Large Mass Hierarchy Research Articles

CP phase in modular flavor models and discrete Froggatt-Nielsen models

We study the large mass hierarchy and CP violation in the modular symmetric quark flavor models without fine-tuning. Mass matrices are written in terms of modular forms. Modular forms near the modular fixed points are approximately given by ϵp, where ϵ and p denote the small deviation from the fixed points and their residual charges. Thus, mass matrices have the hierarchical structures depending on the residual charges and have a possibility describing the large mass hierarchy without fine-tuning. Similar structures of mass matrices are also obtained in Froggatt-Nielsen models. Nevertheless, it seems to be difficult to induce a sufficient amount of CP violation by a single small complex parameter ϵ. To realize the large mass hierarchy as well as sizable CP violation, multimoduli are required. We show the mass matrix structures with multimoduli that are consistent with quark flavor observables including the CP phase. We also discuss the origins of the large mass hierarchy and CP violation in such mass matrix structures. Published by the American Physical Society 2024

Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{\\Delta }\\left(96\\right)$$\\end{document}

We study an approach to construct Siegel modular forms from Sp(6, Z). Zero-mode wave functions on T6 with magnetic flux background behave Siegel modular forms at the origin. Then T-symmetries partially break depending on the form of background magnetic flux. We study the background such that three T-symmetries TI, TII and TIII as well as the S-symmetry remain. Consequently, we obtain Siegel modular forms with three moduli parameters (ω1, ω2, ω3), which are multiplets of finite modular groups. We show several examples. As one of examples, we study Siegel modular forms for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{\\Delta }\\left(96\\right)$$\\end{document} in detail. Then, as a phenomenological applicantion, we study quark flavor models using Siegel modular forms for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{\\Delta }\\left(96\\right)$$\\end{document}. Around the cusp, ω1 = i∞, the Siegel modular forms have hierarchical values depending on their TI-charges. We show the deviation of ω1 from the cusp can generate large quark mass hierarchies without fine-tuning. Furthermore CP violation is induced by deviation of ω2 from imaginary axis.

Comparable dark matter and baryon abundances with a heavy dark sector

We propose a scenario that explains the comparable abundances of dark matter (DM) and baryons without any coincidence in the corresponding particle masses. Here, DM corresponds to heavy “dark baryons” in a hidden MSSM-like dark sector, where the supersymmetry breaking scale can be several orders of magnitude larger than in the visible sector. In both sectors a baryon asymmetry is generated via the Affleck-Dine mechanism, and the smaller dark baryon-to-entropy ratio partially compensates the larger dark baryon masses to give similar densities in the two sectors. The large mass hierarchy also naturally results in an asymmetric reheating of these sequestered sectors. Moreover, this scenario predicts uncorrelated DM and baryon isocurvature perturbations.

Boosting asymmetric charged DM via thermalization

We consider a dark sector scenario with two dark matter species with opposite dark U(1) charges and an asymmetric population comprising some fraction of the dark matter abundance. A new mechanism for boosting dark matter is introduced, arising from the large mass hierarchy between the two particles. In the galaxy, the two species thermalize efficiently through dark Rutherford scattering greatly boosting the lighter dark matter particle, far above the virial and escape velocities in the galaxy, while the dark charge prevents it from escaping. We study the consequences of this scenario for direct-detection experiments, assuming a kinetic mixing between the dark photon and the photon. If the charged dark sector makes up 5% of the total DM mass in our galaxy and the mass ratio is between 103–104, we find that current and future experiments may probe the boosted light dark matter for masses down to 100 keV, in a hitherto unexplored parameter range.

Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points

We study quark and lepton mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Quark and lepton masses have a large hierarchy. In addition, mixing angles are large in the lepton sector, while those are small in the quark sector. We find that this structure can be realized in certain flavor models, which are identified by the zero points of the zero-mode wave functions of fermions and Higgs modes. We classify such realistic flavor models. Fixed points $\tau=i$, $e^{2\pi i/3}$ and $i\infty$ of the modulus $\tau$ play a role in realizing a large mass hierarchy through our scenario, where residual $S$, $ST$, and $T$ symmetries remain and the lightest Higgs modes can correspond to eigenstates of residual symmetries at the leading order. As a result, we find that there are 24 flavor models in total which can be realistic in a vicinity of $S$-symmetric vacuum but no flavor models for $ST$ and $T$-symmetric vacua.

Monojet signatures from gluino and squark decays

We study the monojet and dijet channels at the LHC as a tool for searching for squarks and gluinos. We consider two separate R-parity conserving supersymmetric scenarios. In the first scenario we postulate a large mass hierarchy between squarks ( overset{sim }{q} ) and winos ( overset{sim }{W} ), and wino-like neutralino is assumed to be the lightest supersymmetric particle (LSP). The associated squark-wino production, pp → overset{sim }{q}overset{sim }{W} , then leads to a monojet-like signature, where the high pT jet is originated from the squark decay, overset{sim }{q} → q + overset{sim }{W} . We demonstrate that this associated production, as well as the pp → overset{sim }{W}overset{sim }{W} + jets production, have a significant impact on the exclusion limit in the squark-neutralino mass plane. The second scenario postulates that the lighter of the squark and gluino is only a few GeV heavier than the LSP neutralino. The associated squark-gluino production, pp → overset{sim }{q}overset{sim }{g} , then leads to a distinctive monojet signature, where the high pT jet is produced from the decay of the heavier coloured particle into the lighter one ( overset{sim }{q} → q+ overset{sim }{g} for {m}_{tilde{q}} > {m}_{tilde{g}} and overset{sim }{g} → q+ overset{sim }{q} for {m}_{tilde{g}} > {m}_{tilde{q}} ). The lighter coloured particle is effectively regarded as an invisible particle since the decay products are soft due to the approximate mass degeneracy. We recast existing monojet and dijet analyses and find a non-trivial exclusion limit in the squark-gluino mass plane in this scenario.

Multiple mass hierarchies from complex fixed point collisions

A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the real axis and to one another generate multiple hierarchies, some of which can be parametrically enhanced. We illustrate this effect at weak coupling with field-theory examples, and at strong coupling using holography. We also construct complex flows between complex fixed points, including flows that violate the c-theorem.

A multi-component SIMP model with U(1)X\u2192 Z2 \xd7 Z3

Multi-component dark matter scenarios are studied in the model with U(1)X dark gauge symmetry that is broken into its product subgroup Z2 × Z3 á la Krauss-Wilczek mechanism. In this setup, there exist two types of dark matter fields, X and Y, distinguished by different Z2 × Z3 charges. The real and imaginary parts of the Z2-charged field, XR and XI, get different masses from the U(1)X symmetry breaking. The field Y, which is another dark matter candidate due to the unbroken Z3 symmetry, belongs to the Strongly Interacting Massive Particle (SIMP)-type dark matter. Both XI and XR may contribute to Y’s 3 → 2 annihilation processes, opening a new class of SIMP models with a local dark gauge symmetry. Depending on the mass difference between XI and XR, we have either two-component or three-component dark matter scenarios. In particular two- or three-component SIMP scenarios can be realised not only for small mass difference between X and Y, but also for large mass hierarchy between them, which is a new and unique feature of the present model. We consider both theoretical and experimental constraints, and present four case studies of the multi-component dark matter scenarios.

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.

EV-scale sterile neutrinos from an extra dimension

Motivated by the short-baseline neutrino oscillation anomalies that suggest the existence of sterile neutrinos at the eV scale, we construct a scenario of a seesaw mechanism for 3+1 light neutrinos implemented by warped compactification of an extra dimension. As the seesaw mechanism necessitates at least two right-handed neutrinos at mass scales much larger than eV, incorporating an eV-scale sterile neutrino into a seesaw entails large mass hierarchies among the singlet neutrinos. We show that such hierarchies can be naturally explained by moderate fluctuations of the five-dimensional fermion mass parameters.

Large mass hierarchy from a small nonminimal coupling

We propose a simple but novel cosmological scenario where both the Planck mass and the dark energy scale emerge from the same super-Hubble quantum fluctuations of a non-minimally coupled ultra-light scalar field during primordial inflation. The current cosmic and solar-system observations constrain the non-minimal coupling to be small.

Muon g−2 in a U(1) -symmetric two-Higgs-doublet model

We show in this paper that, in a $U(1)$-symmetric two-Higgs-doublet model (2HDM), the two additional neutral Higgs bosons would become nearly degenerate in the large $\tan\beta$ regime, under the combined constraints from both theoretical arguments and experimental measurements. As a consequence, the excess observed in the anomalous magnetic moment of the muon could not be addressed in the considered framework, following the usual argument where these two neutral scalars are required to manifest a large mass hierarchy. On the other hand, we find that, with an $\mathcal{O}(1)$ top-Yukawa coupling and a relatively light charged Higgs boson, large contributions from the two-loop Barr-Zee type diagrams can account for the muon $g-2$ anomaly at the 1$\sigma$ level, in spite of a large cancellation between the scalar and pseudoscalar contributions. Furthermore, the same scenario can survive the tight constraints from the $B$-physics observables.

Pole mass determination in presence of heavy particles

We investigate the determination of the Higgs-boson propagator poles in the MSSM. Based upon earlier works, we point out that in case of a large hierarchy between the electroweak scale and one or more SUSY masses a numerical determination with DR Higgs field renormalization induces higher order terms which would cancel in a more complete calculation. The origin of these terms is the momentum dependence of contributions involving at least one of the heavy particles. We present two different methods to avoid their appearance. In the first approach, the poles are determined by expanding around the one-loop solutions. In the second approach, a “heavy-OS” Higgs field renormalization is employed in order to absorb the momentum dependence of heavy contributions. We will find that the first approach leads to an unwanted behavior of the Higgs boson mass predictions close to crossing points where two Higgs bosons that mix with each other are almost mass degenerate. These problems are avoided in the second approach, which became the default approach used in the public code FeynHiggs. Despite the discussion being very specific to the MSSM, the argumentation and the methods presented in this work are straightforwardly applicable to the determination of propagator poles in other models involving a large mass hierarchy.

The flavor-locked flavorful two Higgs doublet model

We propose a new framework to generate the Standard Model (SM) quark flavor hierarchies in the context of two Higgs doublet models (2HDM). The ‘flavorful’ 2HDM couples the SM-like Higgs doublet exclusively to the third quark generation, while the first two generations couple exclusively to an additional source of electroweak symmetry breaking, potentially generating striking collider signatures. We synthesize the flavorful 2HDM with the ‘flavor-locking’ mechanism, that dynamically generates large quark mass hierarchies through a flavor-blind portal to distinct flavon and hierarchon sectors: dynamical alignment of the flavons allows a unique hierarchon to control the respective quark masses. We further develop the theoretical construction of this mechanism, and show that in the context of a flavorful 2HDM-type setup, it can automatically achieve realistic flavor structures: the CKM matrix is automatically hierarchical with |Vcb| and |Vub| generically of the observed size. Exotic contributions to meson oscillation observables may also be generated, that may accommodate current data mildly better than the SM itself.

From the Trees to the Forest: A Review of Radiative Neutrino Mass Models

A plausible explanation for the lightness of neutrino masses is that neutrinos are massless at tree level, with their mass (typically Majorana) being generated radiatively at one or more loops. The new couplings, together with the suppression coming from the loop factors, imply that the new degrees of freedom cannot be too heavy (they are typically at the TeV scale). Therefore, in these models there are no large mass hierarchies and they can be tested using different searches, making their detailed phenomenological study very appealing. In particular, the new particles can be searched for at colliders and generically induce signals in lepton-flavor and lepton-number violating processes (in the case of Majorana neutrinos), which are not independent from reproducing correctly the neutrino masses and mixings. The main focus of the review is on Majorana neutrinos. We order the allowed theory space from three different perspectives: (i) using an effective operator approach to lepton number violation, (ii) by the number of loops at which the Weinberg operator is generated, (iii) within a given loop order, by the possible irreducible topologies. We also discuss in more detail some popular radiative models which involve qualitatively different features, revisiting their most important phenomenological implications. Finally, we list some promising avenues to pursue.

De Sitter thin brane model

We discuss the large mass hierarchy problem in a braneworld model which represents our acceleratively expanding universe. The Randall-Sundrum (RS) model with warped one extra dimension added to flat 4-dimensional space-time cannot describe our expanding universe. Here, we study instead the de Sitter thin brane model. This is described by the same action as that for the RS model, but the 4-dimensional space-time on the branes is $\rm dS_4$. We study the model for both the cases of positive 5-dimensional cosmological constant $\Lambda_5$ and negative one. In the positive $\Lambda_5$ case, the 4-dimensional large hierarchy necessitates a 5-dimensional large hierarchy, and we cannot get a natural explanation. On the other hand, in the negative $\Lambda_5$ case, the large hierarchy is naturally realized in the 5-dimensional theory in the same manner as in the RS model. Moreover, another large hierarchy between the Hubble parameter and the Planck scale is realized by the ${\mathcal O}(10^2)$ hierarchy of the 5-dimensional quantities. Finally, we find that the lightest mass of the massive Kaluza-Klein modes and the intervals of the mass spectrum are of order $10^2\,\rm GeV$, which are the same as in the RS case and do not depend on the value of the Hubble parameter.

Large mass hierarchies from strongly-coupled dynamics

Besides the Higgs particle discovered in 2012, with mass 125 GeV, recent LHC data show tentative signals for new resonances in diboson as well as diphoton searches at high center-of-mass energies (2 TeV and 750 GeV, respectively). If these signals are confirmed (or other new resonances are discovered at the TeV scale), the large hierarchies between masses of new bosons require a dynamical explanation. Motivated by these tentative signals of new physics, we investigate the theoretical possibility that large hierarchies in the masses of glueballs could arise dynamically in new strongly-coupled gauge theories extending the standard model of particle physics. We study lattice data on non-Abelian gauge theories in the (near-)conformal regime as well as a simple toy model in the context of gauge/gravity dualities. We focus our attention on the ratio $R$ between the mass of the lightest spin-2 and spin-0 resonances, that for technical reasons is a particularly convenient and clean observable to study. For models in which (non-perturbative) large anomalous dimensions arise dynamically, we show indications that this mass ratio can be large, with $R>5$. Moreover, our results suggest that $R$ might be related to universal properties of the IR fixed point. Our findings provide an interesting step towards understanding large mass ratios in the non-perturbative regime of quantum field theories with (near) IR conformal behaviour.

Superheavy Dark Matter in the Supersymmetric Economical 3-3-1 Model

We suggest the supersymmetric particles contained in the supersymmetric economical 3-3-1model were produced during the heating time. They have not been thermodynamic equilibrium when it frozeout. It leads to the lightest supersymmetric particle can be a good candidate for superheavy dark matter.With assumption the lightest supersymmetric particle is Bino, we show that the correct contribution of thesuperheavy dark matter species to the present critical density requires the Bino mass is order 1012 GeVand there is not exists a large mass hierarchy of the superpartner in the considered model.

27pSD-10 階層性問題と膨張宇宙

27pSD-10 階層性問題と膨張宇宙

Perturbative stability along the supersymmetric directions of the landscape

We consider the perturbative stability of non-supersymmetric configurations in \U0001d4a9=1 supergravity models with a spectator sector not involved in supersymmetry breaking. Motivated by the supergravity description of complex structure moduli in Large Volume Compactifications of type IIB-superstrings, we concentrate on models where the interactions are consistent with the supersymmetric truncation of the spectator fields, and we describe their couplings by a random ensemble of generic supergravity theories. We characterise the mass spectrum of the spectator fields in terms of the statistical parameters of the ensemble and the geometry of the scalar manifold. Our results show that the non-generic couplings between the spectator and the supersymmetry breaking sectors can stabilise all the tachyons which typically appear in the spectator sector before including the supersymmetry breaking effects, and we find large regions of the parameter space where the supersymmetric sector remains stable with probability close to one. We discuss these results about the stability of the supersymmetric sector in two physically relevant situations: non-supersymmetric Minkowski vacua, and slow-roll inflation driven by the supersymmetry breaking sector. For the class of models we consider, we have reproduced the regimes in which the KKLT and Large Volume Scenarios stabilise all supersymmetric moduli. We have also identified a new regime in which the supersymmetric sector is stabilised at a very robust type of dS minimum without invoking a large mass hierarchy.