MeasuringtheFifthStructureFunctionin

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1 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 1/ MeasuringtheFifthStructureFunctionin H( e, e p)n G.P. Gilfoyle, R. Burrell, C. Copos, K. Gill, K. Greenholt, M. Jordan, (Richond) W.K. Brooks, (USM) J.D. Lachniet, B.P. Quinn, (CMU) M.F. Vineyard (Union) Outline 1. Introduction and Background.. Extracting the Fifth Structure Function.. Event Selection and Corrections. 4. Results and Preliinary Coparison with Theory. 5. Conclusions.

2 CLAS Collaboration Meeting, Oct, 1-1, 1 p. / Scientific Motivation Establish a baseline for the hadronic odel to eet so we can clearly see the transition to quark-gluon degrees of freedo. The deuteron is an essential testing ground because it is the siplest nucleus. Differing ix of relativistic corrections (RC), eson-exchange currents (MEC), final-state interactions (FSI), and isobar configurations (IC) depending on kineatics. Learn ore about FSI in quasielastic kineatics. The fifth structure function is zero in PWIA and is doinated by FSI. Deuteron as neutron target, N N interaction... Short-Range Correlations (SRC).

3 CLAS Collaboration Meeting, Oct, 1-1, 1 p. / Soe Necessary Background Goal: Measure the iaginary part of the quasielastic (QE) LT interference ter (fifth structure function) of H( e, e p)n at Q 1 (GeV/c) (σ LT I(Jz fi ( q) J y fi ( q))). The cross section is d σ dωdω e dω p = σ L + σ T + σ LT cos(φ pq )+ σ T T cos(φ pq ) + hσ LT sin(φ pq) where h = ±1 for different bea helicities. Use a variation of the helicity asyetry extracted fro the φ pq -dependent oents of the data in each p = q p p bin. bea helicity R π π σ± sin φ pq dφ pq sin φ pq ± = R π π σ± dφ pq = ± σ LT (σ L + σ T ) = ±A LT Get rid of a sinusoidally-varying background, by taking the difference of the two helicities A ««sin φ pq + sin φ pq = LT + α acc A LT + α acc = A LT

4 CLAS Collaboration Meeting, Oct, 1-1, 1 p. / Soe Necessary Background Goal: Measure the iaginary part of the quasielastic (QE) LT interference ter (fifth structure function) of H( e, e p)n at Q 1 (GeV/c) (σ LT I(Jz fi ( q) J y fi ( q))). The cross section is d σ dωdω An e aside: = σ dω p L + σ T + σ LT cos(φ pq )+ σ T T cos(φ pq ) + hσ LT sin(φ pq) Past easureents in the literature of A LT used a slightly different for. where h = ±1 for different bea helicities. In particular, for fixed, sall-solid-angle spectroeters the helicity asy- a variation was deterined of the helicity using asyetry ex- Useetry tracted fro the φ pq -dependent oents of the data in each p = q p p bin. A h (Q, p, φ pq = 9 ) = bea σ+ 9 helicity σ 9 σ R π σ + π sin φ pq ± = σ± sin φ pq dφ9 + = LT σ σ 9 L + σ T σ T T pq σ R LT π = ± π σ± dφ pq (σ L + σ T ) = ±A LT where the subscripts refer to φ pq = 9 and there is an additional ter σ T T in the denoinator. The contribution of this ter is sall. Get rid of a sinusoidally-varying background, by taking the difference of the two helicities A ««sin φ pq + sin φ pq = LT + α acc A LT + α acc = A LT

5 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 4/ Existing Measureents of Helicity Asyetry Several results fro Bates in the 199 s for different structure functions and kineatics (i.e. quasielastic, dip region) using the Out-Of-Plane Spectroeter. See S.Gilad, et al., NP A61, 76c, (1998) and references therein. JLab efforts to easure deuteron structure functions in quasielastic kineatics θ c pq W. Boeglin etal. PRL, 17, 651 (11) - extracted high-oentu coponent of deuteron wave function. C. Hanretty et al. Hall A E8-8 - deuteron electrodisintegration near threshold; analysis in progress. M. Mayer Data ining project - extracting fifth structure function fro E6 data.

CLAS Collaboration Meeting, Oct, 1-1, 1 p. 5/ The Data Set Analyze data fro the E5 run period in Hall B. Two bea energies, 4. GeV and.56 GeV, with noral torus polarity (electrons inbending).

6 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 5/ The Data Set Analyze data fro the E5 run period in Hall B. Two bea energies, 4. GeV and.56 GeV, with noral torus polarity (electrons inbending). One bea energy.56 GeV with reversed torus polarity (electron outbending) to reach lower Q. Recorded about. billion triggers, Q =. 5.(GeV/c). Dual target cell with liquid hydrogen and deuteriu. Bea polarization:.76 ±.17 Liited statistics at 4. GeV so only lower energy data shown here.

7 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 6/ Event Selection Cuts and Corrections For electrons CC photoelectrons n phe > 5 Energy-oentu atch.5p e.1 < E total <.5p e +.6 Reject pions ec_ei.1 and nphe 5 EC track fiducial dc_ysc 165(dc_xsc 8)/8 EC fiducial No tracks within 1 c of the end of a strip Egiyan threshold cut p e ( ec_threshold).1 Electron fiducial Protopopescu et al., CLAS-NOTE -7. Select target 11.5 c < v z < 8. c Moentu corrections Ki et al., CLAS-Note For protons Proton fiducial cut Nyazov et al., CLAS-NOTE 1-1. ep vertex cut v z (e) v z (proton) 1.5 c ass cut.88 MeV/c < p < 1. MeV/c Moentu corrections K. Y. Ki et al., CLAS-NOTE 1-18 Bea charge.6 GeV, reversed field:.996 ±.7 asyetry.6 GeV, noral field:.9944 ±.7 Radiation EXCLURAD Gilfoyle et al., CLAS-NOTE 5-

8 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 7/ Quasielastic Electron Selection Start with the residual epx ass W n. Counts GeV, noral torus polarity Counts GeV, reversed torus polarity Fit the neutron peak in the distribution to deterine the the W n resolution σ n. Set the W n cut at the pion threshold inus σ n to reove pion containation. Effect of W n cut on the Bjorken x distribution W n cut W n W n :8:1 (GeV) (GeV) Counts GeV, noral torus polarity Black - ep Red - ep+w x :4:47 Bj n Counts W n cut.6 GeV, reversed torus polarity Black - ep Red - ep+w n x Bj

9 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 8/ Quasielastic Electron Selection Consider p e = p e (easured) p e (calculated) where p e (calculated) is extracted fro the angles. (GeV/c) e p.5.6 GeV, reversed torus polarity QE events GeV, noral polarity ep events, W cut on n GeV, reversed polarity ep events, W cut on n θ e (deg) p (GeV/c) e p (GeV/c) e Set the p e cut at the slope change. Effect on the Bjorken x distribution. EXCLURAD used to correct for radiative effects. Counts GeV, noral torus polarity Black - ep Red - ep+w n Green - ep+w p + n x :56:1 Bj e Counts GeV, reversed torus polarity Black - ep Red - ep+w n Green - ep+w p + n e x Bj

10 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 9/ Preliinary A LT Results for D( e,e p)n A LT A LT E=.6 GeV Noral torus polarity.5 D(e,e p)n Preliinary E=.6 GeV Reversed torus polarity Counts ) Counts ( H(e,e )X E=.6 GeV Reversed torus polarity Q =.6 (GeV/c) E=.6 GeV Noral torus polarity Q =.96 (GeV/c) p (GeV/c) :5: Q (GeV/c)

11 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 1/ Consistency Checks Check bea helicity with ep e π. A LT..6 GeV, noral torus polarity A LT..6 GeV, reversed torus polarity At p GeV/c the asyetry should go to zero p (GeV/c) p (GeV/c) The sin φ pq weighted distributions should give the sae results as fitting the φ pq dependence. A LT GeV, noral torus polarity Red - <sin φ > pq Blue - sin φ Fit pq A LT GeV, reversed torus polarity Black - <sin φ > pq Blue - sin φ Fit pq p (GeV/c) p (GeV/c)

12 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 11/ Consistency Checks Use GSIM to validate analysis algoriths. Paraeterize easured helicity asyetries. A LT GeV, reversed torus polarity GSIM results Blue - bin averaged input curve Red - input curve A LT = a 1 x + a x a x + a 4 x + a 5 x 4 + a 6 x 6.4. Quasi-Elastic Event Generator (QUEEG) Feri otion of proton - Hulthen oentu distribution + isotropic direction. Boost to oving proton frae and elastically scatter electron fro proton. Choose φ pq fro paraeterized distribution. Boost back to the lab frae. Send events through GSIM and the sae analysis routines used on the data :7:7 A LT :9: p (GeV/c).6 GeV, noral torus polarity GSIM results Blue - bin averaged input curve Red - input curve p (GeV/c)

13 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 1/ Inventory of Systeatic Uncertainties Methods for Largest Effects 1. Changed cut position by ±1% and took half the difference of A LT.. Changed threshold by ±σ where σ is the uncertainty in the width of the neutron peak.. Half the difference of the change in A LT with the radiative corrections on and off. 4. Sae as Reaining details in draft CLAS Analysis Note. Row Quantity δa LT 1 Nuber of CC Photoelectrons <.4 W n cut <. RC correction <. 4 p cut <. 5 p e cut <. 6 EC track coordinate cut <. 7 EC sapling fraction <. 8 EC pion threshold <. 9 electron/proton fiducial cuts <. 1 Bea Polarization <.1 11 Bea charge asyetry <.1 Main contributions to the systeatic uncertainty and axiu values for both data sets.

14 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 1/ Inventory of Systeatic Uncertainties Methods for Largest Effects 1. Changed cut position by ±1% and took half the difference of A LT.. Changed threshold by ±σ where σ is the uncertainty in the width of the neutron peak.. Half the difference.1 of the change in A LT with the radiative corrections.8 on and off. A LT 4. Sae as Reaining details.in draft CLAS Analysis Note. Row Quantity δa LT 1 Nuber of CC Photoelectrons <.4 W n cut <. RC correction <. Syste atic un certain ty,.6 GeV 4 p cut <. Red Nor al torus polarity Blue Reversed torus polarity 5 p e cut <. 6 EC track coordinate cut <. 7 EC sapling fraction <. 8 EC pion threshold <. 9 electron/proton fiducial cuts <. 1 Bea Polarization <.1 11 Bea charge asyetry < p GeV c Main contributions to the systeatic uncertainty and axiu values for both data sets.

15 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 1/ Preliinary Results with Uncertainties A LT H(e,e p)n Noral torus polarity.6 GeV A LT H(e,e p)n Reversed torus polarity.6 GeV (GeV/c) p (GeV/c) p

16 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 14/ Preliinary Coparison With Theory 1. Arenhövel (black) - Non-relativistic Schrödinger Equation with RC, MEC, IC, and FSI. Averaged over the CLAS acceptance.. Laget (green) - Diagraatic approach for Q = 1.1 GeV (lower panel) and Q =.7 GeV (upper panel).. Jeschonnek and Van Orden (JVO in red) - Relativistic calculation in IA, Gross equation for the deuteron ground state, SAID paraeterization of the NN scattering aplitude for FSI. Off-shell for factor cutoff set to Λ N = 1. GeV (PRC, 81, 148, 1). Averaged over the CLAS acceptance. A LT A LT E=.6 GeV Noral torus polarity H(e,e p)n Preliinary E=.6 GeV Reversed torus polarity Red - JVO Green - Laget Black - Arenhoeval p (GeV/c) :18:17

17 χ / ndf / 9 Constant 1.9e+5 ± 1.517e+ Mean.946 ±.1 Siga.495 ±.1 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 15/ Effect of Narrow W cut Counts :45:8 1. The original A LT results at Bates easured a narrow range in the energy transfer at the QE peak. This is equivalent to a narrow cut in W, the residual ass for inclusive electron events.. To copare our results with the Bates easureents we added a W cut. It is wider that the Bates one (1 MeV versus 17 MeV) in order to obtain adequate statistics. 1.6 GeV, noral torus polarity W (GeV) Counts χ / ndf 8 / 7 Constant 4.549e+5 ±.41e+.6 GeV, reversed Mean.95 ±. torus polarity Siga.764 ±.4.6 GeV, reversed torus polarity W (GeV) A LT A LT E=.6 GeV Noral torus polarity.5 Additional W cut H(e,e p)n Preliinary E=.6 GeV Reversed torus polarity Additional W cut Red - JVO Green - Laget Black - Arenhoeval p (GeV/c) :6:6

18 χ / ndf / 9 Constant 1.9e+5 ± 1.517e+ Mean.946 ±.1 Siga.495 ±.1 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 15/ Effect of Narrow W cut Counts :45:8 1. The original A LT results at Bates easured a narrow range in the energy transfer at the QE peak. This is equivalent to a narrow cut in W, the residual ass for inclusive electron events.. To copare our results with the Bates easureents we added a W cut. It is wider that the Bates one (1 MeV versus 17 MeV) in order to obtain adequate statistics. 1.6 GeV, noral torus polarity W (GeV) Counts χ / ndf 8 / 7 Constant 4.549e+5 ±.41e+.6 GeV, reversed Mean.95 ±. torus polarity Siga.764 ±.4.6 GeV, reversed torus polarity W (GeV) A LT A LT E=.6 GeV Noral torus polarity.5 Additional W cut H(e,e p)n Preliinary E=.6 GeV Reversed torus polarity Additional W cut Red - JVO Green - Laget Black - Arenhoeval (GeV/c) :6:6 :4:55 p

19 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 16/ Conclusions The sin φ pq technique works well including the subtraction of the two different bea helicities to eliinate sinusoidal coponents of the acceptance. We observe a % dip in A LT at p MeV/c in both.6-gev data sets. In the low-q data ( Q =.6 (GeV/c) ) the JVO calculation shows reasonable agreeent with the data across the full p range. In the high-q data ( Q =.96 (GeV/c) ) the JVO calculation predicts a uch greater dip than observed. At low p, the calculations by Arenhövel reproduce the low-q data, but diverge (they re too negative) above p = 5 MeV/c. At high-q, the calculation predicts too great a dip. At low Q, the Laget calculations reproduce the low-p data, but predicts to great a dip at higher p. At high Q, the calculation reproduces the agnitude of the dip. The effect of the narrow W cut on A LT for the high-q data is a puzzle.

20 Additional Slides CLAS Collaboration Meeting, Oct, 1-1, 1 p. 17/

21 Effect of spin-orbit FSI forces calculated by JVO CLAS Collaboration Meeting, Oct, 1-1, 1 p. 18/

22 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 19/ Corrections Moentu corrections. Deterine θ e for elastically scattered electrons and extract W. Miniize the difference between W and M p as a function of the electron θ e and φ e and for each data set. W Data Set.875 ±.7 GeV.6 GeV, reversed torus polarity.879 ±.8 GeV.6 GeV, noral torus polarity.87 ±. GeV 4. GeV, noral torus polarity Radiative corrections. Expected the to be sall (they were in the G n M the sae data set). They weren t sall enough. First, need to see the easured, preliinary A LT. analysis fro

23 CLAS Collaboration Meeting, Oct, 1-1, 1 p. / Radiative Corrections (RC) EXCLURAD - Applies a ore sophisticated ethod than the usual approach of Mo and Tsai or Schwinger to account for exclusive easureents. See CLAS-Note 5- and Afanasev et al., PRD 66, 744 (). They aren t sall enough to ignore. Method Calculate polarized and unpolarized RC surfaces as functions of cos θ pq and φ pq over broad range of Q. Convert cos θ pq to p. Store results in a three diensional histogra in ROOT. Interpolate this histogra to get RC(Q, p, φ pq ) and apply it as a weight event-by-event. Q (GeV ):.,.5,.8, 1.1, 1.4, 1.7. RCpol RCunpol 1.1 Q.8 GeV cosθ

24 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 1/ Choosing vcut Soe of the quantities needed to correct for radiative effects are shown in the plot. The tail is integrated using the covariant inelasticity v defined as v = Λ u = W + h u + E(M + E sin θ r ) E h W + E(M + E θ sin ) where u is the ass of the undetected hadron, Λ is the four-oentu of the issing or undetected particles, and W = M + M(E E ) 4EE sin θ and the quantities E, E, and θ are deterined by the electron kineatics. The hadron energy E h is deterined by the choice of the angle of the outgoing hadron relative to q, the three-vector of the oentu transfer. The asses M, h, and u are all known. E res= choose E > E one-half intrinsic resolution res Region of integration fro E lo to E hi E is the bea energy E is the peak energy of the scattered electron radiative tail E lo E E E hi ω E res E

25 CLAS Collaboration Meeting, Oct, 1-1, 1 p. / Effect of Radiative Corrections A LT Black - no RC Red - with RC A LT GeV, noral torus polarity Effect of radiative correction A LT Preliinary.6 GeV, noral torus polarity p (GeV/c) Black - no RC Red - with RC A LT p (GeV/c) GeV, reversed torus polarity Effect of radiative correction The radiative correction turns out to be uch saller than the statistical uncertainty Preliinary.6 GeV, reversed torus polarity p (GeV/c) p (GeV/c)

26 CLAS Collaboration Meeting, Oct, 1-1, 1 p. / Systeatic Uncertainties.1 CC photoelectron cut uncertainty.1 Effect of changing W n cut.6 GeV Red Nor al torus polarity.6 GeV.5 Blue Reversed torus polarity.5 A LT. A LT..5.5 Red Nor al torus polarity Blue Reversed torus polarity p GeV c p GeV c.1 Syste atic uncertainty due to Proton Mass Cut.1 Syste atic uncertainty due to Radiative Corrections.5.6 GeV Red Nor al torus polarity Blue Reversed torus polarity.5.6 GeV Red Nor al torus polarity Blue Reversed torus polarity A LT. A LT p GeV c p GeV c

27 CLAS Collaboration Meeting, Oct, 1-1, 1 p. 4/ Consistency Checks - Bea helicity ep e pπ Coparison K.Joo and C.Sith, CAN 1-8. A LT <A LT >= ±.9, Q =.4-.7 GeV K. Joo and C. Sith <A LT >= -.17 ±.19, Q =.15-. GeV This work Run Nuber

Measurements of the Fifth Structure Function of the Deuteron

Measurements of the Fifth Structure Function of the Deuteron G.P. Gilfoyle, R. Burrell, C. Copos, K. Gill, K. Greenholt, M. Jordan, University of Richmond, Richmond, VA, 3173 W.K. Brooks, Universidad Técnica