On Direct Search for Dark Matter in Scattering Processes within Yukawa Model

Nowadays, no dark matter candidates have been discovered. We consider two possible reasons for that, both related to the approach of on-peak resonance searching for. As is believed usually, a new particle suits the conditions that the ratio of the width to the mass is less than 1–3% and a narrow-width approximation (NWA) is applicable to identify such type resonant peak in the invariant mass spectrum of the collision products. In the present paper, in the framework of a generalized Yukawa model, we find out the properties of the searched particle, when its width is larger than a maximal one expected during experiments, and, so, this state could be confused with a noise. We also ascertain the values of particle’s parameters, when the NWA is not applicable and estimate the width value, when it happens. These estimations are relevant to interactions between the Standard model and dark matter particles. Such approach is focused on the role of couplings and mass values introduced in the model describing the interaction of visible and dark matters.

Comparative Analysis of Woods-Saxon and Yukawa Model Nuclear Potentials

In this paper, we model the nuclear potential using Woods-Saxon and Yukawa interaction as the mean field in which each nucleon experiences a central force due to rest of the nucleons. The single particle energy states are obtained by solving the time independent Schrodinger wave equation using matrix diagonalization method with infinite spherical well wave-functions as the basis. The best fit model parameters are obtained by using variational Monte-Carlo algorithm wherein the relative mean-squared error, christened as chi-squared value, is minimized. The universal parameters obtained using Woods-Saxon potential are found to be matched with literature reported data resulting a chi-square value of 0.066 for neutron states and 0.069 for proton states whereas the chi-square value comes out to be 1.98 and 1.57 for neutron and proton states respectively by considering Yukawa potential. To further assess the performance of both the interaction potentials, the model parameters have been optimized for three different groups, light nuclei up to 16O - 56Ni, heavy nuclei 100Sn - 208Pb and all nuclei 16O - 208Pb. It is observed that Yukawa model performed reasonably well for light nuclei but did not give satisfactory results for the other two groups while Woods-Saxon potential gives satisfactory results for all magic nuclei across the periodic table.

Renormalization group improvement of the effective potential: an EFT approach

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

One-loop divergences

This chapter focuses on one-loop calculations and related issues such as practical renormalization and the derivation of beta functions. The general result for the one-loop divergences from chapter 13 is applied to a sequence of practical calculations. The starting point is the derivation of vacuum divergences of free matter fields. The beta functions in the vacuum sector are calculated. Asymptotic freedom is discussed. In addition, examples of one-loop divergences in interacting theories are elaborated, including the Yang-Mills field coupled to fermions and scalars, and the Yukawa model.

Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a ℤ2-symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $$ \overline{g} $$ g ¯ , and is expected to have a critical point at a tuned value $$ {\overline{g}}_{\ast } $$ g ¯ ∗ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the ℤ2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $$ \overline{g} $$ g ¯ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C-function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

Dark matter polarization operator in the generalized Yukawa model

Nowadays, no dark matter candidates have been discovered. We consider the possible reason for that which is related to the approach of on-peak resonance searching for. As is believed usually, a new particle has small width and a narrow width approximation is applicable to identify such type resonant peak in the invariant mass spectrum of collision products. In the present paper, in the framework of the generalized Yukawa model, we find out the propertiesof the searched particle when its width is larger than a maximal one expected during experiments and so this state could be missed as a noise. Usually, the new particle width is considered as an arbitrary parameter. Here, we obtain the width of the dark matter particle from an imaginary part of polarization operators. Then the width is analyzed as explicit function of the couplings and masses in the underlying model of the dark matter. The corresponding constraints on the model parameters are obtained. Role of the one-loop mixing of visible and dark matter fields is investigated and constraint on the mixing angle value is derived. These estimations are quite general and, in particular, relevant to interactions between the particles of the Standard model and dark matter.