Weakly-Interacting Massive Particles in Non-supersymmetric SO(10) Grand Unified Models

Non-supersymmetric SO(10) grand unified theories provide a framework in which the stability of dark matter is explained while gauge coupling unification is realized. In this work, we systematically study this possibility by classifying weakly interacting DM candidates in terms of their quantum numbers of $\text{SU}(2)_L \otimes \text{U}(1)_Y$, $B-L$, and $\text{SU}(2)_R$. We consider both scalar and fermion candidates. We show that the requirement of a sufficiently high unification scale to ensure a proton lifetime compatible with experimental constraints plays a strong role in selecting viable candidates. Among the scalar candidates originating from either a 16 or 144 of SO(10), only SU(2)$_L$ singlets with zero hypercharge or doublets with $Y=1/2$ satisfy all constraints for $\text{SU}(4)_C \otimes \text{SU}(2)_L \otimes \text{SU}(2)_R$ and $\text{SU}(3)_C \otimes \text{SU}(2)_L \otimes \text{SU}(2)_R \otimes \text{U}(1)_{B-L}$ intermediate scale gauge groups. Among fermion triplets with zero hypercharge, only a triplet in the 45 with intermediate group $\text{SU}(4)_C \otimes \text{SU}(2)_L \otimes \text{SU}(2)_R$ leads to solutions with $M_{\rm GUT} > M_{\rm int}$ and a long proton lifetime. We find three models with weak doublets and $Y=1/2$ as dark matter candidates for the $\text{SU}(4)_C \otimes \text{SU}(2)_L \otimes \text{SU}(2)_R$ and $\text{SU}(4)_C \otimes \text{SU}(2)_L \otimes \text{U}(1)_R$ intermediate scale gauge groups assuming a minimal Higgs content. We also discuss how these models may be tested at accelerators and in dark matter detection experiments.Comment: 43 pages, 3 figure

Implications of Gravitational Waves for Supersymmetric Grand Unification

Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above $10^{14}\, \mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow the possible range of the cosmic string scale and restricts the unified couplings and the unification scale by requiring gauge coupling unification. As an indirect consequence of the high cosmic string scale, the monopole abundance places non-trivial constraints on the theory. These are complementary to the proton decay constraints and probe different facets of supersymmetric $SO(10)$ unification theories.Comment: 9 pages, 1 figure, 3 table

Dark Matter Models in Non-Supersymmetric SO(10) Unification Models

University of Minnesota Ph.D. dissertation. June 2017. Major: Physics. Advisor: Keith Olive. 1 computer file (PDF); viii, 107 pages.This thesis studies systematically non-supersymmetric models that contain dark matter candidates. The stability of the dark matter is guaranteed by a remnant Z 2 symmetry embedded naturally in SO(10). We build models base on various dark matter production mechanism, including the non-equilibrium thermal dark matter scenario, the weakly interactive massive particle scenario, and the asymmetric dark matter scenario. Although we start from very general assumptions on the choice of dark matter representation and the symmetry breaking pattern, the number of viable models is severely restricted by the requirement of gauge coupling unification. These models are then checked against several phenomenological constraints, such as the light neutrino masses, direct detection bounds on dark matter candidates and the proton decay lifetime. Finally, we demonstrate that the vacuum stability problem of the Standard Model can be evaded by one of our scalar dark matter models

Dark Matter and Gauge Coupling Unification in Non-supersymmetric SO(10) Grand Unified Models

Unlike minimal SU(5), SO(10) provides a straightforward path towards gauge coupling unification by modifying the renormalization group evolution of the gauge couplings above some intermediate scale which may also be related to the seesaw mechanism for neutrino masses. Unification can be achieved for several different choices of the intermediate gauge group below the SO(10) breaking scale. In this work, we consider in detail the possibility that SO(10) unification may also provide a natural dark matter candidate, stability being guaranteed by a leftover $Z_2$ symmetry. We systematically examine the possible intermediate gauge groups which allow a non-degenerate, fermionic, Standard Model singlet dark matter candidate while at the same time respecting gauge coupling unification. Our analysis is done at the two-loop level. Surprisingly, despite the richness of SO(10), we find that only two models survive the analysis of phenomenological constraints, which include suitable neutrino masses, proton decay, and reheating.Comment: 39 pages, 8 figures. Version accepted for publication in Physical Review

Post-Inflationary Dark Matter Bremsstrahlung

Dark matter may only interact with the visible sector efficiently at energy scales above the inflaton mass, such as the Planck scale or the grand unification scale. In such a scenario, the dark matter is mainly produced out of equilibrium during the period of reheating, often referred to as UV freeze-in. We evaluate the abundance of the dark matter generated from bremsstrahlung off the inflaton decay products assuming no direct coupling between the inflaton and the dark matter. This process generally dominates the production of dark matter for low reheating temperatures where the production through the annihilations of particle in the thermal plasma becomes inefficient. We find that the bremsstrahlung process dominates for reheating temperatures $T_{\mathrm{RH}} \lesssim 10^{10}$ GeV, and produces the requisite density of dark matter for a UV scale $\simeq 10^{16}$ GeV. As examples, we calculate numerically the yield of the dark matter bremsstrahlung through gravitation and dimension-6 vector portal effective interactions.Comment: 19 pages, 5 figure

Federated Unlearning via Active Forgetting

The increasing concerns regarding the privacy of machine learning models have catalyzed the exploration of machine unlearning, i.e., a process that removes the influence of training data on machine learning models. This concern also arises in the realm of federated learning, prompting researchers to address the federated unlearning problem. However, federated unlearning remains challenging. Existing unlearning methods can be broadly categorized into two approaches, i.e., exact unlearning and approximate unlearning. Firstly, implementing exact unlearning, which typically relies on the partition-aggregation framework, in a distributed manner does not improve time efficiency theoretically. Secondly, existing federated (approximate) unlearning methods suffer from imprecise data influence estimation, significant computational burden, or both. To this end, we propose a novel federated unlearning framework based on incremental learning, which is independent of specific models and federated settings. Our framework differs from existing federated unlearning methods that rely on approximate retraining or data influence estimation. Instead, we leverage new memories to overwrite old ones, imitating the process of \textit{active forgetting} in neurology. Specifically, the model, intended to unlearn, serves as a student model that continuously learns from randomly initiated teacher models. To preserve catastrophic forgetting of non-target data, we utilize elastic weight consolidation to elastically constrain weight change. Extensive experiments on three benchmark datasets demonstrate the efficiency and effectiveness of our proposed method. The result of backdoor attacks demonstrates that our proposed method achieves satisfying completeness