Compton Scattering on He-3
We present first calculations for Compton scattering on $^3$He. The objective of the calculation is an extraction of the neutron polarizabilities.
nucl-th↗
arXiv subjects
D. R. Phillips
Publications and source records attributed to D. R. Phillips.
How low-energy weak reactions can constrain three-nucleon forces and the neutron-neutron scattering length
We show that chiral symmetry and gauge invariance enforce relations between the short-distance physics that occurs in a number of electroweak and pionic reactions on light nuclei. Within chiral perturbation theory this is manifested via the appearance of the same axial isovector two-body contact term in pi- d -> n n gamma, p-wave pion production in NN collisions, tritium beta decay, pp fusion, nu d scattering, and the hep reaction. Using a Gamow-Teller matrix element obtained from calculations of pp fusion as input we compute the neutron spectrum obtained in pi- d -> n n gamma. With the short-distance physics in this process controlled from p p -> d e+ nu_e the theoretical uncertainty in the nn scattering length extracted from pi- d -> n n gamma is reduced by a factor larger than three, to <~0.05 fm.
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Deuteron Matrix Elements in Chiral Effective Theory at Leading Order
We consider matrix elements of two-nucleon operators that arise in chiral effective theories of the two-nucleon system. Generically, the short-distance piece of these operators scales as 1/r^n, with r the relative separation of the two nucleons. We show that, when evaluated between the leading-order wave functions obtained in this effective theory, these two-nucleon operators are independent of the cutoff used to renormalize the two-body problem for n=1 and 2. However, for n greater than or equal to 3 general arguments about the short-distance behavior of the leading-order deuteron wave function show that the matrix element will diverge.
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The Three-Boson System at Next-To-Next-To-Leading Order
We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R >> a_2, with a_2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R^3/a_2^3). Since corrections of O(R/a_2) and O(R^2/a_2^2) can be straightforwardly included in the integral equation's kernel, a unique solution for 1+2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with the recent three-dimensional Faddeev calculations of Roudnev and collaborators that used phenomenological inter-atomic potentials.
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The near threshold N N -> d pi reaction in chiral perturbation theory
The near-threshold n p -> d pi0 cross section is calculated in chiral perturbation theory to next-to-leading order in the expansion parameter sqrt{M m_pi}/Lambda_chi. At this order irreducible pion loops contribute to the relevant pion-production operator. While their contribution to this operator is finite, considering initial-and final-state distortions produces a linear divergence in its matrix elements. We renormalize this divergence by introducing a counterterm, whose value we choose in order to reproduce the threshold n p -> d pi0 cross section measured at TRIUMF. The energy-dependence of this cross section is then predicted in chiral perturbation theory, being determined by the production of p-wave pions, and also by energy dependence in the amplitude for the production of s-wave pions. With an appropriate choice of the counterterm, the chiral prediction for this energy dependence converges well.
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Using chiral perturbation theory to extract the neutron-neutron scattering length from pi- d -> n n gamma
The reaction pi- d -> n n gamma is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the elementary pi- p -> gamma n amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a_nn from the shape of the entire pi- d -> n n gamma spectrum using our calculation in its present stage would thus be possible at the +-0.8 fm level. A fit to the FSI peak only would allow an extraction of a_nn with a theoretical uncertainty of +-0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the $nn$ rescattering wave function dominates. This suggests that the quoted theoretical error of +-0.3 fm for the most recent pi- d -> n n gamma measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly--and thus reducing the error--is briefly discussed.
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Electron-deuteron scattering in the equal-time formalism: beyond the impulse approximation
Using a three-dimensional formalism that includes relativistic kinematics, the effects of negative-energy states, approximate boosts of the two-body system, and current conservation, we calculate the electromagnetic form factors of the deuteron up to Q^2 of 4 GeV^2. This is done using a dynamical boost for two-body systems with spin. We first compute form factors in impulse approxmation, but then also add an isoscalar meson-exchange current of pion range that involves the gamma-pi contact operator associated with pseudovector pi-N coupling. We also consider effects of the rho-pi-gamma meson-exchange current. The experimentally measured quantities A, B, and t20 are calculated over the kinematic range probed in recent Jefferson Laboratory experiments. The rho-pi-gamma meson-exchange current provides significant strength in A at large Q^2 and the gamma-pi contact-term exchange current shifts t20, providing good agreement with the JLab data. Relativistic effects and the gamma-pi meson-exchange current do not provide an explanation of the B observable, but the rho-pi-gamma current could help to provide agreement if a nonstandard value is used for the tensor rho-N coupling that enters this contribution.
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Delta Effects in Pion-Nucleon Scattering and the Strength of the Two-Pion-Exchange Three-Nucleon Interaction
We consider the relationship between P-wave pi-N scattering and the strength of the P-wave two-pion-exchange three-nucleon interaction (TPE3NI). We explain why effective theories that do not contain the delta resonance as an explicit degree of freedom tend to overestimate the strength of the TPE3NI. The overestimation can be remedied by higher-order terms in these ``delta-less'' theories, but such terms are not yet included in state-of-the-art chiral EFT calculations of the nuclear force. This suggests that these calculations can only predict the strength of the TPE3NI to an accuracy of +/-25%.
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Nucleon Polarizabilities from Low-Energy Compton Scattering
An effective field theory is used to give a model-independent description of Compton scattering at energies comparable to the pion mass. The amplitudes for scattering on the proton and the deuteron, calculated to fourth order in small momenta in chiral perturbation theory, contain four undetermined parameters that are in one-to-one correspondence with the nucleon polarizabilities. These polarizabilities are extracted from fits to data on elastic photon scattering on hydrogen and deuterium. For the proton we find: alpha_p = 12.1 +/- 1.1 +/- 0.5, beta_p = 3.4 +/- 1.1 +/- 0.1, both in units of 10^{-4} fm^3. For the isoscalar polarizabilities we obtain: alpha_N = 13.0 +/- 1.9 +3.9/-1.5 (in the same units) while beta_N is consistent with zero, within sizeable error bars.
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Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)
We study Compton scattering in systems with A=1 and 2 using chiral perturbation theory up to fourth order. For the proton we fit the two undetermined parameters in the O(Q^4) $γ$p amplitude of McGovern to experimental data in the region $ω,\sqrt{|t|} \leq 180$ MeV, obtaining a chi^2/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: alpha_p=12.1 +/- 1.1 (stat.) +/- 0.5 (theory) and beta_p=3.4 +/- 1.1 (stat.) +/- 0.1 (theory), both in units of 10^{-4} fm^3. We also compute Compton scattering on deuterium to O(Q^4). The $γ$d amplitude is a sum of one- and two-nucleon mechanisms, and contains two undetermined parameters, which are related to the isoscalar nucleon polarizabilities. We fit data points from three recent $γ$d scattering experiments with a chi^2/d.o.f.=26.6/20, and find alpha_N=13.0 +/- 1.9 (stat.) +3.9/-1.5 (theory) and a beta_N that is consistent with zero within sizeable error bars.
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Chiral effective field theory of Delta(1232) and Compton scattering
A new power-counting scheme for a chiral effective field theory that includes Delta degrees of freedom is briefly described and applied to the nucleon Compton scattering.
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Supernovae and Light Neutralinos: SN1987A Bounds on Supersymmetry Revisited
For non-universal gaugino masses, collider experiments do not provide any lower bound on the mass of the lightest neutralino. We review the supersymmetric parameter space which leads to light neutralinos, $M_\lsp \lsim {\cal O}(1\gev)$, and find that such neutralinos are almost pure bino. In light of this, we examine the neutralino lower mass bound obtained from supernova 1987A (SN1987A). We consider the production of binos in both electron-positron annihilation and nucleon-nucleon binostrahlung. For electron-positron annihilation, we take into account the radial and temporal dependence of the temperature and degeneracy of the supernova core. We also separately consider the Raffelt criterion and show that the two lead to consistent results. For the case of bino production in $NN$ collisions, we use the Raffelt criterion and incorporate recent advances in the understanding of the strong-interaction part of the calculation in order to estimate the impact of bino radiation on the SN1987A neutrino signal. Considering these two bino production channels allows us to determine separate and combined limits on the neutralino mass as a function of the selectron and squark masses. For $M_\lsp \sim 100 \mev$ values of the selectron mass between 300 and 900 GeV are inconsistent with the supernova neutrino signal. On the other hand, in contrast to previous works, we find that SN1987A provides almost no bound on the squark masses: only a small window of values around 300 GeV can be excluded, and even then this window closes once $M_\lsp \gsim 20 \mev$.
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The S-Wave Pion-Nucleon Scattering Lengths from Pionic Atoms using Effective Field Theory
The pion-deuteron scattering length is computed to next-to-next-to-leading order in baryon chiral perturbation theory. A modified power-counting is then formulated which properly accounts for infrared enhancements engendered by the large size of the deuteron, as compared to the pion Compton wavelength. We use the precise experimental value of the real part of the pion-deuteron scattering length determined from the decay of pionic deuterium, together with constraints on pion-nucleon scattering lengths from the decay of pionic hydrogen, to extract the isovector and isoscalar S-wave pion-nucleon scattering lengths, a^- and a^+, respectively. We find a^-=(0.0918 \pm 0.0013) M_π^{-1} and a^+=(-0.0034 \pm 0.0007) M_π^{-1}.
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Deuteron Compton Scattering in Chiral Perturbation Theory
Compton scattering on the deuteron is studied in the framework of baryon chiral perturbation theory to third order in small momenta, for photon energies of order the pion mass. The scattering amplitude is a sum of one- and two-nucleon mechanisms with no undetermined parameters. Our results are in good agreement with the intermediate energy experimental data, and a comparison is made with the recent higher-energy data obtained at SAL.
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Numerical renormalization using dimensional regularization: a simple test case in the Lippmann-Schwinger equation
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to renormalize the amplitude and produce a finite solution to the integral equation for all energies. This can be done either algebraically or numerically. In the latter case dimensional regularization can be implemented by solving the integral equation in a lower number of dimensions, fixing the potential strength, and computing the phase shifts, while taking the limit as the number of dimensions approaches three. We demonstrate that these steps can be carried out in a numerically stable way, and show that the results thereby obtained agree with those found when the renormalization is performed algebraically to four significant figures.
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Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system
The central tenet of effective theory is that the details of short-distance physics will not have a significant impact on low-energy observables. Here we perform an analysis of electron-deuteron scattering at low momentum transfers which is based on effective field theory. We show that in our approach the deuteron electromagnetic form factors $F_C$ and $F_M$ indeed are largely insensitive to the short-range $NN$ potential at momenta $Q$ up to about 700 MeV. We also find that the effective field theory approach to deuteron electromagnetic structure provides a systematic justification for many features which have been seen in potential model calculations of the same quantities.
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Electron-deuteron scattering in a current-conserving description of relativistic bound states: including meson-exchange-current contributions
Using a three-dimensional formalism that includes relativistic kinematics, the effects of negative-energy states, approximate boosts of the two-body system, and current conservation we calculate the electromagnetic form factors of the deuteron up to $Q^2=6$ GeV$^2$. This is done both in impulse approximation and with a $ρπγ$ meson-exchange current included. The experimentally-measured quantities $A$, $B$, and $T_{20}$ are calculated over the kinematic range probed in recent Jefferson Laboratory experiments. The meson-exchange current provides significant strength in $A$ at large $Q^2$, but has little impact on $B$ or $T_{20}$.
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Compton Scattering on the Deuteron in Baryon Chiral Perturbation Theory
Compton scattering on the deuteron is studied in the framework of baryon chiral perturbation theory to third order in small momenta, for photon energies of order the pion mass. The scattering amplitude is a sum of one- and two-nucleon mechanisms with no undetermined parameters. Our results are in good agreement with existing experimental data, and a prediction is made for higher-energy data being analyzed at SAL.
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