The Drell-Hearn-Gerasimov Sum-Rule at Polarized HERA S. D. Bass a, M. M. Brisudova b and A. De Roeck c a Institut fur Theoretische Kernhysik, Universitat Bonn, Nussallee 4{6, D-535 Bonn, Germany b Theoretical Division, MSB83, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A. c DESY, Deutsches Elektronen Synchrotron Notkestrasse 85, D-607 Hamburg, Germany Abstract We discuss the otential of olarized HERA to measure the sin deendent art of the total hotoroduction cross-section at large s. The Drell-Hearn-Gerasimov sum-rule [] (for reviews see [, 3]) for sin deendent hotoroduction relates the dierence of the two cross-sections for the absortion of a real hoton with sin anti-arallel A and arallel P to the target sin to the square of the anomalous magnetic moment ofthetarget nucleon, (DHG) 4 m = Z d th ( A P )(): () Here is the (LAB) energy of the exchanged hoton, m is the nucleon mass and is the anomalous magnetic moment. The rst direct test of the Drell-Hearn-Gerasimov sum-rule will be made in exeriments which are lanned or underway at the ELSA, GRAAL, LEGS and MAMI facilities. These exeriments will measure ( A P ) u to a hoton LAB energy = 3GeV ( s :5GeV). They will make a recise measurement of nucleon resonance contributions to (DHG), thus testing multiole analyses of unolarized single-ion hotoroduction data [4], as well as the contributions from strangeness roduction and vector meson dominance. There is no elastic contribution to (DHG). The high-energy art of ( A P ) is exected to be determined by Regge theory for s :5GeV. In this note we briey review ossible Regge contributions to ( A P ) and summarise the resent knowledge of these contributions
from low Q (' 0:45GeV ) inclusive hotoroduction. Finally, we discuss the contribution that olarized HERA could make to the measurement of these high s Regge contributions to the Drell-Hearn-Gerasimov sum-rule. At large centre of mass energy squared (s = m + m ), soft Regge theory redicts [5, 6, 7] A P! N 3 s a + N 0 s f + N g ln s s + N PP () ln s Here a and f are the intercets of the isovector a (60) and isoscalar f (85) and f (40) Regge trajectories, which are usually taken between -0.5 and 0.0 [5]. ( We note, however, that the isotrilet art of the dee inelastic structure function g behaves like x 0:5 in the range (0:0 < x < 0:) in the SLAC data [0], corresonding to an eective Regge intercet a (Q ) ' +0:5 at the relatively low dee inelastic Q ' 3 5GeV.) The ln s=s term is induced by any vector comonent to the short range exchange otential [7] { for examle, two nonerturbative gluon exchange [9]. The = ln s term reresents any omeron-omeron cut contribution to ( A P ). The mass arameter is a tyical hadronic 0:5GeV. The coecients N 3, N 0, N g and N PP in Equ.() are to be determined from exeriment. Besides their imortance for a recise test of the DHG sum-rule, the soft Regge contributions to ( A P ) form a baseline for investigations of DGLAP and BFKL small x behaviour in g, the nucleon's rst sin deendent structure function. To estimate the Regge contribution to ( A P )atq =0we take the low Q data from the E-43 [] and SMC [] exeriments (0.5GeV <Q <0:7GeV ) on A = A P (3) A + P This low Q data has the following features. First, the sin asymmetries A and A d show no signicant Q deendence in the range of each exeriment. Secondly, the isoscalar deuteron asymmetry A d is consistent with zero in both the E-43 and SMC low Q bins. There is a clear ositive roton asymmetry in the E-43 data, signalling a strong isotrilet term in ( A P ) at s ' GeV. The SMC A data is less clear: combining the SMC low Q A data yields a ositive value for A. However, the majority of these SMC oints are consistent with zero. In Table we combine the low Q data to obtain one oint corresonding to each exeriment. We imose the cut (Q 0:7GeV, s :5GeV), so that the mean Q is less than 0:5GeV for each exeriments, and so that our data set is well beyond the resonance region. We assume that the large sa is aroximately indeendent ofq between Q = 0 and Q '0.5 GeV. For the total hotoroduction cross-section we take ( A + P )=67:7s +0:0808 + 9s 0:4545 (4)
Table : A at large s and low Q Exeriment hq i s A A d (Q 0:7GeV, s :5GeV) E-43 0.45 3.5 0:077 0:06 +0:008 0:0 SMC 0.45 6.7 0:064 0:04 0:03 0:00 (in units of b), which is known to rovide a good Regge t for s between.5gev and 50GeV [8]. (Here, the s +0:0808 contribution is associated with omeron exchange and the s 0:4545 contribution is associated with the isoscalar! and isovector trajectories.) Since the E-43 low Q data shows a clearly ositive A with the smallest exerimental error, we choose to normalise to E-43. We estimate ( A P ) ' 0b at (Q =0; s=3:5gev) (5) The small isoscalar deuteron asymmetry A d indicates that the isoscalar contribution to A in the E-43 data is unlikely to be more than 30%. In Fig. we show the asymmetry A as a function of s between.5 and 50 GeV for the four dierent would-be Regge behaviours for ( A P ): that the high energy behaviour of ( A P )isgiven. entirely by the (a ;f ) terms in Equ.() with Regge intercet either (a) (conventional) or (b) + (motivated by the observed small x behaviour of ( n) g ),. by taking /3 isovector (conventional) a and /3 two non-erturbative gluon exchange contributions at s =3:5GeV, 3. by taking /3 isovector (conventional) a and /3 omeron-omeron cut contributions at s =3:5GeV. Photoroduction cross-sections can be measured in e collisions at HERA at high s energies. The dominant rocesses in e collisions are interactions where the hoton is on mass shell. The electron is scattered under aroximately zero degrees with resect to the electron beam direction, which at HERA means that it remains in the beamie. The energy of the scattered electron E 0 e is however reduced to E 0 e = E e E, with E e the incident electron energy and E the emitted hoton energy. The HERA machine magnets in the beamline, which
steer the beam into a closed orbit, act as a sectrometer on these o-momentum electrons. The exeriments H and ZEUS have installed calorimeters to detected these kicked out electrons along the beamline. In case of H calorimeters (stations) are installed at three locations: at 8 m, 30 m and 44 m distance from the interaction oint [3]. The stations accet (tag) electrons from dierent momentum ranges, which corresond to s ranges of 80-90 GeV, 50-50 GeV and 60-5 GeV resectively. At the central energy value of each region the accetance of these devices amounts to 5%, 85% and 70% resectively. The locations of the stations may change as a result of the HERA luminosity ugrade, and are resently under study. Equ.4 shows that the cross section is large, of order of hundreds of microbarns. The hoton energy sectrum emitted from an electron beam is given in the Weizsacker-Williams aroximation [4]. An integrated e luminosity at HERA of b can yield about N = 500K events in each of the 30 m and 44 m stations, and about 0 times less in the 8 m station. The collider exeriments record resently unolarized e collisions. Around the year 000, sin rotators will be installed for the electrons, converting the natural transverse olarization of the electron beam into a hysics whise more useful longitudinal one. Studies are being made to have also the roton beam at HERA olarize [5] which would enable olarized e and thus olarized collisions. Note however that the olarization of the hoton beam will be reduced by a factor D = y( y)=(y +( y)), the so called deolarization factor. Here y = s =s e. For the three stations the measurements are at y = 0:09; 0:44 and 0.90, leading to values of D = 0:094; 0:5 and 0.98. The measured asymmetries at HERA are corresondingly reduced by this factor. If HERA is fully olarized, event samles of the order of 00-500 b will be collected, with exected beam olarizations P e = P = 0:7. In the small asymmetry aroximation the error on the asymmetries, A can be calculated as =(P e P N). Due to data-taking bandwidths and trigger roblems resently not all tagged events are recorded. Assuming a data taking rate of Hz for these events, also in future, leads to about 40 M events/year giving a reachable recision A = =(P e P N) = 0:0003. It is however not excluded that novel techniques in triggering, data-taking and data storage will become available and can be installed for the exeriments, which would allow to collect all roduced events, amounting to aroximately 5,000M events in total for the three stations in a eriod of 3 to 5 years. This would lead to maximal reachable recisions of A =3:0 5 for a measurement at the 30m and the 44m station, and A =0 4 for a measurement at the 8m station. Note that when comared with the true asymmetries as shown in Fig., the deolarization factor D reduces the eective sensitivities with the numbers given above. Given the rojected asymmetries, olarized HERA with A =0:0003 would be sensitiveat s = 50GeV to a ( A P ) falling no faster than s. Taking the
conventional, a =, it would be sensitive to a two non-erturbative gluon exchange contribution which is not less than 30% in the E-43 data and to a omeron-omeron cut contribution which is not less than 3% in the E-43 data. At s = 50GeV, olarized HERA would be sensitive to( A P ) which falls no faster than s 0:6 and to a omeron-omeron cut contribution which is no less than 6% of the E-43 A. We note that a zero-result (no signicant signal) would ut an uer bound on the Regge contribution to the Drell-Hearn-Gerasimov integral. Suort from the Alexander von Humboldt Foundation (SDB) and the United States Deartment of Energy (MMB) is gratefully acknowledged. References [] S.D. Drell and A.C. Hearn, Phys. Rev. Lett. 6 (966) 50; S.B. Gerasimov, Yad. Fiz. (965) 839. [] S. D. Bass, Mod. Phys. Lett. A (997) 05 and Proc. Zeuthen Worksho: Dee Inelastic Scattering o Polarized Targets: Theory Meets Exeriment (DESY, Zeuthen) [3] D. Drechsel, Prog. Part. Nucl. Phys. 34 (995) 8. [4] I. Karliner, Phys. Rev. D7 (973) 77; R.L. Workman and R.A. Arndt, Phys. Rev. D45 (99) 789; A.M. Sandor, C.S. Whisnant and M. Khandaker, Phys. Rev. D50 (994) R668. [5] R.L. Heimann, Nucl. Phys. B64 (973) 49; J. Ellis and M. Karliner, Phys. Lett. B3 (988) 73. [6] S.D. Bass and M.M. Brisudova, Bonn rerint TK-97-0 (997). [7] F.E. Close and R.G. Roberts, Phys. Lett. B336 (994) 57. [8] P.V. Landsho, Proc. Zuoz Summer School, PSI Proceedings 94-0 (994) 35, he-h/94050. [9] S.D. Bass and P.V. Landsho, Phys. Lett. B336 (994) 537. [0] The E-43 Collaboration (K. Abe et al.), Phys. Rev. Lett. 74 (995) 346; The E-54 Collaboration (K. Abe et al.), Phys. Rev. Lett. 79 (997) 6. [] The E-43 Collaboration (K. Abe et al.), Phys. Lett. B364 (995) 6.
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0. + 3 0.0 A 0.00 SMC 3 E43 + (a) (b) () (3) 0.000 0 00 s Figure : The asymmetry A as a function of s for dierent Regge behaviours for ( A P ): given entirely by (a) the (a ;f ) terms in Equ.() with Regge intercet either (conventional) or (b) + ; () by /3 isovector (conventional) a and /3 two non-erturbative gluon exchange contributions at s =3:5GeV; (3) by /3 isovector (conventional) a and /3 omeron-omeron cut contributions at s =3:5GeV.