Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

Regularization,renormalization and “peratization” in effective field theory for two nucleons

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, the renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff \( \Lambda\) as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit \( \Lambda\) \( \rightarrow\) ∞ yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.     

On the effective action and field renormalization for variationalλø4

We perform a study of the effective action within the gaussian variational approach for λλ₃₊₁⁴ with the aim of understanding better field renormalization. The difficulties in obtaining a finite effective action in this approach are made clear.     

Ambiguities in theη-nucleon scattering length determination

The positive sign of theη-nucleon scattering lengthb _ηN was predicted in [1] assuming the resonance mechanism for theπ ^?p → ηn reaction. We demonstrate that

1. the assumption about thet-channel mechanism of the reaction leads tob _ηN < 0 and
2. the experimental data on theη production cross section are equally compatible with both resonance andt-channel mechanisms.

     

Isospin-breaking corrections in the pion–deuteron scattering length

It is shown that isospin-breaking corrections to the pion–deuteron scattering length can be very large, because of the vanishing of the isospin-symmetric contribution to this scattering length at leading order in chiral perturbation theory. We further demonstrate that these corrections can explain the bulk of the discrepancy between the recent experimental data on pionic hydrogen and pionic deuterium. We also give the first determination of the electromagnetic low-energy constant f₁$f_1$.     

n + p → d + γ in effective field theory

The radiative capture process n + p → d + γ provides clear evidence for meson exchange currents in nuclear physics. We compute this process at low energies using a recently developed power counting for the effective field theory that describes nucleon-nucleon interactions. The leading order contribution to this process comes from the photon coupling to the nucleon magnetic moments. At subleading order there are other contributions. Among these are graphs where the photon couples directly to pions, i.e. meson exchange currents. These diagrams are divergent and require the presence of a local four-nucleon-one-photon counterterm. The coefficient of this operator is determined by the measured cross section, σ^expt = 334.2±0.5 mb, for incident neutrons with speed |v| = 2200 m/s.     

Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].     

Perturbative effective theory in an oscillator basis?

The effective interaction problem in nuclear physics is believed to be highly nonperturbative, requiring extended high-momentum spaces for accurate solution. We trace this to difficulties that arise at both short and long distances when the included space is defined in terms of a basis of harmonic oscillator Slater determinants. We show, in the simplest case of the deuteron, that both difficulties can be circumvented, yielding highly perturbative results in the potential even for modest (approximately 4 variant Planck's over 2pi omega) included spaces.     

The loop expansion for the effective potential in theP(φ)2 quantum field theory

We study the loop expansion for the effective potential, defined as the Fenchel transform (convex conjugate) of the pressure in an external field, in theP()₂ quantum field theory. For values of the classical fielda for which the classical potentialU ₀(a)=P(a)+1/2m ² a ² equals its convex hull and has nonvanishing curvature we prove that the 1-PI loop expansion is asymptotic as 0. We also give an example of a double well classical potential for which the 1-PI loop expansion fails to be asymptotic, and find the true asymptotics.This paper is a condensed version of the author's Ph.D. thesis for the Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Y4     

Analysis of data on proton-proton scattering in the energy range 100–1300 MeV

The results of a partial-wave analysis of data on proton-proton interaction in the energy range 100–1300 MeV are presented. The real parts of phase shifts were found for states of orbital angular momentum up to L = 9, while their imaginary parts were determined for states of orbital angular momentum up to L = 5. The sixth parameter of the S matrix was introduced in order to describe states of total angular momentum J = 2 and 4. The inelasticity thresholds were chosen individually for each state and were found to be substantially different from one another. The resulting solution was characterized by χ ² = 1.155 per point in the case where the number of experimental data was 12 841 and by a large imaginary part of the phase shift in the ³ P ₂-wave state at the edge of the energy range. Special features of the interaction in orbital states are discussed along with the energy dependence of integrated amplitudes and amplitudes of the scattering matrix at zero angle.     

On the ππ-scattering lengths in the theory with effective Lagrangian

Use of the effective Lagrangian incorporating both the scalar and pseudoscalar mesons gives a possibility to calculate the ππ-scattering lengths without attraction of the ChPT theory.     

Charge independence breaking and charge symmetry breaking in the nucleon–nucleon interaction from effective field theory

We discuss charge symmetry and charge independence breaking in an effective field theory approach for few-nucleon systems. We systematically introduce strong isospin-violating and electromagnetic operators in the theory. The charge dependence observed in the nucleon–nucleon scattering lengths is due to one-pion exchange and one electromagnetic four-nucleon contact term. This gives a parameter free expression for the charge dependence of the corresponding effective ranges, which is in agreement with the rather small and uncertain empirical determinations. We also compare the low energy phase shifts of the nn and the np system. We present a classification scheme for corrections to the leading order results and show that power counting explains previously made phenomenological observations.     

Existence of the critical point in φ4 field theory

We consider the ⁴ quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m() decreases continuously to zero as the bare mass parameter approaches a critical value _c from above. In three dimensions the critical point _c is in the single phase region and the physical mass vanishes there,m( _c )=0.A consequence of our results is that the critical exponentv governing the approach to infinite correlations is bounded below (rigorously) by its classical value, 1/2.Supported in part by the National Science Foundation under Grant MPS74-13252