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Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 137
Author(s):  
Vadim V. Varlamov ◽  
Larisa D. Pavlova ◽  
Olga S. Babushkina

The group theoretical description of the periodic system of elements in the framework of the Rumer–Fet model is considered. We introduce the concept of a single quantum system, the generating core of which is an abstract C*-algebra. It is shown that various concrete implementations of the operator algebra depend on the structure of the generators of the fundamental symmetry group attached to the energy operator. In the case of the generators of the complex shell of a group algebra of a conformal group, the spectrum of states of a single quantum system is given in the framework of the basic representation of the Rumer–Fet group, which leads to a group-theoretic interpretation of the Mendeleev’s periodic system of elements. A mass formula is introduced that allows giving the termwise mass splitting for the main multiplet of the Rumer–Fet group. The masses of elements of the Seaborg table (eight-periodic extension of the Mendeleev table) are calculated starting from the atomic number Z=3 and going to Z=220. The continuation of the Seaborg homology between lanthanides and actinides is established with the group of superactinides. A 10-periodic extension of the periodic table is introduced in the framework of the group-theoretic approach. The multiplet structure of the extended table’s periods is considered in detail. It is shown that the period lengths of the system of elements are determined by the structure of the basic representation of the Rumer–Fet group. The theoretical masses of the elements of 10th and 11th periods are calculated starting from Z=221 and going to to Z=364. The concept of hypertwistor is introduced.


Author(s):  
S. Haddad

The effective nucleon mass splits into two components, one for the proton and another for the neutron, in the case of adding the isovector coupling channel of the nuclear interaction, while being the same in the case of considering only the isoscalar coupling. A quantitative measure of the splitting is defined by the root mean square (RMS) value of the effective nucleon mass splitting and applied to the effective nucleon mass splitting in lead and tin isotopes. The isospin splitting of the effective nucleon mass is found to increase almost linearly with the asymmetry parameter.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Bin Zhu ◽  
Murat Abdughani

Abstract The existence of a light mediator is beneficial to some phenomena in astroparticle physics, such as the core-cusp problem and diversity problem. It can decouple from Standard Model to avoid direct detection constraints, generally realized by retard decay of the mediator. Their out-of-equilibrium decay process changes the dark matter (DM) freeze-out via temperature discrepancy. This type of hidden sector (HS) typically requires a precision calculation of the freeze-out process considering HS temperature evolution and the thermal average of the cross-section. If the mediator is light sufficiently, we can not ignore the s-wave radiative bound state formation process from the perspective of CMB ionization and Sommerfeld enhancement. We put large mass splitting between DM and mediator, different temperature evolution on the same theoretical footing, discussing the implication for DM relic density in this HS. We study this model and illustrate its property by considering the general Higgs-portal dark matter scenario, which includes all the relevant constraints and signals. It shows that the combination of BBN and CMB constraint favors the not-too-hot HS, rinf< 102, for the positive cubic interaction of mediator scenario. On the other hand, the negative cubic interaction is ruled out except for our proposed blind spot scenario.


2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Bikash Thapa ◽  
Ng. K. Francis

AbstractWe present an S$$_4$$ 4 flavour symmetric model within a minimal seesaw framework resulting in mass matrices that leads to TM$$_1$$ 1 mixing. Minimal seesaw is realized by adding two right-handed neutrinos to the Standard Model. The model predicts Normal Hierarchy (NH) for neutrino masses. Using the constrained six-dimensional parameter space of the model, we have evaluated the effective Majorana neutrino mass, which is the parameter of interest in neutrinoless double beta decay experiments. The possibility of explaining baryogenesis via resonant leptogenesis is also examined within the model. A non-zero, resonantly enhanced CP asymmetry generated from the decay of right-handed neutrinos at the TeV scale is studied, considering flavour effects. The evolution of lepton asymmetry is discussed by solving the set of Boltzmann equations numerically and obtain the value of baryon asymmetry to be $$|\eta _B| = 6.3 \times 10^{-10}$$ | η B | = 6.3 × 10 - 10 with the choice of right-handed neutrino mass, $$M_1 = 10$$ M 1 = 10 TeV and mass splitting, $$d \simeq 10^{-8}$$ d ≃ 10 - 8 .


2021 ◽  
Vol 81 (10) ◽  
Author(s):  
C. Cazzaniga ◽  
P. Odagiu ◽  
E. Depero ◽  
L. Molina Bueno ◽  
Yu. M. Andreev ◽  
...  

AbstractWe report the results of a search for a new vector boson ($$ A'$$ A ′ ) decaying into two dark matter particles $$\chi _1 \chi _2$$ χ 1 χ 2 of different mass. The heavier $$\chi _2$$ χ 2 particle subsequently decays to $$\chi _1$$ χ 1 and an off-shell Dark Photon $$ A'^* \rightarrow e^+e^-$$ A ′ ∗ → e + e - . For a sufficiently large mass splitting, this model can explain in terms of new physics the recently confirmed discrepancy observed in the muon anomalous magnetic moment at Fermilab. Remarkably, it also predicts the observed yield of thermal dark matter relic abundance. A detailed Monte-Carlo simulation was used to determine the signal yield and detection efficiency for this channel in the NA64 setup. The results were obtained re-analyzing the previous NA64 searches for an invisible decay $$A'\rightarrow \chi \overline{\chi }$$ A ′ → χ χ ¯ and axion-like or pseudo-scalar particles $$a \rightarrow \gamma \gamma $$ a → γ γ . With this method, we exclude a significant portion of the parameter space justifying the muon g-2 anomaly and being compatible with the observed dark matter relic density for $$A'$$ A ′ masses from 2$$m_e$$ m e up to 390 MeV and mixing parameter $$\varepsilon $$ ε between $$3\times 10^{-5}$$ 3 × 10 - 5 and $$2\times 10^{-2}$$ 2 × 10 - 2 .


2021 ◽  
Vol 57 (9) ◽  
Author(s):  
R. Frezzotti ◽  
G. Gagliardi ◽  
V. Lubicz ◽  
F. Sanfilippo ◽  
S. Simula

AbstractWe propose a scheme of lattice twisted-mass fermion regularization which is particularly convenient for application to isospin breaking (IB) QCD and QED calculations, based in particular on the so called RM123 approach, in which the IB terms of the action are treated as a perturbation. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the $$\pi ^+ - \pi ^0$$ π + - π 0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized with opposite values of the Wilson parameter r. These correlation functions are found to be affected by much smaller statistical fluctuations, with respect to the analogous functions in which quark and antiquark fields are regularized with the same value of r. Two numerical application of this scheme, that we call rotated twisted-mass, within pure QCD and QCD + QED respectively, are also provided for illustration.


2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Jason Arakawa ◽  
Tim Tait

We examine a real electroweak triplet scalar field as dark matter, abandoning the requirement that its relic abundance is determined through freeze out in a standard cosmological history (a situation which we refer to as `miracle-less WIMP’). We extract the bounds on such a particle from collider searches, searches for direct scattering with terrestrial targets, and searches for the indirect products of annihilation. Each type of search provides complementary information, and each is most effective in a different region of parameter space. LHC searches tend to be highly dependent on the mass of the SU(2) charged partner state, and are effective for very large or very tiny mass splitting between it and the neutral dark matter component. Direct searches are very effective at bounding the Higgs portal coupling, but ineffective once it falls below \lambda_{\text{eff}} \lesssim 10^{-3}λeff≲10−3. Indirect searches suffer from large astrophysical uncertainties due to the backgrounds and JJ-factors, but do provide key information for \sim∼ 100 GeV to TeV masses. Synthesizing the allowed parameter space, this example of WIMP dark matter remains viable, but only in miracle-less regimes.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Juan Carlos Criado ◽  
Abdelhak Djouadi ◽  
Manuel Pérez-Victoria ◽  
José Santiago

Abstract We present an effective field theory describing the relevant interactions of the Standard Model with an electrically neutral particle that can account for the dark matter in the Universe. The possible mediators of these interactions are assumed to be heavy. The dark matter candidates that we consider have spin 0, 1/2 or 1, belong to an electroweak multiplet with arbitrary isospin and hypercharge and their stability at cosmological scales is guaranteed by imposing a ℤ2 symmetry. We present the most general framework for describing the interaction of the dark matter with standard particles, and construct a general non-redundant basis of the gauge-invariant operators up to dimension six. The basis includes multiplets with non-vanishing hypercharge, which can also be viable DM candidates. We give two examples illustrating the phenomenological use of such a general effective framework. First, we consider the case of a scalar singlet, provide convenient semi-analytical expressions for the relevant dark matter observables, use present experimental data to set constraints on the Wilson coefficients of the operators, and show how the interplay of different operators can open new allowed windows in the parameter space of the model. Then we study the case of a lepton isodoublet, which involves coannihilation processes, and we discuss the impact of the operators on the particle mass splitting and direct detection cross sections. These examples highlight the importance of the contribution of the various non-renormalizable operators, which can even dominate over the gauge interactions in certain cases.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Carolina Arbeláez ◽  
Claudio Dib ◽  
Kevin Monsálvez-Pozo ◽  
Iván Schmidt

Abstract We implement a minimal linear seesaw model (LSM) for addressing the Quasi-Dirac (QD) behaviour of heavy neutrinos, focusing on the mass regime of MN ≲ MW. Here we show that for relatively low neutrino masses, covering the few GeV range, the same-sign to opposite-sign dilepton ratio, Rℓℓ, can be anywhere between 0 and 1, thus signaling a Quasi-Dirac regime. Particular values of Rℓℓ are controlled by the width of the QD neutrino and its mass splitting, the latter being equal to the light-neutrino mass mν in the LSM scenario. The current upper bound on mν1 together with the projected sensitivities of current and future |UN ℓ|2 experimental measurements, set stringent constraints on our low-scale QD mass regime. Some experimental prospects of testing the model by LHC displaced vertex searches are also discussed.


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