Fermion Number Violation Research Articles

Dyonium induced fermion number violation

Dyonium induced fermion number violation is studied in a SU(2)L×U(1)Y gauge theory with a doublet Higgs field. Dyonium is a generalization of Nambu's monopolium, having finite sized pair of dyon and anti-dyon, connected with a thin string under the linear plus Coulomb force.1This is a follow-up of the author's paper on monopolium induced neutrino mass (including the lepton and baryon number violations), studied with a SO(10) Grand Unified model in 1983. To fulfill the requirement from the chiral anomaly or its index theorem, an electric field should be excited in parallel to the dipole magnetic field. This crucial dynamical problem, not fully answered then, has been solved, by considering not monopolium but dyonium.The fermionic zero modes in the dyonium background fields are necessary in evaluating the transition rate of the fermion number violation processes. Their Dirac equation can be reduced to a single component partial differential equation, similar to the renormalization group equation, which may be useful to estimate the reaction rates.

Missing final state puzzle in the monopole-fermion scattering

It has been known that when a charged fermion scatters off a monopole, the fermion in the s-wave component must flip its chirality, i.e., fermion number violation must happen. This fact has led to a puzzle; if there are two or more flavors of massless fermions, any superposition of the fermion states cannot be the final state of the s-wave scattering as it is forbidden by conservation of the electric and flavor charges. The unitary evolution of the state vector, on the other hand, requires some interpretation of the final states. We solve the puzzle by finding new particle excitations in the monopole background, where multi-fermion operators exhibit condensation. The particles are described as excitations of closed-string configurations of the operators.

Flavon magnetobaryogenesis

In this paper, we explore the evolution of baryon asymmetry as well as the hypermagnetic field in the early universe with an assumption that the flavon of the Froggatt-Nielsen carries an asymmetry. Through the decay of the flavon to Standard Model fermions, this asymmetry is transferred to fermions, where the right-handed electron keeps its asymmetry while its Yukawa interaction is out of thermal equilibrium. Through the existence of the flavon, we can ensure that the freezing-in temperature of the right-handed electron is closer to the electroweak phase transition than the Standard cosmology scenario. With this trick, the asymmetry in the right-handed electron is saved for a longer time. Moreover, the injection of the asymmetry to the right-handed electron is gradual, which helps the preservation of the asymmetry in the right-handed sector significantly. Due to the intimate relationship between fermion number violation and the helicity of the hypermagnetic field, some of the asymmetry is used to amplify the hypermagnetic field which itself helps to preserve the remnant asymmetry through keeping the Yukawa processes out of thermal equilibrium. We find the sweet region of the parameter space that can produce the right asymmetry in the baryons while generating a large hypermagnetic field by the time of the electroweak phase transition.

Contributions to theUY(1)Chern-Simons term and the evolution of fermionic asymmetries and hypermagnetic fields

We study simultaneous evolution of electron, neutrino and quark asymmetries, and large scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range $100$GeV$\leq T\leq 10$TeV, taking into account the chirality flip processes via inverse Higgs decays and fermion number violation due to Abelian anomalies. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The $\textrm{U}_{\textrm{Y}}(1)$ Chern-Simons term affects the resulting anomalous magnetohydrodynamic (AMHD) equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition ($T_{EW} \sim 100$GeV) for a variety of critical ranges for their initial values at $T=10$TeV. We first investigate the results of this sign change, by directly comparing our results with those obtained in one of the previous works and find that matter asymmetry generation increases considerably in the presence of a strong hypermagnetic field. Furthermore, we find that a strong hypermagnetic field can generate matter asymmetry starting from absolutely zero asymmetry, while matter asymmetry can generate a hypermagnetic field provided the initial value of the latter is nonzero.

One-loop fermionic corrections to the instanton transition in the two dimensional chiral Higgs model

The one-loop fermionic contribution to the probability of an instanton transition with fermion number violation is calculated in the chiral Abelian Higgs model in $1+1$ dimensions, where the fermions have a Yukawa coupling to the scalar field. The dependence of the determinant on fermionic, scalar, and vector mass is determined. We show in detail how to renormalize the fermionic determinant in partial wave analysis, which is convenient for computations.

Fermion-number violation in regularizations that preserve fermion-number symmetry

There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance (``fermion number''). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers gauge invariance to all orders in perturbation theory by including suitable counterterms. At the nonperturbative level, an apparent conflict then arises between the chiral U(1) symmetry of the regularized theory and the existence of 't Hooft vertices in the renormalized theory. The only possible resolution of the paradox is that the chiral U(1) symmetry is broken spontaneously in the enlarged Hilbert space of the covariantly gauge-fixed theory. The corresponding Goldstone pole is unphysical. The theory must therefore be defined by introducing a small fermion-mass term that breaks explicitly the chiral U(1) invariance and is sent to zero after the infinite-volume limit has been taken. Using this careful definition (and a lattice regularization) for the calculation of correlation functions in the one-instanton sector, we show that the 't Hooft vertices are recovered as expected.

Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds

Real-time anomalous fermion number violation is investigated for massless chiral fermions in spherically symmetric SU(2) Yang-Mills gauge field backgrounds which can be weakly dissipative or even nondissipative. Restricting consideration to spherically symmetric fermion fields, the zero-eigenvalue equation of the time-dependent effective Dirac Hamiltonian is studied in detail. For generic spherically symmetric SU(2) gauge fields in Minkowski spacetime, a relation is presented between the spectral flow and two characteristics of the background gauge field. These characteristics are the well-known ``winding factor,'' which is defined to be the change of the Chern-Simons number of the associated vacuum sector of the background gauge field, and a new ``twist factor,'' which can be obtained from the zero-eigenvalue equation of the effective Dirac Hamiltonian but is entirely determined by the background gauge field. For a particular class of (weakly dissipative) Luscher-Schechter gauge field solutions, the level crossings are calculated directly and nontrivial contributions to the spectral flow from both the winding factor and the twist factor are observed. The general result for the spectral flow may be relevant to electroweak baryon number violation in the early universe.

The overlap passes a chiral dynamical test in two dimensions

A certain U(1) model in 2 dimensions, describing four right handed unit charged Weyl fermions interacting with one doubly charged left handed Weyl fermion, is exactly soluble and has massless Majorana-Weyl composites. Instanton induced fermion number violation is essential for 't Hooft anomaly consistency. The associated 't Hooft vertex can be analytically computed in the continuum, including finite size corrections. This number is reproduced in a dynamical simulation employing the overlap.

Anomalous Decay of Heavy Fermions by Electroweak Instanton

The presence of a heavy fermion doublet in the electroweak instanton probably leads to unsuppressed fermion number nonconservation. By calculating numerically the effective potential barrier of electroweak instanton with heavy fermion in Minkowski space by using semiclassical approximation, it is shown that, if the mass of heavy fermion exceeds a critical value [Formula: see text] TeV (for MH = MW), the tunneling by electroweak instanton should be unsuppressed and the heavy fermion decays with fermion number violation. The dependence of critical fermion mass on the Higgs mass is also presented.

Collision-induced decays of electroweak solitons: Fermion number violation with two and few initial particles.

We consider a variant of the standard electroweak theory in which the Higgs sector has been modified so that there is a classically stable weak scale soliton. We explore fermion-number-violating processes which involve soliton decay. A soliton can decay by tunneling under the sphaleron barrier, or the decay can be collision induced if the energy is sufficient for the barrier to be traversed. We present a classical solution to the Minkowski space equations of motion in which a soliton is kicked over the barrier by an incoming pulse. This pulse corresponds to a quantum coherent state with a mean number of $W$ quanta $\ensuremath{\sim}\frac{2.5}{{g}^{2}}$ where $g$ is the SU(2) gauge coupling constant. We also give a self-contained treatment of the relationship between classical solutions, including those in which solitons are destroyed, and tree-level quantum amplitudes. Furthermore, we consider a limit in which we can reliably estimate the amplitude for soliton decay induced by collision with a single $W$ boson. This amplitude depends on $g$ like $\mathrm{exp}(\ensuremath{-}c{g}^{\ensuremath{-}\frac{1}{3}})$, and is larger than that for spontaneous decay via tunneling in the same limit. Finally, we show that in soliton decays light $\mathrm{SU}{(2)}_{L}$ doublet fermions are anomalously produced. Thus we have a calculation of a two-body process with energy above the sphaleron barrier in which fermion number is violated.

Electroweak baryogenesis in supersymmetric models.

The baryon density which may be produced during the electroweak phase transition in supersymmetric models is computed, taking into account the previously neglected effects of transport, strong and weak anomalous fermion number violation, thermal scattering, and a new method for computing CP-violating processes during the transition. We can account for the observed baryon asymmetry, provided new CP-violating phases are greater than \ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}2}$--${10}^{\mathrm{\ensuremath{-}}4}$, and some superpartners are light enough to be relevant during the transition, which takes place at a temperature of 50--100 GeV. In one case, the light superpartners are the top squarks and the charginos and/or the neutralinos; in another case the top squarks and both Higgs doublets are light. Our calculation is easily extended to the case of a general two Higgs model, where we find sufficient baryogenesis provided that a certain combination of parameters in the Higgs potential leads to a CP-violating space-dependent phase in the top quark mass of order ${10}^{\mathrm{\ensuremath{-}}3}$. \textcopyright{} 1996 The American Physical Society.

A lattice construction of chiral gauge theories

We formulate chiral gauge theories non-perturbatively, using two different cutoffs for the fermions and gauge bosons. We use a lattice with spacing b to regulate the gauge fields in standard fashion, while computing the chiral fermion determinant on a finer lattice with spacing f ⪡ b. This determinant is computed in the background of f-lattice gauge fields, obtained by gauge-covariantly interpolating b-lattice gauge fields. The notorious doublers that plague lattice theories containing fermions are decoupled by the addition of a Wilson term. In chiral theories such a term breaks gauge invariance explicitly. However, the advantage of the two-cutoff regulator is that gauge invariance can be restored to O( f 2/ b 2) by a one-loop subtraction of calculable local gauge field counterterms. We show that the only obstruction to this procedure is the presence of an uncancelled gauge anomaly among the fermion representations. We conclude that for practical purposes, it suffices to choose f/b ∼ b/L, where L is the physical volume of the system. In our construction it is simple to prove the Adler-Bardeen theorem for anomalies in global currents to all orders. The related subject of fermion-number violation is also studied. Finally, we discuss the prospects for improving the efficiency of our algorithm.

Fermion number violation in the background of a gauge field in Minkowski space

Anomalous fermion number violation is studied in the background of a pure SU(2) gauge field in Minkowski space using the method of N. Christ. It is demonstrated that the chiral fermion number is violated by at most an integer amount. Then the method is applied for a spherically symmetric Minkowski space classical gauge field in the background. These classical gauge fields are finite energy solutions to pure SU(2) equations of motion with in general non-integer topological charge. We show that in the classical background which during a finite time-interval matches such solutions the fermion number violation is integer and non-zero. In particular, we calculate the violation of the fermiion number in the presence of Lüscher-Schechter solutions. The meaning of the anomaly equation and applications to QCD and electroweak theory are briefly discussed. We also comment on the relation of the results of this paper to the previous work.

Anomalous violation of conservation laws in Minkowski space

We consider the evolution of quantum Fermi fields in Minkowski gauge field backgrounds. Our motivation is the study of anomalous fermion number violating processes. We derive selection rules for fermion scattering amplitudes which relate the violation of fermionic charge to the change in winding between early and late times of the vacuum part of the gauge field. We find that the amount of fermion number violation is always integer, even when the topological charge of the gauge field is fractional. As an explicit example, we apply our results to spherically symmetric Minkowski solutions.

Anomalous violation of conservation laws in Minkowski space: spontaneously broken gauge theories

We extend our previous results on the evolution of quantum Fermi fields in Minkowski gauge field backgrounds to the case of spontaneously broken gauge theories. We obtain a selection rule which relates the amount of fermion number violation to the change in Higgs winding number of the configuration. This selection rule is applicable to any classical solution which dissipates at both early and late times.

Spherical shells of a classical gauge field and their topological charge as a perturbative expansion.

We consider the classical equations of motion of $SU(2)$ gauge theory, without a Higgs field, in Minkowski space. We work in the spherical ansatz and develop a perturbative expansion in the coupling constant $g$ for solutions which in the far past look like freely propagating spherical shells. The topological charge $Q$ of these solutions is typically non-integer. We then show that $Q$ can be expressed as a power series expansion in $g$ which can be nonzero at finite order. We give an explicit analytic calculation of the order $g^5$ contribution to $Q$ for specific initial pulses. We discuss the relation between our findings and anomalous fermion number violation, and speculate on the physical implications of our results.

FERMIONS IN THE INSTANTON-ANTI-INSTANTON VALLEY AND HIGH-ENERGY ELECTROWEAK INTERACTIONS

We consider the behavior of fermions in the background of instanton-anti-instanton valley fields. Several different physics problems, from the high-energy electroweak interactions to the study of vacuum structure of QCD and of large orders of perturbation theory, are related to this problem. The spectrum of the Dirac operator in such a background is studied in detail. We present an approximation for the fermion correlation function when the instanton-anti-instanton separation (R) is large compared to their sizes (ρ). The situation where the instanton-anti-instanton overlap and melt is studied through the behavior of the Chern-Simons number as a function of R/ρ and x4. Applying our results to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there is no theoretical basis for expecting anomalous cross-sections to become observable at energies in the 10 TeV region.

FERMION NUMBER VIOLATION AND A TWO-DIMENSIONAL HIGGS MODEL

The investigation of topological properties of the gauge field in a two-dimensional Higgs model can help in understanding anomalous fermion number violation.

Fermion Modes in Instanton-Anti-Instanton Background in (1 + 0)-Dimensional Model

We evaluate the eigenvalues of Dirac operator in the background of instanton-anti-instanton configuration (I-$\bar{{\rm I}}$), in a simple (1+0)-dimensional model, and find that quasi-zero-mode disappears for the closely localized I-$\bar{{\rm I}}$ configurations. This result suggests that the configurations which are dominant at high energy in the valley method are actually non-anomalous ones and irrelevant to fermion number violation. Hence, there seems to be no theoretical basis for expecting anomalous cross section to become observable at energies of 10 Tev region in Weinberg-Salam theory.

Sphalerons and baryogenesis

The author reviews recent studies of sphaleron-induced fermion-number violation at high temperatures and its relevance to the early Universe.