Electroweak Model Research Articles

Nuclear and Detector Sensitivities for Neutrinoless Double Beta-Decay Experiments

Neutrinoless double beta-decay (DBD) is of current interest in high-sensitivity frontiers of particle physics. The decay is very sensitive to Majorana neutrino masses, neutrino CP phases, right-handed weak interactions, and others, which are beyond the standard electroweak model. DBDs are actually ultrarare events, and thus, DBD experiments with ultrahigh sensitivity are required. Critical discussions are presented on nuclear and detector sensitivities for high-sensitivity DBD experiments to study the neutrino masses in the normal and inverted mass hierarchies.

The Standard Model of Particle Physics as a Conspiracy Theory and the Possible Role of the Higgs Boson in the Evolution of the Early Universe

I am considering Veltman's "The Infrared - Ultraviolet Connection" addressing the issue of quadratic divergences and the related huge radiative correction predicted by the electroweak Standard Model (SM) in the relationship between the bare and the renormalized theory, commonly called "the hierarchy problem" which usually is claimed that this has to be cured. After the discovery of the Higgs particle at CERN, which essentially completed the SM, an amazing interrelation of the leading interaction strengths of the gauge bosons, the top-quark and the Higgs boson showed up amounting that the SM allows for a perturbative extrapolation of the running couplings up to the Planck scale. The central question concerns the stability of the electroweak vacuum, which requires that the running Higgs self-coupling stays positive. Although several evaluations seem to favor the meta-stability within the experimental and theoretical parameter-uncertainties, one should not exclude the possibility that other experiments and improved matching conditions will be able to establish the absolute stability of the SM vacuum in the future. I will discuss the stable vacuum scenario and its impact on early cosmology, revealing the Higgs boson as the inflaton. It turns out that the Standard Model's presumed "hierarchy problem" and similarly the "cosmological constant problem" resolve themselves when we understand the SM as a low energy effective tail that is emergent from a cutoff-medium at the Planck scale. "The Infrared - Ultraviolet Connection" conveyed by the Higgs boson mass renormalization appears in a new light when the energy dependence of the SM couplings is taken into account. The bare Higgs boson mass square then changes sign below the Planck scale where it is activating the Higgs mechanism.

Laser effect on the final products of Z-boson decay

Experimentalists have long sought a method that allows them to control the branching ratios of an unstable particle decay and direct some decay to follow one specific desired channel without another. The powerful laser could make this a reality. In this letter and within the framework of the standard electroweak model, we investigate theoretically the laser effect on the branching ratios of different Z-boson decay modes by calculating analytically the Z-boson decay into a fermion–antifermion pai in the presence of a circularly polarized electromagnetic field. It is found that, at high intensities, the Z-boson could only decay invisibly into neutrinos, and its decay into any other pair of charged fermions becomes impossible due to the increase in the effective mass that fermions acquire inside the electromagnetic field. The influence of the laser frequency and intensity on the lifetime is also included in order to confirm the surprising result obtained for the pion lifetime in a previous paper (Mouslih 2020 Phys. Rev. D 102 073006).

Spectral action in matrix form

Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang–Mills theory. We illustrate the procedure for the toy electroweak model.

Spin-dipole nuclear matrix element for the double beta decay of 76Ge by the (3He, t) charge-exchange reaction

Nuclear matrix elements (NMEs) for double beta decays (DBDs) are crucial for studying the neutrino mass and other neutrino properties beyond the standard electro-weak model by measuring neutrino-less DBDs. The spin-dipole (SD) Jπ = 2− NME is one of the major components associated with the DBD NME. The SD NME for 76Ge was derived for the first time by using the 74,76 Ge (3He, t) at RCNP Osaka. The obtained SD NME for the 76Ge → 76As ground-state transition is in natural units. This is smaller by a coefficient around k ≈ 0.2 with respect to the quasi-particle model NME . The impact of the reduced (quenched) SD NME on DBD neutrino studies is discussed.

String landscape and fermion masses

Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution $P({\cal Q})$ of a physical quantity $\cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${\cal Q}=0$ as a signature of string theory. In the Racetrack K\"ahler uplift model, where $P(\Lambda)$ of the cosmological constant $\Lambda$ peaks sharply at $\Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $\Lambda$ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $\sum m_{\nu} \simeq 0.0592$ eV, with an upper bound $\sum m_{\nu} <0.066$ eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.

Nonperturbative path integral quantization of the electroweak model: The Maxwell integration

The non-perturbative path integral quantization of the electroweak model is confronted with an apparent instability when integrating over the Maxwell potential $A_{\mu}$ due to the fast growth of the box graphs $AAAA$ and $AAAZ$ for large amplitude variations of $A_{\mu}$. $Z_{\mu}$ is from the vector part of the weak neutral current. These graphs are unavoidable because they are conditionally convergent and have to be isolated in the model's exact Euclidean one-loop effective action arising from its fermion determinants. A previous QED calculation of the large amplitude variation of its fermion determinant for a class of random potentials showed that the $AAAA$ box graph cancels in this limit. Using this result it is shown that within the electroweak model large amplitude variations of $A_{\mu}$ for fixed $Z_{\mu}$ in a superposition of these fields cancel the $AAAA$ and $AAAZ$ graphs, thereby removing an apparent obstacle to the model's non-perturbative quantization. A negative paramagnetic term in the remainder opposes the effective action's growth for such variations. Its calculation requires knowledge of the degeneracy of the bound states of a charged fermion in the four-dimensional magnetic fields generated by the functional measure of $A_{\mu}$.

Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity

We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the oblique correction parameters S and U can also be written in terms of the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It is found that perturbative unitarity of the scattering amplitudes involving the Higgs bosons and the longitudinal gauge bosons demands the flatness of the scalar manifold. The relationship between the finiteness of the electroweak oblique corrections and perturbative unitarity of the scattering amplitudes is also clarified in this language: we verify that once the tree-level unitarity is ensured, then the one-loop finiteness of the oblique correction parameters S and U is automatically guaranteed.

Direct determination of sin2ϑeffℓ at hadron colliders

We discuss the renormalization of the electroweak Standard Model at 1-loop using the leptonic effective weak mixing angle as one of the input parameters. We evaluate the impact of this choice in the prediction of the forward-backward asymmetry for the neutral current Drell-Yan process. The proposed input scheme is suitable for a direct determination of the effective leptonic weak mixing angle from the experimental data.

Neutrino masses in an SU(4)otimes U(1)-electroweak model with a scalar decuplet

A neutrino mass model is suggested within an SU(4)otimes U(1)-electroweak theory. The smallness of neutrino masses can be guaranteed by a seesaw mechanism realized through Yukawa couplings to a scalar SU(4)-decuplet. In this scheme the light active neutrinos are accompanied by heavy neutrinos, which may have masses at different scales, including those within eV–MeV scales investigated quite intensively in both particle physics and astrophysics/cosmology. The flavour neutrinos are superpositions of light neutrinos and a small fraction of heavy neutrinos with the mixing to be determined by the model’s parameters (Yukawa coupling coefficients or symmetry breaking scales). The distribution shape of the Yukawa couplings can be visualized via a model-independent distribution of the neutrino mass matrix elements derived by using the current experimental data. The absolute values of these Yukawa couplings are able to be determined if the symmetry breaking scales are known, and vice versa. With reference to several current and near future experiments, detectable bounds of these heavy neutrinos at different mass scales are discussed and estimated.

Ultraviolet complete quantum field theory and particle model

An ultraviolet complete particle model is constructed for the observed particles of the standard model. The quantum field theory associates infinite derivative entire functions with propagators and vertices, which make quantum loops finite and maintain Poincar\'e invariance and unitarity of the model. The electroweak model $SU(2)\times U(1)$ group is treated as a broken symmetry group with non-vanishing experimentally determined boson and fermion masses. A spontaneous symmetry breaking of the vacuum by a scalar Higgs field is not invoked to restore boson and fermion masses to the initially massless $SU(2)\times U(1)$ Lagrangian of the standard model. The hierarchy naturalness problem of the Higgs boson mass is resolved and the model contains only experimentally observed masses and coupling constants. The model can predict a stable vacuum evolution. Experimental tests to distinguish the standard model from the alternative model are proposed. The finite quantum field theory can be extended to quantum gravity.

Artificial versus Substantial Gauge Symmetries: A Criterion and an Application to the Electroweak Model

To systematically answer the generalized Kretschmann objection, I propose a mean to make operational a criterion widely recognized as allowing one to decide whether the gauge symmetry of a theory is artificial or substantial. My proposition is based on the dressing field method of gauge symmetry reduction, a new simple tool from mathematical physics. This general scheme allows one in particular to straightforwardly argue that the notion of spontaneous symmetry breaking is superfluous to the empirical success of the electroweak theory. Important questions regarding the context of justification of the theory then arise.

Electroweak phase transition with three phases in the SU(2)1 ⊗ SU(2)2 ⊗ U(1)Y model

Our analysis shows that SM-like electroweak phase transition (EWPT) in the [Formula: see text] (2-2-1) model is a first-order phase transition at the 200 GeV scale (the SM scale). Its strength [Formula: see text] is about 1–2.7 and the masses of new gauge bosons are larger than 1.7 TeV when the second VEV is larger than 535 GeV in a three-stage EWPT scenario and the coupling constant of [Formula: see text] group must be larger than 2. Therefore, this first-order EWPT can be used to fix VEVs and the coupling constant of the gauge group in electroweak models.

Radiative corrections of order O(αEe/mN) to Sirlin’s radiative corrections of order O(α/π) to the neutron lifetime

We calculate the radiative corrections of order O(alpha E_e/m_N) as next-to-leading order corrections in the large nucleon mass expansion to Sirlin's radiative corrections of order O(alpha/pi) to the neutron lifetime. The calculation is carried out within a quantum field theoretic model of strong low-energy pion--nucleon interactions described by the linear sigma-model (LsM) with chiral SU(2)xSU(2) symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with SU(2)_L x U(1)_Y symmetry of the Standard Electroweak Model (SEM). Such a quantum field theoretic model is some kind a hadronized version of the Standard Model (SM). From a gauge invariant set of the Feynman diagrams with one-photon exchanges we reproduce Sirlin's radiative corrections of order O(alpha/pi), calculated to leading order in the large nucleon mass expansion, and calculate next-to-leading corrections of order O(alpha E_e/m_N). This confirms Sirlin's confidence level of the radiative corrections O(alpha E_e/m_N). The contributions of the LsM are taken in the limit of the infinite mass of the scalar isoscalar sigma-meson. In such a limit the LsM reproduces the results of the current algebra (Weinberg, Phys. Rev. Lett. {\bf 18}, 188 (1967)) in the form of effective chiral Lagrangians of pion-nucleon interactions with non--linear realization of chiral SU(2)xSU(2) symmetry. In such a limit the L$\sigma$M is also equivalent to Gasser-Leutwyler's chiral quantum field theory or chiral perturbation theory (ChPT) with chiral SU(2)xSU(2)symmetry and the exponential parametrization of a pion-field (Ecker, Prog. Part. Nucl. Phys. {\bf 35}, 1 (1995)).

Impact of fermionic electroweak multiplet dark matter on vacuum stability with one-loop matching

We investigate the effect of fermionic electroweak multiplet dark matter models on the stability of the electroweak vacuum using two-loop renormalization group equations (RGEs) and one-loop matching conditions. Such a treatment is crucial to obtain reliable conclusions, compared with one-loop RGEs and tree-level matching conditions. In addition, we find that the requirement of perturbativity up to the Planck scale would give strong and almost mass-independent constraints on the Yukawa couplings in the dark sector. We also evaluate these models via the idea of finite naturalness for the Higgs mass fine-tuning issue.

Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

Within the standard [Formula: see text] theory of weak interactions, Quantum Electrodynamics (QED) and the linear [Formula: see text]-model [Formula: see text] of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron [Formula: see text]-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order [Formula: see text], induced by hadronic structure of the nucleon, to the rate of the neutron [Formula: see text]-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative [Formula: see text]-decay and neutron [Formula: see text]-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective [Formula: see text] vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and [Formula: see text], which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the [Formula: see text], where the effective [Formula: see text] vertex of hadron–lepton current–current interactions is caused by the [Formula: see text]-electroweak-boson exchange.

New Cosmology: The Global Dynamics of the Higgs Quantum Space and the Accelerated Expansion of the Universe

This work investigates the nature of the empty space and of the energy accelerating expansion of the universe, within the context of the Higgs theory. It is consensus among the cosmologists that dark energy, accelerating the expansion of the universe, is energy of the empty space (vacuum) itself. According to the Higgs theory, empty space (vacuum) is filled up by a real quantum fluid medium, closely analogous to the superconducting condensate, giving mass to the elementary particles by the Higgs mechanism. This spatial medium is the holder of the vacuum energy. Current theories describe the empty space (vacuum) in terms of the stress-energy tensor of a perfect fluid and estimate the vacuum energy density in terms of zero-point energies of the various force fields. They come to the scandalous conclusion that the vacuum energy density is 120 decimal orders of magnitude larger than shown by the observations. In the context of the Higgs theory, empty space, far from a perfect fluid, is a very strongly correlated boson condensate, a perfect quantum fluid ruled by the principles of quantum physics and governed by a powerful order parameter. This order parameter is stabilized by a huge energy gap that, according to the Glashow-Weinberg-Salam electroweak model, achieves more than 200 GeV. This huge energy gap very strongly suppresses the quantum fluctuations and the zero-point energies. This lets clear that estimating the vacuum energy density in terms of the zero-point energies cannot be correct. The expanding universe does not create more and more vacuum energy and does not expand against a negative pressure. The universe is an adiabatic system that conserves the total mass-energy and expansion only reduces the vacuum energy density. Calculations within this context show that the vacuum energy density converges closely to the observed value.

Gauge properties of hadronic structure of nucleon in neutron radiative beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

Within the standard [Formula: see text] theory of weak interactions, Quantum electrodynamics (QED) and the linear [Formula: see text]-model (L[Formula: see text]M) of strong low-energy hadronic interactions, we analyze gauge properties of hadronic structure of the neutron and proton in the neutron radiative [Formula: see text]-decay. We show that the Feynman diagrams, describing contributions of hadronic structure to the amplitude of the neutron radiative [Formula: see text]-decay in the tree-approximation for strong low-energy interactions in the L[Formula: see text]M, are gauge invariant. In turn, the complete set of Feynman diagrams, describing the contributions of hadron–photon interactions in the one-hadron-loop approximation, is not gauge invariant. In the infinite limit of the scalar [Formula: see text]-meson, reproducing the current algebra results (S. Weinberg, Phys. Rev. Lett. 18, 188 (1967)), and to leading order in the large nucleon mass expansion the Feynman diagrams, violating gauge invariance, do not contribute to the amplitude of the neutron radiative [Formula: see text]-decay in agreement with Sirlin’s analysis of strong low-energy interactions in neutron [Formula: see text] decays. We assert that the problem of appearance of gauge noninvariant Feynman diagrams of hadronic structure of the neutron and proton is related to the following. The vertex of the effective [Formula: see text] weak interactions does not belong to the combined quantum field theory including the L[Formula: see text]M and QED. We argue that gauge invariant set of Feynman diagrams of hadrons, coupled to real and virtual photons in neutron [Formula: see text] decays, can be obtained within the combined quantum field theory including the Standard Electroweak Model (SEM) and the L[Formula: see text]M, where the effective [Formula: see text] vertex of weak interactions is a result of the [Formula: see text]-electroweak boson exchange.

Derivation of spontaneously broken gauge symmetry from the consistency of effective field theory II: Scalar field self-interactions and the electromagnetic interaction

We extend our study of deriving the local gauge invariance with spontaneous symmetry breaking in the context of an effective field theory by considering self-interactions of the scalar field and inclusion of the electromagnetic interaction. By analyzing renormalizability and the scale separation conditions of three-, four- and five-point vertex functions of the scalar field, we fix the two couplings of the scalar field self-interactions of the leading order Lagrangian. Next we add the electromagnetic interaction and derive conditions relating the magnetic moment of the charged vector boson to its charge and the masses of the charged and neutral massive vector bosons to each other and the two independent couplings of the theory. We obtain the bosonic part of the Lagrangian of the electroweak Standard Model as a unique solution to the conditions imposed by the self-consistency conditions of the considered effective field theory.

Penning-Trap Mass Measurements in Atomic and Nuclear Physics

Penning-trap mass spectrometry in atomic and nuclear physics has become a well-established and reliable tool for the determination of atomic masses. In combination with short-lived radioactive nuclides it was first introduced at ISOLTRAP at the Isotope Mass Separator On-Line facility (ISOLDE) at CERN. Penning traps have found new applications in coupling to other production mechanisms, such as in-flight production and separation systems. The applications in atomic and nuclear physics range from nuclear structure studies and related precision tests of theoretical approaches to description of the strong interaction to tests of the electroweak Standard Model, quantum electrodynamics and neutrino physics, and applications in nuclear astrophysics. The success of Penning-trap mass spectrometry is due to its precision and accuracy, even for low ion intensities (i.e., low production yields), as well as its very fast measurement cycle, enabling access to short-lived isotopes. The current reach in relative mass precision goes beyond δ m/ m=10−8, the half-life limit is as low as a few milliseconds, and the sensitivity is on the order of one ion per minute in the trap. We provide a comprehensive overview of the techniques and applications of Penning-trap mass spectrometry in nuclear and atomic physics.