements for both channels are in reasonable agreement with previous measurements. The non-zero $gX^2Y$ term for the decay mode $\eta\to\pi^+\pi^-\pi^0$ is confirmed, as reported by the KLOE Collaboration, while the other higher-order terms are found to be insignificant. Dalitz plot asymmetries in the $\eta\to\pi^+\pi^-\pi^0$ decay are also explored and are found to be consistent with charge conjugation invariance. In addition, a cusp effect is investigated in the $\eta\to\pi^0\pi^0\pi^0$ decay, and no obvious structure around the $\pi^+\pi^-$ mass threshold is observed.

Perturbative QCD analysis of exclusive processes e+e−→VP and e+e−→TP

We study the $e^+e^-\to VP$ and $e^+e^-\to TP$ processes in the perturbative QCD approach based on $k_T$ factorization, where the $P,V$ and $T$ denotes a light pseudo-scalar, vector and tensor meson, respectively. We point out in the case of $e^+e^-\to TP$ transition due to charge conjugation invariance, only three channels are allowed: $e^+e^-\to a_2^{\pm} \pi^\mp$, $e^+e^-\to K_2^{*\pm} K^\mp$ and the V-spin suppressed $e^+e^-\to K_2^{*0} \bar K^0+\overline K_2^{*0} K^0 $. Cross sections of $e^+e^-\to VP$ and $e^+e^-\to TP$ at $\sqrt{s}=3.67$ GeV and $\sqrt{s}=10.58$ GeV are calculated and the invariant mass dependence is found to favor the $1/s^4$ power law. Most of our theoretical results are consistent with the available experimental data and other predictions can be tested at the ongoing BESIII and forthcoming Belle-II experiments.

Dissipative hydrodynamics with higher-form symmetry

A theory of parity-invariant dissipative fluids with q-form symmetry is formulated to first order in a derivative expansion. The fluid is anisotropic with symmetry SO(D − 1 − q) × SO(q) and carries dissolved q-dimensional charged objects that couple to a (q + 1)-form background gauge field. The case q = 1 for which the fluid carries string charge is related to magnetohydrodynamics in D = 4 spacetime dimensions. We identify q+7 parity-even independent transport coefficients at first order in derivatives for q > 1. In particular, compared to the q = 1 case under the assumption of parity and charge conjugation invariance, fluids with q > 1 are characterised by q extra transport coefficients with the physical interpretation of shear viscosity in the SO(q) sector and current resistivities. We discuss certain issues related to the existence of a hydrostatic sector for fluids with higher-form symmetry for any q ≥ 1. We extend these results in order to include an interface separating different fluid phases and study the dispersion relation of capillary waves finding clear signatures of anisotropy. The formalism developed here can be easily adapted to study hydrodynamics with multiple higher-form symmetries.

Baryogenesis in nonminimally coupled f(R) theories

We generalize the mechanism for gravitational baryogensis in the context of $f(R)$ theories of gravity, including a nonminimal coupling between curvature and matter. In these models, the baryon asymmetry is generated through an effective coupling between the Ricci scalar curvature and the net baryon current that dynamically breaks Charge Conjugation, Parity and Time Reversal (CPT) invariance. We study the combinations of characteristic mass scales and exponents for both non-trivial functions present in the modified action functional and establish the allowed region for these parameters: we find that very small deviations from General Relativity are consistent with the observed baryon asymmetry and lead to temperatures compatible with the subsequent formation of the primordial abundances of light elements. In particular, we show the viability of a power-law nonminimal coupling function $f_2(R) \sim R^n$ with $ 0 < n \lesssim 0.078 $ and determine its characteristic curvature scale.

Prompt photon yield and elliptic flow from gluon fusion induced by magnetic fields in relativistic heavy-ion collisions

We compute photon production at early times in semi-central relativistic heavy-ion collisions from non-equilibrium gluon fusion induced by a magnetic field. The calculation accounts for the main features of the collision at these early times, namely, the intense magnetic field and the high gluon occupation number. The gluon fusion channel is made possible by the magnetic field and would otherwise be forbidden due to charge conjugation invariance. Thus, the photon yield from this process is an excess over calculations without magnetic field effects. We compare this excess to the difference between PHENIX data and recent hydrodynamic calculations for the photon transverse momentum distribution and elliptic flow coefficient $v_2$. We show that with reasonable values for the saturation scale and magnetic field strength, the calculation helps to better describe the experimental results obtained at RHIC energies for the lowest part of the transverse photon momentum.

Entanglement entropy and Möbius transformations for critical fermionic chains

Entanglement entropy may display a striking new symmetry under Möbius transformations. This symmetry was analysed in our previous work for the case of a non-critical (gapped) free homogeneous fermionic chain invariant under parity and charge conjugation. In the present work we extend and analyse this new symmetry in several directions. First, we show that the above mentioned symmetry also holds when parity and charge conjugation invariance are broken. Second we extend this new symmetry to the case of critical (gapless) theories. Our results are further supported by numerical analysis. For some particular cases, analytical demonstrations show the validity of the extended symmetry. We finally discuss the intriguing parallelism of this new symmetry and space-time conformal transformations.

Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the covariant spectator theory

The pion form factor is calculated in the framework of the charge-conjugation invariant Covariant Spectator Theory. This formalism is established in Minkowski space and the calculation is set up in momentum space. In a previous calculation we included only the leading pole coming from the spectator quark (referred to as the relativistic impulse approximation). In this paper we also include the contributions from the poles of the quark which interacts with the photon and average over all poles in both the upper and lower half planes in order to preserve charge conjugation invariance (referred to as the $C$-symmetric complete impulse approximation). We find that for small pion mass these contributions are significant at all values of the four-momentum transfer $Q^2$ but, surprisingly, do not alter the shape obtained from the spectator poles alone.

Unified Wigner–Ville distribution and ambiguity function in the linear canonical transform domain

In this paper, we propose a novel integral transform by combining the generalized Wigner–Ville distribution (WDL) with the linear canonical transform (LCT). The new integral transform unifies the WDL and the generalized ambiguity function (AFL), and then can be considered as a generalization of the classical Wigner–Ville distribution (WVD) and ambiguity function (AF). Some useful properties of the new integral transform are derived, including conjugation symmetry property, conjugation invariance of LCT, marginal properties, shifting properties, anti-derivative property and Moyal formula. The relationships between the new integral transform and other common time–frequency analysis tools are discussed, such as the LCT, the short-time Fourier transform (STFT) and the short-time linear canonical transform (STLCT). The applications of the newly defined integral transform in the detection of one-component and bi-component linear frequency-modulated (LFM) signals embedded in white Gaussian noise are investigated. The comparisons of the detection performance of the new integral transform with that of the WDL and AFL are also performed to show the preponderance of the proposed techniques. The simulation results indicate that the new integral transform achieves better detection performance than the WDL and AFL.

Relativistic Stark resonances in a simple exactly soluble model for a diatomic molecule

A simple 1D relativistic model for a diatomic molecule with a double-point interaction potential is solved exactly in a constant electric field. The Weyl–Titchmarsh–Kodaira method is used to evaluate the spectral density function, allowing the correct normalization of continuum states. The boundary conditions at the potential wells are evaluated using Colombeau’s generalized function theory along with charge conjugation invariance and general properties of self-adjoint extensions for point-like interactions. The resulting spectral density function exhibits resonances for quasi-bound states, which move in the complex energy plane as the model parameters are varied. It is observed that for a monotonically increasing interatomic distance, the ground-state resonance can either go deeper into the negative continuum or can give rise to a sequence of avoided crossings, depending on the strength of the potential wells. For the sufficiently low electric field strength or small interatomic distance, the behavior of resonances is qualitatively similar to non-relativistic results.

Test of charge conjugation invariance in the decay of theηmeson intoπ+π−π0

In this work we present the preliminary results of the analysis of the pp->pp eta(->pp pi(+)pi(-)pi(0) reaction aiming to test the charge conjugation symmetry C in strong interactions. Based on approximately $10^5$ identified eta->pi(+)pi(-)pi(0) decay events we have extracted asymmetry parameters sensitive to C symmetry violation for different isospin values of the final state and we have established that all are consistent with zero within the obtained accuracy.

Symmetry and mass degeneration in multi-Higgs-doublet models

We investigate possible symmetry properties of the scalar sector of Multi-Higgs-Doublet Models, and, to some extent, the generalization of such models to gauge groups other than SU(2) L × U(1) Y . In models with C (charge conjugation) invariance, and where certain quartic terms are not present, the scalar potential is invariant under a group larger than the gauge group, O(4) when the Higgs fields are doublets. If the Higgs fields develop aligned vacuum expectation values, this symmetry will break to an O(3) subgroup, which in general is further broken by loop corrections involving the gauge bosons. Assuming such corrections are small, the physical properties of the Higgs sector will approximately organize into representations of SO(3). If the vacuum expectation values of the Higgs fields are aligned in the direction of the C even fields, the mass spectra of the charged and C odd sectors will be degenerate. Moreover, if the Higgs fields develop a pair of non-aligned vacuum expectation values, so that the charge conjugation symmetry is spontaneously broken (but not the U(1) electromagnetic gauge invariance), a pair of light charged pseudo-Goldstone bosons will appear.

κ-DEFORMED DIRAC EQUATION

We construct a Dirac equation in κ-Minkowski spacetime and analyze its implications. This κ-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, a. We show that the κ-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the hydrogen atom spectrum is modified due to the κ-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter a, which are a few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

Formation of antihydrogen in the ground state

Cross sections for antihydrogen formation in the ground state for the process [Formula: see text] + Ps(nlm) → [Formula: see text](1s) + e– have been calculated using charge conjugation and time reversal invariance. Calculations are based on a two-state approximation method, used by the author earlier for positron–hydrogen charge -exchange process (e+ – H → Ps(nlm) + p). Cross-section results are reported in the intermediate- and high-energy region (20 keV – 500 keV). PACS No.: 36.10.Dr

Pomeron-Quark Coupling from Charge ConjugationInvariance

Based on the charge conjugation invariance and the vacuum propertyof the Pomeron, we point out that the commonly used vector vertexof the Pomeron coupling to quark is incorrect since it contradictswith the Pomeron property. We also claim that the soft Pomeroncould be a tensor glueball ξ(2230) with quantum numbersIGJPC = 0+2++ and total decay widthΓtot≃100 MeV, which lies on the soft Pomerontrajectory αp = 1.08+0.20t. Therefore, the couplingvertex of the soft Pomeron to quark should be tensorial which isinvariant under the charge conjugation and can explain why theinadequate vector coupling, γμ, of the soft Pomeron toquark is successful in dealing with Pomeron physics.

Charge conjugation invariance of the vacuum and the cosmological constant problem

We propose a method of field quantization which uses an indefinite metric in a Hilbert space of state vectors. The action for gravity and the standard model includes, as well as the positive energy fermion and boson fields, negative energy fields. The Hamiltonian for the action leads through charge conjugation invariance symmetry of the vacuum to a cancellation of the zero-point vacuum energy and a vanishing cosmological constant in the presence of a gravitational field. To guarantee the stability of the vacuum, we introduce a Dirac sea “hole” theory of quantization for gravity as well as the standard model. The vacuum is defined to be fully occupied by negative energy particles with a hole in the Dirac sea, corresponding to an anti-particle. We postulate that the negative energy bosons in the vacuum satisfy a para-statistics that leads to a para-Pauli exclusion principle for the negative energy bosons in the vacuum, while the positive energy bosons in the Hilbert space obey the usual Bose–Einstein statistics. This assures that the vacuum is stable for both fermions and bosons. Restrictions on the para-operator Hamiltonian density lead to selection rules that prohibit positive energy para-bosons from being observable. The problem of deriving a positive energy spectrum and a consistent unitary field theory from a pseudo-Hermitian Hamiltonian is investigated.

Test of Charge Conjugation Invariance

We report on the first determination of upper limits on the branching ratio (BR) of eta decay to pi0pi0gamma and to pi0pi0pi0gamma. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(eta-->pi0pi0gamma)<5 x 10(-4) at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(eta-->pi0pi0pi0gamma)<6 x 10(-5) at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions.

Broken symmetries and dilepton production from gluon fusion in a quark gluon plasma

The observational consequences of certain broken symmetries in a thermalised quark gluon plasma are elucidated. The signature under study is the spectrum of dileptons radiating from the plasma, through gluon fusion. Being a pure medium effect, this channel is non-vanishing only in plasmas with explicitly broken charge conjugation invariance. The emission rates are also sensitive to rotational invariance through the constraints imposed by Yang's theorem. This theorem is interpreted in the medium via the destructive interference between various multiple scattering diagrams obtained in the spectator picture. Rates from the fusion process are presented in comparison with those from the Born term.

A strategy for the analysis of semi-inclusive deep inelastic scattering

We present a strategy for the systematic extraction of a vast amount of detailed information on polarized parton densities and fragmentation functions from semi-inclusive deep inelastic scattering l + N → l + h + X , in both LO and NLO QCD. A method is suggested for estimating the errors involved in the much simpler, and therefore much more attractive, LO analysis. The approach is based upon a novel interplay with data from inclusive DIS and from e + e − → hX , and leads to a much simplified form of the NLO expressions. No assumptions are made about the equality of any parton densities and the only symmetries utilised are charge conjugation invariance and isotopic spin invariance of strong interactions.

Charge-Conjugation Invariance of the Spectator Equations

In response to recent critcism, we show how to define the spectator equations for negative energies so that charge conjugation invariance is preserved. The result, which emerges naturally from the application of spectator principles to systems of particles with negative energies, is to replace all factors of the external energies $W_i$ by $\sqrt{W^2_i}$, insuring that the amplitudes are independent of the sign of the energies $W_i$.