slac-pub-2605 - SLAC - Stanford University

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2. Constraints on Hadronic Wavefunctions -16- The quark distribution amplitudes @(xi,Q) Q2 -. / d kl Jl(Xi, kli) which control exclusive reactions at large momentum transfer, and the quark probability distributions q(xi,Q) ~~d2k~ I~(Xi,kli) I2 ( summed over all Fock states), which control inclusive reactions at large momentum transfer, are each deter- mined by the hadronic Fock state wavefunctions $(xi,kLi). In principle the Jib i,kLi) describe all hadronic matrix elements. A central goal of hadronic physics will be to utilize these wavefunctions to unify short and long distance physics, and make contact with hadronic spectroscopy, low momentum transfer reactions, and the whole range of non-perturbative physics. Although the complete specification of hadronic wavefunctions clearly will require a solution of the non-perturbative bound state problem in QCD, there is a large number of properties of the wavefunctions which can be derived from the theory and experimental phenomena. In this section we will discuss the following constraints C3J: (a) The predictions of perturbative QCD for the large transverse momentum tail of the Fock state infinite momentum wavefunction $(kli,xi). These results, which also follow from the operator product expansion near the light-cone [131, lead to evolution equations Cl,21 for the process-independent distribution amplitudes $(xi,Q) which control large transverse momentum exclusive reactions such as form factors, and for the distribution functions G q,,(x,,Q> and G glH(xi,Q) which control large transverse momentum inclusive reactions. (b) Exact boundary conditions for the valence Fock state meson wavefunctions from the meson decay amplitudes. In particular we shall show how the x"+yy decay amplitude for msssless quarks specifies the pion wavefunction at - zero k I. This is a new type of low energy theorem for the pion wavefunction which is consistent with chiral symmetry and the triangle anomaly for the axial vector current C181. This large-distance result, together with the constraint on the valence wavefunction at short distance from the r+uv leptonic decay amplitude, leads to a number of new results for the parameterization of the
-17- pion wavefunction. In particular, we show that the probability of finding the valence lq state in the total pion wavefunction is -0.2 to 0.25, for a broad range of confining potentials. (c) As noted above the wavefunction for the Fock states of the hadrons on the light-cone (or at infinite momentum frame) $, h) 'kLi 'xi, Z si) completely specify the quark and gluon particle content of the hadrons. The coherent aspects of the wavefunction are required for constructing the distribution amplitudes which are not only necessary for exclusive processes, but also for the multi-particle, high twist subprocesses which enter inclusive reactions and control transverse momentum smearing effects. We show that the evolution equations which specify the large Q2 behavior of the distribution amplitudes and of incoherent distribution functions G are correctly applied for Q2 ) cc?>, where is the mean value of the off-shell (light-cone/infinite momentum frame) energy in the Fock state wavefunction ( Zt+rn2 1 Bc&'~ ----g-- . i i=l i To first approximation, is the "starting point" Qg for evolution due to perturbative effects in QCD. (2.1) Let us now discuss the constraints on meson wavefunctions imposed by their decay constants. The leptonic decays of the mesons give an important constraint on the valence Iq wavefunction at the origin. As shown in Ref. Cl,21 lim $M(xi,Q) = aOx1x2 = Q-+- for R for pL where fr 2 93 MeV is the pion decay constant for r'-+u'v and f,, Z 107 MeV is (2.2) the leptonic decay constant from p" + e+e-. The analogous result holds for all zero helicity mesons. Because the Q2-+m distribution amplitude has zero
Page 1 and 2: EXCLUSIVE PROCESSES AND HADRON DYNA
Page 3 and 4: 1. Introduction -3- One of the most
Page 5 and 6: -5- where by momentum conservation
Page 7 and 8: -7- our analysis of these processes
Page 9 and 10: -9- processes with large momentum t
Page 11 and 12: form factor. It is also clear then
Page 13 and 14: -13- not already included in the le
Page 15: -15- scale-constant A is relatively
Page 19 and 20: I QC2)(k,,xi,si) = -19- -+2 kL + m2
Page 21 and 22: where 4 non-pert(xi) = I -21- [d2kl
Page 23 and 24: -23- perturbative or perturbative c
Page 25 and 26: -25- where, because of the large ms
Page 27 and 28: -27- 32n2 a2 (Q2) s(Q2) = yj- 6 c b
Page 29 and 30: -29- of just two basic form factors
Page 31 and 32: -31- short distances. Their contrib
Page 33 and 34: -33- straightforward perturbative e
Page 35 and 36: -35- tudinal (sin2b) at large z at
Page 37 and 38: -37- Detailed predictions for each
Page 39 and 40: 0 0.2 0.4 0.6 0.8 1.0 z2 = cm2 (8)
Page 41 and 42: I invariance and spin structure of
Page 43 and 44: -43- (8) Some of the most important
Page 45 and 46: -45- REFERENCES 1. Brodsky, S. J. a
Page 47 and 48: 19. 20. 21. 22. 23. 24. 25. 26. 27.
Page 49: -49- 50. See, e.g., R%kl, R., Brods

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