Physics of Atomic Nuclei, Vol. 66, No. 7, 2003, pp. 1282–1288. Translated from Yadernaya Fizika, Vol. 66, No. 7, 2003, pp. 1322–1328. Original Russian Text Copyright c  2003 by Mokeev, Ripani, Anghinolfi, Battaglieri, De Vita, Golovach, Ishkhanov, Markov, Osipenko, Ricco, Sapunenko, Taiuti, Fedotov. ELEMENTARY PARTICLES AND FIELDS Theory Helicity Components of the Cross Section for Double Charged-Pion Production by Real Photons on Protons V. I. Mokeev 1) , M. Ripani 2) , M. Anghinolfi 2) , M. Battaglieri 2) , R. De Vita 2) , E. N. Golovach 1) , B. S. Ishkhanov 1) , N. S. Markov 3) , M. V. Osipenko 1) , G. Ricco 2) , V. V. Sapunenko 2) , M. Taiuti 2) , and G. V. Fedotov 3) Institute of Nuclear Physics, Moscow State University, Vorob’evy gory, Moscow, 119899 Russia Received October 9, 2002 Abstract—The helicity components σ 1/2 and σ 3/2 of the cross section for double charged-pion production by real photons on a nucleon are calculated within a phenomenological approach developed previously. A high sensitivity of the σ 1/2 –σ 3/2 asymmetry to the contribution of nucleon resonances having strongly different electromagnetic helicity amplitudes A 1/2 and A 3/2 is demonstrated. This feature is of importance for seeking “missing” baryon states. c  2003 MAIK “Nauka/Interperiodica”. 1. INTRODUCTION Experiments with polarized electron (photon) beams and polarized proton targets made it possible to determine the cross sections σ 1/2 and σ 3/2 corre- sponding to the total proton and photon helicities of 1/2 and 3/2 in the initial states both for the inclusive channel and for various exclusive channels [1–6]. Interest in studying the helicity components σ 1/2 and σ 3/2 is motivated by the following factors. On the basis of the most general theoretical prin- ciples, Gerasimov [7] and Drell and Hern [8] (GDH in the following) predicted the value of the integral I GDH =  (σ 1/2 - σ 3/2 ) dν ν , (1) where σ 1/2 and σ 3/2 are the total photoabsorption cross sections for the case in which the total photon– proton helicity is 1/2 and 3/2, respectively, while ν is thephotonenergy.Itfollowsfrom[7,8]thattheGDH integral must take the value of -204 μbatthephoton point. The experimental results reported in [1, 2] were compared with the predictions made in [7, 8]. The definition of I GDH can be extended to the case of virtual-photon absorption, I GDH = I GDH (Q 2 ), where Q 2 is the sign-reversed square of the virtual-photon 4-momentum. The investigation of the Q 2 depen- dence of I GDH in [4] revealed that, for Q 2 > 1.0 GeV 2 , 1) Institute of Nuclear Physics, Moscow State University, Vorob’evygory, Moscow, 119899 Russia. 2) Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Genova,Italy. 3) Faculty of Physics, Moscow State University, Vorob’evy gory, Moscow,119899 Russia. its behavior obeys the 1/Q 2 law.Thisbehaviorfollows from the calculations within perturbative QCD in the region Q 2 > 5 GeV 2 ,butexperimentaldataareinac- cord with the asymptotic behavior of photon–proton interaction at lower values of Q 2 down to 1 GeV 2 . The integral I GDH grows fast from the photon point to Q 2 ≈ 1–2 GeV 2 , and its absolute value de- creases approximately by an order of magnitude at Q 2 =1.0 GeV 2 . Under the assumption of photon interaction with proton partons, the difference σ 1/2 - σ 3/2 isdeterminedbythedifferenceoftheprobabilities of finding a parton with spin orientation along and against the photon-spin direction. Thus, the integral I GDH is related to the contribution of the parton spin to the total proton spin. According to the analyses performed in [9, 10], the contribution of the parton spin to the total nucleon spin in the asymptotic region (Q 2 > 1.0 GeV 2 )doesnotexceed30%;atthephoton point (Q 2 =0 GeV 2 ), the main contribution to the nucleon spin comes from constituent quarks. Thus, the variation in the quantity Q 2 over the interval from 0 to 1.0 GeV 2 leads to a significant variation in the helicity amplitudes of photon–proton interaction and in the contribution of the quark spin to the total proton spin. In order to understand mech- anisms behind such strong changes in the spin struc- ture of the photon–proton interaction, it is necessary to analyze contributions of various exclusive channels to the cross-section difference σ 1/2 - σ 3/2 . A detailed description of the Q 2 and W (W is the total energy in the c.m. frame) dependences of the cross sections σ 1/2 and σ 3/2 and of the GDH integral 1063-7788/03/6607-1282$24.00 c  2003 MAIK “Nauka/Interperiodica”