###### Abstract

For the - interaction, the perturbative expansion of the effective chiral Lagrangian (PT) can be limited to terms quartic in momenta and masses (O(p)), or to higher order. The abnormal intrinsic parity (chiral anomaly) component of the lagrangian leads to interesting predictions for the processes and . These are described by the amplitudes F and F, respectively. We demonstrate that the O(p) value of F disagrees with existing data, while the O(p) value is nearly consistent. We describe how Fermilab experiment E781 can get improved data for tests of the chiral anomaly.

Preprint TAUP-2176-94, Sept. 1994, Bulletin Board - 9409307

Contribution: Proceedings of the Conference on Physics with GeV-Particle Beams,

Juelich, Germany, Aug. 1994, World Scientific, Eds. H. Machner and K. Sistemich.

[.3CM] CHIRAL ANOMALY TESTS

[.3CM] Murray A. Moinester

[.3CM] School of Physics and Astronomy,

Raymond and Beverly Sackler Faculty of Exact Sciences,

Tel Aviv University, 69978 Ramat Aviv, Israel

E-mail:

[1cm]

The Chiral Axial Anomaly can be studied with a 600 GeV pion beam in FNAL experiment E781 [russ]. For the - interaction, the O(p) chiral lagrangian [gl, donn1] includes Wess-Zumino-Witten (WZW) terms [wzw, bij3], which lead to a chiral anomaly term [wzw, bij3, anti] in the divergence equations of the currents. This leads directly to interesting predictions [bij3, ter] for the processes and ; and other processes as well [bij3, ben]. The two processes listed are described by the amplitudes F and F, respectively. The F vertex was first described by Adler, Bell, and Jackiw [abj].

The chiral anomaly term leads to a prediction for F and F in terms of , the number of colors in QCD; and f, the charged pion decay constant. We use and f= 92.4 0.2 MeV in the equations given previously [bij3, anti] for these amplitudes. This f value is from Holstein [hols1], and Marciano and Sirlin [mar]; since the PDG [pdg] value 93.2 does not account completely for radiative corrections [hols1, mar]. The value we use differs from f= 90. 5. MeV estimated by Antipov et al. [anti], and leads therefore also to different conclusions regarding the agreement of data and theory. The O(p) F prediction [bij3] is:

(1) |

in agreement with experiment [bij3]. The F prediction is:

(2) |

We estimate a theoretical uncertainty of 0.2 GeV from f and including the accuracy of the O(p) prediction. The latter is of order [gl, donn1] m , where sets the scale [gl, donn1] for the PT expansion. The O(p) relationship between these two amplitudes was first given by Terentev [ter]:

(3) |

The experimental confirmation of eq. 2 would demonstrate that the O(p) terms are sufficient to describe F.

The amplitude F was measured by Antipov et al. [anti] at Serpukhov with 40 GeV pions. Their study involved pion production by a pion in the nuclear Coulomb field via the Primakoff reaction:

where Z is the nuclear charge. The 4-momentum of each particle is , , , , , respectively. In the one-photon exchange domain, eq. 4 is equivalent to:

and the 4-momentum of the virtual photon is k = -. The cross section formula for the eq. 4 reaction was given in Ref. 6, and depends on , and on t, s, t, t, Z. Here t is the squared four-momentum transfer to the nucleus, is the invariant mass of the final state, t is the squared 4-momentum transfer between initial and final in eq. 5, is the minimum value of t to produce a mass , and the virtual photon target density is proportional to Z. The Antipov et al. data sample (roughly 200 events) covered the ranges and . The small t-range selects events predominantly associated with the exchange of a virtual photon, for which the target nucleus acts as a spectator.

The experiment [anti] yielded F. The uncertainties do not include estimated 10% errors [anti, amen] arising from extrapolating F to threshold (s, t approaching zero); for data taken in the s-range of Antipov et al. The cited experimental result differs from the O(p) expectation (eq. 2) by at least two standard deviations. Therefore, in contrast to the conclusion of Antipov et al, we conclude that the chiral anomaly prediction at O(p) is not confirmed by the available data.

Bijnens et al. [bij3, bij1] studied higher order PT corrections in the abnormal intrinsic parity (anomalous) sector. They included one-loop diagrams involving one vertex from the WZW term, and tree diagrams from the O(p) lagrangian. They determine parameters of the lagrangian via vector meson dominance (VMD) calculations. The higher order corrections are small for F. For F, they increase the lowest order value from 7% to 12%. The one-loop and O(p) corrections to F are comparable in strength. The loop corrections to F are not constant over the whole phase space, due to dependences on the momenta of the 3 pions. The average effect is roughly 10%, which then changes the theoretical prediction by 1. GeV. Given the VMD assumption, we make a rough uncertainty estimate of 30% for this contribution. The prediction, including the errors given previously in eq. 2, is then:

almost consistent with the data. The limited accuracy of the existing data, together with the new calculations of Bijnens et al., motivate an improved and more precise experiment.

We use the Primakoff cross section formula [anti] for the reaction of eq. (4), with the O(p) value, to calculate the expected cross section for an incident 600 GeV energy. The cross section is about 100 nb for a C target for an s interval of 4-10 m; while the total inelastic cross section is roughly 192 mb. The number of pion interactions in the target during the E781 beam time is estimated to be about . Therefore, the expected number of two-pion events for this s-interval is about . The large number of events will allow analysis of the data separately in different intervals of s. This is important because uncertainties [anti, amen] due to and contributions increase with s; and to control systematic uncertainties. The contributions (near the -resonance s-value, and near the two-pion threshold) can be seen in the data of Jensen et al. [jens] for the Primakoff reaction . For reaction (4) in the s interval from 4-6 m, we expect roughly an order of magnitude less events than in the interval to 10 m. This number of events is still large enough to give excellent statistical error.

Another reaction [amen] to determine F also uses a virtual photon:

whereby an incident high energy pion scatters inelasticly from a target electron in an atomic orbit. The number of such events observed by Amendolia et al. [amen] was 36 for a Hydrogen target, corresponding to a cross section of 2.1 0.5 nb. The experiment did not extract a value for F; but smaller cross section uncertainties are in any case needed for a precision chiral anomaly test. For this reaction on a carbon target, as in Fermilab E781, the expected cross section per atom is roughly 10. nb., and the number of expected events is roughly 2000. The experimental backgrounds [amen] for this reaction have been described; and their minimization would lead to a high quality complementary determination of F.

The reaction is also approved for study at CEBAF [rm] by measuring cross sections near threshold using tagged photons. The accuracy of this method is limited by the uncertainties associated with the needed Chew-Low [cl] extrapolation to the pion pole. F can also be studied at a low energy electron-positron collider in the near threshold reaction .

In conclusion, the experimental result of Antipov et al. differs with the chiral anomaly prediction at O(p) by at least two standard deviations. At O(p), considering the experimental and theoretical uncertainties, the data and prediction are nearly consistent. How well does PT work in the anomalous sector? How anomalous is the real world anyhow? We described how the Fermilab E781 experiment can give improved answers to these questions via studies of reactions (4) and (7). The 1 MHz pion flux at Fermilab will enable significantly improved statistics, compared to the previous experiments. In E781, at the 600 GeV higher energy, and also at lower value of s; the strong contribution to reaction (4) is negligible [in, ber]. This should significantly reduce the systematic uncertainty.

Acknowledgements

Discussions on this subject with J. Bijnens, L. Frankfurt,
S. Gerzon, B. Holstein, H. Leutwyler, S. Nussinov, E. Piasetzky, and J. Russ
are acknowledged. This work was supported by the U.S.-Israel Binational
Science Foundation (BSF), Jerusalem, Israel.

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