Charged Fermions Research Articles

QED as a many-body theory of worldlines. II. All-order S -matrix formalism

In arXiv:2206.04188, we developed a first-quantized worldline formalism for all-order computations of amplitudes in QED. In particular, we demonstrated in this framework an all-order proof of the infrared safety of the Faddeev-Kulish (FK) S-matrix for virtual exchanges in the scattering of charged fermions. In this work, we extend the worldline formalism for both the Dyson and FK S-matrix to consider further the emission and absorption of arbitrary numbers of photons. We show how Low's theorem follows in this framework and derive Weinberg's theorem for the exponentiation of IR divergences. In particular, we extend our all-order proof of the IR safety of the FK S-matrix to both virtual exchanges and real photon emissions. We argue that the worldline approach leads to a modern Wilsonian interpretation of the IR safety of the FK S-matrix and provides a novel template for the treatment of IR divergences in real-time problems. Using Grassmannian integration methods, we derive a simple and powerful result for N-th rank vacuum polarization tensors. Applications of these methods will be discussed in follow-up work.

Decay law of magnetic turbulence with helicity balanced by chiral fermions

In plasmas composed of massless electrically charged fermions, chirality can be interchanged with magnetic helicity while preserving the total chirality through the quantum chiral anomaly. The decay of turbulent energy in plasmas such as those in the early Universe and compact stars is usually controlled by certain conservation laws. In the case of zero total chirality, when the magnetic helicity density balances with the appropriately scaled chiral chemical potential to zero, the total chirality no longer determines the decay. We propose that in such a case, an adaptation to the Hosking integral, which is conserved in nonhelical magnetically dominated turbulence, controls the decay in turbulence with helicity balanced by chiral fermions. We show, using a high resolution numerical simulation, that this is indeed the case. The magnetic energy density decays and the correlation length increases with time just like in nonhelical turbulence with vanishing chiral chemical potential. But here, the magnetic helicity density is nearly maximum and shows a scaling with time t proportional to t−2/3. This is unrelated to the t−2/3 decay of magnetic energy in fully helical magnetic turbulence. The modulus of the chiral chemical potential decays in the same fashion. This is much slower than the exponential decay previously expected in theories of asymmetric baryon production from the hypermagnetic helicity decay after axion inflation.Received 1 February 2023Accepted 4 April 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L022028Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAstrophysical fluid dynamicsCosmologyMagnetohydrodynamic turbulenceGravitation, Cosmology & AstrophysicsPlasma PhysicsFluid Dynamics

Aspects of the electroweak Skyrmion

We consider certain aspects of the electroweak Skyrmion (EWS). We discuss the case of EWS with dynamical Higgs and find numerical solutions for various values of the cutoff scale. Our results are qualitatively similar to the ones present in the literature, but we find a considerable lower mass than previous studies. We discuss the quantization of the light degrees of freedom and prove that the EWS is a boson. We consider the interaction between fermions and the EWS and the transfer of fermionic charge onto the soliton. We consider the large distance structure of the soliton and the interaction between two well separated EWSs. We find that the classical EWS has a magnetic dipole moment. We discuss the lifetime of the metastable soliton. Finally, we discuss some phenomenological and cosmological consequences of our results.

A two-generational SU(7) model with extended weak sector: mass hierarchies, mixings, and the flavor non-universality

We study a possible gauge symmetry breaking pattern in an SU(7) grand unified theory, which describes the mass origins of all electrically charged SM fermions of the second and the third generations. Two intermediate gauge symmetries of {mathcal{G}}_{341}equiv textrm{SU}{(3)}_cotimes textrm{SU}{(4)}_Wotimes textrm{U}{(1)}_{X_0} and {mathcal{G}}_{331}equiv textrm{SU}{(3)}_cotimes textrm{SU}{(4)}_Wotimes textrm{U}{(1)}_{X_1} arise above the electroweak scale. SM fermion mass hierarchies between two generations can be obtained through a generalized seesaw mechanism. The mechanism can be achieved with suppressed symmetry breaking VEVs from multiple Higgs fields that are necessary to avoid tadpole terms in the Higgs potential. Some general features of the SU(7) fermion spectrum will be described, which include the existence of vectorlike fermions, the tree-level flavor changing weak currents between the SM fermions and heavy partner fermions, and the flavor non-universality between different SM generations from the extended weak sector.

Codimension-2 defects and higher symmetries in (3+1)D topological phases

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2ℤ2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2ℤ2×ℤ2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral (D_nDn) and alternating (A_6A6) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4H4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6A6 gauge theory.

Collision of two interacting electrons on a mesoscopic beam splitter: Exact solution in the classical limit

Experiments on collisions of isolated electrons guided along the edges in quantum Hall setups can mimic mixing of photons with the important distinction that electrons are charged fermions. In the so-called electronic Hong-Ou-Mandel (HOM) setup uncorrelated pairs of electrons are injected towards a beamsplitter. If the two electron wave packets were identical, Fermi statistics would force the electrons to scatter to different detectors, yet this quantum antibunching may be confounded by Coulomb repulsion. Here we model an electronic HOM experiment using a quadratic 2D saddle point potential for the beamsplitter and unscreened Coulomb interaction between the two injected electrons subjected to a strong out-of-plane magnetic field. We show that classical equations of motion for the drift dynamics of electrons' guiding centers take on the form of Hamilton equations for canonically conjugated variables subject to the saddle point potential and the Coulomb potential where the dynamics of the center-of-mass coordinate and the relative coordinate separate. We use these equations to determine collision outcomes in terms of a few experimentally tuneable parameters: the initial energies of the uncorrelated electrons, relative time delay of injection and the shape of the saddle point potential. A universal phase diagram of deterministic bunching and antibunching scattering outcomes is presented with a single energy scale characterizing the increase of the effective barrier height due to interaction of coincident electrons. We suggest clear-cut experimental strategies to detect the predicted effects and give analytical estimates of conditions when the classical dynamics is expected to dominate over quantum effects.

Quantum backflow for a massless Dirac fermion on a ring

We study the quantum backflow problem for a massless charged Dirac fermion constrained to move on a ring of radius R. Using the relativistic current operator for states of definite magnetic quantum number it is shown that quantum backflow takes place on the ring. We also study the backflow problem on the line and it is shown that unlike massive fermions, massless fermions do not exhibit quantum backflow.

Photon splitting corrections to soft-photon resummation

In this paper we present an algorithm to add photon-splitting corrections to the Yennie-Frautschi-Suura-style soft-photon resummation available in the Sherpa MonteCarlo event generator. Photon-splitting corrections enter at NNLO in QED and, as these effects are not incorporated in the standard QED FSR resummations, their size is larger than the pure hard photon-emission corrections at the same order. We introduce different lepton dressing strategies which incorporate further leptons and hadrons in addition to the customary photons, and discuss their sensitivity to dressing parameters such as the cone size. Finally, we quantify the effects of photon splittings into charged fermions and scalars under different such dressing strategies on Z → e+e− decays and find effects of up to 1% for suitably inclusive dressing strategies independent of the dressing cone size, and up to 9% if only photons are used in the dressing procedure with large dressing cones.

Fermionic and bosonic greybody factors as well as quasinormal modes for charged Taub NUT black holes

The paper studies the spinorial wave equations, namely the Dirac and the Klein–Gordon equations, as well as the greybody radiations and quasinormal modes (QNMs) of the charged Taub NUT black hole (CTNBH). To obtain fermionic greybody factors (GFs) and QNMs, we study the charged fermions by employing the Dirac equation. To this end, we use a null tetrad in the Newman–Penrose formalism. Then, we separate the Dirac equation into radial and angular sets. Using the obtained radial equations, we convert them into the typical one dimensional Schrödinger-like wave equations with the aid of tortoise coordinate and derive the effective potentials. For bosonic GFs and QNMs, we study the Klein–Gordon equation in the CTNBH geometry and obtain the radial equation. We then derive the effective potential and investigate the effect of NUT parameter on it. We show that while the fermionic QNMs and GFs individually increase with the increasing NUT parameter, the increase of bosonic GFs with increasing NUT parameter is overwhelmingly greater than that of the bosonic QNMs.

Synchrotron radiation by slowly rotating fermions

We study the synchrotron radiation emitted by a charged fermion, rotating as a part of a larger system, in a constant magnetic field $B$ parallel to the axis of rotation. The rotation is classical and independent of the magnetic field. The angular velocity of rotation $\mathrm{\ensuremath{\Omega}}$ is assumed to be much smaller than the inverse magnetic length $\sqrt{qB}$, which allows us to ignore the boundary effects at $r=1/\mathrm{\ensuremath{\Omega}}$. We refer to such rotation as slow, even though in absolute value it may be an extremely rapid rotation. Using the exact solution of the Dirac equation, we derived the intensity of electromagnetic radiation, its spectrum, and its chirality. We demonstrate by explicit numerical calculation that the effect of rotation on the radiation intensity increases with the particle energy. Depending on the relative orientation of the vectors $\mathbf{\ensuremath{\Omega}}$ and $\mathbit{B}$ and the sign of the electric charge, the rotation can either strongly enhance or strongly suppress the radiation.

Optical Channeling of Low Energy Antiprotons in Thin Crystal Targets

A relevant aspect of the interactions between charged fermions and crystal targets is coherence, which can exist at both classical and quantum levels. In the case of antiprotons crossing crystal targets, there are theories and measurements of classical-level coherence effects, in particular, channeling effects. For the present study, we assume the existence of a low-energy regime where the electrostatic interactions between an antiproton and the crystal atoms lead to a local loss in the beam flux as their leading effect. We expect this assumption to be well-justified for antiproton (p¯) energies below 100 eV, with a progressive transition to a standard “Rutherford regime” in the energy range 100–1000 eV. Under these conditions, the target can be treated as an optical absorber with a periodical structure, which can be simplified by considering a multi-layer planar structure only. As in standard optics, wave absorption is accompanied by interference and diffraction. Assuming sub-nanometer ranges for the relevant parameters and a realistic angular spread for the antiproton beam, we find narrow-angle focusing effects that reproduce the classical channeling effect at a qualitative level. We also find that diffraction dominates over interference, although this may strongly depend on the target details.

Thermodynamics and weak cosmic censorship conjecture with pressure in the rotating BTZ black holes

As a charged spinning fermion drops into a charged rotating BTZ black hole, we investigate the laws of thermodynamics and weak cosmic censorship conjecture with and without pressure, respectively. For the case without pressure, the first law, second law, as well as the weak cosmic censorship are found to be valid. While for the case with pressure, though the first law is still valid, the second law and the weak cosmic censorship conjecture are found to be violable, depending on the charge, angular momentum, AdS radius, and their variations. In addition, in both cases, the configurations of the extremal black holes are found to be stable since the final states of the extremal black holes are still extremal black holes. While for the near-extremal black holes, their configurations are not stable.

B-anomalies in a twin Pati-Salam theory of flavour including the 2022 LHCb {R}_{K^{left(ast right)}} analysis

We perform a comprehensive phenomenological analysis of the twin Pati-Salam theory of flavour, focussing on the parameter space relevant for interpreting the B-anomalies via vector leptoquark U1 exchange. This model provides a very predictive framework in which the U1 couplings and the Yukawa couplings find a common origin via mixing of chiral quarks and leptons with vector-like fermions, providing a direct link between the B-anomalies and the fermion masses and mixing. We propose and study a simplified model with three vector-like fermion families, in the massless first family approximation, and show that the second and third family charged fermion masses and mixings and the B-anomalies can be simultaneously explained and related. The model has the proper flavour structure to be compatible with all low-energy observables, and leads to predictions in promising observables such as τ → 3μ, τ → μγ and Bto {K}^{left(ast right)}nu overline{nu} at Belle II and LHCb. The model also predicts a rich spectrum of TeV scale gauge bosons and vector-like fermions, all accessible to the LHC. In this updated version we have included an extended analysis considering the new 2022 LHCb data on {R}_{K^{left(ast right)}} , which has slightly shifted the preferred parameter space with respect to the 2021 case. The model can still explain the {R}_{D^{left(ast right)}} anomalies at 1σ in a narrow window, however we expect small deviations from the SM on the {R}_{K^{left(ast right)}} ratios, to be tested in the future via more precise measurements by the LHCb collaboration. We also predict RD = {R}_{D^{ast }} , with future measurements shifting the world averages to slightly smaller central values.

Anomalous and axial Z′ contributions to g−2

We study the effects of an anomalous Z′ boson on the anomalous magnetic moment of the muon (g – 2), and especially the impact of its axial coupling. We mainly evaluate the negative contribution to (g – 2) of such couplings at one-loop and look at the anomalous couplings generated at two loops. We find areas of the parameter space, where the anomalous contribution becomes comparable and even dominant compared to the one-loop contribution. We show that in such cases, the cutoff of the theory is sufficiently low, so that new charged fermions can be found in the next round of collider experiments. We comment on the realization of such a context in string theory orientifolds.

Two-Field Model of Gravitational-Scalar Instability and Formation of Supermassive Black Holes in the Early Universe

Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a two-component statistical system of scalarly charged degenerate fermions, a numerical model of the cosmological evolution of gravitational-scalar perturbations in the presence of classical and phantom scalar fields is constructed and studied. The gravitational-scalar instability at early stages of expansion arises in the model under study at sufficiently large scalar charges, and the instability develops near unstable points of the vacuum doublet. Short-wave perturbations of the free phantom field turn out to be stable at stable singular points of the vacuum doublet. It is shown that for sufficiently large scalar charges, mass perturbations can grow to the values of masses black hole seeds (BHS).

Wash-in leptogenesis after axion inflation

CP violation and the violation of baryon-minus-lepton number B−L do not necessarily have to occur simultaneously in order to accomplish successful leptogenesis. Instead, it suffices if new CP-violating interactions at high energies result in primordial charge asymmetries, which are then reprocessed into a nonvanishing B−L asymmetry by right-handed neutrinos (RHNs) at lower energies. In this paper, we study this novel mechanism known as wash-in leptogenesis, utilizing axion inflation as the source of high-scale CP violation. We specifically consider axion inflation coupled to the Standard Model hypercharge sector, which results in the dual production of hypermagnetic helicity and fermionic charge asymmetries. Although the survival of these charges is endangered by sphaleron processes, magnetic diffusion, and the chiral plasma instability, we find a large range of viable scenarios. We consistently account for RHN flavor effects and coherence among the Standard Model lepton flavors across a wide range of RHN masses. We find a lower bound of 105···9 GeV on the mass of the lightest RHN involved in wash-in leptogenesis, depending on the onset of turbulence in the chiral plasma and the Hubble scale of inflation. Our model is representative of a broader class of new leptogenesis scenarios and suggests interesting observational signatures with regard to intergalactic magnetic fields, primordial black holes, and gravitational waves.

Relic challenges for vector-like fermions as connectors to a dark sector

New dark sectors consisting of exotic fields that couple only very feebly to the Standard Model (SM) have strong theoretical motivation and may be relevant to explaining the abundance of dark matter (DM). An important question for such sectors is how they connect to the SM. For a dark sector with a new gauge interaction, a natural connection arises from heavy vector-like fermions charged under both the visible and dark gauge groups. The gauge charges of such fermions imply that one or more of them is stable in the absence of additional sources of dark symmetry breaking. A generic challenge for such connectors is that they can produce too much dark matter or interact too strongly with nuclei if they were ever thermalized in the early universe. In this paper we study this challenge in a simple connector theory consisting of new vector-like electroweak doublet and singlet fermions that also transform under the fundamental representation of a new Abelian gauge force, and we show that these connectors in their minimal form are almost always ruled out by existing direct DM searches. To address this challenge, we investigate two solutions. First, we study mitigating scattering on nuclei by introducing a Majorana mass term for the singlet. And second, we investigate a mixing with SM leptons that allows the connectors to decay while remaining consistent with cosmological tests and searches for charged lepton flavour violation. Both solutions rely on the presence of a dark Higgs field with a specific charge.

Gravitational-Scalar Instability of Cosmological Model Based on Two-Component System of Degenerate Scalarly Charged Fermions with Asymmetric Higgs Interaction. I. Equations for Perturbations

A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed system of differential equations describing the unperturbed state of a homogeneous and isotropic system and a system of self-consistent evolution equations of small perturbations are constructed.

Gravitational-Scalar Instability of Cosmological Model Based on Two-Component System of Degenerate Scalarly Charged Fermions with Asymmetric Higgs Interaction. II. WKB-approximation

Gravitational-Scalar Instability of Cosmological Model Based on Two-Component System of Degenerate Scalarly Charged Fermions with Asymmetric Higgs Interaction. II. WKB-approximation

Viable quark-lepton Yukawa ratios and nucleon decay predictions in SU(5) GUTs with type-II seesaw

We investigate the viability of predictive schemes for quark-lepton Yukawa ratios and nucleon decay in non-supersymmetric SU(5) Grand Unified Theories (GUTs) where neutrino masses are generated by a type II seesaw mechanism. The scalar sector of the considered scenario contains 5-, 24- and 45-dimensional representations plus a 15-dimensional representation for realizing the type II seesaw. Predictions for the ratios of the quark and lepton Yukawa couplings emerge when the relevant entries of the Yukawa matrices are generated from single joint GUT operators (i.e. under the condition of single operator dominance). Focusing on the 2nd and 3rd family and hierarchical Yukawa matrices, we show that only two sets of predictions, yτyb=32, yμys=92 and yτyb=2, yμys=6 are viable. To further investigate both options, we extend the minimal scenarios to two “toy models”, including the 1st family of charged fermions, and calculate the models' predictions, e.g. for the nucleon decay rates and for the masses of the light relics that are potentially within reach of colliders.