Predictive power of grand unification from quantum gravity

Abstract If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content of the grand unified model. In turn, the direction of spontaneous breaking of the grand-unified gauge symmetry becomes predictable. For the flow of the couplings below the Planck mass, gauge and Yukawa interactions compete for the determination of the minimum of the effective potential.

Download Full-text

Full spectrum and genetic algorithm-selected spectrum-based chemometric methods for simultaneous determination of azilsartan medoxomil, chlorthalidone, and azilsartan: Development, validation, and application on commercial dosage form

Open Chemistry ◽

10.1515/chem-2021-0022 ◽

2021 ◽

Vol 19 (1) ◽

pp. 205-213

Author(s):

Hany W. Darwish ◽

Abdulrahman A. Al Majed ◽

Ibrahim A. Al-Suwaidan ◽

Ibrahim A. Darwish ◽

Ahmed H. Bakheit ◽

...

Keyword(s):

Genetic Algorithm ◽

Simultaneous Determination ◽

Predictive Power ◽

Principal Component Regression ◽

Selection Procedure ◽

Principal Component ◽

Chemometric Methods ◽

Full Spectrum ◽

Azilsartan Medoxomil

Abstract Five various chemometric methods were established for the simultaneous determination of azilsartan medoxomil (AZM) and chlorthalidone in the presence of azilsartan which is the core impurity of AZM. The full spectrum-based chemometric techniques, namely partial least squares (PLS), principal component regression, and artificial neural networks (ANN), were among the applied methods. Besides, the ANN and PLS were the other two methods that were extended by genetic algorithm procedure (GA-PLS and GA-ANN) as a wavelength selection procedure. The models were developed by applying a multilevel multifactor experimental design. The predictive power of the suggested models was evaluated through a validation set containing nine mixtures with different ratios of the three analytes. For the analysis of Edarbyclor® tablets, all the proposed procedures were applied and the best results were achieved in the case of ANN, GA-ANN, and GA-PLS methods. The findings of the three methods were revealed as the quantitative tool for the analysis of the three components without any intrusion from the co-formulated excipient and without prior separation procedures. Moreover, the GA impact on strengthening the predictive power of ANN- and PLS-based models was also highlighted.

Download Full-text

Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

Journal of High Energy Physics ◽

10.1007/jhep01(2021)180 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Guillem Domènech ◽

Mark Goodsell ◽

Christof Wetterich

Keyword(s):

Quantum Gravity ◽

Top Quark ◽

Quark Mass ◽

Scalar Potential ◽

Planck Scale ◽

Neutrino Masses ◽

Top Quark Mass ◽

Vacuum Stability ◽

Intermediate Scale ◽

Yukawa Couplings

Abstract A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson MH and the top quark Mt. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed MH∼ 125 GeV results in the prediction for the top quark mass Mt∼ 171 GeV, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of an SU(2) triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to Mt ∼ 172.5 GeV for a triplet mass of M∆ ∼ 108GeV. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of Mt due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.

Download Full-text

Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽

10.3390/universe7020045 ◽

2021 ◽

Vol 7 (2) ◽

pp. 45

Author(s):

Christof Wetterich

Keyword(s):

Quantum Gravity ◽

Top Quark ◽

Particle Physics ◽

Scalar Potential ◽

Scalar Fields ◽

The Standard Model ◽

Scaling Potential ◽

Realistic Description ◽

The Masses ◽

Dynamical Dark Energy

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.

Download Full-text

Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽

10.3390/sym13061044 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1044

Author(s):

Daniel Jones ◽

Jeffery A. Secrest

Keyword(s):

Gauge Symmetry ◽

Symmetry Group ◽

Lie Group ◽

Cartan Subalgebra ◽

Natural Extension ◽

Grand Unification ◽

Raising And Lowering Operators ◽

Higher Dimensional ◽

Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

Download Full-text

Symmetry breaking at high temperatures in large N gauge theories

Journal of High Energy Physics ◽

10.1007/jhep08(2021)148 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Soumyadeep Chaudhuri ◽

Eliezer Rabinovici

Keyword(s):

Fixed Point ◽

Phase Transitions ◽

Symmetry Breaking ◽

High Temperatures ◽

Gauge Theories ◽

Scalar Fields ◽

Temperature Limit ◽

Spontaneous Breaking ◽

Critical Temperatures ◽

Weakly Coupled

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

Download Full-text

Ultraviolet fixed point and generalized flow equation of quantum gravity

Physical Review D ◽

10.1103/physrevd.65.025013 ◽

2001 ◽

Vol 65 (2) ◽

Cited By ~ 223

Author(s):

O. Lauscher ◽

M. Reuter

Keyword(s):

Fixed Point ◽

Quantum Gravity ◽

Flow Equation

Download Full-text

THE CURRENT PROBLEMS OF THE MINIMAL SO(10) GUT AND THEIR SOLUTIONS

International Journal of Modern Physics E ◽

10.1142/s0218301307006836 ◽

2007 ◽

Vol 16 (05) ◽

pp. 1489-1503 ◽

Cited By ~ 4

Author(s):

TAKESHI FUKUYAMA ◽

TATSURU KIKUCHI ◽

NOBUCHIKA OKADA

Keyword(s):

Predictive Power ◽

Blow Up ◽

Gauge Coupling ◽

Neutrinoless Double Beta Decay ◽

Double Beta Decay ◽

Grand Unification ◽

Warped Extra Dimension ◽

Gut Scale ◽

Gauge Couplings ◽

Yukawa Sector

This talk consists of two parts. In part I we review how the minimal renormalizable supersymmetric SO (10) model, an SO (10) framework with only one 10 and one [Formula: see text] Higgs multiplets in the Yukawa sector, is attractive because of its highly predictive power. Indeed it not only gives a consistent predictions on neutrino oscillation data but also gives reasonable and interesting values for leptogenesis, LFV, muon g - 2, neutrinoless double beta decay etc. However, this model suffers from problems related to running of gauge couplings. The gauge coupling unification may be spoiled due to the presence of Higgs multiplets much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. In part II we consider the minimal SO (10) model in the warped extra dimension and show a possibility to solve these problems.

Download Full-text