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Where%is%the%Proton%Spin?%
Kevin%R.%Wood%Abhay%Deshpande,%Stacy%Karthas%
September%21,%2015%
1%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
2%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
Where%is%the%Proton%Spin?%
Quark&Polariza,on&
%@%%SLAC@Yale%&%EMC%polarized%DIS%measurements%
Gluon&Polariza,on&
%@%%RHIC%polarized%proton@proton%collisions%
Parton&Angular&Momentum&
%@%%Plans%for%the%EIC%
Summary%
Spin%from%Quarks?%
Qp = +1= qq∑
?%
The%charge%of%the%proton%is%completely%accounted%for%by%the%sum%of%that%of%its%consQtuent%quarks.%
s = ± 12
s = − 12
s = + 12
u%q = 2
3
u%q = 2
3
d%q = − 1
3
Sp =12= Sq ≡
12ΔΣ∑?%
Is%the%situaQon%for%the%spin%of%the%proton%analogous%to%that%of%its%charge?%
3%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
• %%Use%deep%inelasQc%scaUering%of%polarized%(&%electrically%charged)%lepton%beam%off%%%%%%protons%polarized%parallel%and%anQ@parallel%with%respect%to%the%beam%
4%
longitudinally%polarized%lepton%beam%
fixed%proton%targets%polarized%(anQ@)parallel%to%beam%
θ↑↑ ↓
• %%Measure%the%asymmetry%in%differenQal%cross%secQon%[1]:%
%%%%where%E%is%the%energy%of%the%incoming%lepton%and%E’%that%of%the%scaUered%lepton%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
A =dσ ↑↓( )− dσ ↑↑( )dσ ↑↓( ) + dσ ↑↑( ) dσ ≡
d 2σ E,E ',θ( )dΩdE '
Measuring%Quark%PolarizaQon%Inside%the%Proton%%
5%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
• %%Experimentally,%one%counts%the%number%of%scaUered%leptons%(per%energy%and%solid%angle)%and%calculates%the%asymmetry%[2]:%
• %%If%the%naïve%model%menQoned%previously%holds%true,%we%would%expect%this%asymmetry%%%%%to%be%%Δ%=%1/3%%
θ
γ*%
s = ± !
2 s = − !
2
s = + !
2
Δ =N ↑↓( )− N ↑↑( )N ↑↓( ) + N ↑↑( )
• %%Leptons%interacts%with%a%quark%electro@%%%%magneQcally%via%a%virtual%photon%(spin%1)%
• %%Thus%the%lepton%switches%its%spin%state%from%+½%%%%%%to%@½%by%emiing%a%+1%spin%photon%
• %%Absorbing%this%photon%changes%the%spin%state%%%%of%the%quark%(spin%½%parQcles);%only%spin%@½%%%%%quarks%can%do%this%
• %%The%anQ@aligned%protons%has%twice%as%many%%%%%%spin%@½%quarks%as%the%aligned%protons%
Measuring%Quark%PolarizaQon%Inside%the%Proton%%
Kevin%R.%Wood%%%%%@%%%%%Proton%Spin% 6%
(1978)%SLAC@Yale:%DIS%with%polarized%~25%GeV%electrons%[1]%
(1989)%EMC:%DIS%with%polarized%~200%GeV%muons%[3]%
The&quarks’&spins&only&account&for&a&small&por,on&(~30%)&of&the&Proton’s&spin!&
Measuring%Quark%PolarizaQon%Inside%the%Proton%%
Kevin%R.%Wood%%%%%@%%%%%Proton%Spin% 7%
More%to%the%Proton%
Sp =12≠ 12ΔΣ
But%the%proton%also%consists%of%gluons!%
Gluons%are%spin%1%parQcles..%
Could%there%be%a%net%gluon%polarizaQon%within%the%proton%to%account%for%the%spin?%
Sp =12= 12ΔΣ + Δg?%
[5]%
Kevin%R.%Wood%%%%%@%%%%%Proton%Spin% 8%
Measuring%Gluon%PolarizaQon%Inside%the%Proton%%
• %%The%RelaQvisQc%Heavy%Ion%Collider%(RHIC)%then%measured%the%contribuQon%from%the%%%%%%gluon%spin%(spin%1%parQcle)%
• %%Collide%longitudinally%polarized%protons%with%(anQ)aligned%polarizaQons%
• %%Measure%cross%secQon%asymmetry%for%neutral%pion%producQon%
π
• %%π%%tags%a%strong%interacQon%(mediated%by%%%%%gluons)%
• %%An%emiUed%gluon%will%only%be%absorbed%by%%%%%a%parton%with%the%proper%spin%
Kevin%R.%Wood%%%%%@%%%%%Proton%Spin% 9%
Measuring%Gluon%PolarizaQon%Inside%the%Proton%%
There%is%a%net%gluon%polarizaQon%within%the%proton!%
…%But%it’s%sQll%not%enough%
Gluons&only&contribute&an&addi,onal&~30%&of&the&proton’s&total&spin.&
Where%is%the%addiQonal%~40%%of%the%protons%spin?%
In%the%orbital%moQon%of%the%partons?&
Sp =12≠ 12ΔΣ + Δg
Sp =12= 12ΔΣ + Δg + Lq + Lg
?%
Phys.%Rev.%LeU.%115,%092002%(2015)%
Kevin%R.%Wood%%%%%@%%%%%Proton%Spin% 10%
Measuring%the%Parton%Angular%Momentum%
• %%The%proposed%Electron%Ion%Collider%(EIC)%plans%to%take%advantage%of%the%resoluQon%from%%%%polarized%DIS%experiments%and%the%highly%relaQvisQc%protons%from%collider%experiments%
*%Will%also%drasQcally%improve%the%precision%of%%%%ΔΣ%and%Δg%
[5]%
Summary%
11%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
The%proton%gets%its%spin%from%a%variety%of%its%consQtuents,%not%just%the%valence%quarks.%
We%can%measure%the%various%contribuQons%from%polarized%DIS%and%collision%experiments.%
There%is%sQll%spin%that%is%unaccounted%for,%but%the%next%generaQon%experiment,%EIC,%hopes%to%seUle%the%maUer.%
Understanding%of%the%proton%spin%can%be%applied%to%other%to%other%hadrons.%
References%
[1]%%Phys.%Rev.%LeU.%41&(2)%70@73%(1978)%
[2]%%Gerhard%K.%Mallot,%Spin*of*the*nucleon*in*deep*inelas2c*lepton*sca3ering*experiments,*Conf.:920126—4*(1992)*
[3]%%Nucl.%Phys.%B%328&1@35%(1989)%
[4]%%Phys.%Rev.%LeU.%115,%092002%(2015)%[5]%%arXiv:1212.1701%Electron%Ion%Collider:%The%Next%QCD%FronQer%
Cover%art:%hUp://www.physastro.iastate.edu/research/highlights/unlocking@mystery@proton@spin%
12%Kevin%R.%Wood%%%%%@%%%%%Proton%Spin%
