Seagull Terms Research Articles

One-loop effective actions and higher spins. Part II

In this paper we continue and improve the analysis of the effective actions obtained by integrating out a scalar and a fermion field coupled to external symmetric sources, started in the previous paper. The first subject we study is the geometrization of the results obtained there, that is we express them in terms of covariant Jacobi tensors. The second subject concerns the treatment of tadpoles and seagull terms in order to implement off-shell covariance in the initial model. The last and by far largest part of the paper is a repository of results concerning all two point correlators (including mixed ones) of symmetric currents of any spin up to 5 and in any dimensions between 3 and 6. In the massless case we also provide formulas for any spin in any dimension.

Axial gravity, massless fermions and trace anomalies

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.

Functional form of the imaginary part of the atomic polarizability

The dynamic atomic polarizability describes the response of the atom to incoming electromagnetic radiation. The functional form of the imaginary part of the polarizability for small driving frequencies omega has been a matter of long-standing discussion, with both a linear dependence and an omega^3 dependence being presented as candidate formulas. The imaginary part of the polarizability enters the expressions of a number of fundamental physical processes which involve the thermal dissipation of energy, such as blackbody friction, and non-contact friction. Here, we solve the long-standing problem by calculating the imaginary part of the polarizability in both the length (d.E) as well as the velocity-gauge (p.A) form of the dipole interaction, verify the gauge invariance, and find general expressions applicable to atomic theory; the omega^3 form is obtained in both gauges. The seagull term in the velocity gauge is found to be crucial in establishing gauge invariance.

COUPLING ELECTROMAGNETISM TO GLOBAL CHARGE

It is shown that an alternative to the standard scalar quantum electrodynamics (QED) is possible. In this new version, there is only global gauge invariance as far as the charged scalar fields are concerned, although local gauge invariance is kept for the electromagnetic field. The electromagnetic coupling has the form jμ(Aμ +∂μB) where B is an auxiliary field and the current jμ is Aμ independent, so that no "sea gull terms" are introduced. As a consequence of the absence of sea gulls, it is seen that no Klein paradox appears in the presence of a strong square well potential. In a model of this kind, spontaneous breaking of symmetry does not lead to photon mass generation, instead the Goldstone boson becomes a massless source for the electromagnetic field. When spontaneous symmetry breaking takes place infrared questions concerning the theory and generalizations to global vector QED are discussed. In this framework, Q-Balls and other nontopological solitons that owe their existence to a global U(1) symmetry can be coupled to electromagnetism and could represent multiply charged particles now in search in the large hadron collider (LHC). Furthermore, we give an example where an "Emergent" Global Scalar QED can appear from an axion–photon system in an external magnetic field. Finally, formulations of Global Scalar QED that allow perturbative expansions without sea gulls are developed.

Nuclear polarization in muonic208Pb

We calculate nuclear-polarization energy shifts in muonic ${}^{208}\mathrm{Pb}.$ We employ a relativistic field-theoretical calculation and evaluate the ladder, cross, and seagull terms of the two-photon exchange diagrams in both the Feynman and Coulomb gauges. Gauge independence is very well satisfied with the calculated nuclear-polarization energies. Using these results, we analyze fine-structure splitting energies of muonic ${}^{208}\mathrm{Pb}$ because of the presence of the persisting discrepancies between experiment and calculation. The present nuclear-polarization energies explain about half of the anomaly in the $\ensuremath{\Delta}2p$ fine-structure splitting energy, and only one-fourth of the anomaly in the $\ensuremath{\Delta}3p$ fine-structure splitting energy.

Nuclear polarization in hydrogenlike82208Pb81+

We calculate nuclear-polarization energy shifts for hydrogenlike $^{208}_{~82}$Pb$^{81+}$. A retarded transverse part as well as the Coulomb part is taken into account as the electromagnetic interaction between an electron and the nucleus. With a finite charge distribution for the nuclear ground state and the random-phase approximation to describe the nuclear excitations, we obtain nuclear polarization energy of the $1s_{1/2}$ state as --38.2 (--37.0) meV in the Feynman (Coulomb) gauge. For the $2s_{1/2}$, $2p_{1/2}$ and $2p_{3/2}$ states, they are --6.7 (--6.4), --0.2 (--0.2) and +0.0 (+0.0) meV, respectively. The seagull term in the two-photon exchange diagrams is shown to be quite important to obtain the gauge invariance of the nuclear polarization energies.

Two-dimensional chiral anomaly in differential regularization

The two-dimensional chiral anomaly is calculated using differential regularization. It is shown that the anomaly emerges naturally in the vector and axial Ward identities on the same footing as the four-dimensional case. The vector gauge symmetry can be achieved by an appropriate choice of the mass scales without introducing the seagull term. We have analyzed the reason why such a universal result can be obtained in differential regularization.

Do the seagull terms really survive for the electric polarizability of the nucleon?

The seagull terms for the electric polarizability of the nucleon are shown indeed to vanish, if one introduces fluctuations around the Skyrmion configuration, and the origin of the electric polarizability cannot after all be attributed to the seagull terms in the Skyrme model.

Constant-cutoff approach to electric seagull terms in the soliton Hamiltonian

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. Using the constant-cutoff approach, we then study theSU(2) soliton Hamiltonian, which does not contain the electric seagull terms, and show that if the fields are restricted to the collective subspace, the electric seagull terms are induced in the effective Hamiltonian similarly to the case of the complete Skyrme model. These terms are consistent with gauge invariance and leading-term predictions of the chiral perturbation calculation of the electric polarizability.

Meson-baryon-baryon vertex function and the Ward-Takahashi identity.

Ohta proposed a solution for the well-known difficulty of satisfying the Ward-Takahashi identity for a photo-meson-baryon-baryon amplitude (\ensuremath{\gamma}MBB) when a dressed meson-baryon-baryon (MBB) vertex function is present. He obtained a form for the \ensuremath{\gamma}MBB amplitude which contained, in addition to the usual pole terms, longitudinal seagull terms which were determined entirely by the MBB vertex function. He arrived at his result by using a Lagrangian which yields the MBB vertex function at tree level. We show that such a Lagrangian can be neither Hermitian nor charge conjugation invariant. We have been able to reproduce Ohta's result for the \ensuremath{\gamma}MBB amplitude using the Ward-Takahashi identity and no other assumption, dynamical or otherwise, and the most general form for the MBB and \ensuremath{\gamma}MBB vertices. However, contrary to Ohta's finding, we find that the seagull terms are not robust. The seagull terms extracted from the \ensuremath{\gamma}MBB vertex occur unchanged in tree graphs, such as in an exchange current amplitude. But the seagull terms which appear in a loop graph, as in the calculation of an electromagnetic form factor, are, in general, different. The whole procedure says nothing about the transverse part of the (\ensuremath{\gamma}MBB) vertex and its contributions to the amplitudes in question. \textcopyright{} 1996 The American Physical Society.

Nucleon electric polarizability in soliton models and the role of the seagull terms

The full Hamiltonian of the soliton models contains no electric seagull terms. Here it is shown that if one restricts the fields to the collective subspace then electric seagull terms are induced in the effective Hamiltonian. These effective seagull contributions are consistent with gauge invariance. They also reproduce the leading nonanalytic behavior of a large $N_c$ chiral perturbation theory calculation of the electric polarizability.

Nuclear polarization corrections for the S-levels of electronic and muonic deuterium

We calculate the second-order corrections to the atomic energy level shifts in ordinary and muonic deuterium due to virtual excitations of the deuteron which are important for ongoing and planned precise experiments in these systems. We use a method for light atoms in which the shift is expressed as integrals over the longitudinal and transverse inelastic structure functions of the nucleus and employ the structure functions arising from separable NN potentials. Special emphasis is put on gauge invariance which requires a consistent inclusion of interaction currents and seagull terms. The effect of the D-wave component of the deuteron is investigated for the leading longitudinal contribution. We also estimate the shift for pionic deuterium.

PHOTOPRODUCTION OF WEAK VECTOR BOSONS IN A SPINOR THEORY

We put forward the hypothesis that the weak W boson be a compound of two 2-component Lorentz spinors. The resulting novel γWW vertex is no gauge field structure. Nevertheless, the Born amplitude of γγ→WLWL respects partial-wave unitarity. As in the Yang-Mills case, the amplitude consists of a direct term, a crossed term, and a sea-gull term, and no unobserved particles are to be involved to get the “good” high-energy behavior. This is due to an imaginary pseudoscalar γWW interaction term. Significant differences between angular distributions and total cross sections of the non-Abelian case and the case of the composite bosons are displayed. The unitarity constraint applied to the reaction γγ→WTWT leads to the prediction of the existence of a composite charged weak scalar Φ±. It constitutes the spin 0 state of the constituents forming W±. Furthermore, the existence of a second and heavy scalar-vector pair ω-X is predicted. These weak boson states are found to exclude the presence of a seagull graph. In the threshold region, the total cross section of γγ→WW in the compositeness case is smaller than in the non-Abelian case. In a broad intermediate energy region it can be larger. Upper unitarity mass-bounds are estimated. They suggest mΦ≈mw so that Φ± might be discovered by forthcoming experiments. The structure of the γΦW, γXW and γωW transition vertices can be inferred without making recourse to unitarity. However, unitarity requires that the mass relation mΦ/mW=mω/mX be valid.

Lorentz spinors in elastic WW scattering and neutral currents

We propose a novel electroweak unification scheme that can be interpreted in terms of compositeness and an effective Lagrangian and show that it leads to a good high-energy behaviour of the reactions WW→WW, νν→WW and ee→WW. The weak vector bosons are no more gauge fields. The description of the reactions WLWL→WLWL and WTWL→WLWL becomes simpler than in the non-Abelian case: no seagull term is necessary and no scalar boson must be exchanged to get a good high-energy behaviour. We obtain a low-energy neutral current phenomenology that is identical with the usual one. The LEP II process ee→WW is analysed in some detail. The relative sign of the individual amplitudes can be determined. We find clear Lorentz spinor signals. They would be indicative of the existence of a Z′-boson as well as a heavy neutrino (N). The upper unitarity mass boundmN<890 GeV is derived.

Pion photoproduction in the Skyrme model and low-energy theorem

We investigate pion photoproduction on the nucleon in the Skyrme model. We employ the formulation, which was recently developed by Hayashi et al., that the full pion field is treated as an interpolating field between asymptotic in and out fields. It is shown that the amplitude of the pion photoproduction is correctly given by the direct and the crossed baryon-pole terms, and the equal-time commutator terms between the axial-vector current and the electromagnetic current and between the pion field and the latter. We show that the lowest-order Kroll-Ruderman and the pion pole terms are reproduced, and that the seagull terms inherent to the Skyrme model are present. Further, the threshold behavior of the amplitude is discussed.

Born amplitudes and seagull term in meson-soliton scattering

The meson-soliton scattering for the ⊘ 4 theory in 1 + 1 dimensions is calculated. We show that when the seagull term from the equal time commutator is included in addition to the Born amplitudes, the t-matrix from the reduction formula approach is identical to that of the potential scattering with small quantum fluctuations to leading order in weak coupling. The seagull term is equal to the Born term in the potential scattering. This confirms the speculation that the leading order Yukawa coupling is derivable from the classical soliton.

Schwinger terms of the super-Virasoro algebra in (1,0) superspace.

We calculate the Schwinger terms of the super-Virasoro algebra for the heterotic string, and the associated anomalous seagull terms, directly from the Lorentz and super-Weyl anomalies using the (1,0) superspace formalism. The various supercurrents in (1,0) superspace are also discussed.

Schwinger terms, seagulls and the Virasoro anomaly

A formalism is presented which allows the calculation of anomalous Schwinger terms, seagull terms and the Virasoro anomaly of the bosonic string directly from the Weyl anomaly.

Casimir effect, the gauge problem and seagull terms

Much recent interest in the classic Casimir effect problem has urged us to treat this phenomenon carefully by giving special attention to the gauge problem, which has been almost entirely swept under the carpet in the past, and to seagull terms. By quantising in the so-called Coulomb gauge, where the dynamical degrees of freedom are apparent and the quantisation problem is unambiguous, the expression for the Casimir effect is derived by explicitly taking into account seagull terms. Although a physical quantity ought to be gauge independent a specific gauge, nevertheless, has to be chosen for its evaluation.

Nuclear polarization shifts in light muonic atoms

A consistent nonrelativistic expression for the energy shift in muonic atoms due to second-order processes is derived under the assumption that the muon is weakly bound. The transverse contribution is shown to be finite only if the two-photon (“seagull”) amplitude is taken into account as required by gauge invariance. Numerical results are presented for muonic 12C using a recently developed model for the nuclear response function. The total transverse contributions to the energy shift are found to be small although dependent to some extent on the detailed high-momentum behaviour of the seagull term.