Nonzero Fermion Mass Research Articles

Mass-induced confinement near the sill of the conformal window

We revisit standard arguments for hyperscaling of the spectrum when a non-zero fermion mass is introduced to a gauge-fermion theory which is conformal in the infrared limit. With some general assumptions, we argue that the induced confinement scale will be significantly enhanced near the edge of the conformal to confining transition. This enhancement can allow for the fermion mass to be arbitrarily small compared to the confinement scale. This scale separation may allow for apparent spontaneous breaking of chiral symmetry within the conformal window, which may be of interest for construction of dilaton effective field theories in this regime.

Mass perturbation theory in the 2-flavor Schwinger model with opposite masses with a review of the background

I discuss the 2-flavor Schwinger model with θ = 0 and small equal and opposite fermion masses (or θ = π with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special mass term modifies the conformal sector without breaking the conformal symmetry. I show in detail how mass-perturbation-theory works for correlators of flavor-diagonal fermion scalar bilinears. The result provides quantitative evidence that the theory has no mass gap for small non-zero fermion masses. The massive fermions are bound into conformally invariant unparticle stuff. I show how the long-distance conformal symmetry is maintained when small fermion masses are turned on and calculate the relevant scaling dimensions for small mass. I calculate the corrections to the 2- and 4-point functions of the fermion-bilinear scalars to leading order in perturbation theory in the fermion mass and describe a straightforward procedure to extend the calculation to all higher scalar correlators. I hope that this model is a useful and non-trivial example of unparticle physics, a sector with unbroken conformal symmetry coupled to interacting massive particles, in which we can analyze the particle physics in a consistent approximation.

Phase structure of the (1+1)-dimensional massive Thirring model from matrix product states

Employing matrix product states as an ansatz, we study the non-thermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with non-zero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behaviour, and serve as an important ingredient for controlling the continuum extrapolation of the model.

Casimir force variability in one-dimensional QED systems

The Casimir force between two short-range charge sources, embedded in a background of one dimensional massive Dirac fermions, is explored by means of the original $\ln\text{[Wronskian]}$ contour integration techniques. For identical sources with the same (positive) charge, we find that in the non-perturbative region the Casimir interaction between them can reach sufficiently large negative values and simultaneously reveal the features of a long-range force in spite of nonzero fermion mass, that could significantly influence the properties of such quasi-one-dimensional QED systems. For large distances $s$ between sources we recover that their mutual interaction is governed first of all by the structure of the discrete spectrum of a single source, in dependence on which it can be tuned to give an attractive, a repulsive, or an (almost) compensated Casimir force with various rates of the exponential fall-down, quite different from the standard $\exp (-2 m s)$ law. By means of the same $\ln\text{[Wronskian]}$ techniques, the case of two $\delta$-sources is also considered in a self-consistent manner with similar results for the variability of the Casimir force. A quite different behavior of the Casimir force is found for the antisymmetric source-anti-source system. In particular, in this case, there is no possibility for a long-range interaction between sources. The asymptotics of the Casimir force follows the standard $\exp (-2 m s)$ law. Moreover, for small separations between sources, the Casimir force for symmetric and antisymmetric cases turns out to be of opposite sign.

Casimir interactions between two short-range Coulomb sources

We calculate the Casimir interaction between two short range extended charge sources, embedded in a background of one dimensional massive Dirac fermions. We explore both the induced polarization density ρvac(x) and the corresponding integral charge Qvac, as well as the Casimir energy Evac and its contribution to the interaction between sources. For sources with the same charge, by means of the novel ln[Wronskian] contour integration techniques we find that the interaction energy between two sources can exceed sufficiently large negative values and simultaneously reveal the features of a long-range force in spite of non-zero fermion mass, which could significantly influence the properties of such quasi-one-dimensional systems. For large distances between sources we recover that their mutual interaction is governed first of all by the structure of the discrete spectrum of a single source, in dependence on which it can be tuned to give an attractive, a repulsive, or an (almost) compensated Casimir force with various rates of the exponential fall-down, quite different from the standard exp(−2ms) law.

Chiral effects in gauge theories and the chiral chemical potential

The chiral balance is broken as a result of an anomaly relation for the axial current in a strongly magnetized electron–positron gas in QED. The pair creation process, due to the decay of longitudinal axial photons (out of light cone), induces an imbalanced chirality and contributes to a chiral current along the external magnetic field B. In our case, a pseudo‐vector longitudinal mode generates the chiral charge density. A chiral chemical potential is not necessary. Only an electromagnetic chemical potential is introduced, but the chiral effect is valid even when it vanishes. A nonzero fermion mass is assumed, which is usually considered vanishing. The introduction of a chiral chemical potential in the frame of electroweak theory at finite temperature and density is discussed. It is not compatible with the Standard Model, since the spontaneous symmetry breaking prevents the conservation of the weak neutral charge.

Chiral current generation in QED by longitudinal photons

We report the generation of a pseudovector electric current having imbalanced chirality in an electron–positron strongly magnetized gas in QED. It propagates along the external applied magnetic field B as a chiral magnetic effect in QED. It is triggered by a perturbative electric field parallel to B, associated to a pseudovector longitudinal mode propagating along B. An electromagnetic chemical potential was introduced, but our results remain valid even when it vanishes. A nonzero fermion mass was assumed, which is usually considered vanishing in the literature. In the quantum field theory formalism at finite temperature and density, an anomaly relation for the axial current was found for a medium of massive fermions. It bears some analogy to the Adler–Bell–Jackiw anomaly. From the expression for the chiral current in terms of the photon self-energy tensor in a medium, it is obtained that electrons and positrons scattered by longitudinal photons (inside the light cone) contribute to the chiral current, as well as the to pair creation due to longitudinal photons (out of light cone). In the static limit, an electric pseudovector current is obtained in the lowest Landau level.

Discussion for the Solutions of Dyson-Schwinger Equations at <i>m</i> ≠ 0 in QED<sub>3</sub>

In the case of nonzero fermion mass, within a range of Ansatze for the full fermion-boson vertex, we show that Dyson-Schwinger equation for the fermion propagator in QED3 has two qualitatively distinct dynamical chiral symmetry breaking solutions. As the fermion mass increases and reaches to a critical value mc, one solution disappears, and the dependence of mc on the number of fermion flavors is also given.

Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions

I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, N\'ogradi and Schroeder [Z. Fodor, K. Holland, J. Kuti, D. Nogradi, and C. Schroeder, Phys. Lett. B 703, 348 (2011).]. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length $\ensuremath{\xi}$ with the fermion mass ${m}_{q}$, $\ensuremath{\xi}\ensuremath{\sim}{m}_{q}^{\ensuremath{-}1/{y}_{m}}$ with ${y}_{m}\ensuremath{\sim}1.35$. Shortcomings of the analysis are discussed.

Erratum: Testing effective Yukawa couplings in Higgs boson searches at the Tevatron and LHC [Phys. Rev. D82, 113014 (2010)

We explore the possibility that, while the Higgs mechanism provides masses to the weak-gauge bosons at the electroweak scale as in the standard model, fermion masses are generated by an unknown mechanism at a higher energy scale. At low energies, the standard model can then be regarded as an effective field theory, where fermion masses explicitly break the electroweak SU(2)_L \times U(1)_Y gauge symmetry. If \Lambda is the renormalization scale where the renormalized Yukawa couplings vanish, then at energies lower than \Lambda, effective Yukawa couplings will be radiatively induced by nonzero fermion masses. In this scenario, Higgs-boson decays into photons and weak gauge-bosons pairs are in general quite enhanced for a light Higgs. However, depending on \Lambda, a substantial decay rate into b \bar{b} can arise, that can be of the same order as, or larger than, the enhanced H\to gamma gamma rate. A new framework for Higgs searches at hadron colliders is outlined, vector-boson fusion becoming the dominant production mechanism at the CERN LHC, with an important role also played by the WH/ZH associated production. A detailed analysis of the Higgs branching fractions and their implications in Higgs searches is provided, versus the energy scale \Lambda.

Testing effective Yukawa couplings in Higgs boson searches at the Tevatron and LHC

We explore the possibility that, while the Higgs mechanism provides masses to the weak-gauge bosons at the electroweak scale as in the standard model, fermion masses are generated by an unknown mechanism at a higher energy scale. At low energies, the standard model can then be regarded as an effective field theory, where fermion masses explicitly break the electroweak $\mathrm{SU}(2{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{Y}}$ gauge symmetry. If $\ensuremath{\Lambda}$ is the renormalization scale where the renormalized Yukawa couplings vanish, then at energies lower than $\ensuremath{\Lambda}$, effective Yukawa couplings will be radiatively induced by nonzero fermion masses. In this scenario, Higgs boson decays into photons and weak gauge-bosons pairs are in general quite enhanced for a light Higgs. However, depending on $\ensuremath{\Lambda}$, a substantial decay rate into $b\overline{b}$ can arise that can be of the same order as, or larger than, the enhanced $H\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ rate. A new framework for Higgs searches at hadron colliders is outlined, vector-boson fusion becoming the dominant production mechanism at the CERN LHC, with an important role also played by the $WH/ZH$ associated production. A detailed analysis of the Higgs branching fractions and their implications in Higgs searches is provided, versus the energy scale $\ensuremath{\Lambda}$.

Chiral symmetry breaking and monopole dynamics in noncompactQED3coupled to a four-Fermi interaction

We present results from the first lattice simulations of three dimensional non-compact quantum electrodynamics (QED3) with N_f four-component fermion flavors coupled to a weak Z(2) chirally invariant four-fermi interaction. Results with $N_f \ge 4$ show that the scaling near the strong coupling chiral transition or sharp crossover is determined by the 3d Gross Neveu ultraviolet-stable renormalization group fixed point. Small deviations of the N_f=4 critical exponents from the respective Gross Neveu ones, hint at evidence for non-zero fermion mass generated by the gauge fields dynamics that might have been enhanced by the four-fermi coupling. It is also shown that the scaling region is suppressed at weak four-fermi couplings and large N_f values. Measurements of i) a monopole susceptibility which is the polarizability of the monopole configurations, and ii) the density of isolated monopoles, imply that for $N_f \ge 1$ and weak gauge couplings the monopoles do not affect the theory's confining properties, because they are shielded.

Erratum: Mass zeros in the one-loop effective actions of QED in1+1and3+1dimensions [Phys. Rev. D62, 125007 (2000)

It is known that the one-loop effective action of ${QED}_2$ is a quadratic in the field strength when the fermion mass is zero: all potential higher order contributions beyond second order vanish. For nonzero fermion mass it is shown that this behavior persists for a general class of fields for at least one value of the fermion mass when the external field's flux $\Phi$ satisfies $0<|e\Phi|<2\pi$. For ${QED}_4$ the mass-shell renormalized one-loop effective action vanishes for at least one value of the fermion mass for a class of smooth, square integrable background gauge fields provided a plausible zero-mass limit exists.

Ee4fγ—A program for e+e−→4f,4f γ with nonzero fermion masses

A computer program ee4f γ for calculating cross-sections of any four fermion final state of e + e −-annihilation at high energy and the corresponding bremsstrahlung reaction that is possible in the framework of the Standard Model is presented. As the fermion masses are arbitrary, the cross-sections for channels that do not contain e + and/or e − in the final state can be computed without any collinear cut, the on-shell top quark production can be studied and the Higgs boson exchange can be incorporated in a consistent way. The program can be used as a Monte Carlo generator of unweighted events as well. Program summary Title of program: ee4f γ Version: 1.0 (February 2004) Catalogue identifier: ADTQ Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers: all Operating systems: Unix/Linux Programming language used: FORTRAN 90 CPC Program Library subprograms used: RANLUX, ACPR RANLUX 79 (1994) 111—a random number generator Memory required to execute with typical data: 4.0 Mb No. of bits in a word: 32 No. of bytes in distributed program, including test data, etc.: 364 490 No. of lines in distributed program, including test data, etc.: 45 278 Distribution format: tar gzip file Nature of physical problem: Description of all e + e −→4 fermions and corresponding bremsstrahlung reactions that are possible in the Standard Model (SM) to lowest order and with nonzero fermion masses at center of mass energies typical for next generation linear colliders. Such reactions are relevant, typically, for W-pair or intermediate mass Higgs boson production and decay. Method of solution: Matrix elements are calculated with the helicity amplitude method. The phase space integration is performed numerically utilizing a multi-channel Monte Carlo method. Restrictions on complexity of the problem: No higher order effects are taken into account, except for assuming the fine structure constant and the strong coupling at the appropriate scale and partial summation of those one particle irreducible loop corrections which are inducing the (fixed) finite widths of unstable particles. Typical running time: The running time depends strongly on a selected channel and desired precision of the result. The results of the appended test run have been obtained on a 800 MHz Pentium III processor with the use of Absoft FORTRAN 90 compiler in about 9 minutes. In order to obtain a precision level below one per mile a few million calls to the integrand are required. This results in less than one hour running time for the fastest channel e +e −→ν μ ν ̄ μν τ ν ̄ τ and more than 100 hours running time for the slowest channel e + e −→ e + e − e + e −. However, the typical running time for channels that are relevant for the W-pair or Higgs boson production is several hours.

Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions

It is known that the one-loop effective action of ${\mathrm{QED}}_{2}$ is a quadratic in the field strength when the fermion mass is zero: all potential higher order contributions beyond second order vanish. For a nonzero fermion mass it is shown that this behavior persists for a general class of fields for at least one value of the fermion mass when the external field's flux $\ensuremath{\Phi}$ satisfies $0l|e\ensuremath{\Phi}|l2\ensuremath{\pi}.$ For ${\mathrm{QED}}_{4}$ with (anti-)self-dual fields the mass-shell renormalized one-loop effective action vanishes for at least one value of the fermion mass provided a plausible zero-mass limit exists.

Quadratic effective action for QED inD=2,3dimensions

We calculate the effective action for quantum electrodynamics (QED) in $D=2,3$ dimensions at the quadratic approximation in the gauge fields. We analyze the analytic structure of the corresponding nonlocal boson propagators nonperturbatively in $k/m.$ In two dimensions for any nonzero fermion mass, we end up with one massless pole for the gauge boson. We also calculate in $D=2$ the effective potential between two static charges separated by a distance L and find it to be a linearly increasing function of L in agreement with the bosonized theory (massive sine-Gordon model). In three dimensions we find nonperturbatively in $k/m$ one massive pole in the effective bosonic action leading to screening. Fitting the numerical results we derive a simple expression for the functional dependence of the boson mass upon the dimensionless parameter ${e}^{2}/m.$

The hard bremsstrahlung correction to $e^+ e^- \to 4f$ with finite fermion masses: results for $e^+ e^- \to u \bard} \mu^- \bar{\nu}_{\mu}$

An improved efficient method of calculating the hard bremsstrahlung correction to e^+ e^- -> 4f for non-zero fermion masses is presented. The non-vanishing fermion masses allow us to perform the phase space integrations to the very collinear limit. We therefore can calculate cross sections independent of angular cuts. Such calculations are important for background studies. Results are presented for the total and some differential cross sections for e^+ e^- -> u d-bar mu^- nu and the corresponding hard bremsstrahlung process. The latter is of particular interest for a detailed investigation of the effects of final state radiation. In principle, the process e^+ e^- -> u d-bar mu^- nu gamma is also interesting since it helps to set bounds on possible anomalous triple and quartic gauge boson couplings involving photons. The size of mass effects is illustrated by comparing the final states u d-bar mu^- nu (gamma), c s-bar mu^- nu (gamma) and u d-bar tau^- nu(gamma).

Instantons in the Schwinger model.

The known calculations of the fermion condensate $<\bar{\psi}\psi>$ and the correlator $<\bar{\psi}\psi(x) ~\bar{\psi}\psi(0)>$ have been interpreted in terms of {\em localized} instanton solutions minimizing the {\em effective} action. Their size is of order of massive photon Compton wavelength $\mu^{-1}$. At high temperature, these instantons become quasistatic and present the 2-dimensional analog of the `walls' found recently in 4-dimensional gauge theories. In spite of the static nature of these solutions, they should not be interpreted as `thermal solitons' living in Minkowski space: the mass of these would-be solitons does not display itself in the physical correlators. At small but nonzero fermion mass, the high-T partition function of $QED_2$ is saturated by the rarefied gas of instantons and antiinstantons with density $\propto m~\exp\{-S^{inst.}\}~=~m~\exp\{-\pi T/\mu\}$ to be confronted with the dense strongly correlated instanton-antiinstanton liquid saturating the partition function at $T=0$.

The four-Fermi model in three dimensions at non-zero density and temperature

The four-Fermi model with discrete chiral symmetry is studied in three dimensions at non-zero chemical potential and temperature using the hybrid Monte Carlo algorithm. The number of fermion flavors is chosen large ( N f = 12) to compare with analytic results. A first order chiral symmetry restoring transition is found at zero temperature with a critical chemical potential μ c in good agreement with the large N f calculations. The critical index v of the correlation length is measured in good agreement with analytic calculations. The two-dimensional phase diagram (chemical potential vs. temperature) is mapped out quantitatively. Finite size effects on relatively small lattices and non-zero fermion mass effectsare seen to smooth out the chiral transition dramatically.

Renormalization-scheme-invariant QCD and QED: The method of effective charges

We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding St\uckelberg---Peterman---Gell-Mann---Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter $\ensuremath{\Lambda}$, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass $\stackrel{^}{m}$ is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales.