Deviation from bimaximality due to Planck scale effects

We study the effects of neutrino mass hierarchy, above the GUT scale. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bi-maximal. Quantum gravity (Planck scale effects) lead to an effective SU(2)L×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the above masses and mixing. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino mass square difference for normal and invert neutrino mass hierarchy, namely modified dispersion relation for \(\Delta_{31}'\) above the GUT scale.

Neutrino mixing lead to a non zero contribution to the dark energy of the universe. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. The mechanism of neutrino mixing is a possible candidate to contribute the cosmological dark energy. Quantum gravitational (Planck scale) effects lead to an effective SU(2)L×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor. In this paper, we discuss the three flavor neutrino mixing and cosmological dark energy contributes due to Planck scale effects.

We study corrections to tribimaximal (TBM) neutrino mixing from renormalization group (RG) running and from Planck scale effects. We show that while the RG effects are negligible in the standard model (SM), for quasidegenerate neutrinos and large $\mathrm{tan}\ensuremath{\beta}$ in the minimal supersymmetric standard model (MSSM) all three mixing angles may change significantly. In both these cases, the direction of the modification of ${\ensuremath{\theta}}_{12}$ is fixed, while that of ${\ensuremath{\theta}}_{23}$ is determined by the neutrino mass ordering. The Planck scale effects can also change ${\ensuremath{\theta}}_{12}$ up to a few degrees in either direction for quasidegenerate neutrinos. These effects may dominate over the RG effects in the SM, and in the MSSM with small $\mathrm{tan}\ensuremath{\beta}$. The usual constraints on neutrino masses, Majorana phases or $\mathrm{tan}\ensuremath{\beta}$ stemming from RG running arguments can then be relaxed. We quantify the extent of Planck scale effects on the mixing angles in terms of ``mismatch phases'' which break the symmetries leading to TBM. In particular, we show that when the mismatch phases vanish, the mixing angles are not affected in spite of the Planck scale contribution. Similar statements may be made for $\ensuremath{\mu}--\ensuremath{\tau}$ symmetric mass matrices.

We show that both the Planck and electroweak mass scales can be generated from conformal gravity via the Coleman–Weinberg mechanism of dimensional transmutation. At the first step, the Planck scale is generated via the Coleman–Weinberg mechanism in the sector of conformal gravity, which means that radiative corrections associated with gravitons induce spontaneous symmetry breakdown of a local conformal symmetry. At the second step, the vacuum expectation value of a scalar field is transmitted to the sector of the standard model via a potential involving the conformally invariant part and the contribution from the Coleman–Weinberg mechanism, thereby generating the electroweak scale. The huge hierarchy between the two scales can be explained in terms of a very tiny coupling constant between the scalar and the Higgs field in a consistent way.

We show that both the Planck and electroweak mass scales can be generated from conformal gravity via the Coleman–Weinberg mechanism of dimensional transmutation. At the first step, the Planck scale is generated via the Coleman–Weinberg mechanism in the sector of conformal gravity, which means that radiative corrections associated with gravitons induce spontaneous symmetry breakdown of a local conformal symmetry. At the second step, the vacuum expectation value of a scalar field is transmitted to the sector of the standard model via a potential involving the conformally invariant part and the contribution from the Coleman–Weinberg mechanism, thereby generating the electroweak scale. The huge hierarchy between the two scales can be explained in terms of a very tiny coupling constant between the scalar and the Higgs field in a consistent way.

The extension of the Standard Model of particle physics by sterile neutrinos can naturally explain the smallness of neutrino masses as observed by neutrino oscillation and nuclear beta decay experiments. These hypothetical particles, also referred to as heavy neutrinos in the mass eigenbasis, can give rise to a testable phenomenology when they have masses around the electroweak scale. Hence they are actively searched for at, for instance, colliders such as the Large Hadron Collider. The proposed future colliders, which are currently in the design phase, will be more powerful than the operated colliders to date. The new possibilities which they provide to search for sterile neutrinos and to test the neutrino mass mechanism in the not too far future have therefore to be assessed. In this thesis, various aspects of the sterile neutrino phenomenology as well as various searches for sterile neutrinos at colliders are investigated. In particular, we study the contributions from sterile neutrinos to the Higgs boson production mechanism at colliders, the implications of long-lived heavy neutrinos that lead to displaced vertex events, lepton-number violation as the manifestation of heavy neutrino-antineutrino oscillations, lepton-flavour violation as the consequence of leptonic mixing, the possibilities to resolve heavy neutrino-antineutrino oscillations, how to test the viable leptogenesis parameter space, and their implications to collider searches. These collider studies are investigated in the context of low scale seesaw scenarios featuring ns = 2 sterile neutrinos with masses in the range of O(1 GeV) and O(1 TeV), which constitutes the benchmark scenario. Within the benchmark scenario, analytical calculations, and analyses of Monte Carlo generated event samples are performed. The investigated collider studies demonstrate promising avenues to test sterile neutrinos at future colliders. This contains novel possible search strategies by the search for Higgs bosons produced from heavy neutrinos and by probing the effects from heavy neutrino-antineutrino oscillations via the displaced vertex search. The assessed capabilities of the future colliders with respect to the sterile neutrino searches contribute to the physics case of the future colliders.

A universe without weak interactions is constructed that undergoes big-bang nucleosynthesis, matter domination, structure formation, and star formation. The stars in this universe are able to burn for billions of years, synthesize elements up to iron, and undergo supernova explosions, dispersing heavy elements into the interstellar medium. These definitive claims are supported by a detailed analysis where this hypothetical ''Weakless Universe'' is matched to our Universe by simultaneously adjusting Standard Model and cosmological parameters. For instance, chemistry and nuclear physics are essentially unchanged. The apparent habitability of the Weakless Universe suggests that the anthropic principle does not determine the scale of electroweak breaking, or even require that it be smaller than the Planck scale, so long as technically natural parameters may be suitably adjusted. Whether the multi-parameter adjustment is realized or probable is dependent on the ultraviolet completion, such as the string landscape. Considering a similar analysis for the cosmological constant, however, we argue that no adjustments of other parameters are able to allow the cosmological constant to raise up even remotely close to the Planck scale while obtaining macroscopic structure. The fine-tuning problems associated with the electroweak breaking scale and the cosmological constant therefore appear to be qualitatively different from the perspective of obtaining a habitable universe.

The extension of the Standard Model by heavy right-handed neutrinos can simultaneously explain the observed neutrino masses via the seesaw mechanism and the baryon asymmetry of the Universe via leptogenesis. If the mass of the heavy neutrinos is below the electroweak scale, they may be found at the LHC, BELLE II, NA62, the proposed SHiP experiment or a future high-energy collider. In this mass range, the baryon asymmetry is generated via CP-violating oscillations of the heavy neutrinos during their production. We study the generation of the baryon asymmetry of the Universe in this scenario from first principles of non-equilibrium quantum field theory,including spectator processes and feedback effects. We eliminate several uncertainties from previous calculations and find that the baryon asymmetry of the Universe can be explained with larger heavy neutrino mixing angles, increasing the chance for an experimental discovery. For the limiting cases of fast and strongly overdamped oscillations of right-handed neutrinos, the generation of the baryon asymmetry can be calculated analytically up to corrections of order one.

In this work, discuss neutrino masses and mixings in the framework of a minimal S3 symmetric extension of the Standard Model. In this model, the mass matrices of all fermions take the same generic form with two texture zeroes. The mass matrices of the neutrinos and charged leptons are re-parameterized in terms of their eigenvalues, then the neutrino mixing matrix, VPMNS, is computed and exact, explicit analytical expressions for the neutrino mixing angles as functions of the masses of neutrinos and charged leptons are obtained in excellent agreement with the latest experimental data. We also compute the branching ratios of some selected flavour-changing neutral current (FCNC) processes, as well as the contribution of the exchange of neutral flavour-changing scalars to the anomaly of the magnetic moment of the muon, as functions of the masses of charged leptons and the neutral Higgs bosons. We find that the S3 × Z2 flavour symmetry and the strong mass hierarchy of the charged leptons strongly suppress the FCNC processes in the leptonic sector, well below the present experimental bounds by many orders of magnitude. The contribution of FCNC's to the anomaly of the muon's magnetic moment is small, but not negligible.

Recent developments in string theory have led to ``realistic string compactifications which lead to moduli stabilization while generating a hierarchy between the Electroweak and Planck scales at the same time. However, this seems to suggest a rethink of our standard notions of cosmological evolution after the end of inflation and before the beginning of BBN. This epoch is crucial for addressing the issues of neutrino masses, baryon asymmetry, Dark Matter (DM) abundance and the moduli (gravitino) problem. We argue that within classes of realistic string compactifications as defined above, there generically exists a light modulus with a mass comparable to that of the gravitino which is typically much smaller than the Hubble parameter during inflation. Therefore, it is destabilized and generates a large late-time entropy when it decays. Thus, all known elegant mechanisms of generating the baryon asymmetry of the Universe in the literature have to take this fact into account. In this work, we find that it is still possible to naturally generate the observed baryon asymmetry of the Universe as well as light left-handed neutrino masses from a period of Affleck-Dine (AD) leptogenesis shortly after the end of inflation, in classes of realistic string constructions with a minimal extension of the MSSM below the unification scale (consisting only of right-handed neutrinos) and satisfying certain microscopic criteria described in the text. The AD mechanism has already been used to generate the baryon asymmetry in the literature; however in this work we have embedded the above mechanism within a framework well motivated from string theory and have tried to describe the epoch from the end of inflation to the beginning of BBN in a complete and self-consistent manner. The consequences of our analysis are as follows. The lightest left-handed neutrino is required to be virtually massless. The moduli (gravitino) problem can be naturally solved in this framework both within gravity and gauge mediation. The observed upper bound on the relic abundance constrains the moduli-matter and moduli-gravitino couplings since the DM is produced non-thermally within this framework. Finally, although not a definite prediction, the framework naturally allows a light right-handed neutrino and sneutrinos around the electroweak scale which could have important implications for the nature of DM as well as the LHC.

We suggest a renormalizable standard model extension based on S4 symmetry that accommodates the recent observed neutrino oscillation pattern. Through the type-I seesaw mechanism, the smallness of the active neutrino mass and its hierarchy are produced. The model generates the updated data on neutrino parameters in which the reactor neutrino mixing angle θ13, the atmospheric neutrino mixing θ23, and the Dirac phase δ for both NH and IH belong to 1σ range, while the solar mixing angle θ12 = 35.70° belongs to 2σ range. The effective masses are found to be 〈 mee〉 = 5.74 meV for NH and 〈 mee〉 = 48.1 meV for IH within their allowed constraints.

Lectures on flavor physics presented at the 2012 CERN HEP Summer School. Content: 1) flavor physics within the Standard Model, 2) phenomenology of B andD decays, 3) flavor physics beyond the Standard Model. In the limit of unbroken electroweak symmetry none of the basic constituent of matter could have a non-vanishing mass. The problem of quark and lepton masses is therefore intimately related to the other big open question in particle physics: which is the mechanism behind the breaking of the electroweak symmetry, or which is the mechanism responsible for the non-vanishing masses of the weak force carriers (theW andZ bosons). Within the SM these two problems are both addressed by the Higgs mechanism: the masses of quarks and leptons, as well as the masses ofW andZ bosons, are the result of the interaction of these basic fields (both matter constituents and force carriers) with a new type of field, the Higgs scalar field, whose ground state breaks spontaneously the electroweak symmetry. The recent observation by the ATLAS and CMS experiments of a new state compatible with the properties of the Higgs boson (or the spin-0 excitation of the Higgs field) has significantly reinforced the evidences in favor of the Higgs mechanisms and the validity of the SM. However, we have also clear indications that this theory is not complete: the phenomenon of neutrino oscillations and the evidence for dark matter cannot be explained within the SM. The SM is also affected by a serious theoretical problem because of the instability of the Higgs sector under quantum corrections. We have not yet enough information to unambiguously determine how this theory should be extended; however, most realistic proposals point toward the existence of new degrees of freedom in the TeV range, possibly accessible at the high-pT experiments at the LHC. The description of quark and lepton masses in terms of the Higgs mechanism is particularly un- satisfactory since the corresponding interactions is not controlled by any symmetry principle, contrary to all other known interactions, resulting in a large number of free parameters. Beside determining quark masses, the interaction of the quarks with the Higgs is responsible for the peculiar pattern of mixing of

In the standard interaction scenario, a direct measurement of absolute neutrino masses via neutrino oscillations is not feasible, as the oscillations depend only on the mass-squared differences. However,scalar non-standard interactions (SNSI) can introduce sub-dominant terms in the neutrino oscillation Hamiltonian that can directly affect the neutrino mass matrix, thereby making SNSI a unique tool for neutrino mass measurements. In this work, for the first time, we constrain the absolute masses of neutrinos by probing SNSI in a neutrino oscillation experiment. We show that a bound on the neutrino mass can be induced in the presence of SNSI at DUNE. We note that the constraints on the neutrino mass are much better for ημμ and ηττ as compared to ηee for both NO and IO scenarios. We have also explored the constraints on the neutrino mass for different choices of δCP and θ23 for both neutrino mass orderings. This study shows that SNSI can serve as an interesting avenue to constrain the absolute neutrino masses in long-baseline neutrino experiments via neutrino oscillations.

<p><strong>The future of theoretical physics is unclear. Two large areas that fall under the umbrella of theoretical physics are cosmology and quantum gravity. Modern cosmology is relatively a much younger field than quantum gravity, and both of these fields require further developments of general relativity. In this thesis we do not hope to resolve the problems facing modern cosmology or theories of quantum gravity. Rather, we will conduct original research into aspects of general relativity that may be used in the future to aid the development and testing of theories of cosmology and quantum gravity.</strong></p><p>It is our view that the largest problem facing astrophysics and cosmology stem from the existence of the dark sector of the Universe. The implication here being that more than ninety percent of the energy density of the Universe is “missing in action” and seemingly consists of dark energy and dark matter. Furthermore, it is apparent that there exist conceptual flaws in our understanding of observational concepts such as expansion versus motion and observer biases. To this end, we investigate the standard spacetime metric used in cosmology, the Friedmann–Lemaˆıtre-Roberston–Walker (FLRW) metric in a peculiar coordinate system — the Painlev´e–Gullstrand coordinates. In this coordinate system (slicing), space is no longer expanding, rather, the galaxies are receding from each other. We hope this will aid in the understanding of expansion, motion, curvature, and observer bias with future work. We further investigate the possibility of black holes in cosmology being directly coupled to the accelerated expansion of the Universe — in other words, black holes as a source for dark energy. However, we show that this is highly implausible.</p><p>Relatively recently it has been postulated that the near black hole horizon limit may be a regime where quantum gravity effects become relevant i.e., quantum gravity may not be restricted to near the Planck scale. We investigate a curious model of black and white holes that shows how one may transition into the other over a finite period of time. This is research conducted in the near horizon limit of the Schwarzschild black hole. We introduce a time dependent function into the usual Schwarzschild black hole spacetime (leaving this new spacetime not a simple coordinate transformed version of the original). This function allows the black hole to transition into a white hole. Importantly, the action for this transition can be shown to be zero, meaning it can be added to the Feynman path integral at no cost.</p><p>Finally, we move to investigating the black hole memory effect. During the last decade, there has been an interesting connection made between the Bondi– Metzner–Sachs (BMS) group — an infinite dimensional group of symmetries found at null infinity — and the gravitational memory effect. In particular, it was shown that the passage of a gravitational wave that alters a Schwarzschild black hole is seen as a supertranslation of the spacetime at null infinity. We extend these calculations to the Kerr and Kerr–Newman black holes. Hence, showing that there may be a way to verify the abstract mathematical ideas predicated on the BMS group by detection of the memory effect in future observations.</p><p>It is our hope that when future gravitational wave detectors such as the laser-interferometer-space-antenna (LISA) are launched, research conducted in this thesis may shed light on how the memory may relate to black holes in their asymptotic & near horizon limits to aid our understanding of the nature of quantum gravity.</p>

We study a neutrino mass model with [Formula: see text] discrete flavor symmetry using a type-I seesaw mechanism. The inclusion of extra flavons in our model leads to deviations from the exact tribimaximal mixing pattern resulting in a nonzero [Formula: see text] consistent with the recent experimental results and a sum rule for light neutrino masses is also obtained. In this framework, a connection is established among the neutrino mixing angles-reactor mixing angle ([Formula: see text]), solar mixing angle ([Formula: see text]), and atmospheric mixing angle ([Formula: see text]). This model also allows us a prediction of Dirac CP-phase and Jarlskog parameter [Formula: see text]. The octant of the atmospheric mixing angle [Formula: see text] occupies the lower octant. Our model prefers Normal Hierarchy (NH) than Inverted Hierarchy (IH). We use the parameter space of our model of neutrino masses to study the neutrinoless double beta decay parameter [Formula: see text].