Effective Field Theory Calculations Research Articles

Determining the7Li(n,γ) cross section via Coulomb dissociation of8Li

The applicability of Coulomb dissociation reactions to determine the cross section for the inverse neutron capture reaction was explored using the reaction 8Li(gamma,n)7Li. A 69.5 MeV/nucleon 8Li beam was incident on a Pb target, and the outgoing neutron and 7Li nucleus were measured in coincidence. The deduced (n,gamma) excitation function is consistent with data for the direct capture reaction 7Li(n,gamma)8Li and with low-energy effective field theory calculations.

Measurements of the γ*p → Δ reaction at low Q2

We report new p$(\vec{e},e^\prime p)\pi^\circ$ measurements in the $\Delta^{+}(1232)$ resonance at the low momentum transfer region utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The mesonic cloud dynamics are predicted to be dominant and appreciably changing in this region while the momentum transfer is sufficiently low to be able to test chiral effective calculations. The results disagree with predictions of constituent quark models and are in reasonable agreement with dynamical calculations with pion cloud effects, chiral effective field theory and lattice calculations. The reported measurements suggest that improvement is required to the theoretical calculations and provide valuable input that will allow their refinements.

Interplay between spin-crossover and magnetic interactions in a BEG model

A two-dimensional Blume-Emery-Griffiths spin-1 model with spin-phonon interaction is introduced to investigate the thermodynamic properties of Prussian Blue Analogs and Spin-crossover materials. The quadrupolar interaction parameter is assumed to depend on the temperature in the form K = αkBT while the crystal-field depends both on the ligand-field strength and the degeneracy ratio between high spin (HS) and low spin (LS) states as in some previous works. The model is solved by means of two statistical-mechanical methods: kinetic Monte Carlo simulations and corrective effective field theory calculations. Our calculations indicate that by tuning α, the spin-crossover transition changes to a sharp first order transition where the HS fraction, nHS changes discontinuously. Second order transitions are observed in the presence of magnetic ordering when the nearest-neighbor coupling constant J exceeds some critical value Jc which depends on α and other model parameters. Below Jc, simple spin-transition occurs at an equilibrium temperature Teq that is very sensitive to the values of the degenaracy ratio and the ligand-field. Competition between model parameters lead to interesting phase diagrams. Some of them are displayed for varying values of the coupling J and also in the specific case where J and K are of the same order of magnitude. Thermal hysteresis loops have been calculated by Monte Carlo simulations and also by using the self-consistent equations in the case of long-lived metastable states showing strong dependence on model parameters.

Unambiguous identification of the second 2+ state in 12C and the structure of the Hoyle state.

The second J(π)=2+ state of 12C, predicted over 50 years ago as an excitation of the Hoyle state, has been unambiguously identified using the 12C(γ,α0)(8)Be reaction. The alpha particles produced by the photodisintegration of 12C were detected using an optical time projection chamber. Data were collected at beam energies between 9.1 and 10.7 MeV using the intense nearly monoenergetic gamma-ray beams at the HIγS facility. The measured angular distributions determine the cross section and the E1-E2 relative phases as a function of energy leading to an unambiguous identification of the second 2+ state in 12C at 10.03(11) MeV, with a total width of 800(130) keV and a ground state gamma-decay width of 60(10) meV; B(E2:2(2)+→0(1)+)=0.73(13)e(2) fm(4) [or 0.45(8) W.u.]. The Hoyle state and its rotational 2+ state that are more extended than the ground state of 12C presents a challenge and constraints for models attempting to reveal the nature of three alpha-particle states in 12C. Specifically, it challenges the ab initio lattice effective field theory calculations that predict similar rms radii for the ground state and the Hoyle state.

Effective field theory and Ab-initio calculation of p-type (Ga, Fe)N within LDA and SIC approximation

Based on first-principles spin-density functional calculations, using the Korringa–Kohn–Rostoker method combined with the coherent potential approximation, we investigated the half-metallic ferromagnetic behavior of (Ga, Fe)N co-doped with carbon within the self-interaction-corrected local density approximation. Mechanism of hybridization and interaction between magnetic ions in p-type (Ga, Fe)N is investigated. Stability energy of ferromagnetic and disorder local moment states was calculated for different carbon concentration. The local density and the self-interaction-corrected approximations have been used to explain the strong ferromagnetic interaction observed and the mechanism that stabilizes this state. The transition temperature to the ferromagnetic state has been calculated within the effective field theory, with a Honmura–Kaneyoshi differential operator technique.

Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order

We calculate via the effective field theory (EFT) approach the next-to-next-to-leading order (NNLO) spin1-spin2 conservative potential for a binary. Hereby, we first demonstrate the ability of the EFT approach to go at NNLO in post-Newtonian (PN) corrections from spin effects. The NNLO spin1-spin2 interaction is evaluated at fourth PN order for a binary of maximally rotating compact objects. This sector includes contributions from diagrams, which are not pure spin1-spin2 diagrams, as they contribute through the leading-order spin accelerations and precessions, that should be first taken into account here. The fact that the spin is derivative-coupled adds significantly to the complexity of computations. In particular, for the irreducible two-loop diagrams, which are the most complicated to evaluate in this sector, irreducible two-loop tensor integrals up to order 4 are required. The EFT calculation is carried out in terms of the nonrelativistic gravitational (NRG) fields. However, not all of the benefits of the NRG fields apply to spin interactions, as all possible diagram topologies are realized at each order of $G$ included. Still, the NRG fields remain advantageous, and thus there was no use of automated computations in this work. Our final result can be reduced, and a corresponding Hamiltonian may be derived.

Symmetry Restoration by Acceleration

The restoration of spontaneous symmetry breaking for a scalar field theory for an accelerated observer is discussed by the one-loop effective potential calculation and by considering the effective potential for composite operators. Above a critical acceleration, corresponding to the critical restoration temperature,T_c, for a Minkowski observer by Unruh relation, i.e. a_c/2\pi=T_c, the symmetry is restored. This result confirms other recent calculations in effective field theories that symmetry restoration can occur for an observer with an acceleration larger than some critical value. From the physical point of view, a constant acceleration is locally equivalent to a gravitational field and the critical acceleration to restore the spontaneous symmetry breaking corresponds to a huge gravitational effect which, therefore, prevents boson condensation.

Measurement of the partial cross sectionsσTT,σLT, and(σT+ɛσL)of the1H(e,e′π+)nreaction in theΔ(1232)resonance

We report new precision p(e,e' pi+})n measurements in the Delta(1232) resonance at Q2 = 0.127(GeV/c)2 obtained at the MIT-Bates Out-Of-Plane scattering facility. These are the lowest, but non-zero, Q2 measurements in the pi+ channel. The data offer new tests of the theoretical calculations, particularly of the background amplitude contributions. The chiral effective field theory and Sato-Lee model calculations are not in agreement with this experiment.

Effective field theory calculation of conservative binary dynamics at third post-Newtonian order

We reproduce the two-body gravitational conservative dynamics at third post-Newtonian order for spinless sources by using the effective field theory methods for the gravitationally bound two-body system, proposed by Goldberger and Rothstein. This result has been obtained by automatizing the computation of Feynman amplitudes within a Mathematica algorithm, paving the way for higher-order computations not yet performed by traditional methods.

Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach

We use an effective field theory (EFT) approach to calculate the next to leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex sector of the NLO spin effects, previously derived within the EFT approach. In particular, it requires the inclusion of non-stationary cubic self-gravitational interaction, as well as the implementation of a spin supplementary condition (SSC) at higher orders. The EFT calculation is carried out in terms of the non-relativistic gravitational field parametrization, making the calculation more efficient with no need to rely on automated computations, and illustrating the coupling hierarchy of the different gravitational field components to the spin and mass sources. Finally, we show explicitly how to relate the EFT derived spin results to the canonical results obtained with the ADM Hamiltonian formalism. This is done using non-canonical transformations, required due to the implementation of covariant SSC, as well as canonical transformations at the level of the Hamiltonian, with no need to resort to the equations of motion or the Dirac brackets.

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h0.

Erratum: Limits of custodial symmetry [Phys. Rev. D80, 095001 (2009)

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zbb coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) x U(1)_X = SU(2)_L x SU(2)_R x P_{LR} x U(1)_X symmetry that protects the Zbb coupling. This symmetry is softly broken to the gauged SU(2)_L x U(1)_Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M to 0) and standard-model-like (M to infinity) limits. In this simple model, we find that the experimental limits on the Zbb coupling favor smaller M while the presence of a potentially sizable negative contribution to T strongly favors large M. A fit to all precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limits the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to alpha T, alpha S and the Zbb coupling in this model arise from an effective operator coupling right-handed top-quarks to the Z-boson, and how the effects on these observables are correlated. We contrast this toy model with extra-dimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to alpha T and the Zbb coupling, while leaving the standard model contributions essentially unchanged.

Few-body Studies at the High Intensityγ-Ray Source (HIγS)

The HIγS facility is making it possible to perform studies of few body systems at a new level of accuracy and precision. A study of the photodisintegration of the deuteron using 100% linearly polarized beams at 14 and 16 MeV has determined the splittings of the three p-wave amplitudes involved in this process for the first time. These results show that the relativistic contributions, which when included in the theory lead to a positive value of the GDH integrand above 8 MeV, are valid. The near threshold data on the photodisintegration of the deuteron provide results which are used to extract the forward spin-polarizability of the deuteron for the first time. The experimental value is in good agreement with a recent effective field theory calculation. Measurements of the absolute differential cross section of the 3He(γ,n)pp reaction have been completed at three γ-ray energies. The measurements were made at incident γ-ray energies of 12.8, 13.5, and 14.7 MeV. It has been found that the shape of the outgoing neutron energy distribution at a given scattering angle at 12.8 MeV disagrees with current theoretical predictions. At these energies, the shape is consistent with a phase-space-only shape. At the higher energies, the measurements agree with theory.

Limits of custodial symmetry

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the $Z{b}_{L}{\overline{b}}_{L}$ coupling from large corrections. This ``doublet-extended standard model'' adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an $O(4)\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}\ensuremath{\sim}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}\ifmmode\times\else\texttimes\fi{}{P}_{LR}\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$ electroweak symmetry by a Dirac mass $M$ for the new doublet; adjusting the value of $M$ allows us to explore the range of possibilities between the $O(4)$-symmetric ($M\ensuremath{\rightarrow}0$) and standard-model-like ($M\ensuremath{\rightarrow}\ensuremath{\infty}$) limits. In this simple model, we find that the experimental limits on the $Z{b}_{L}{\overline{b}}_{L}$ coupling favor smaller $M$ while the presence of a potentially sizable negative contribution to $\ensuremath{\alpha}T$ strongly favors large $M$. Comparison with precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limit the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to $\ensuremath{\alpha}T$, $\ensuremath{\alpha}S$, and the $Z{b}_{L}{\overline{b}}_{L}$ coupling in this model arise from an effective operator coupling right-handed top quarks to the $Z$ boson, and how the effects on these observables are correlated. We contrast this toy model with extradimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to $\ensuremath{\alpha}T$ and the $Z{b}_{L}{\overline{b}}_{L}$ coupling, while leaving the standard model contributions essentially unchanged.

Chiral effective field theory calculations of neutrino processes in dense matter

We calculate neutrino processes involving two nucleons at subnuclear densities using chiral effective field theory. Shorter range noncentral forces reduce the neutrino rates significantly compared with the one-pion exchange approximation currently used in supernova simulations. For densities $\ensuremath{\rho}<{10}^{14} \mathrm{g} {\mathrm{cm}}^{\ensuremath{-}3}$, we find that neutrino rates are well constrained by nuclear interactions and nucleon-nucleon scattering data. As an application, we calculate the mean-square energy transfer in scattering of a neutrino from nucleons and find that collision processes and spin-dependent mean-field effects dominate over the energy transfer due to nucleon recoil.

Δ-baryon electromagnetic form factors in lattice QCD

We develop techniques to calculate the four $\ensuremath{\Delta}$ electromagnetic form factors using lattice QCD, with particular emphasis on the subdominant electric quadrupole form factor that probes deformation of the $\ensuremath{\Delta}$. Results are presented for pion masses down to approximately 350 MeV for three cases: quenched QCD, two flavors of dynamical Wilson quarks, and three flavors of quarks described by a mixed action combining domain-wall valence quarks and dynamical staggered sea quarks. The magnetic moment of the $\ensuremath{\Delta}$ is compared with chiral effective field theory calculations and the $\ensuremath{\Delta}$ charge density distributions are discussed.

Effective field theory calculation of second post-Newtonian binary dynamics

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.

Proton–proton fusion in pionless effective theory

The proton–proton fusion reaction, pp→de+ν, is studied in pionless effective field theory (EFT) with di-baryon fields up to next-to leading order. With the aid of the di-baryon fields, the effective range corrections are naturally resummed up to the infinite order and thus the calculation is greatly simplified. Furthermore, the low-energy constant which appears in the axial-current-di-baryon–di-baryon contact vertex is fixed through the ratio of two- and one-body matrix elements which reproduces the tritium lifetime very precisely. As a result we can perform a parameter free calculation for the process. We compare our numerical result with those from the accurate potential model and previous pionless EFT calculations, and find a good agreement within the accuracy better than 1%.

Four-fermion production near the W pair-production threshold

We perform a dedicated study of the four-fermion production process e − e + → μ − ν ¯ μ u d ¯ X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, Γ W / M W , and the non-relativistic velocity v of the W boson up to next-to-leading order in Γ W / M W ∼ α ew ∼ v 2 . We find that the dominant theoretical uncertainty in M W is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into δ M W ≈ 10 – 15 MeV , and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.

Pion-mass dependence of three-nucleon observables

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the 1 S 0 scattering length and effective range, the deuteron binding energy, the 3 S 1 effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse 3 S 1 and 1 S 0 scattering lengths vanishing at m π crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m π in the region between the physical pion mass and m π = m π crit .