International Journal of Modern Physics A

Quantum vorticity occurs in superfluidity, which arises from a spatial variation of the quantum phase. As such, it can occur in diverse systems over a wide range of scales, from the electroweak sector and QCD of the standard model of particle theory, through the everyday world, to the cosmos. I review the observable manifestations, and their unified description in terms of an order parameter that is a complex scalar field.

We rederive in a physical manner the Weyl anomaly in two-dimensional space–time by considering the Dirac Sea. It is regularized by some bosonic extra species which are formally negatively counted. In fact, we calculate the trace of the energy–momentum tensor in the Dirac Sea in presence of background gravitational field. It has to be regularized, since the Dirac Sea is bottomless and thus causes divergence. The new regularization method consists in adding various massive bosonic species some of which are to be counted negative in the Dirac Sea. The mass terms in the Lagrangian of the regularization fields have a dependence on the background gravitational field.

With the recent measurements of ${\psi }^{\prime }$ and $\mathrm{J/\psi }$ decay into octet-baryon pairs, we study the relative phase between the strong and the electromagnetic amplitudes, and find a large phase by fitting the present data. The fits take into account the details of experimental effects, including energy spread and initial state radiation. We also predict some branching fractions of ${\psi }^{\prime }$ decays and the continuum production rates at the $\mathrm{J/\psi }$ mass based on the relative phase and absolute amplitudes obtained from the fits.

We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger–Lambert–Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and nonlinear gauges. Remarkably, for Delbourgo–Jarvis–Baulieu–Thierry–Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost–antighost condensation. Further, we discuss the ghost–antighost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.

We introduce the concept of a variational tricomplex, which is applicable both to variational and nonvariational gauge systems. Assigning this tricomplex with an appropriate symplectic structure and a Cauchy foliation, we establish a general correspondence between the Lagrangian and Hamiltonian pictures of one and the same (not necessarily variational) dynamics. In practical terms, this correspondence allows one to construct the generating functional of a weak Poisson structure starting from that of a Lagrange structure. As a byproduct, a covariant procedure is proposed for deriving the classical BRST charge of the BFV formalism by a given BV master action. The general approach is illustrated by the examples of Maxwell’s electrodynamics and chiral bosons in two dimensions.

We reconsider the gauge hierarchy problem from the viewpoint of effective field theories and a high-energy physics, motivated by the alternative scenario that the standard model holds up to a high-energy scale such as the Planck scale. The problem is restated as the question whether it is possible to construct a low-energy effective theory and the interaction with heavy particles, without spoiling the structure of a high-energy physics supported by an excellent concept. Based on this reinterpretation, we give a conjecture that theories with hidden fermionic symmetries can be free from the gauge hierarchy problem and become candidates of the physics beyond and/or behind the standard model, and present toy models with particle-ghost symmetries as illustrative examples and a prototype model for the grand unification.

We study the rare decays $K_L^0\to {\pi }^0\nu \bar{\nu }$, $B^{+}\to {\pi }^{+}\nu \bar{\nu }$, $B^{+}\to K^{\ast +}\nu \bar{\nu }$ and $B\to X_s\nu \bar{\nu }$ for the search of NSIs. We want to constrain the NSIs by using these reactions. We show that there is a strong dependence of these reactions on new physics free parameter ${ϵ}_{\tau \tau }^{QL}$, where $Q=u$, $c$, $t$. We include second and third generation of quarks in the loop for these decays. We show that the $K_L^0\to {\pi }^0\nu \bar{\nu }$ is providing very precise bounds as compared to all other semileptonic decays, having neutrinos in their final state. We further show that the interference between standard model and NSIs is giving dominant contribution for $B^{+}\to {\pi }^{+}\nu \bar{\nu }$, $B^{+}\to K^{\ast +}\nu \bar{\nu }$ and $B\to X_s\nu \bar{\nu }$. We point out that the constraints for ${ϵ}_{\tau \tau }^{cL}$ and ${ϵ}_{\tau \tau }^{tL}$ are more precise as compared to ${ϵ}_{\tau \tau }^{uL}$. The analysis of $B^{+}\to {\pi }^{+}\nu \bar{\nu }$, $B^{+}\to K^{\ast +}\nu \bar{\nu }$ and $B\to X_s\nu \bar{\nu }$, provide us that the $u$-quark induced Br of NSIs are giving very small contribution. We also compare these decays to the decays of charm and kaons having neutrinos in the final state.

The Higgs boson $H$ has the largest coupling to the top quark $t$ among the standard model (SM) fermions. This is one of the ideal places to investigate new physics beyond SM. In this work, we study the potential of determining Higgs boson $CP$ properties at the LHC and future 33 TeV and 100 TeV $pp$ colliders by analyzing various operators formed from final states variables in $t\bar{t}H$ production. The discrimination power from SM coupling is obtained with Higgs boson reconstructed from $H\to \gamma \gamma$ and $H\to b\bar{b}$. We find that $t\bar{t}b\bar{b}$ process can provide more than $3\sigma$ discrimination power with $300{\mathrm{\text{fb}}}^{-1}$ integrated luminosity in a wide range of allowed Higgs to top couplings for the LHC, the 33 TeV and 100 TeV colliders. For $t\bar{t}\gamma \gamma$ the discrimination power will be below $3\sigma$ at the LHC, while for 33 TeV and 100 TeV colliders, more than $3\sigma$ sensitivity can be reached.

Hypernuclei ${}_Y^4\mathrm{\text{He}}$, ${}_Y^4\mathrm{\text{H}}$, ${}_{YY}^4\mathrm{\text{He}}$, ${}_{YY}^4\mathrm{\text{H}}$, where $Y=\Lambda$, ${\Sigma }_0$, ${\Sigma }_{+}$, ${\Sigma }_{-}$, with the atomic (baryon) number $A=B=4$, are described by the relativistic twelve-quark equations in the framework of the dispersion relation technique. Hypernuclei as the systems of interacting quarks and gluons are considered. The relativistic twelve-quark amplitudes of hypernuclei, including the constituent quarks of three flavors $u$, $d$, $s$ are calculated. The approximate solutions of these equations are obtained using a method based on extraction of leading singularities of the amplitudes. The poles of the multiquark amplitudes allow us to determine the masses and the binding energy of hypernuclei with $A=4$. The mass and the binding energy of state ${}_{\Lambda \Lambda }^4\mathrm{\text{H}}$ with the isospin projection $I_3=0$ and the spin-parity $J^P=0^{+}$ is equal to $M=4118\mathrm{\text{MeV}}$ and $B=-8\mathrm{\text{MeV}}$, respectively. We predict the mass spectrum of hypernuclei with $A=4$, which is valuable for further experimental study of the hypernuclei.