Measurements of polarized photo-pion production on longitudinally polarized HD and Implications for Convergence of the GDH Integral
LEGS Spin Collaboration, S. Hoblit, A.M. Sandorfi, K. Ardashev, C. Bade, O. Bartalini, M. Blecher, A. Caracappa, A. D'Angelo, A. d'Angelo, R. Di Salvo, A. Fantini, C. Gibson, H. Glueckler, K. Hicks, A. Honig, T. Kageya, M. Khandaker, O.C. Kistner, S. Kizilgul, S. Kucuker, A. Lehmann, M. Lowry, M. Lucas, J. Mahon, L. Miceli, D. Moricciani, B. Norum, M. Pap, B. Preedom, H. Seyfarth, C. Schaerf, H. Stroeher, C.E. Thorn, C.S. Whisnant, K. Wang, X. Wei
aa r X i v : . [ h e p - e x ] A ug Measurements of ~ H ~ D ( ~γ, π ) and Implications for Convergence of the GDH Integral S. Hoblit,
1, 2, ∗ A. M. Sandorfi, † K. Ardashev,
1, 3
C. Bade, O. Bartalini, M. Blecher, A. Caracappa, A. D’Angelo, A. d’Angelo, R. Di Salvo, A. Fantini, C. Gibson, H. Gl¨uckler, K. Hicks, A. Honig, T. Kageya, M. Khandaker, O. C. Kistner, S. Kizilgul, S. Kucuker, A. Lehmann, M. Lowry, M. Lucas, J. Mahon, L. Miceli, D. Moricciani, B. Norum, M. Pap, B. Preedom, H. Seyfarth, C. Schaerf, H. Str¨oher, C. E. Thorn, C. S. Whisnant, K. Wang, and X. Wei (LSC Collaboration) Deptartment of Physics, University of Virginia, Charlottesville, VA 22901 Physics Department, Brookhaven National Laboratory, Upton, NY 11973 Deptartment of Physics, University of South Carolina, Columbia, SC 29208 Department of Physics, Ohio University, Athens OH 45701 Universit`a di Roma “Tor Vergata” and INFN-Sezione di Roma2, Rome, Italy Physics Deptartment, Virginia Polytechnic Inst. & State Univ., Blacksburg, VA 24061 Forschungszentrum J¨ulich GmbH, D-52425 J¨ulich, Germany Deptartment of Physics, Syracuse University, Syracuse, NY 13210 Norfolk State University, Norfolk and Jefferson Lab, Newport News, VA 23606 James Madison University, Harrisonburg, VA 22807 (Dated: October 29, 2018)We report new measurements of inclusive π production from frozen-spin HD for polarized photonbeams covering the ∆(1232) resonance. These provide data simultaneously on both H and D withnearly complete angular distributions of the spin-difference cross sections entering the Gerasimov-Drell-Hearn (GDH) sum rule. Recent results from Mainz and Bonn exceed the GDH prediction forthe proton by 22 µ b, suggesting as yet unmeasured high-energy components. Our π ◦ data reveala different angular dependence than assumed in Mainz analyses and integrate to a value that is 18 µ b lower, suggesting a more rapid convergence. Our results for deuterium are somewhat lower thanpublished data, considerably more precise and generally lower than available calculations. PACS numbers: 13.60.Hb, 13.60.Le, 14.20.Gk, 25.20.Lj, 27.10.+h
In 1966 three sets of authors, Gerasimov [1], Drell andHearn [2] and Hosoda and Yamamoto [3] independentlyderived a sum rule for the anomalous magnetic moment( κ ) of spin S = 1 / P ) andanti-parallel ( A ) photon and target spin alignments, Z ∞ ω σ P − σ A ω dω = 4 Sπ α (cid:16) κm (cid:17) . (1)In recent literature this relation for S = 1 / GDH sum rule . Hosoda andYamamoto also showed that the same relation holds forspin S = 1 nuclei, such as the deuteron [4]. This ex-pression follows from a Gell-mann–Goldberger–Thirringdispersion relation for the forward elastic (Compton) am-plitude [5], provided that the spin-flip Compton ampli-tude vanishes at high energy at least as fast as 1 /ln ( ω ).Because of the latter requirement, this sum rule is notfundamental, in that no underlying theory falls if it isviolated. Rather, convergence of the above integral to avalue different from the right side of eqn. 1 would revealan interesting property of a very high-energy process.For the proton and deuteron, the right hand side ofeqn. 1 reduces to 204 µb and 0.7 µb , respectively. Re-cently, a collaboration from Mainz and Bonn has ex- perimentally checked the GDH sum rule for the proton[6], and at least consistency with calculations for thedeuteron over a limited energy range [7]. Their protonmeasurements spanned the energy range from 0.2 to 2.9GeV and yielded 254 ± ± µ b, exceeding the sumrule expectation. Multipole analyses such as SAID [8]or MAID [9] agree that a contribution of − µb is ex-pected from the near threshold region below 0.2 GeV.This would require an as yet unmeasured − µb fromhigh energies to restore agreement with the expectationsof eqn. 1, which is possible since some negative contribu-tions have been suggested by Regge models [10, 11].We report here new measurements of inclusive π photo-production from a polarized HD target, spanning a rangeof polarized photon energies covering the P ∆ reso-nance. The experiments were performed at the LaserElectron Gamma Source (LEGS) at Brookhaven Na-tional Laboratory with tagged circular polarized γ -raysbetween 190 and 420 MeV. The general characteristics ofthe LEGS photon beams are discussed in ref [12]. Herethe photon polarization averaged between 60% to 99%and was cycled between left and right circular states atrandomly chosen times averaging every few minutes.The polarized target consisted of solid hydrogen-deuteride (HD), held in a frozen-spin state. The materialwas condensed in a variable temperature cryostat, wherethe NMR polarization monitoring system was calibratedat 2 K, transferred to a dilution refrigerator for polariza-tion at ∼
15 mK and 15 Tesla, held there for typically 3months to reach the frozen-spin state, and finally trans-ferred to an In-Beam Cryostat (IBC) operating at 0.3 K,where a thin 0.9 Tesla solenoid maintained the H andD orientations. The polarization cycle will be detailedin a separate publication. Some aspects are discussed in[13]. Data were collected during two running periods inFall 2004 and Spring 2005, the first emphasizing H po-larization, with initial polarizations of P ( H ) = 0 .
59 and P ( D ) = 0 .
07, and the second using increased D polariza-tion following an RF transfer of spin between H and D,with P ( H ) = 0 .
32 and P ( D ) = 0 .
33. Mid-way througheach period the H polarization was flipped with an RFtransition. This produced four distinct data blocks withdiffering target polarizations, during which the in-beamspin relaxation times for polarized H and D ranged from 7to 15 months. The polarization was monitored frequentlywith a cross-coil NMR system within the IBC [14].For these measurements, pions were detected in a large
Spin Asymmetry (SASY) calorimeter. An array of 432NaI(Tl) detectors, an
XBOX , surrounded the target cov-ering laboratory (Lab) angles from 45 ◦ to 135 ◦ . A cylin-drical array of plastic neutron detectors was positionedbetween the XBOX and the IBC. (Results for exclusivechannels will be discussed elsewhere.) A forward wallconsisting of 31 cm of plastic scintillators, backed by anarray of 176 Pb-Glass crystals detected reaction productsat Lab angles between 10 ◦ and 40 ◦ . The configurationof these detectors was optimized for neutral pions, witheither two decay photons detected in the XBOX or onein the XBOX and the other in the forward wall. Thisprovided nearly complete coverage for π ◦ detection.Two-pion production is negligible throughout our en-ergy range [15]. As a result, spectra at a fixed angleand tagged energy are dominated by 2-body (from H) orquasi-2-body (from D) kinematics. The energy of recon-structed neutral pions is compared to the 2-body expec-tation in Fig. 1 for one of 10 angle bins, 17 tagged energybins and 4 target polarization groups. The simulated re-sponse (blue curve) is in excellent agreement. The spinasymmetry is evident in the left and right panels, whichshow yields for parallel and anti-parallel beam and targetspin alignments. Charged pion spectra are very similar.The only unpolarizable nucleons in the target are foundin a mesh of 50 µm Al wires used to conduct away heatduring polarization and in pCTFE (C ClF ) windowsof the target cell. Their contributions are determinedthrough empty cell measurements (black area in Fig. 1).We discuss here inclusive π production, integrated overazimuthal angles, for which the differential cross sectionfrom polarized HD can be written as [13, 16], dσ ( θ, E γ ) = dσ HD − P cγ P H ˆ E H − P cγ P VD ˆ E D + p / P TD ˆ T , (2) E missing (MeV) ! + H D " X
320 MeV75 o Lab P "" " N o r m a li z e d Y i e l d -100 -50 0 50 100 E missing (MeV) ! + H D " XA
320 MeV75 o Lab $ " " FIG. 1: Differences between 2-body kinematics and the mea-sured π ◦ energy are shown in red, for parallel (left) and anti-parallel (right) beam and target spin alignments. Simulatedenergy differences are shown as the solid (blue) curves. Emptycell contributions are shaded in black. where P cγ is the circular beam polarization, P H is thehydrogen polarization, P VD and P TD are the deuteronvector and tensor polarizations, respectively, and asubscript zero (0) denotes an unpolarized cross sec-tion. Here we have designated the numerator of a spinasymmetry with a carat, so that ˆ E H = dσ H E H =1 / (cid:2) dσ H ( A ) − dσ H ( P ) (cid:3) , ˆ E D is the corresponding quan-tity for deuterium and p / T = p / dσ D T =1 / (cid:2) dσ D ( A ) + dσ D ( P ) − dσ D (cid:3) is the deuteron tensorobservable, following the convention of [16].The data set consists of four distinct blocks with dif-ferent target polarizations, each containing roughly equalamounts of data with right and left circular photon po-larization. These eight data groups overdetermine thefour observables of eqn. 2. Fits varying ˆ T produced atmost few percent changes in dσ HD , compared to fixingˆ T to zero, and no perceptible changes to ˆ E H and ˆ E D .Here we focus on results of fits with ˆ T fixed to zero.Sample angular distributions of the unpolarized crosssection at the peak of the ∆(1232) are shown in Fig. 2(solid circles). To compare with other available deuterondata we have subtracted the well-known proton cross sec-tions as parameterized by SAID(FA07k) [8]. Here weshow results for the Fall’04 data for which the deuterontensor polarization was negligible.The normalization scale was checked by comparingD( γ, π ◦ )X cross sections to data collected with the samedetector array using a liquid D target of known length(open circles in Fig. 2). The Fall’04 target was grownslowly and its length agreed with that expected from theknown amount of HD gas. The Spring’05 target wasgrown rapidly and its cross section scale was normal-ized to the Fall’04 D( γ, π ◦ )X by fitting to the interval110 ◦ ≤ θ πLab ≤ ◦ where both our fits and the calcula-tions of [16] agree that ˆ T is negligible.Differential spin-difference cross sections, [ dσ H ( P ) − dσ H ( A )] = − E H , for polarized H are shown in Fig. 3as solid circles for energies near the peak of the ∆. Since ! " Lab (deg)
304 MeV d $ L a b ( µ b / s r ) D( % , " )X ! " ± Lab (deg) D( % , " ± )X304 MeV FIG. 2: Unpolarized cross sections (solid circles) forD( γ, π ◦ )X, left, and D( γ, π ± )X, right, at E γ = 304 MeV, de-duced by subtracting SAID(FA07k) predictions [8] for p( γ, π )from fitted HD results. For the π ◦ channel, LEGS data from aliquid D target are shown as open circles, while crosses andhatched-boxes are from [17] and [15]. For the π ± channel,open boxes are constructed from π − pp [18] and the π − /π + ratio data of [19]. The curves are calculations from [16]. E ! = 320 MeV " Lab E ! = 320 MeV-40-200204060 0 45 90 135 E ! = 304 MeV d $ H ( P ) - d $ H ( A ) ( µ b / s r ) -40-200204060 0 45 90 135 d $ H ( P ) - d $ H ( A ) ( µ b / s r ) E ! = 304 MeV " Lab H( ! , ) % % H( ! , + ) % % FIG. 3: Angular dependence of the [ P − A ] spin-differencecross section for polarized H at beam energies near the ∆peak. The full data are solid (red) circles. Unpolarized limits(solid red squares) at 0 ◦ and 180 ◦ are the means of SAID [8]and MAID [9]. Open diamonds are from Mainz [20], interpo-lated to these energies. Predictions from SAID and MAID aredotted (black) and dashed (green) curves, respectively. Solid(blue) lines show Legendre fits to our data. the pion has zero spin, at 0 ◦ and 180 ◦ the H spin differ-ence reduces to − dσ H . For these angles, the mean ofSAID(FA07k) [8] and MAID(2007) [9] were used (solidsquares). The Mainz H-Butanol results for π + are invery good agreement with the present data, both hereand at other energies. SAID and MAID multipole pre-dictions, which include the Mainz data in their fits, repro-duce the angular dependence of the π + spin difference.The Mainz π ◦ differential spin difference data are againin good agreement with our results, although they havea very limited angular range [20]. However, forward of80 ◦ in the laboratory, our spin-difference results drop be-low the multipole prediction of SAID and MAID. Thistrend occurs mainly near the ∆ peak. At energies 40MeV higher or lower, SAID and MAID π ◦ predictionsare quite close to our data.The angular distributions of the π spin-difference crosssections have been fitted to a Legendre expansion (solidblue curves in Fig. 3). The integration of these distri-butions are shown as the open (red) crosses in Fig. 4.Our total spin difference for π + from polarized H (Fig. 4,top) is in excellent agreement with Mainz results [20],although limited to energies above 270 MeV by absorp-tion in the neutron detectors surrounding the HD target.The π ◦ spin-difference is lower than the Mainz results inthe region of the ∆ peak (Fig. 4, second panel from top),reflecting the differences in the angular distributionsAnother method of obtaining total cross sections is tosimply count pions in the full detector. This techniquewas used in Mainz experiments. All quasi-4 π detectorshave efficiencies that vary with angle, which must be cor-rected using simulations. However, it is important to useaccurate angular distributions to distribute events in suchsimulations to avoid biasing results, particularly whencross sections vary rapidly with angle. Counting neutralpions in the SASY detector, with efficiencies correctedby simulation using measured angular distributions, re-sults in the solid (red) circles of Fig. 4. This agrees withdirect integration of the angular distributions, and hassmaller uncertainties since it avoids propagating errorsfrom multiple background subtractions.Systematic uncertainties on the cross section scale as-sociated with target length, flux normalizations and pos-sible geometrical differences between the detector and thesimulations are estimated at 3.5%. Photon beam polar-izations are known to 1%. Systematic uncertainties ontarget polarization vary between data groups. Their ef-fect produces a 5.1% uncertainty in the integrated spin-difference. The total systematic uncertainty in GDH(p)is then 6.3%.The π ◦ contribution to the running GDH integral forthe proton is plotted against the upper limit of integra-tion in Fig. 4 (third panel from top). From 200 MeV to420 MeV, our integrated result is 125.4 ± µ b. Inte-gration of the Mainz data over the same interval gives142.9 ± µ b [20]. This difference of -17.5 ± µ b -1000100200 ! H ( P )- ! H ( A ) ( µ b ) H( " , + ) $ $ H( " , % ) $ $ ! H ( P )- ! H ( A ) ( µ b ) MainzLEGS R unn i n g G D H ( µ b ) – 18 µ b H( " , % ) $ $ D( " , % )X $ $ E " (MeV) ! D ( P )- ! D ( A ) ( µ b ) FIG. 4: Total π + and π ◦ spin-difference cross sections forpolarized H (top two panels) and for π ◦ production from po-larized D (bottom). Open (red) crosses result from an angleintegration of the differential spin difference ( π ◦ crosses areshifted by +3 MeV for clarity). Solid (red) circles result fromcounting π ’s in the detector, using the measured angular de-pendences in a simulation to correct for varying efficiencies.Mainz results, using the latter method, are shown as open di-amonds [7, 20]. The π ◦ contribution to the running GDH(p)is plotted in the second to bottom panel against the upperlimit of integration. Curves are as in Fig. 2 and Fig. 3. appears to originate from a limited energy range. Ap-plying this correction to the full Mainz+Bonn result, to-gether with the -28 µ b contribution from energies below0.2 GeV, would bring their GDH(p) total down to 208 ± ±
14 (sys) µ b, where we have combined here thesystematic uncertainties from both experiments. This isto be compared with 204 µ b for the right side of eqn. 1and removes the need for additional canceling contribu-tions from higher energies to achieve agreement with theGDH(p).The integrated spin difference for π ◦ production fromthe deuteron is shown in the bottom panel of Fig. 4.These are somewhat lower than the Mainz results of [7]and considerably more precise. The calculation of [16]is shown as the solid curve. While certainly in proxim-ity to the data, further theoretical work will be needed to address the discrepancies which are largest in the π ◦ channel (Fig. 2 as well).In summary, while our charged- π data from polarizedH agree with Mainz, our π ◦ results near the peak of the∆ reveal a different angular distribution than what wasassumed in Mainz analyses. As a result, our π ◦ contri-bution to eqn. 1 is 18 µ b less than the Mainz result for Hand suggests that a high-energy Regge tail is not needed.Our results for polarized D are lower than the trend of theMainz data and have considerably smaller uncertainties.The data are also lower than recent deuteron calculationsand point to the need for additional theoretical work tounderstand the GDH(D) convergence.This work was supported by the U.S. Dept. of Energyunder Contract No. DE-AC02-98-CH10886, by the Isti-tuto Nazionale di Fisica Nucleare, Italy, and by the U.S.National Science Foundation. We are indebted to Mr.F. Lincoln for his expert technical assistance. We thankDrs. C. Commeaux, J.-P. Didelez and G. Rouill´e for theircollaboration during the early stages of the HD target de-velopment. One of us (AMS) would like to thank Drs. A.Fix and H. Arenh¨ovel for supplying their deuteron cal-culations and for many clarifying discussions, as well asDr. T.-S. H. Lee for stimulating interactions. ∗ Corresponding author: [email protected] † Corresponding author: sandorfi@jlab.org[1] S. B. Gerasimov, Sov. J. Nucl. Phys. , 430 (1966).[2] S. D. Drell and A. C. Hearn, Phys. Rev. Lett. , 908(1966).[3] M. Hosoda and K. Yamamoto, Prog. Theor. Phys. ,425 (1966).[4] M. Hosoda and K. Yamamoto, Prog. Theor. Phys. ,426 (1966).[5] M. Gell-Mann, M. L. Goldberger, and W. E. Thirring,Phys. Rev. , 1612 (1954).[6] H. Dutz et al., Phys. Rev. Lett. , 32003 (2004).[7] J. Ahrens et al., Phys. Rev. Lett. , 202303 (2006).[8] R. A. Arndt, W. J. Briscoe, I. I. Strakovsky, and R. L.Workman, Phys. Rev. C , 55213 (2002).[9] D. Drechsel, O. Hanstein, S. S. Kamalov, and L. Tiator,Nucl. Phys. A , 145 (1999).[10] S. Simula et al., Phys. Rev. D , 34017 (2002).[11] K. Helbing, Prog. Part. Nucl. Phys. , 451 (2003).[12] G. Blanpied et al., Phys. Rev. C , 25203 (2001).[13] A. M. Sandorfi et al., in Proc. NSTAR 2005: Physics ofExcited Nucleons , edited by S. Capstick, V. Crede, andP. M. Eugenio (World Scientific, New Jersey, 2006).[14] C. Thorn and A. Caracappa, AIP Conf. Proc. , 397(2008).[15] B. Krusche et al., Eur. Phys. J. A , 309 (1999).[16] A. Fix and H. Arenhovel, Phys. Rev. C , 64005 (2005).[17] U. Siodlaczek et al., Eur. Phys. J. A , 365 (2001).[18] P. Benz et al., Nucl. Phys. B , 158 (1973).[19] T. Fujii et al., Nucl. Phys. B , 395 (1977).[20] J. Ahrens et al., Eur. Phys. J. A21