ELSEVIER Nuclear Physics A623 (1997) 376c-380c

N U C L E A R PHYSICS A

E x c e r p t s f r o m t h e P a n e l Se s s i on

J. Gasser

Institut fiir theoretische Physik der Universit£t Bern Sidlerstr. 5, CH-3012 Bern, Switzerland

Many matrix elements of hadronic currents can be probed at the CEBAF facility, as well as at DA~NE. The kinematical regions explored axe, however, often different - this makes a concerted effort to measure these processes very attractive.

1. P H Y S I C S A T C E B A F A N D A T D A ~ N E

Here I discuss a few processes, relevant for chiral perturbation theory (CHPT), that can be measured at CEBAF and at DA~NE. 1

1 . 1 . E l e c t r o m a g n e t i c f o r m f a c t o r s o f m e s o n s

In Fig. 1 are shown transitions that contain meson matrix elements of the electromag- netic current. At CEBAF (DAffNE) the momentum transfer is spacelike (timelike). I refer to the contribution of Baker for a more detailed discussion of these processes. Here I just mention that the expression for the electric charge radius of the neutral kaon is finite at one loop in CHPT [1], with no low energy constant (LEC) contributing at leading

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Figure 1. Meson matriz elements of the electromagnetic current (P=lr, K, ~}. The double line stands for the scattered nucleus or nucleon.

*Work supported in part by Swiss National Science Foundation 1I do not have at my disposal the contributions from the other speakers, and I apologize to those whose work is therefore not properly referred to in the following.

0375-9474/97/$17.00 © 1997 - Elsevier Science B.V. All rights reserved. PII: S0375-9474(97)00459-4

J. Gasser~Nuclear Physics A623 (1997) 376c-380c 377c

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Figure 2. Matrix elements governed by the ehiral anomaly.

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Figure 3. More anomalous matrix elements.

order. It will certainly be very interesting to have a precise experimental determination of this quantity.

1.2. Chiral anomal i e s In his talk, Bernstein discussed the coupling of the neutral pion to two photons. The

vertex function

f dzei(q,~+a2,,)(OlTj,(z)j,,(y)l~rO(p)) ,,,.~, 2 = ~ ql,q,~F(q,,q~); f = (ql + q2)",

receives its leading order contribution in the chiral expansion from the chiral anomaly [2]. At vanishing momentum transfer q~ = 0, the square IF(0,0)[ z of the form factor is proportional to the width of the neutral pion. Processes that contain this transition matrix element are displayed in Fig. 2. Note that at CEBAF, the photons are spacelike, whereas the last diagram (relevant for DA~NE) contains one real and one timelike photon. A precise determination of F(0, 0) would be interesting, because it would allow one to investigate isospin breaking effects in this transition. The momentum dependence of this form factor is an effect of order pe in CHPT, such that a measurement of the slopes 0F(0, O)/Oq~ would allow one to pin down some of the couplings at order p6 in the effective lagrangian [3]. Further anomalous processes are shown in figure 3.

378c J. Gasser~Nuclear Physics A623 (1997) 376c-380c

e , , e e e

Figure 4. Measuring the pion Compton amplitude 7~r --, q,~r (CEBAF) and the crossed process "Y7 --~ ~r~r at DA%NE.

1 . 3 . P i o n p o l a r i z a b i l i t i e s

The diagrams in figure 4 display relevant processes for Compton scattering 77r --~ 7~r, again illustrating the different kinematical regimes explored at CEBAF and at DA~NE. These processes have been discussed quite frequently in the recent literature [4], because they again contain amplitudes that can be well described in the framework of CHPT. A precise experimental determination of the amplitude in the low energy region would be very welcome.

2. D I S C U S S I O N P A R T

Here I wish to comment - in more detail than it was possible in the panel session - on two questions that were asked to the panelists.

I. Suppose that the low energy constants in the effective lagrangian of QCD have been pinned down - what comes next?

The couplings L1, . . . , Llo at order p4 are already known to rather good precision (for a recent update, see Ref. [6] ). Open issues are the following:

1. One should make sure that all processes ate described with these constants at the corresponding accuracy. A well known recent example where this did not seem to be the case is the reaction 73, --* lr°Ir °. The relevant matrix element receives its leading contribution at one loop order [7] - in addition, the couplings Li do not contribute to this accuracy. The predicted [7] cross section for 3,-), ~ a'°a "° disagrees with the Crystal Ball data [8] even near threshold. This fact generated some doubts as to the validity of the chiral expansion in this case. However, once the calculation had been carried out to two-loop order [9], the discrepancy disappeared. This example illustrates that one has to know the size of the corrections to a prediction, before one can judge its reliability.

J Gasser~Nuclear Physics A623 (1997) 376c-380c 379c

2. On a more fundamental level, even if the Li's provide a compatible set for all known data, the question remains whether they are really the low energy constants of QCD. Indeed, in the framework of QCD, the Li's can in principle be calculated in terms of the renormalization group invariant scale AQcD and of the heavy quark masses - the LEC's are on the same footing as other static quantities like masses, decay constants, magnetic moments etc. The situation is pictured in figure 5.

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Figure 5. The Li's can be determined either from data or from the underlying theory.

The determination of the LEC's in the framework of QCD will therefore be a natural next step in the programme - for an outline of the procedure see Refs. [10,11]. Once we will know what the values of the LEC's in QCD are, we will be confronted with two possible situations: either, there is nice agreement between the data and QCD. Or, one finds that the values of some of the LEC's in QCD do not agree with those determined from the data. Both possibilities are interesting, although not equally S O . 2

[ ~. Would it be interesting to measure ~-decays? [

The decay ?7 --* 7ra'a" gives information on the ratio of light quark masses [13,14]. At the same time, CHPT makes precise predictions for the Dalitz plot distribution of these transitions. It would certainly be worthwhile to measure these decays again, provided that the luminosities achieved and the detectors available allow one to do a good job and to improve on the present statistical and systematic experimental uncertainties in the relevant quantities. I refer to Ref. [14] for a recent discussion of the issue. Apart from the three pion channel, eta decays offer a rich spectrum of other decays, that would be very worthwhile to study experimentally and theoretically. I refer to Scherer's contribution to this workshop, and to Ref. [15] for reviews.

2This comparison has been carried oat in the linear sigma model, at one loop level [12]. Not surprisingly, it was found that, in this case, the predicted relations among the LEC's are not consistent with the data.

380c J. Gasser~Nuclear Physics A623 (1997) 376c-380c

I thank the organizers for the invitation to this interesting workshop.

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