E up to Q 2 =13.5

Transcription

1 G n M E up to Q 2 =13.5 (GeV/c) 2 by Ratio Method Form factors Combining n & p form factors GMn by ratio method Hall A GMn 1

2 In one-photon exchange approx. 2 j ien( p f ){ F1 ( Q ) 2 i q F2 ( Q )} N( pi ) 2M 2 Where Q q q d ( E, ) Mott[( F1 F2 ) 2 ( F1 F2 ) tan ( )] d 2 Or with d d 2 2 Where Q / 4M G F F and G F F E 1 2 M 1 2 G G E M 2 2 ( E, ) Mott [ 2 GM tan ( )] d Mott 2 2 ( E, ) [ G E G M ] Where d 1 2 Rosenbluth separation 2 1/ 1 2(1 )tan ( / 2)

3 Non-relativistic interpretation: G E and G M are F.T. of charge and magnetization density Relativistic: G E (Q 2 ) and G M (Q 2 ) are F.T. components of distributions in Breit frame for that Q 2. Boost back to common target frame is (highly) non-trivial. 3

4 Combining neutron and proton form factors G p G Isovector form factor E/ M E/ M insensitive to disconnected quark loops. Ideal test case for lattice-qcd n Model-independent extraction of individual u/d flavor contributions. (assuming s-quark contributions are negligible) Notation: F d and F u are d- and u-quark (plus anti-quark) contributions associated with proton current. F F p 1,2 n 1,2 2 1 u d F1,2 F } 1, ,2 2 d 1 u F1, 2 F1,2 3 3 F 2F F F u 1, 2 d 12, F p n 1,2 2F p n 1,2 1,2 4

5 Separated quark form factors (extracted using all four nucleon form factors) set sum rules on GPDs q dx H ( x,, Q ) F ( Q ) 2 q 2 1 q dx E ( x,, Q ) F ( Q ) 2 q 2 2 5

6 The Hall A G Mn Measurement E

7 n G M Ratio Method: Measure quasi-elastic scattering from deuteron tagged by coincident nucleon: d(e,e p) and d(e,e n) R '' d d d d d e e (, ' n) nucl. n( e, e') d corr. d d d neutron Electric d ( e, e' p) p( e, e') R / Mott d d 1 n G n E GM 2 2 Mott d d p( ee, ') Many systematic effects (experimental and theory) cancel in ratio. Expect very small correction for Electric because small form factor and large kinematic weighting of Magnetic G n M p( ee, ') 2 7

8 Systematics Ratio Method is insensitive to: Target thickness Target density R Beam current Beam structure Live time (electron) trigger efficiency Electron track reconstruction Electron acceptance '' d d d d d ( e, e' n) d( e, e' p) Important to understand: Neutron efficiency/proton efficiency HCal almost ideal Neutron acceptance/proton acceptance 8

9 Technique Ratio Method: Measure quasi-elastic scattering from deuteron tagged by coincident nucleon: d(e,e p) and d(e,e n) BigBite as electron arm (Beam left) Identifies q-vector ( ) q *** Add pretty picture of experiment **** HCal-J as hadron detector with CDet in front (Beam right) 48D48 (SBS spectrometer magnet) Deflects protons vertically on HCal-J to distinguish from neutrons Fiducial cut in BigBite selects high, matched acceptance for n and p. 9

10 Electron arm Existing BigBite spectrometer Instrumented with GEMs from SBS GRINCH BB Timing Hodo GEMs 10

11 GMn Layout BB SBS and HCal 11

12 Calibration Layout HRS-L SBS HCal 12

13 proposed configuration Q 2 E Beam BB SBS d BB d 48D48 48D48 field Luminosity dhcal (GeV/c) 2 (GeV) (deg.) (deg.) (m) (m) integral (T-m) (10 38 /A/cm 2 /s) (m) & 9 3.5/6.0 modified calibration of HCal using L-HMS at kinematics of config. 1 &3 configuration Q 2 E Beam BB SBS d BB d 48D48 48D48 field Luminostiy dhcal (GeV/c) 2 (GeV) (deg.) (deg.) (m) (m) integral (T-m) (10 38 /A/cm 2 /s) (m) (2.8?) (2.8?) (2.8?) L-HRS , , ,

14 Hadron Calorimeter (HCal) built for Super BigBite Spectrometer Iron/scintillator sampling calorimeter 12X24 identical modules High energy-deposition - High threshold - High Luminosity Excellent spatial resolution -Tight cut on nucleon direction (wrt q-vector) High efficiency for n and p - Nearly equal (cancel in ratio) 14

15 Calibration of HCal Elastic electrons in BigBite for p(e,e )p Dedicated run on LH2 target using HRS to measure p + in p(, p + )n with bremsstrahlung end point method. At p n = 3 & 4 GeV/c with HCal at 17 m 15

16 E W. Brooks, G. Gilfoyle, J. Lachniet, W. Vineyard E B. Quinn, J. Annand, R. Gilman, B. Wojtsekhowski 16

17 Status Equipment nearing end of construction Assembly and commissioning at JLab in progress ERR last week (Thur/Fri) Awaiting (Just received) formal committee response Several recommendations to address Hope for successful review before next scheduling meeting Possible schedule Complete commissioning by end of 2018 Begin installation in hall early 2019? Long 10mo (5-6 mo) installation period Ready to run fall 2019? 17

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21 Nuclear Corrections Corrections to d(e,e n) and d(e,e p) almost identical cancel in ratio Arenhovel (low Q 2 ) finds small (<1% when wide-angle tail is cut) corrections at 1 GeV/c and decreasing at larger Q 2 Q 2 (GeV/c) FSI corr. S. Jeschonnek found ratio of full calc (S. Jeschonnek and J.W. Van Orden Phys. Rev. C 62 (2000) ) to PWIA calc. for Kinematics of earlier CLAS e5 measurements. Ratio almost identical for n and p tiny corrections Additional nuclear effects due to Fermi motion manifest as PWIA calculation of coefficients a,b,c, and d: R PWIA 2 2 n n agm bge c.f. R cg d G G G n n GM GE Free p p p 2 p 2 M E M E Q 2 (GeV/c) PWIA corr Using Jechonnek s code, found R PWIA /R Free (neglecting neutron Electric form factor) for planned kinematics and cuts. < 0.5% 21

22 Two-photon Corrections Usual complication of two-photon corrections is for separation of small form factor from large one. Small epsilon-dependence has big effects. We extract the larger Magnetic form factor. d 2 2 Mott (, ') E n d G M n G n ee d d d p( e, e') d p p( e, e') (1 ) (1 ) Corrections may not tend to cancel in ratio (P.G. Blunden, W. Melnitchouk and J.A.Tjon, Phys. Rev. C 72 (2005) ). Recent results at these kinematics: Q 2 =16 GeV 2 n - p =-0.15% Q 2 =18 GeV 2 n - p = 1.8 % Not specific to ratio technique, affect any elastic cross section measurement at these kinematics n p IR divergent n (full) 22