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1 !"#"$%&!"'()%'&*$&+,-*%./0*1),2$3& 4)"#%-1$&5#,6"-*$3&,%&7"8"-'1$&9,:;& >?++4<&H1)),:1-,21$ +!4<&H1)),:1-,21$?+5&5D-*$3&E""2$3?$,B"*FG&H? E,.&IG&JKII

2 LB"&M"(%-,)&H(--"$%&,$=&M(#)"1$&0"#%1-& scattering. The spatial structure of the nucleon reflects in N1-F&N,#%1-' 5%-,$3"&O(,-C'&"P*'%&*$&%B"&$(#)"1$&,%&'B1-%&=*'%,$#"&'#,)"'Q& simplest spatial map of the interior of neutrons and protons are the electromagnetic form factors, which lead to a picture R1&%B".&D),.&,&-1)"&*$&"),'2#&D-1%1$&'#,6"-*$3S of the average spatial distributions of charge and magnetism. 0.2 ] 4πr 2 ρbreit [fm 1 ] observed in both deep-inelastic scattering experiments with hadron coincidences at HERMES and in hadron production in polarized proton-proton collisions at RHIC. The latter echoed an earlier result from Fermilab at lower energies, where perturbative QCD was not thought to be applicable. At HERMES, but not yet definitively at RHIC, measurements have disentangled the contributions due to quark transverse spin preferences and transverse motion preferences within a transversely polarized proton. The motional preferences are intriguing because they require spin-orbit correlaexperiments have revealed the proton s internal makeup with ever-increasing precision, largely through the use of electron QCD the distributions of the elementary quarks and gluons, as well as their motion and spin polarization. Charge and Magnetization Distributions of Protons and Neutrons. The fundamental quantities that provide the -1 [fm 4 r 2 Breit ? r [fm] Figure 2.5: On the left is the distribution of the charge within the neutron, the combined result of experiments around the globe that use polarization techniques in electron scattering. On the right is that of the (much larger) proton distribution for reference. The widths of the colored bands represent the uncertainties. A decade ago, as described in the 1999 NRC report (The Core of Matter, the Fuel of Stars, National Academies Press [1999]), our knowledge of neutron structure was quite limited and unable to constrain calculations, but as promised, advances in polarization techniques led to substantial improvement.?''(f"&t&o(,-c&u,v1-&#1$%-*:(21$'&%1&v"#%1-&w1-f&w,#%1-';&x ( G&X = G&X ' 26 QCD and the Structure of Hadrons HB,-3"& 5.FF"%-. + T&"O(,21$'& Y*%B T&($C$1Y$'

3 E",'(-*$3&5%-,$3"&0"#%1-&N1-F&N,#%1-'! Z! 2 ~ 10"4 Q 2 GeV 2 For a proton: ~ few parts per million Forward angle Backward angle Anapole radiative corrections are problematic G Z E,M =(1 4 sin 2 θ W )G p E,M Gn E,M G s E,M For a spin=0,t=0 4 He: G s E only! For deuterium: Enhanced G A

4 4PD"-*F"$%,)&ZV"-V*"Y 5?E+94 1D"$&3"1F"%-.G& *$%"3-,2$3G& :,#C/,$3)"&1$).?` ZD"$&3"1F"%-. N,'%&#1($2$3&#,)1-*F"%"-&W1-& :,#C3-1($=&-"a"#21$ N1-Y,-=&,$=&b,#CY,-=&,$3)"' >?++4< +-"#*'*1$&'D"#%-1F"%"-G& *$%"3-,2$3 N1-Y,-=&,$3)"G&,)'1& `>"&,%&)1Y&] J >?++4</T;&X 4' &[&KQ\J&X E '& &,%&] J &^&KQ_J&X"0 J XK &&&&&&&&ZD"$&3"1F"%-. N,'%&#1($2$3&Y*%B&F,3$"2#&'D"#%-1F"%"-&[&LZN& W1-&:,#C3-1($=&-"a"#21$ N1-Y,-=&,$=&b,#CY,-=&,$3)"'&1V"-&,&-,$3"&1W&] J

5 c1-)=&=,%,&1$&x ' all forward-angle proton data η = τ Gp M G p E Q 2 $"!# $"$# s GE $"! $!$"$# 6$+89:.;1<421.9=>?&((*@!? 7?&((*@!?9 all low Q 2 data &7 %&'()*+,-./ 6 & !$"!!$"!# 2 Q ~ 0.1 GeV 2!!"#!!!$"# $ $"#!!"# G s M At Q 2 =~0.1 GeV 2, G s < few percent of G p Form Factor error: precision of EMFF (including 2!) and Anapole correction Significant systematic uncertainty in higher Q 2 points

6 X)1:,)&d%&1W&,))&Y1-)=&=,%, 5*FD)"&d%; 7 <+ $=$> +?@ 7 A+ $=$B +!"#$"%&'()*+$,''$-./')$),#,$0 1$ 2$3456$7*8 1 $ 73$7'.9,'$*//./$,''.-*)$#.$:.,#$-"#;$(%"#$&.%+#/,"%# R,%,&'"%&,DD",-'&%1&'B1Y&#1$'*'%"$%&D-"W"-"$#"&W1-&D1'*2V"&"8"#% 5*3$*d#,$%&#1$%-*:(21$'&,%&B*3B"-&] J &,-"&$1%&-()"=&1(%Q&

7 3 Data Quality 3.1 Detector Acceptances 0"-.&#)",$&'"D,-,21$&1W "),'2#&"V"$%'&:.&>!5&1D2#' Detector acceptances are checked to ensure that the detector is well aligned and not imposing geometric cut to skew the Q2. The top two plots in Fig. 3.1 are S0 triggered plots, and the bottom two are detector triggered plots. The S0 paddles are much bigger than the detector and covers the entire detector plane. The detector x/y distribution plots with detector triggers look identical to the S0 triggered plots, indicating that the detector does not impose any geometric cuts on the acceptance. Elastic Inelastic detector '""'&1$).&"),'2#&"V"$%' LHRS Detector Plane Dist. -3! Quad !10 Detector Plane y (m) Detector Plane x (m) Detector Plane x (m) Dipole 10 9",=&/&9(#*%"&H"-"$C1V&5B1Y"-&H,)1-*F"%"-50 DB1%1%(:"&#(--"$%&*$%"3-,%"=&1V"-&dP"=&2F"&D"-*1=' RMS Entries e Detector Plane x (m) Detector Plane x (m) RHRS Detector Plane Dist Psuedo-random, -50 rapid helicity flip det Trigger 0-0.2! S0 Trigger Dist. LHRS Detector Plane S0 Trigger Detector Plane y (m) Q Q Detector Plane y (m) Detector Plane y (m) 100 target RHRS Detector Plane Dist. -3! Detector Plane x (m) Detector Plane x (m) det Trigger Detector Plane x (m) Detector Plane x (m) Figure 3.1: Detector acceptance plots with S0 and detector triggers. The bounding box is the outline of the detector with the PMT located at about 1.2m in x. 1 The cuts used to generate these plots are -20&& LHRS::"P.hapadcL>550 && L.tr.n==1 abs(extgtcor_l.th)<0.07 && abs(extgtcor_l.ph)<0.07 && abs(extgtcor_l.dp)<0.05" parts per million RHRS::"P.hapadcR>700 && R.tr.n==1 && abs(extgtcor_r.th)<0.07 && abs(extgtcor_r.ph)<0.07 && abs(extgtcor_r.dp)<0.05"!

8 f? +0 && f? +0 &i&? +0 & gddfh +1),-*j,21$ KQJKJ KQk\l ] J &E",'(-"F"$% KQI_K KQ_ml b,#c3-1($=' KQIn` KQkJl 9*$",-*%. KQIJn KQ\`l N*$*%"&?##"D%,$#" KQK`k KQJKl N,)'"&?'.FF"%-*"' KQK`I KQIml L1%,)&5.'%"F,2#& KQT\T IQ`nl 5%,2'2#' KQmm_ TQJml L1%,)&4PD"-*F"$%,)& KQk\T TQ\nl Linearity Studies Compton + Moller polarimeters HRS Backgrounds more later from Megan Friend, CMU Spectrometer Calibration more later from Kiadtisak Saenboonruang, UVa LEDs Pulser Electronics PMT DIFF ENABLE BASELINE ENABLE Flexio Board ADC Board Data Acquisition System more later from Rupesh Silwal, UVa Systematic uncertainties are well controlled - experiment is statistics dominated

9 +0 A RAW = ± (stat) ppm This includes beam asymmetry correction (-0.01 ppm) charge normalization (0.20 ppm) Position Differences micron diff_bpm4bx OUT / IN from slow spin reversals to cancel systematics L-,a"#%1-.&,%&%,-3"%& OUT A= / nm IN A= / nm,v"-,3"=&%1&qt$fgqkq\$-,=& AVG A= / nm diff_bpm12x OUT A= / nm IN A= / nm AVG A= / nm slug parts per million OUT A= / ppm, N=381,! 2 = 1.00, P=0.51 IN A= / ppm, N=409,! 2 = 1.09, P=0.09 AVG A= / ppm, N=791,! 2 = 1.05, P= data slug Additional corrections are then applied: backgrounds (1.1%) acceptance averaging (0.5%) beam polarization (11%) TQJ_l&g'%,%ho&IQ`nl&g'.'%h %1%,)&#1--"#21$&pJQ\l&[&D1),-*j,21$?$,).'*'&b)*$="=&o&JQ\&DDF combined 2-arm data

10 A PV = ± (stat) ± (syst) ppm Q 2 = ± (GeV/c) 2

11 A PV = ± (stat) ± (syst) ppm Q 2 = ± (GeV/c) 2?gX '^Kh&^&/J`QI\k&DDF&C&KQ T&DDF

12 A PV = ± (stat) ± (syst) ppm Q 2 = ± (GeV/c) 2?gX '^Kh&^&/J`QI\k&DDF&C&KQ T&DDF X ' 4&[&KQ\J&X ' E&^&&&& &&&&&&&&&&&KQKK\&C&KQKIK g'%,%h& C&KQKK`g'.'%h &C&KQKKk gnnh

13 N*%G&c1-)=&R,%, Wtih HAPPEX-3 result at Q 2 = GeV 2 : X ' 4&[&KQ\J&X ' E&^&&&&&KQKK\&C&KQKIK g'%,%h& C&KQKK`g'.'%h &C&KQKKk gnnh

14 H1$'*="-*$3&1$).&%B"&`&>?++4<&F",'(-"F"$%' HAPPEX-III (2011) s G +0.52G E s M 2 2 Q = GeV High precision Small systematic error HAPPEX-II He (2006) s GE 2 2 Q = GeV Clean theoretical interpretation HAPPEX-II (2006) s G +0.09G E s M 2 2 Q = GeV HAPPEX-I (1999) s G +0.39G E s M 2 2 Q = GeV A PV - A NS / A NS

15 c1-)=&r,%,&1$&5%-,$3"&nn HAPPEX-3 Q 2 = 0.62 GeV s GE 0 G0-forward % 95% G G0-backward ( 1 H) s M &>?++4</@@@&D-1V*="'&,&#)",$G&D-"#*'"&F",'(-"&1W&? +0 &,%&] J^KQ_J&X"0 J G&,$=&d$='&%B,%&*%&*'& #1$'*'%"$%&Y*%B&$1&'%-,$3"$"''&#1$%-*:(21$Q&& &Recent lattice results indicate values smaller than these FF uncertainties &N(-%B"-&*FD-1V"F"$%'&*$&D-"#*'*1$&Y1()=&-"O(*-"&,==*21$,)&%B"1-"2#,)&,$=&"FD*-*#,)& *$D(%&W1-&*$%"-D-"%,21$

16 &c",c&hb,-3"&r*'%-*:(21$&1w&>",v.&m(#)"* M(#)",-&%B"1-.&D-"=*#%'&,&$"(%-1$& r'c*$s&1$&b",v.&$(#)"* 208 Pb M"(%-1$&=*'%-*:(21$&*'&$1%&,##"''*:)"&%1& %B"&#B,-3"/'"$'*2V"&DB1%1$Q D-1%1$ $"(%-1$ 4)"#%-*#&#B,-3" I K c",c&#b,-3" pkqkk I PREX (Pb-Radius EXperiment) Q 2 ~ 0.01 GeV 2 5 o scattering angle A PV ~ 0.6 ppm Rate ~1.5 GHz! M EM = 4"# Q 2 F p Q 2 ( ) [ ( ) " F ( n Q 2 )] M NC PV = G F ( 2 1 " 4sin2 # W )F p Q 2 A PV " G F Q2 4#$ 2 ( ) ( ) F n Q 2 F p Q 2

17 E",'(-"F"$%'&1W&$"(%-1$&'C*$!Proton-Nucleus Elastic Pion, alpha, d Scattering Pion Photoproduction Heavy ion collisions Rare Isotopes (dripline) Involve strong probes Magnetic scattering Most spins couple to zero. PREX Electroweak probe Theory MFT fit mostly by data other than neutron densities

18 ?&#-(#*,)&#,)*:-,21$&D1*$%&W1-&$(#)",-&%B"1-. The single measurement of Fn translates to a measurement of Rn via mean-field nuclear models Skyrme covariant meson covariant point coupling D,%)$E*,+(/"%F$/ G $H"%+$).-%$ #;*$+IEE*#/I$*%*/FI F n (Q 2 )/N r n! r p (fm) ( R.J. Furnstahl ) r n in 208 Pb (fm) 0.1 Skyrme relativistic meson relativistic point coupling symmetry energy a 4 (MeV)

19 Nuclear Structure: Symmetry energy variation with neutron density is a fundamental observable that remains elusive. Reflects poor understanding of symmetry energy of nuclear matter = the energy cost of n.m. density ratio proton/ neutrons Slope unconstrained by data Adding Rn from 208 Pb will eliminate the dispersion in the plot. Slide adapted from J. Piekarewicz

20 Crab Nebula N-1F& JKk +:&%1&,&M"(%-1$&5%,- R n calibrates the equation of state of neutron rich matter pressure density Crust Thickness Explain Glitches in Pulsar Frequency? Combine PREX R n with observed neutron star radii Phase Transition to Exotic Core? Strange star? Quark Star? Some neutron stars seem too cold Cooling by neutrino emission (URCA) 0.2 fm URCA probable, else not

21 PREX Physics Output Measured Asymmetry Correct for Coulomb Distortions Weak Density at one Q 2 20% corrections, calculated to precision by multiple groups Atomic Parity Violation Small Corrections for G n E G s MEC E Neutron Density at one Q 2 Mean Field & Other Models Assume Surface Thickness Good to 25% (MFT) Neutron Stars Slide adapted from C. Horowitz see later talk in last session R n

22 HB,))"$3*$3&4PD"-*F"$% Similar to the HAPPEX measurements Use Hall A spectrometers integrating technique Electronics noise new low-noise ADCs Ultimate goal: 20 ppb absolute measurement 3% relative error "(A PV )/A PV ~ 3% "(R n )/R n ~ 1% see later talk by Luis Mercado Low energy electron beam polarimetry Compton Polarimeter upgrade IR to Green light Integrating photon detection Moller Polarimeter upgrade to SC magnet FADC DAQ upgrade 10X more precise than any previous e - -nucleus scattering! Beam False Asymmetries Source optimization - reduce position difference and spot-size asymmetry Injector magnetic spin manipulation New modulation system for calibrating corrections Transverse Asymmetry see later talk by Bob Michaels Target survivability Precise kinematics calibration Water cell calibration High rate tracking with GEMS Low current beam position monitors see later talk by Zafar Ahmed

23 \ 1 &5"D%(F&%1&,(3F"$%&%B"&>!5 HRS-L Septum Magnet collimator HRS-R collimator target calibration collimators

24 >*3B&!"'1)(21$&5D"#%-1F"%"- Carbon Carbon Ground State Lead p (GeV/c) 2.6 MeV p (GeV/c) C 1st excited state C Pb Momentum (GeV/c) Pb excited states Ground States Detector integrates the elastic peak. Backgrounds from inelastics are suppressed. Negligible contributions from inelastic events rescattering in spectrometer

25 +,-*%.&](,)*%.&b",f microns Points: Not sign corrected Helicity Correlated Position Differences < ~ 4 nm Average with signs = what exp t feels Injector spin manipulation proved important for cancellation microns Slug # ( ~ 1 day)

26 Systematic Errors &&4--1-&&&51(-#"?:'1)(%"&&&gDDFh!"),2V"&&g&&l&h J.',/"K,L.%$gIh 3433MN N4N "#$%!!&'(%%#)*+#'&(2) 3433M1 N4N O*#*&#./$$P"%*,/"#I 3433MN N4N QRA$$P"%*,/"#I 3433N3 341 S*+&,T*/"%F 34333N 3 U/,%+V*/+*$$J.',/"K,L.%$ 3433N1 341$ 0 1$$$$ gih 34331W 34X$ U,/F*#$$U;"&Y%* N N1 R$$Z+IEE*#/I$$$gJh X [%*',+L&$$\#,#*+ 3 3 LZL?9 KQKITK JQK (1) Normalization Correction applied (2) Nonzero correction (the rest assumed zero)

27 +!4<&?'.FF"%-. A RAW = ± (stat) ppm This includes beam asymmetry correction (-40 ppb) charge normalization (96 ppb) Araw (ppm) OUT / IN, L/R from slow spin reversals to cancel systematics Additional corrections are then applied: backgrounds (1.1%) acceptance averaging (0.3%) beam polarization (11%) Slug ~ 1 day?$,).'*'&b)*$="=&o&jkk&dd:

28 +!4<&?'.FF"%-. A RAW = ± (stat) ppm This includes beam asymmetry correction (-40 ppb) charge normalization (96 ppb) Araw (ppm) OUT / IN, L/R from slow spin reversals to cancel systematics Additional corrections are then applied: backgrounds (1.5%) acceptance averaging (0.3%) beam polarization (11%) Slug ~ 1 day?$,).'*'&b)*$="=&o&jkk&dd: ppm 9.2 % 2.0 % at Q 2 = GeV 2! Statistics limited ( 9% )! Systematic error goal achieved! (2%)

29 ?'.FF"%-.&)",='&%1&! $ Neutron Skin = R N - R P = fm Preliminary estimate from C.J. Horowitz Shufang Ban, C.J. Horowitz, R. Michaels arxiv: [nucl-th] ( theory curve, not integrated over acceptance )

30

31 First electroweak observation of the neutron skin of a heavy nucleus (CL =95%)

32 N(%(-"&!($&#,$&-",#B&DB.'*#'&31,) Proposal for a 2nd run is under development Pb Major experimental questions have been answered! Lead sandwich target Precision polarimetry at 1 GeV HRS optics optimization Source performance Transverse Asymmetry Must address: Beam vacuum issues Neutron radiation in the Hall (shielding, reduced beam collimation)

33 ZD21$'&W1-&1%B"-&$(#)"* Plans to pursue 48 Ca far from 208 Pb closer comparison to microscopic calculation compatible with 12 GeV! 5 o scattering at 2 GeV : new septum required Additional measurements could address Rn in other nuclei shape dependence? isotope dependence? E (GeV) Rate 50 µa) APV (ppm) days to 1% on Rn 208 Pb Sn R N Surface thickness 48 Ca R N Surface thickness Parity Violating Electron Scattering Measurements of Neutron Densities Shufang Ban, C.J. Horowitz, R. Michaels arxiv: [nucl-th]

34 +!4<&&;&&5(FF,-.&& LB"&F1'%&D-"#*'"&F",'(-"F"$%&1W&")"#%-1$/ $(#)",-&'#,6"-*$3&,'.FF"%-.&."%;&_J&DD:t& N($=,F"$%,)&&&M(#)",-&&&+B.'*#'&&Y*%B&F,$.&&&,DD)*#,21$'?#B*"V"=&&,&&nl&&'%,%Q&"--1-&&*$&&?'.FF"%-.;& Ju&")"#%-1Y",C&1:'"-V,21$&1W&$"(%-1$&'C*$ 5(##"''&*$&"PD"-*F"$%,)&%"#B$*O(";& '.'%"F,2#&"--1-'&#,$&:"&#1$%-1))"= +-1D1',)&W1-&,&'"#1$=&-($&*'&*$&D-"D,-,21$