Electroweak Standard Model Research Articles

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.

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.

Protecting the stability of the electroweak vacuum from Planck-scale gravitational effects

We investigate the stability of the Standard-Model Electroweak (EW) vacuum in the presence of Planck-scale suppressed operators of the type $\phi^{2n}/M^{2n-4}_{\rm P}$ that involve the Higgs field $\phi$ and could in principle be induced by quantum gravity effects. We show how minimal embeddings of the Standard Model (SM) in supergravity (SUGRA) can stabilize the EW vacuum against such operators up to very high values of the induced supersymmetry breaking scale $M_{\cal S}$, which may well be above the onset of the so-called SM metastability scale of $10^{11}$ GeV. In particular, we explicitly demonstrate how discrete $R$ symmetries could be invoked to suppress the occurrence of harmful Planck-scale operators of the form $\phi^{2n}/M^{2n-4}_{\rm P}$ to arbitrary higher powers of $n$. We analyze different scenarios of Planck-scale gravitational physics and derive lower limits on the power $n$ that is required in order to protect our EW vacuum from dangerous rapid decay. The significance of our results for theories of low-scale quantum gravity is illustrated.

Update of the global electroweak fit and constraints on two-Higgs-doublet models

We present an update of the global fit of the Standard Model electroweak sector to latest experimental results. We include new kinematic top quark and W boson mass measurements from the LHC, a sin !^2theta ^{ell }_{mathrm{eff}} result from the Tevatron, and a new evaluation of the hadronic contribution to alpha (M_Z^2). We present tests of the internal consistency of the electroweak Standard Model and updated numerical predictions of key observables. The electroweak data combined with measurements of the Higgs boson coupling strengths and flavour physics observables are used to constrain parameters of two-Higgs-doublet models.

Scalar dark matter explanation of the DAMPE data in the minimal left-right symmetric model

Left-Right symmetric model (LRSM) has been an attractive extension of the Standard Model (SM) which can address the origin of parity violation in the SM electroweak (EW) interactions, generate tiny neutrino masses, accommodate dark matter (DM) candidates and provide a natural framework for baryogenesis through leptogenesis. In this work we utilize the minimal LRSM to study the recently reported DAMPE results of cosmic $e^+e^-$ spectrum which exhibits a tentative peak around 1.4 TeV, while satisfying the current neutrino data. We propose to explain the DAMPE peak with a complex scalar DM $\chi$ in two scenarios: 1) $\chi\chi^* \to H_1^{++}H_1^{--} \to \ell_i^+\ell_i^+\ell_j^-\ell_j^-$; 2) $\chi\chi^* \to H_{k}^{++}H_{k}^{--} \to \ell_i^+\ell_i^+\ell_j^-\ell_j^-$ accompanied by $\chi\chi^* \to H_1^+ H_1^- \to \ell_i^+ \nu_{\ell_i} \ell_j^- \nu_{\ell_j}$ with $\ell_{i,j}=e,\mu,\tau$ and $k=1,2$. We fit the theoretical prediction on $e^+e^-$ spectrum to relevant experimental data to determine the scalar mass spectrum favored by the DAMPE excess. We also consider various constraints from theoretical principles, collider experiments as well as DM relic density and direct search experiments. We find that there are ample parameter space which can interpret the DAMPE data while passing the constraints. Our explanations, on the other hand, usually imply the existence of other new physics at the energy scale ranging from $10^7 {\rm GeV}$ to $10^{11} {\rm GeV}$. Collider tests of our explanations are also discussed.

High precision analytical description of the allowed β spectrum shape

Beta decay is a process that reveals the structure of the standard model and its possible extensions. This reviews provides a description of the allowed beta-spectrum shape in view of ongoing and planned measurements searching for physics beyond the standard electroweak model and weak magnetism. The formalism presents a description of the underlying physics. The derived expression for both Fermi and Gamow-Teller transitions is accurate for low to medium Z nuclei.

Cosmological implications of Higgs near-criticality.

The Standard Model electroweak (EW) vacuum, in the absence of new physics below the Planck scale, lies very close to the boundary between stability and metastability, with the last option being the most probable. Several cosmological implications of this so-called 'near-criticality' are discussed. In the metastable vacuum case, the main challenges that the survival of the EW vacuum faces during the evolution of the Universe are analysed. In the stable vacuum case, the possibility of implementing Higgs inflation is critically examined.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'.

Amplitudes, recursion relations and unitarity in the Abelian Higgs model

The Abelian Higgs model forms an essential part of the electroweak standard model: it is the sector containing only Z0 and Higgs bosons. We present a diagram-based proof of the tree-level unitarity of this model inside the unitary gauge, where only physical degrees of freedom occur. We derive combinatorial recursion relations for off-shell amplitudes in the massless approximation, which allows us to prove the cancellation of the first two orders in energy of unitarity-violating high-energy behaviour for any tree-level amplitude in this model. We describe a deformation of the amplitudes by extending the physical phase space to at least 7 spacetime dimensions, which leads to on-shell recursion relations à la BCFW. These lead to a simple proof that all on-shell tree amplitudes obey partial-wave unitarity.

The standard electroweak model in the noncommutative DFR space–time

The noncommutative (NC) framework elaborated by Doplicher, Fredenhagen and Roberts (DFR) has a Lorentz invariant space–time structure in order to be considered as a candidate to understand the physics of the early Universe. In DFR formalism, the NC parameter [Formula: see text] is a coordinate operator in an extended Hilbert space and it has a conjugate momentum. Since [Formula: see text] and [Formula: see text] are independent coordinates, the Moyal–Weyl (MW) product can be used in this framework. With these elements, in this work, we have constructed the standard electroweak model. To accomplish this task, we have begun with the MW-product basis group of symmetry. After that we have introduced the spontaneous symmetry breaking and the hypercharge in DFR framework. The electroweak symmetry breaking was analyzed and the masses of the new bosons were computed. Finally, the gauge symmetry and gauge transformations were discussed.

Quantum stabilization of a hedgehog type of cosmic string

Within a slightly simplified version of the electroweak standard model we investigate the stabilization of cosmic strings by fermion quantum fluctuations. Previous studies of quantum energies considered variants of the Nielsen–Olesen profile embedded in the electroweak gauge group and showed that configurations are favored for which the Higgs vacuum expectation value drops near the string core and the gauge field is suppressed. This work found that the strongest binding was obtained from strings that differ significantly from Nielsen–Olesen configurations, deforming essentially only the Higgs field in order to generate a strong attraction without inducing large gradients. Extending this analysis, we consider the leading quantum correction to the energy per unit length of a hedgehog type string, which, in contrast to the Nielsen–Olesen configuration, contains a pseudoscalar field. To employ the spectral method we develop the scattering and bound state problems for fermions in the background of a hedgehog string. Explicit occupation of bound state levels leads to strings that carry the quantum numbers of the bound fermions. We discuss the parameter space for which stable, hedgehog type cosmic strings emerge and reflect on phenomenological consequences of these findings.

Exotic electroweak signals in the twin Higgs model

The Twin Higgs model is the preeminent example of a theory of neutral naturalness, where the new particles that alleviate the little hierarchy problem are Standard Model (SM) singlets. The most promising collider search strategy, based on rare Higgs decays, is nevertheless not effective in significant regions of the parameter space of the low energy theory. This underlines the importance of phenomenological studies on ultraviolet completions of the Twin Higgs model, which must lie at a scale lower than 5-10 TeV. We pursue this course in the context of non-supersymmetric completions, focusing on exotic fermions that carry SM electroweak and twin color charges, as well as on exotic vectors that transform as the bi-fundamental of the electroweak or color groups. Both $Z_2$-preserving and $Z_2$-breaking mass spectra are considered for the exotic fermions. In the former case they must be heavier than $\sim 1$ TeV, but can still be sizably produced in the decays of the color bi-fundamental vector. In the $Z_2$-breaking scenario, the exotic fermions can have masses in the few hundred GeV range without significantly increasing the fine-tuning. Once pair-produced through the electroweak interactions, they naturally form bound states held together by the twin color force, which subsequently annihilate back to SM particles. The associated resonance signals are discussed in detail. We also outline the phenomenology of the electroweak bi-fundamental vectors, some of which mix with the SM $W$ and $Z$ and can therefore be singly produced in hadron collisions.

Operational Spacetimes

Time, positions and spacetimes are modelled by groups and subgroup classes. Their Hilbert space representations define particles and interactions. Electroweak spacetime, proposed as nature-realized manifold, represents the homogeneous groups of the electroweak standard model. The leptonic and hadronic (quark) sectors, characteristic for particles and interactions, are related to the embedded time and position operations, respectively.

Three-loop vacuum integrals with arbitrary masses

Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, analytical results for integrals with only one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.

An Introduction to the Massive Helicity Formalism with applications to the Electroweak SM

The power of the helicity formalism has been appreciated recently from its application to the massless case, where plenty of formal aspects of multi-legs amplitudes have been derived. However, in order to extend the formalism to the realistic cases, such as the electroweak Standard Model and QCD with massive quarks, some extra inputs are needed. We discuss first the formalism needed to evaluate amplitudes expressed with the modern notation for massive fermions and vectors based on a thorough treatment of Proca vector fields. Then, we present some examples of elementary processes where it is shown how the formalism leads to tremendous simplifications, these include 2-body decays Z → ƒƒ, h → ƒƒ and h → W-W+ as well as the 3-body decay h → V ƒ' f̄.

Probing new physics scales from Higgs and electroweak observables at e + e − Higgs factory

New physics beyond the standard model (SM) can be model-independently formulated via dimension-6 effective operators, whose coefficients (cutoffs) characterize the scales of new physics. We study the probe of new physics scales from the electroweak precision observables (EWPO) and the Higgs observables (HO) at the future $e^+e^-$ Higgs factory (such as CEPC). To optimize constraints of new physics from all available observables, we establish a scheme-independent approach. With this formulation, we treat the SM electroweak parameters and the coefficients of dimension-6 operators on equal footing, which can be fitted simultaneously by the same $\chi^2$ function. As deviations from the SM are generally small, we can expand the new physics parameters up to linear order and perform an analytical $\chi^2$ fit to derive the potential reach of the new physics scales. We find that the HO from both Higgs produnction and decay rates can probe the new physics scales up to 10TeV (and to 44TeV for the case of gluon-involved operator $\mathcal{O}_g$), and the new physics scales of Yukawa-type operators can be probed by the precision Higgs coupling measurements up to (13-25)TeV. Further including the EWPO can push the limit up to 35TeV. From this prospect, we demonstrate that the EWPO measured in the early phase of a Higgs factory can be as important as the Higgs observables. These indirect probes of new physics scales at the Higgs factory can mainly cover the energy range to be directly explored by the next generation hadron colliders of pp(50-100TeV), such as the SPPC and FCC-hh.

Energy spectrum of the electroweak Pomeron

In this paper we study the high energy behaviour of Electroweak Standard Model for a nonzero Weinberg angle $\theta_{W}$. We evaluate the spectrum of the electroweak pomeron and demonstrate that the leading intercept is given by $\alpha _{\rm e.w.}4 \ln 2$ and does not depend on the mixing angle $\theta_{W}$. Due to its very small numerical value, we conclude that the high energy behaviour of electroweak theory cannot be discussed without including the QCD Pomeron which, at sufficiently large energies, will dominate.

SU(2/1) gauge-Higgs unification

We discuss a question whether the observed Weinberg angle and Higgs mass are calculable in the formalism based on a construction in which the electroweak gauge group [Formula: see text] is embedded in the graded Lie group [Formula: see text]. Here, we follow original works of Ne’eman and Fairlie believing that bosonic fields take their values in the Lie superalgebra and fermionic fields take their values in its representation space. At the same time, our approach differs significantly. The main one is that while for them the gauge symmetry group is [Formula: see text], here we consider only symmetries generated by its even subgroup, i.e. symmetries of the standard electroweak model. The reason is that such formalism fixes the quartic Higgs coupling and at the same time removes the sign and statistics problems. The main result is that the presented model predicts values of the Weinberg angle and the Higgs mass correctly up to the two-loop level. Moreover, the model sets the unification scale coinciding with the electroweak scale and automatically describes the fermions correctly with the correct quark and lepton charges.

Symmetry breaking patterns of the 3-3-1 model at finite temperature

We consider the minimal version of an extension of the standard electroweak model based on the $SU(3)_c \times SU(3)_L \times U(1)_X$ gauge symmetry (the 3-3-1 model). We analyze the most general potential constructed from three scalars in the triplet representation of $SU(3)_L$, whose neutral components develop nonzero vacuum expectation values, giving mass for all the model's massive particles. {}For different choices of parameters, we obtain the particle spectrum for the two symmetry breaking scales: one where the $SU(3)_L \times U(1)_X$ group is broken down to $SU(2)_L\times U(1)_Y$ and a lower scale similar to the standard model one. Within the considerations used, we show that the model encodes two first-order phase transitions, respecting the pattern of symmetry restoration. The last transition, corresponding to the standard electroweak one, is found to be very weak first-order, most likely turning second-order or a crossover in practice. However, the first transition in this model can be strongly first-order, which might happen at a temperature not too high above the second one. We determine the respective critical temperatures for symmetry restoration for the model.