We prove a new soft-pion theorem for the near-threshold pion production by a hard electromagnetic probe. This theorem relates various near-threshold pion-production amplitudes to the nucleon distribution amplitudes. The new soft-pion theorem is in good agreement with the SLAC data for the structure function F p 2 ͑W, Q 2 ͒ for W 2 # 1.4 GeV 2 and 9 # Q 2 # 30.7 GeV 2 .The amplitudes of the pion production near the threshold by the electromagnetic probeat a not too large virtuality ͑Q 2 ͒ of the photon Q 2 ø L 3 ͞m p (L ϳ 1 GeV is a typical hadronic scale) can be expressed in terms of various nucleon form factors with the help of the soft-pion theorem (SPT) [1][2][3]. For virtualities Q 2 ϳ L 3 ͞m p and larger this SPT does not work, because the SPT of [1-3] corresponds to first taking the chiral limit ͑m p ! 0͒ while Q 2 is kept fixed. To study the parametric domain m p Q 2 ¿ L 3 we consider the opposite sequence of the limits: Q 2 !`first and m p ! 0 second. Since the two limits do not commute, in this way we derive a new "hard-soft" pion theorem (hSPT) for the reaction (1) in the near-threshold region and in the Q 2 kinematics complementary to one of Refs. [1-3], namely, m p Q 2 ¿ L 3 . Our main tool is the QCD factorization theorem for exclusive processes [4,5] (for a recent review and comprehensive list of references, see, e.g., [6]). It allows us to express the pion-production amplitude at large virtuality in terms of the distribution amplitudes (DAs) of the nucleon and of the low-mass pN system. These nonperturbative objects correspond to the minimal three quark ͑3q͒ Fock component of the nucleon and pN systems [7]. We derive a hSPT to relate the corresponding distribution amplitude of the pN system (we call it pN DA) to the nucleon distribution amplitude. This hSPT is valid for the limit when the mass of the pN system (denoted as W) is close to the threshold W th M N 1 m p . The derivation of the similar theorem for DA of the two-pion system near threshold can be found in [8,9].The physical picture of the near-threshold production of pion by a hard electromagnetic probe is as follows. At large Q 2 the emission of the soft pion from the initial state contributes only to large invariant masses W. The emission from the hard interaction part is a higher twist in Q 2 . Hence the emission occurs solely in the final state when a small 3q system produced in the hard interaction expands to a large enough configuration. At this point we are dealing with a soft-pion emission and can apply corresponding near-threshold chiral theory relations.It follows from the QCD factorization theorem [4,5] that the transition matrix element A͑g ‫ء‬ N ! pN 0 ͒ at large Q 2 can be written as (up to the power suppressed terms)where T ͑x, y͒ is the hard part of the process computable in perturbative QCD. The functions F N ͑ y͒, F pN 0 ͑x͒ are distribution amplitudes (light cone wave functions) of the nucleon and of the low-mass pN 0 system. The DA of the nucleon F N ͑ y͒ also enters the QCD description of the nucleon form factor and it...

Hard scattering to a three cluster final state is suggested as a method to probe configurations in hadrons containing small size color singlet cluster and a residual quark-gluon system of a finite mass. Examples of such processes include e + N →could be a pion(kaon) or other state of finite mass which does not increase with momentum transfer (Q 2 ). We argue that different models of the nucleon may lead to very different qualitative predictions for the spectrum of states M X . We find that in the pion model of nonperturbative qq sea in a nucleon the cross section of these reactions is comparable to the cross section of the corresponding two-body reaction. Studies of these reactions are feasible using both fixed target detectors (EVA at BNL, HERMES at DESY) and collider detectors with a good acceptance in the forward direction.

Using the leading order amplitudes of hard exclusive electroproduction of pion pairs we have analyzed the angular distribution of the two produced particles. At leading twist a pion pair can be produced only in an isovector or an isoscalar state. We show that certain components of the angular distribution only get contributions from the interference of the I=1 and the (much smaller) I=0 amplitude. Therefore our predictions prove to be a good probe of isospin zero pion pair production. We predict effects of a measurable size that could be observed at experiments like HERMES. We also discuss how hard exclusive pion pair production can provide us with new information on the effective chiral Lagrangian.Comment: 17 pages, version to appear in Phys. Rev.

An extension of Weinberg's approach is applied to the aa-scattering amplitude of the leading order in 1 / N , . The resulting sum rules (SR's) restrict the masses and widths of aa resonances providing dualitylike properties of the aa amplitude and enable us to express constants of chiral Lagrangians in terms of resonance parameters. The numerical verification of SR's displays agreement with present experimental information and consistency with the results of some models.