International Journal of Modern Physics A

An adinkra is a graph-theoretic representation of space–time supersymmetry. Minimal four-color valise adinkras have been extensively studied due to their relations to minimal 4D, ${𝒩}=1$ supermultiplets. Valise adinkras, although an important subclass, do not encode all the information present when a 4D supermultiplet is reduced to 1D. Eigenvalue equivalence classes for valise adinkra matrices exist, known as ${\chi }_{\mathrm{\text{o}}}$ equivalence classes, where valise adinkras within the same ${\chi }_{\mathrm{\text{o}}}$ equivalence class are isomorphic in the sense that adinkras within a ${\chi }_{\mathrm{\text{o}}}$-equivalence class can be transformed into each other via field redefinitions of the nodes. We extend this to non-valise adinkras, via Python code, providing a complete eigenvalue classification of “node-lifting” for all 36,864 valise adinkras associated with the Coxeter group $B{C}_4$. We term the eigenvalues associated with these node-lifted adinkras Height Yielding Matrix Numbers (HYMNs) and introduce HYMN equivalence classes. These findings have been summarized in a Mathematica notebook that can be found at the HEPTHools Data Repository on GitHub.

We examine a generic field theory in which the field particle has two couplings. It is of particular interest when these are the electroweak, $e$, and the hypothetical magnetoweak, $g$. The new field operators are obtained by replacing the field operators $\mathrm{\Psi }(x)$ of the Standard Model or of similar models by $\tilde{\mathrm{\Psi }}(x)D_q^j(m,m^{\prime })$ where $D_q^j(m,m^{\prime })$ is an element of the $(2j+1)$-dimensional representation of the SLq(2) algebra, which is also the knot algebra. The new field is assumed to exist in two phases distinguished by two values of $q$: $q_e=\frac{e}{q}$ and $q_g=\frac{g}{q}$ which label the electroweak and magnetoweak phases, respectively.

We assume that the observed leptons and quarks are mainly composed of $e$-preons and are in agreement with the observed charge spectrum of leptons and quarks. It is now proposed that there is also a $g$-phase where $g$-leptons and $g$-quarks are composed of mainly $g$-preons. It is assumed that the $g$-charge is very large compared to the $e$-charge and the mass of the $g$-charged particle is even larger since the mass of all of these particles is partially determined by the eigenvalues of ${\bar{D}}_q^j(m,m^{\prime })D_q^j(m,m^{\prime })$, a polynomial in $q$, that multiplies the Higgs mass term and where

Since these values of $q_g/q_e$ indicate that particles in the $g$-phase are much more massive, they should be harder to produce or to observe. Since the remote parts of the universe are at increasingly higher temperatures, magnetic poles are perhaps most likely to be found in deep probes of space as well as in high energy accelerators.

The section entitled “Introduction” was added only after it was generally realized that the birth of the present universe was probably due to a nuclear explosion.

In the framework of the littlest Higgs Model with T-parity (LHT), we investigate the single production of vector-like top partner $T_{+}$ decaying to $Wb$ in the leptonic channel at the high energy $e\gamma$ collision. We utilize the polarized electron beam and photon beam to enhance the signal and propose a search strategy by performing a detector simulation. On the basis of the current limits from the precision electroweak data and Higgs data, we find that the top partner mass can be excluded up to 1350 (1380) GeV with integrated luminosity of 1000 fb${}^{-1}$ and 1400 (1470) GeV with integrated luminosity of 3000 fb${}^{-1}$ for the $\sqrt{s}=2.0$ TeV (2.4 TeV) at the $2\sigma$ level. If the center-of-mass energy can be improved to 3.0 TeV, the limits on the top partner mass will reach 1450 (1550) GeV with integrated luminosities of 1000 (3000) fb${}^{-1}$.

The recent discovery of a Higgs boson at LHC, while establishing the Higgs mechanism as the way of electroweak symmetry breaking, started an era of precision measurements involving the Higgs boson. In an effective Lagrangian framework, we consider the $e^{+}{e}^{-}\to ZHH$ process, at an ILC running at a center-of-mass energy of 500 GeV to investigate the effect of the $ZZH$ and $ZZHH$ couplings on the sensitivity of $HHH$ coupling on this process. Our results show that the sensitivity of the trilinear Higgs self-couplings on this process has somewhat strong dependence on the Higgs-gauge boson couplings. Single- and two-parameter reaches of ILC with integrated luminosity of 1000 fb${}^{-1}$ are obtained on all the effective couplings indicating how these limits are affected by the presence of anomalous $ZZH$ and $ZZHH$ couplings. The kinematic distributions studied to understand the effect of the anomalous couplings, again, show strong influence of $Z$–$H$ couplings on the dependence of these distributions on $HHH$ coupling. Similar results are indicated in the case of the process, $e^{+}{e}^{-}\to \nu \bar{\nu }HH$, considered at a center-of-mass energy of 2 TeV, where the cross-section is large enough. The effect of $WWH$ and $WWHH$ couplings on the sensitivity of $HHH$ coupling is clearly established through our analyses in this process.

We present the complete azimuthal asymmetries at leading twist in terms of fragmentation functions in dihadron production semi-inclusive electron–positron annihilation process. When the nontrivial $𝜃$ vacuum is taken into consideration, the parity symmetry of quantum chromodynamics is violated. As a consequence of the $local$ ${𝒫}$-odd effects, ${𝒫}$-odd fragmentation functions would contribute to the azimuthal asymmetries. Azimuthal asymmetry coming from two interference terms with opposite signs vanishes when sum over many events. This symmetry only survives on the event-by-event basis. Azimuthal asymmetry coming from two interference terms with same signs survives and can be measured to extract the ${𝒫}$-odd fragmentation functions. We also present the hadron polarizations.

A few exact results concerning topological currents in field theories are obtained. It is generally shown that a topological charge cannot generate any kind of symmetry transformation on fields. It is also proven that the existence of a charge that does not generate any kind of symmetry transformation on fields, has to be of topological origin. As a consequence, it is found that in a given theory, superconductivity via Anderson–Higgs route can only occur if the gauge coupling with other fields is minimal. Several physical implications of these results are studied.

In order to understand the possible physical nature of the newly observed resonance $d^{\ast }(2380)$, we calculate the real photo-absorption cross-section on deuteron contributed by the resonance $d^{\ast }$ by considering the electromagnetic transition amplitude of $\gamma +d\to d^{\ast }(2380)$. In our interpretation, the $d^{\ast }(2380)$ is regarded as a compact six-quark system with mainly two components of $\mathrm{\Delta }\mathrm{\Delta }$ and hidden-color clusters $C_8{C}_8$. We find that only the next-to-leading terms contribute the $\gamma +d\to d^{\ast }(2380)$ and the obtained photo-absorption cross-section is quite small which is in the order of 10 nb. Compared with the data measured at ELPH and Mainz recently, it is almost about 20 times smaller.