Predictions Of Chiral Perturbation Theory Research Articles

The TUNL-FELL inverse Compton γ-ray source as a nuclear physics facility

A new technique for producing an intense beam of polarized γ-rays is presented. This High-Intensity Gamma-ray Source (HIGS) will utilize the facilities of the new Duke Free Electron Laser Laboratory. This system includes the LINAC injector, the 1.3 GeV electron storage ring, and the OK-4 undulator.It will be shown that it is possible to tune the electron beam in a manner which allows the FEL photons to backscatter from an electron bunch, all within the ring. This leads to an intense beam of almost 100% linearly polarized γ-rays whose energy can be readily tuned from about 5 to greater than 200 MeV. Furthermore, beam energy spreads of less than 1% can be obtained by pure geometrical collimation. Details of the beam properties and background sources will be presented. It will be shown that this is an ideal beam for nuclear physics and nuclear astrophysics studies. One example of this which takes advantage of the flux, energy resolution and polarization of the beam, is the study of Δ 33 excitations in finite nuclei. These intense polarized beams will also make it possible to perform precision measurements of the nucleon polarizabilities. And we will see that studies in the vicinity of the photo-pion production threshold can provide crucial tests of many of the recent predictions (Low Energy Theorems) of Chiral Perturbation Theory. Our final example will show how the very intense beams available at low energies can be used to determine astrophysically important capture cross sections by measurements of the inverse reactions.

POLARIZABILITY EFFECTS IN PION PHOTOPRODUCTION

We investigate the pion photoproduction reaction γN→γNπ as a probe of pion electromagnetic polarizability. This reaction had been proposed as having the potential to resolve the long standing discrepancy between measurements of pion polarizabilities and the predictions of Chiral Perturbation Theory. We have carried out a series of calculations of ratios of substructure — related to background contributions for energies below the Δ resonance — but have to report that the largest values are found in the high-energy tail of the photon spectrum and that these are of the order of 0.1% for charged pions and 1% for neutral pions. We conclude that these sensitivities are not yet accessible experimentally, and that this regime of energy should be excluded from current consideration.

Threshold π0 electroproduction at the Mainz 3-spectrometer facility

We investigated the threshold H(e,e′p) π 0 reaction at q 2 = −0.1 (GeV/c) 2 as a test of chiral perturbation theory (ChPT), a low energy approximation to QCD. The longitudinal and transverse structure functions were determined by a Rosenbluth separation. The results differ significantly from recent predictions of ChPT.

The reaction πN → ππN at threshold in chiral perturbation theory

In the framework of heavy baryon chiral perturbation theory, we give the chiral expansion for the πN → ππN threshold amplitudes D 1 and D 2 to quadratic order in the pion mass. The theoretical results agree within one standard deviation with the empirical values. We also derive a relation between the two threshold amplitudes of the reaction πN → ππN and the ππ S-wave scattering lengths, a 0 0 and a 2 0, respectively, to order ( M 2 π ). We show that there are uncertainties mostly related to resonance excitation which make an accurate determination of the ππ scattering length a 0 0 from the ππN threshold amplitudes at present very difficult. The situation is different in the ππ isospin two final state. Here, the chiral series converges and one finds a 2 0 = −0.031 ± 0.007 consistent with the one-loop chiral perturbation theory prediction.

A trigger for the identification of pions stopped in an active target

The total cross sections of the π +p → π + π +n and π −p → π + π −n reactions near threshold can be used to obtain scattering lengths which are directly comparable to predictions of chiral perturbation theory. Data for these reactions were taken at TRIUMF using a segmented active scintillator target. The signature of a π + in an active target segment was a prompt pulse caused by the particle stopping, followed by a second pulse due to the π + to μ + decay. TRIUMF 500 Mhz transient digitisers were used to record the scintillator outputs in 2 ns steps so that the double pulses could be identified with high efficiency in off-line data analysis. A second level trigger able to reject events in less than 10 μs was necessary to avoid a prohibitively high deadtime due to the long read-out time of the digitisers. It was implemented with fast ECLine electronics and increased the useful event acquisition rate by a factor of more than forty.

Electromagnetic corrections to the threshold pion-pion charge exchange amplitude and the lifetime of pionium

Abstract We give the electromagnetic corrections (due to the mass difference between π ± and π 0 and the Coulomb potential) to the s-wave threshold parameters in the coupled two-channel ( π + π − , π 0 π 0 ) system. We estimate that the uncertainty in this correction to the threshold charge-exchange amplitude (which determines the lifetime of pionium, i.e. the π + π − bound state) is rather less than the uncertainty in the prediction of chiral perturbation theory for this quantity. We conclude that a measurement of the lifetime for the decay of pionium with an accuracy of about 10% would provide a significant test of the chiral-perturbation theory prediction.

η-decays into three pions

The branching ratios Γ(η → 3π 0) Γ(η → π +π −π 0) = 1.44 ± 0.09 ± 0.10 and Γ(η → γγ) Γ(η → π +π −π 0) = 1.78 ± 0.10 ± 0.13 have been determined using the Crystal Barrel detector at LEAR. The latter ratio yields a partial width of Γ( η → π + π − π 0) = 0.26 ± 0.03 keV using the known value for Γ( η → γγ). The η → π + π − π 0) Dalitz plot is compared to the predictions of chiral perturbation theory.

Light quark dependence of the Isgur-Wise function from QCD sum rules.

We study light quark dependence of the Isgur-Wise function for $B_a\rightarrow D_a$ and $B_a\rightarrow D^{*}_a$ in the framework of QCD sum rules. At zero recoil , all the Isgur-Wise functions equal as required by heavy quark symmetry and at non-zero recoil, the Isgur-Wise function for $B_s$ decay falls faster than that for $B_{u,d}$ decay , which is just contrary to the recent prediction of the heavy meson chiral perturbation theory. As by-products, we also estimate SU(3) breaking effects in the mass and the decay constant.

Electromagnetic moments of the baryon decuplet.

We compute the leading contributions to the magnetic dipole and electric quadrupole moments of the baryon decuplet in chiral perturbation theory. The measured value for the magnetic moment of the $\Omega^-$ is used to determine the local counterterm for the magnetic moments. We compare the chiral perturbation theory predictions for the magnetic moments of the decuplet with those of the baryon octet and find reasonable agreement with the predictions of the large--$N_c$ limit of QCD. The leading contribution to the quadrupole moment of the $\Delta$ and other members of the decuplet comes from one--loop graphs. The pionic contribution is shown to be proportional to $I_z$ (and so will not contribute to the quadrupole moment of $I=0$ nuclei), while the contribution from kaons has both isovector and isoscalar components. The chiral logarithmic enhancement of both pion and kaon loops has a coefficient that vanishes in the $SU(6)$ limit. The third allowed moment, the magnetic octupole, is shown to be dominated by a local counterterm with corrections arising at two loops. We briefly mention the strange counterparts of these moments.

Gamma gamma --> pi 0 pi 0 contribution to the process e+e--->e+e- pi 0 pi 0.

We consider the $O({p}^{4})$ predictions of chiral perturbation theory ($\ensuremath{\chi}\mathrm{PT}$) in the process $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, together with the study of the existing experimental measurements and the planned new ones. At the Frascati $\ensuremath{\Phi}$ factory $\mathrm{DA}\ensuremath{\Phi}\mathrm{NE}$ the rate of the events ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ is large enough to allow for a measurement of the cross section with a good statistical sensitivity. However, a quantitative analysis of the commonly used approximation of considering only real photons for the detection of the $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ signal is still lacking. This motivates us to compute the cross section in $\ensuremath{\chi}\mathrm{PT}$ for the production of ${\ensuremath{\pi}}^{0}$ pairs due to off-shell photons. A measurement of the azimuthal correlations would test the higher order $\ensuremath{\chi}\mathrm{PT}$ corrections independently from the measurement of the cross section. We approximate these corrections by including the contribution of the low-lying vector resonances in the scattering amplitude.

Chiral corrections to the [formula omitted

I study the chiral corrections to the O( p 2) prediction of Chiral Perturbation Theory B K ⋍ 0.29 . I point out that neglecting non-factorizable chiral corrections one obtains B K ⋍ 0.61 ; this result takes into account factorizable chiral corrections to all orders in the chiral expansion. Non-factorizable O( p 4) chiral corrections are computed within the framework of the mean field approximation of the extended Nambu-Jona-Lasinio Model and appear to be negative. I find B K = 0.38 −0.02 +0.10.

Decuplet contributions to hyperon axial vector form factors

We consider the predictions of chiral perturbation theory for SU (3) breaking in the axial vector form factor g 1 measured in semileptonic hyperon decays. Including only octet baryon intermediate states, the non-analytic correlations are ∼ 100%. These corrections are dominated by an SU (3)-symmetric wavefunction renormalization, which explains the fact that the “corrected” predictions still fit the data well. We argue that the large corrections are nonetheless strong evidence that the chiral expansion is breaking down. We theninclude decuplet baryon intermediate states. We find that the effects of a non-zero octet-decuplet mass difference, Δ, significantly changes the pattern of corrections from the Δ = 0 case. The decuplet corrections can cancel the large octet contributions in a non-trivial way, but the corrections no longer favor the SU (6) values of the axial couplings. We also argue the D and F axial couplings cannot be reliably extracted from calculations which keep only the non-analytic corrections.

Unitarity and KL → π0γγ

We discuss the rare decay K L → π 0 γγ. Although the recently measured 2γ-invariant-mass distribution is in quite good agreement with the lowest-order chiral perturbation theory prediction, there seems to be a discrepancy with the calculated branching ratio. We extend the previous computations to next-to-leading order, O( p 6). The two dominant mechanism at this order are emphasized: the two-poin intermediate state and vector meson exchange.

The role of the Δ isobar in chiral perturbation theory and hedgehog soliton models

Hedgehog model predictions for the leading nonanalytic behavior (in m π 2) of certain observables are shown to agree with the predictions of chiral perturbation theory up to an overall factor which depends on the operator. This factor can be understood in terms of contributions of the Δ isobar in chiral loops. These physically motivated contributions are analyzed in an expansion in which both m π and M Δ − M N are taken as small parameters, and are shown to yield large corrections to both hedgehog models and chiral perturbation theory.

Absorption and dispersion of pions at finite temperature

We consider the pole shift in the propagator and analyse both absorptive and dispersive properties of pions at finite temperature. The leading-order term in an expansion in powers of the density is determined by the ππ forward scattering amplitude. We evaluate this amplitude in a semi-phenomenological manner, using chiral perturbation theory at threshold and relying on experimental information at higher energies. In particular we analyse the contributions generated by ρ-exchange and show that they substantially modify the lowest-order prediction of chiral perturbation theory.

The σ-commutator and low-energy πN phase shifts

Presently, the best experimental determination is σ = 53 ± 8 MeV, compared with the prediction of chiral perturbation theory, σ = 36 ± 6 MeV. The experimental value has been very stable since 1974 and requires a 50% increase in accepted masses of up and down quarks to m̂ = (mu + md)/2 = 10.3 ± 1.8 MeV. Almost all the πN data below 300 MeV are consistent with one another and analyticity except those of Frank et al. and Brack et al. The new X-ray result of Beer et al. is consistent with other data within one standard deviation, but is slightly less accurate; a further improvement by a factor of four in the X-ray data seems possible and would be important.

On the validity of chiral perturbation theory for weak hyperon decays

The predictions of chiral perturbation theory for the weak non-leptonic decays of hyperons are examined beyond the leading order. For the S-wave amplitudes we find that the leading corrections to lowest order chiral perturbation theory preserve the vanishing of the Σ + → nπ + amplitude. However, the Lee-Sugawara relation gets a large correction indicating a breakdown of chiral perturbation theory for this relation. For the P-wave amplitudes we find that the leading corrections to lowest order chiral perturbation theory are large indicating a breakdown of chiral perturbation theory for the P-wave amplitudes. The weak semileptonic hyperon decays are determined by baryon matrix elements of the left-handed current. Corrections to the predictions of lowest order chiral perturbation theory for these matrix elements are computed. These corrections are very small.

On the consistency of chiral symmetry and the quark model in proton decay

We have examined an apparent discrepancy between the predictions of chiral perturbation theory and the quark model in proton decay and found that the disagreement is resolved by taking into account a neglected diagram in the quark model. Our results increase the predicted rate for p → π 0e +; in minimal SU(5) this increase leads to a discrepancy with experiment if Λ MS =150 MeV .