Intrinsic Parity Research Articles

19pAL-10 Tau and Hadron decay with intrinsic parity violation in Resonance Chiral Lagrangian

19pAL-10 Tau and Hadron decay with intrinsic parity violation in Resonance Chiral Lagrangian

Study of an anomalous tau lepton decay using a chiral Lagrangian with vector mesons

The hadronic tau decay τ−→ντηπ−π0 occurs through V-A weak current. In this decay mode, the vector current contribution is intrinsic parity violating and the axial current contribution is G parity violating. The latter contribution is suppressed due to tiny isospin breaking. We have computed both vector and axial vector form factors using a chiral Lagrangian with vector mesons including the effect of isospin breaking and intrinsic parity violation. A numerical result of the invariant mass distribution is shown and the structure of ρ resonance can be seen in the distribution with respect to Mπ−π0.

Mortality, ethnicity, and education in an occupational cohort

Purpose – The purpose of this paper is to investigate the relationship between occupational degree requirement and mortality between ethnic groups in a cohort of urban workers. Design/methodology/approach – The study included 118,606 health-insured full-time workers from the New York City Health and Hospitals Corporation (HHC). Mortality rates (MR) and mortality rate ratios (MRR) were calculated for major ethnic categories. Estimates were adjusted for age, sex, and occupational degree requirement. Findings – Prior to adjustment for degree requirement, mortality rates (MRs) by ethnic groups in the Health and Hospitals Corporation were in line with national estimates: highest for blacks, followed by whites, Hispanics, and Asian/Pacific Islander (APIs). After adjustment, the MR for blacks became comparable to whites (mortality rate ratio (MRR)=1.02). The low-Hispanic MR did not change; the Hispanic advantage persisted (MRR=0.66), as did the API advantage (MRR=0.50). Research limitations/implications – Higher education may not substantially change the MR for Hispanics, and it may only account for a portion of the survival advantage among APIs. The findings also suggest that without reducing the disparity in higher education attainment between blacks and whites, equality in other socioeconomic factors may not abolish the disparity in mortality between these groups. Originality/value – This study bypassed common limitations of ethnic mortality studies, with intrinsic parity for certain socio-economic status factors (full-time employment and health care access) across cohort members and consistent ethnic classification across time-points. This includes a cohort of API workers with complete self-identification of ethnicity, which has not been accomplished by previous investigations.

Relativistic dynamics compels a thermalized fermi gas to a unique intrinsic parity eigenstate

The Dirac equation describes the dynamics of a relativistic spin-1/2 particle regarding its spatial motion and intrinsic degrees of freedom. Here we adopt the point of view that the spinors describe the state of a massive particle carrying two qubits of information: helicity and intrinsic parity. We show that the density matrix for a gas of free fermions, in thermal equilibrium, correlates helicity and intrinsic parity. Our results introduce the basic elements for discussing the spin-parity correlation for a Fermi gas: (1) at the ultra-relativistic domains, when the temperature is quite high, , the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature, K, a unique parity dominates (conventionally chosen positive), by to 1, while the helicity goes into a mixed state for spin up and down, and the quantum correlation decoheres. For the antifermions we get the opposite behavior. In the framework of quantum information, our result could be considered as a plausible explanation of why we accept, as a fact (consistent with the experimental observation), that fermions (and antifermions), in our present epoch of a cool universe, have a unique intrinsic parity. The framework for constructing spin-parity entangled states is established.

P stabilizes dark matter and with CP can predict leptonic phases

We find that spontaneously broken parity (P) or left-right symmetry stabilizes dark matter in a beautiful way. If dark matter has a non-real intrinsic parity \pm i (e.g. Majorana fermions), parity can ensure that it cannot decay to all normal particles with real intrinsic parities. However if Majorana couplings are absent either in the Lepton or the dark sector, P symmetry can be redefined to remove relative non-real intrinsic phases. It is therefore predicted that neutrinos and dark matter fermions must have Majorana masses if dark matter is stable due to parity. We also consider vectorlike doublet fermions with intrinsic parity \pm i. Strong CP problem is solved by additionally imposing CP. Leptonic CP phases vanish at the tree level in the minimal strong CP solving model, which is a testable prediction. Experimentally if leptonic CP phases are not found (they are found to be consistent with 0 or \pi) it can be evidence for the type of models in this work where CP is spontaneously or softly broken and there is also a second hidden or softly broken symmetry such as P, Z_2 or Z_4. However leptonic CP violation can be present in closely related or some non-minimal versions of these models.

Low-lying pseudoscalar and vector mesons and their dynamics

In chiral perturbation theory, the leading-order contribution to reactions with pions in the sector of odd intrinsic parity is defined by the Wess-Zumino-Witten structure. This structure is supplemented by a simple vector-meson Lagrangian where the vector mesons are described by antisymmetric tensor fields. With the rho-omega-pion coupling as the only parameter in the sector of odd intrinsic parity, i.e. without additional contact terms, one can achieve a proper description of the single- and double-virtual pion transition form factor and the three-pion production in electron-positron collisions.

Reactions with pions and vector mesons in the sector of odd intrinsic parity

In chiral perturbation theory, the leading-order contribution to reactions with pions in the sector of odd intrinsic parity is defined by the Wess-Zumino-Witten structure. This structure is supplemented by a simple vector-meson Lagrangian where the vector mesons are described by antisymmetric tensor fields. With the rho-omega-pion coupling as the only parameter in the sector of odd intrinsic parity, i.e. without additional contact terms, one can achieve a proper description of the pion transition form factor and the three-pion production in electron-positron collisions.

Reactions with pions and vector mesons in the sector of odd intrinsic parity

The Wess-Zumino-Witten structure is supplemented by a simple vector-meson Lagrangian where the vector mesons are described by antisymmetric tensor fields. With the \rho-\omega-\pi{} coupling as the only parameter in the sector of odd intrinsic parity, i.e. without additional contact terms, one can achieve a proper description of the decay of an \omega-meson into three pions, the single- and double-virtual pion transition form factor and the three-pion production in electron-positron collisions.

Holography, chiral Lagrangian and form factor relations

We derive all the $ \mathcal{O}\left( {{p^6}} \right) $ Chiral Perturbation Theory low-energy constants from a class of gravity dual models of QCD described by the Yang-Mills and Chern-Simons Lagrangian terms, with the chiral symmetry broken through boundary conditions in the infrared. All the constants of the odd intrinsic parity sector are universally determined by those at $ \mathcal{O}\left( {{p^4}} \right) $ in the even sector, together with an extra resonance term. A few relations for the even sector couplings are also extracted. Our estimates reasonably agree with the few available $ \mathcal{O}\left( {{p^6}} \right) $ determinations from alternative phenomenological analyses. Some of the relations between low-energy constants are the manifestation, at large distances, of universal relations that we find between form factors in the even and odd sectors, e.g., between the γ * → ππ and π → γγ * matrix elements.

Holographic QCD integrated back to hidden local symmetry

We develop a previously proposed gauge-invariant method to integrate out infinite tower of Kaluza-Klein (KK) modes of vector and axialvector mesons in a class of models of holographic QCD (HQCD). The HQCD is reduced by our method to the chiral perturbation theory with the hidden local symmetry (HLS) having only the lowest KK mode identified as the HLS gauge boson. We take the Sakai-Sugimoto model as a concrete HQCD, and completely determine the ${\cal O} (p^4)$ terms as well as the ${\cal O}(p^2)$ terms from the DBI part and the anomaly-related (intrinsic parity odd) gauge-invariant terms from the CS part. Effects of higher KK modes are fully included in these terms. To demonstrate power of our method, we compute momentum-dependences of several form factors such as the pion electromagnetic form factors, the $\pi^0$-$\gamma$ and $\omega$-$\pi^0$ transition form factors compared with experiment, which was not achieved before due to complication to handle infinite sums. We also study other anomaly-related quantities like $\gamma^*$-$\pi^0$-$\pi^+$-$\pi^-$ and $\omega$-$\pi^0$-$\pi^+$-$\pi^-$ vertex functions.

TheCoperator inPT-symmetric quantum field theory transforms as a Lorentz scalar

A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorentz group as a scalar.

On the intrinsic parity of black holes

We investigate the intrinsic parity of black holes. It appears that discrete symmetries require the black hole Hilbert space to be larger than suggested by the usual quantum numbers M (mass), Q (charge) and J (angular momentum). Recent results on black hole production in trans-Planckian scattering lead to gravitational effects which do not decouple from low-energy physics. Dispersion relations incorporating these effects imply that the semi-classical black hole spectrum is similar in parity even and odd channels. This result can be generalized to other discrete and continuous symmetries.

Superfluid and conformal phase transitions of two-color QCD

The phase structure of two-color QCD is examined as a function of the chemical potential and the number of light quark flavors. We consider effective Lagrangians for two-color QCD containing the Goldstone excitations, spin-one particles and negative intrinsic parity terms. We discuss the possibility of a conformal phase transition and the enhancement of the global symmetries as the number of flavors is increased. The effects of a quark chemical potential on the spin-one particles and on the negative intrinsic parity terms are analyzed. It is shown that the phase diagram that is predicted by the linearly realized effective Lagrangian at tree-level matches exactly that predicted by chiral perturbation theory.

THE PIN GROUPS IN PHYSICS: C, P AND T

A simple, but not widely known, mathematical fact concerning the coverings of the full Lorentz group sheds light on parity and time reversal transformations of fermions. Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which cover the full Lorentz group. Pin(1, 3) is to O(1, 3) what Spin(1, 3) is to SO(1, 3). The existence of two Pin groups offers a classification of fermions based on their properties under space or time reversal finer than the classification based on their properties under orientation preserving Lorentz transformations — provided one can design experiments that distinguish the two types of fermions. Many promising experimental setups give, for one reason or another, identical results for both types of fermions. These negative results are reported here because they are instructive. Two notable positive results show that the existence of two Pin groups is relevant to physics: • In a neutrinoless double beta decay, the neutrino emitted and reabsorbed in the course of the interaction can only be described in terms of Pin(3, 1). • If a space is topologically nontrivial, the vacuum expectation values of Fermi currents defined on this space can be totally different when described in terms of Pin(1, 3) and Pin(3, 1). Possibly more important than the two above predictions, the Pin groups provide a simple framework for the study of fermions; it makes possible clear definitions of intrinsic parities and time reversal; it clarifies colloquial, but literally meaningless, statements. Given the difference between the Pin group and the Spin group it is useful to distinguish their representations, as groups of transformations on "pinors" and 'spinors", respectively. The Pin(1, 3) and Pin(3, 1) fermions are twin-like particles whose behaviors differ only under space or time reversal. A section on Pin groups in arbitrary spacetime dimensions is included.

(1/2, 1/2) REPRESENTATION SPACE — AN ab initio CONSTRUCT

A careful ab initio construction of the finite-mass (1/2, 1/2) representation space of the Lorentz group reveals it to be a spin-parity multiplet. In general, it does not lend itself to a single-spin interpretation. We find that the (1/2, 1/2) representation space for massive particles naturally bifurcates into a triplet and a singlet of opposite relative intrinsic parties. The textbook separation into spin-1 and spin-0 states occurs only for certain limited kinematical settings. We construct a wave equation for the (1/2, 1/2) multiplet, and show that the particles and antiparticles in this representation space do not carry a definite spin but only a definite relative intrinsic parity. In general, both spin-1 and spin-0 are covariantly inseparable inhabitants of massive vector fields. This last observation suggests that scalar particles, such as the Higgs, are natural inhabitants of massive (1/2, 1/2) representation space.

Different Quantum Field Constructions in the (1/2,0) ⊕ (0,1/2) Representation

We present another concrete realization of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner. Considering the special case of the (1/2,0)⊕ (0,1/2) field and developing the Majorana–McLennan–Case–Ahluwalia construction for neutrino, we show that fermion and its antifermion can have the same intrinsic parity. The construction can be applied to explain the present situation in neutrino physics.

Solution of the Skyrme—Hartree—Fock equations in the Cartesian deformed harmonic oscillator basis II. The program HFODD

We describe the code HFODD which solves the nuclear Skyrme—Hartree—Fock problem by using the deformed Cartesian harmonic oscillator basis. The user has a possibility of choosing among various symmetries of the nuclear HF problem for rotating or nonrotating nuclei; they vary from the non-axial parity-invariant nuclear shapes, through those also breaking the intrinsic parity, towards the least-restrictive case corresponding to only one symmetry plane. The code provides a solution for a complete superdeformed rotational band in an A ∼ 150 nucleus within one CPU hour of the CRAY C-90 supercomputer or within two-three CPU hours of a fast workstation.

Complete leading order analysis in chiral perturbation theory of the decays KL → γγ and KL → ℓ +ℓ −γ

The decays K L → γγ and K L → ℓ +ℓ − γ are studied at the leading order p 6 in chiral perturbation theory. One-loop contributions stemming from the odd intrinsic parity | ΔS| = 1 effective Lagrangian of order p 4 are included and shown to be of possible relevance. They affect the decay K L → γγ adding to the usual pole terms a piece free of counterterm uncertainties. In the case of the K L → ℓ +ℓ − γ decays the dependence of the form factor on the dilepton invariant mass requires a counterterm. The form factor may receive a sizeable contribution from chiral logarithms. Including considerations from the K L → π + π − γ direct emission amplitude, we obtain two consistent scenarios. In one scenario the long distance contributions from the one-loop terms are important, while in the other they are marginal. In both cases the counterterm is shown to be significant.

THEORY OF NEUTRAL PARTICLES: MCLENNAN-CASE CONSTRUCT FOR NEUTRINO, ITS GENERALIZATION, AND A NEW WAVE EQUATION

Continuing our recent argument where we constructed a FNBWW type spin-1 boson having opposite relative intrinsic parity to that of the associated antiparticle, we now study eigenstates of the charge conjugation operator. Based on the observation that if ϕL(pμ) transforms as a (0, j) spinor under Lorentz boosts, then [Formula: see text] transforms as a (j, 0) spinor [with a similar relationship existing between ϕR(pμ) and [Formula: see text] where w ith Θ[j] the well-known Wigner matrix involved in the operation of time reversal] we introduce McLennan-Case type (j, 0)⊗(0, j) spinors. Relative phases between ϕR(pμ) and [Formula: see text] and [Formula: see text] and ϕL(pμ), turn out to have physical significance and are fixed by appropriate requirements. An explicit construction, and a series of physically relevant properties, for these spinors are obtained for spin-1/2 and spin-1 culminating in the construction of a new wave equation and the introduction of Dirac-like and Majorana-like quantum fields.

Extension of the chiral perturbation theory meson Lagrangian to order p6.

We have derived the most general chirally invariant Lagrangian ${\cal L}_6$ for the meson sector at order $p^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\cal L}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion' terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating $p^6$ contributions to simple processes.