scholarly journals Renormalization and radiative corrections to masses in a general Yukawa model

2018 ◽  
Vol 33 (03) ◽  
pp. 1850019 ◽  
Author(s):  
M. Fox ◽  
W. Grimus ◽  
M. Löschner
Keyword(s):  
Scalar Potential ◽  
Vacuum Expectation ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Tree Level ◽  
Majorana Fermion ◽  
Dirac Fermions ◽  
Yukawa Couplings ◽  
Fermion Fields ◽  
The Masses

We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields [Formula: see text], general Yukawa couplings and a [Formula: see text] symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the [Formula: see text] symmetry by vacuum expectation values (VEVs) of the [Formula: see text]. Introducing the shifted fields [Formula: see text] whose VEVs vanish, [Formula: see text] renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the [Formula: see text]. Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme, we compute the self-energies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavor symmetry group.

scholarly journals Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽  
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.

scholarly journals Fermion mass hierarchies from supersymmetric gauged flavour symmetry in 5D

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Ketan Patel
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Fermion Mass ◽  
Order Unity ◽  
Anomaly Cancellation ◽  
Fundamental Parameters ◽  
Yukawa Couplings ◽  
Fifth Dimension ◽  
Fermion Masses ◽  
The Masses

A mechanism to generate realistic fermion mass hierarchies based on supersymmetric gauged U(1)_FU(1)F symmetry in flat five-dimensional (5D) spacetime is proposed. The fifth dimension is compactified on S^1/Z_2S1/Z2 orbifold. The standard model fermions charged under the extra abelian symmetry along with their superpartners live in the 5D bulk. Bulk masses of fermions are generated by the vacuum expectation value of N=2N=2 superpartner of U(1)_FU(1)F gauge field, and they are proportional to U(1)_FU(1)F charges of respective fermions. This decides localization of fermions in the extra dimension, which in turn gives rise to exponentially suppressed Yukawa couplings in the effective 4D theory. Anomaly cancellation puts stringent constraints on the allowed U(1)_FU(1)F charges which leads to correlations between the masses of quarks and leptons. We perform an extensive numerical scan and obtain several solutions for anomaly-free U(1)_FU(1)F, which describe the observed pattern of fermion masses and mixing with all the fundamental parameters of order unity. It is found that the possible existence of SM singlet neutrinos substantially improves the spectrum of solutions by offering more freedom in choosing U(1)_FU(1)F charges. The model predicts Z^\primeZ′ boson mediating flavour violating interactions in both the quark and lepton sectors with the couplings which can be explicitly determined from the Yukawa couplings.

Dependence on the renormalization points in a simple scalar theory

1982 ◽  
Vol 60 (6) ◽  
pp. 789-792
Author(s):  
Gerry McKeon
Keyword(s):  
Scalar Potential ◽  
Scalar Fields ◽  
Simple Theory ◽  
Coupling Constants ◽  
Scalar Theory

One loop corrections to the scalar potential in a simple theory involving two scalar fields [Formula: see text] and ψ are evaluated. The dependence of the renormalized coupling constants on the renormalization points [Formula: see text] and ψ0 are examined. It is found that under the change [Formula: see text], ψ0 → (1 + ε)ψ0, the coupling constants vary according to a set of equations that are independent of the ratio [Formula: see text]. It is shown that the coupling constants are not altered if [Formula: see text] is changed.

scholarly journals FLAVOR SYMMETRY AND VACUUM ALIGNED MASS TEXTURES

2007 ◽  
Vol 16 (05) ◽  
pp. 1427-1436 ◽  
Author(s):  
SATORU KANEKO ◽  
HIDEYUKI SAWANAKA ◽  
TAKAYA SHINGAI ◽  
MORIMITSU TANIMOTO ◽  
KOICHI YOSHIOKA
Keyword(s):  
Scalar Potential ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Flavor Symmetry ◽  
Yukawa Couplings ◽  
Flavor Changing ◽  
Symmetry Approach ◽  
Mass Matrices ◽  
Vanishing Elements ◽  
Higgs Fields

A texture-zeros is an approach to reduce the number of free parameters in Yukawa couplings and it is one of the most attractive ones. In our paper, we discuss the origin of zero-structure in texture-zeros by S3 flavor symmetry approach. Some of electroweak doublet Higgs fields have vanishing vacuum expectation value (VEV) which leads to vanishing elements in quark and lepton mass matrices. Then, the structure of supersymmetric scalar potential is analyzed and Higgs fields have non-trivial S3 charges. As a prediction of our paper, a lower bound of a MNS matrix element, Ue3 ≥ 0.04, is obtained. The suppression of flavor-changing neutral currents (FCNC) mediated by the Higgs fields is discussed and lower bounds of the Higgs masses are derived.

scholarly journals Higgs Portal Inflation with Fermionic Dark Matter

2018 ◽  
Vol 168 ◽  
pp. 06002
Author(s):  
Aditya Aravind ◽  
Minglei Xiao ◽  
Jiang-Hao Yu
Keyword(s):  
Dark Matter ◽  
Scalar Potential ◽  
Scalar Fields ◽  
Fermionic Field ◽  
Planck Data ◽  
Slow Roll ◽  
The Standard Model ◽  
The Masses ◽  
Higgs Portal

We discuss the inflationary model presented in [1], involving a gauge singlet scalar field and fermionic dark matter added to the standard model. Either the Higgs or the singlet scalar could play the role of the inflaton, and slow roll is realized through its non-minimal coupling to gravity. The effective scalar potential is stabilized by the mixing between the scalars as well as the coupling with the fermionic field. Mixing of the two scalars also provides a portal to dark matter. Constraints on the model come from perturbativity and stability, collider searches and dark matter constraints and impose a constraining relationship on the masses of dark matter and scalar fields. Inflationary predictions are generically consistent with current Planck data.

Fermion localization on branes with non-standard kinetic terms

2018 ◽  
Vol 33 (40) ◽  
pp. 1850235 ◽  
Author(s):  
Masoumeh Moazzen Sorkhi ◽  
Esmaeil Mazani
Keyword(s):  
Scalar Field ◽  
Yukawa Coupling ◽  
Zero Mode ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Warp Factor ◽  
Coupling Mechanism ◽  
Fermion Fields ◽  
Derivative Term ◽  
Fermion Localization

In this paper, by using the Yukawa coupling mechanism, we consider the fermion localization in two types of braneworld models driven by real scalar fields with non-standard dynamics. Because of the existing freedom in the form of the Yukawa coupling, we consider two coupling forms between the background scalar field and spinors where one is arising from the geometry shape of the warp factor and the other is a function of the background scalar field containing a derivative scalar-fermion coupling. With two coupling functions, it is shown that the massless zero mode of fermion fields is localized on both branes with generalized dynamic depending on the values of the coupling constants. However, there is no localized mode when the Yukawa coupling only contains a derivative term of the background scalar field. Furthermore, effects of the parameters of the models on the zero mode and fermion effective potential are addressed.

DERIVATION OF A NOVEL RELATION BETWEEN THE MASSES OF THE TOP-QUARK AND AN ELECTROWEAK SCALAR

2000 ◽  
Vol 15 (11) ◽  
pp. 1597-1612
Author(s):  
E. H. LEMKE
Keyword(s):  
Gauge Symmetry ◽  
Top Quark ◽  
Scalar Fields ◽  
Energy Scale ◽  
Coupling Constants ◽  
Spontaneous Breaking ◽  
Precision Data ◽  
Vector Bosons ◽  
Charged Leptons ◽  
The Masses

We start with generating the masses of the charged leptons by gap equations. Then we present analogous radiative masses of the electroweak vector-bosons. We derive them from the global SU (2)L× U (1) symmetry without making recourse to any scalar fields or spontaneous breaking of gauge symmetry. Nevertheless, we find the mixing angle relation [Formula: see text]. Moreover, we find that the radiatively generated masses of Z and W require the existence of a cutoff energy of the order of 1014 GeV, which is just the grand-unification energy scale. We then eliminate the cutoff by renormalizing the two coupling constants and arrive at a function between mW and m top if mZ, [Formula: see text] and sin 2θ eff are given. Comparison with the electroweak precision data shows that the predicted value of mW does reproduce the experimental data though the vacuum loops of the leptons, of the light quarks as well as of possible scalar particles have been ignored. Then, we introduce a doublet of scalar bosons to investigate its effect on the mW prediction. We fix its couplings to the photon, to W as well as Z by localizing SU (2)L× U (1). The radiative mZ and mW results interdict a spontaneous breaking of the gauge symmetry. So there are an elementary charged and neutral scalar field. Their masses are identical. We show that there is no radiative effect of these scalars on the masses of W and Z. However, the scalar fields affect the coupling constants and, by this, the relationship between mW and m top alters. We calculate the modifications and find a relatively small effect. It seems to be comparable in magnitude with the QCD-corrections of the loops of vacuum polarization. Substituting the experimental mW value, we get a relation between m top and m scalar . The mass of the top-quark is increasing with increasing m scalar . In the standard model, m top also increases with increasing m Higgs . The effect of the elementary scalar is however much weaker.

scholarly journals High-temperature electroweak symmetry non-restoration from new fermions and implications for baryogenesis

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Oleksii Matsedonskyi ◽  
Géraldine Servant
Keyword(s):  
High Temperature ◽  
Scalar Potential ◽  
Scalar Fields ◽  
New Physics ◽  
High Temperature Phase ◽  
Tree Level ◽  
Thermal Mass ◽  
Temperature Phase ◽  
Electroweak Symmetry ◽  
Temperature Plasma

Abstract The strength of electroweak symmetry breaking may substantially differ in the early Universe compared to the present day value. In the Standard Model, the Higgs vacuum expectation value (vev ) vanishes and electroweak symmetry gets restored at temperatures above ∼ 160 GeV due to the Higgs field interactions with the high-temperature plasma. It was however shown that new light singlet scalar fields may change this behaviour. The key feature is the non-standard dependence on the Higgs vev of the new particles mass which can vanish at large Higgs vev, inducing a negative correction to the Higgs thermal mass, leading to electroweak symmetry non-restoration at high temperature. We show that such an effect can also be induced by new singlet fermions which on the other hand have the advantage of not producing unstable directions in the scalar potential at tree level, nor bringing additional severe hierarchy problems. As temperature drops, such a high-temperature breaking phase may continuously evolve into the zero-temperature breaking phase or the two phases can be separated by a temporary phase of restored symmetry. We discuss how our construction can naturally arise in motivated models of new physics, such as Composite Higgs. This is particularly relevant for baryogenesis, as it opens a whole class of possibilities in which the baryon asymmetry can be produced during a high temperature phase transition, while not being erased later by sphalerons.

scholarly journals The Family Formula for Leptons and Quarks

2019 ◽  
Author(s):  
Nikola Perkovic
Keyword(s):  
Structure Constant ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Majorana Neutrino ◽  
Fine Structure Constant ◽  
Dirac Fermions ◽  
Strong Argument ◽  
Yukawa Couplings ◽  
Charged Leptons ◽  
G Factors

The problem of Yukawa couplings being arbitrary parameters in the Standard Model Higgs mechanism is a long standing one due to their formulaic dependence on the Higgs Vacuum Expectation Value. We will attempt to solve this problem and provide a strong argument that the Yukawa couplings of charged leptons and down type quarks are not arbitrary parameters in the SM. A new methodology for predicting the Yukawa couplings will be presented by using Compton wavelengths, the Rydberg Constant and g-factors of charged leptons instead of relying on the Higgs VEV. We will then proceed to rewrite this new method in terms of an empirical formula that depends on the running of the fine-structure constant on the Q scale, charge and lepton quantum numbers and g-factors to predict the values of the Yukawa couplings for all three generations of charged leptons and d-type quarks. We will also touch on the subject of neutrinos both as Majorana and Dirac fermions respectively and make a prediction for the lightest possible Majorana neutrino and the differences between Dirac neutrinos and anti-neutrinos. We conclude that the Yukawa couplings are not arbitrary parameters in the SM and that this new formula provides very accurate results.

scholarly journals Quantum aspects of Yukawa model with scalar and axial scalar fields in curved spacetime

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Iosif L. Buchbinder ◽  
Andreza Rairis Rodrigues ◽  
Eduardo Antonio dos Reis ◽  
Ilya L. Shapiro
Keyword(s):  
Effective Potential ◽  
Dimensional Regularization ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Dirac Fermions ◽  
Yukawa Model ◽  
Curved Spacetime ◽  
Renormalization Group Approach ◽  
The One ◽  
Local Momentum

AbstractWe study the Yukawa model with one scalar and one axial scalar fields, coupled to N copies of Dirac fermions, in curved spacetime background. The theory possesses a reach set of coupling constants, including the scalar terms with odd powers of scalar fields in the potential, and constants of non-minimal coupling of the scalar fields to gravity. Using the heat-kernel technique and dimensional regularization, we derive the one-loop divergences, describe the renormalization of the theory under consideration and calculate the full set of beta- and gamma-functions for all coupling constants and fields. As a next step, we construct the renormalized one-loop effective potential of the scalar fields up to the terms linear in scalar curvature. This calculation includes only the contributions from quantum scalar fields, and is performed using covariant cut-off regularization and local momentum representation. Some difficulties of the renormalization group approach to the effective potential in the case under consideration are discussed.

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