Peter Bosted (Jefferson Lab and William and Mary) Spin structure of the nucleon: update from CLAS at JLab Los Alamos, September 2011

Outline Introduction Inclusive spin structure functions Semi-inclusive structure functions Outlook What makes up the Earth?

Why probe with electrons? Interaction via exchange of (mostly) a single photon due to small size of coupling (1/137) in well-understood electro-magnetic interaction (from D. Day)

Why probe with electrons? Interaction via exchange of (mostly) a single photon due to small size of coupling (1/137) in well-understood electro- magnetic interaction To probe inside a nucleon need wave lengths of order 1 fm or less: means high energy (GeV), greater than proton mass which is GeV. Also want high Q 2 Photon has energy and “mass 2 ” Q 2 (from D. Day)

Electron scattering versus, Q 2 (from D. Day) (scattering probability) x=Q 2 /2M

What was learned at SLAC using high and Q 2 (short wavelengths)  Proton made of two “valence” u quarks and one d quark (neutron has two d and one u).  Quarks have charge 2/3 (u) or -1/3 (d).  Quarks have spin 1/2, like protons themselves.  Quarks appear to be point-like (no substructure themselves). Analogy: hitting a single marble as opposed to bags of marbles that break up if you hit them hard enough.  Theory of QCD (quantum chromodynamics) explains change in rates with x=Q 2 /2M via the process of gluon radiation.

What was learned at SLAC using high and Q 2 (short wavelengths)  Proton made of two “valence” u quarks and one d quark (neutron has two d and one u).  Quarks have charge 2/3 (u) or -1/3 (d).  Quarks have spin 1/2, like protons themselves.  Quarks appear to be point-like (no substructure themselves). Analogy: hitting a single marble as opposed to bags of marbles that break up if you hit them hard enough.  Theory of QCD (quantum chromodynamics) explains change in rates with x=Q 2 /2M via the process of gluon radiation.

What was learned at SLAC using high and Q 2 (short wavelengths)  Proton made of two “valence” u quarks and one d quark (neutron has two d and one u).  Quarks have charge 2/3 (u) or -1/3 (d).  Quarks have spin 1/2, like protons themselves.  Quarks appear to be point-like (no substructure themselves). Analogy: hitting a single marble as opposed to bags of marbles that break up if you hit them hard enough.  Theory of QCD (quantum chromodynamics) explains change in rates with x=Q 2 /2M via the process of gluon radiation.

What was learned at SLAC using high and Q 2 (short wavelengths)  Proton made of two “valence” u quarks and one d quark (neutron has two d and one u).  Quarks have charge 2/3 (u) or -1/3 (d).  Quarks have spin 1/2, like protons themselves.  Quarks appear to be point-like (no substructure themselves).  Theory of QCD (quantum chromodynamics) explains change in rates with x=Q 2 /2M via the process of gluon radiation.

What was learned at SLAC using high and Q 2 (short wavelengths)  Proton made of two “valence” u quarks and one d quark (neutron has two d and one u).  Quarks have charge 2/3 (u) or -1/3 (d).  Quarks have spin 1/2, like protons themselves.  Quarks appear to be point-like (no substructure themselves). Analogy: hitting a single marble as opposed to bags of marbles that break up if you hit them hard enough.  Theory of QCD (quantum chromodynamics) explains change in rates with x=Q 2 /2M via the process of gluon radiation.

quarks are elementary particles gluons are force-carrying subatomic particles that bind quarks together Proton Constituents: Quarks and Gluons quarks and gluons are confined in proton and their properties define characteristics of the proton, like its mass and the spin (angular momentum intrinsic to a body)

quarks are elementary particles making up most of mass of our galexy gluons are force-carrying subatomic particles that bind quarks together Proton Constituents: Quarks and Gluons quarks and gluons are confined in proton and their properties define characteristics of the proton, like its mass and the spin (angular momentum intrinsic to a body)

quarks are elementary particles making up most of mass of our galexy gluons are force-carrying subatomic particles that bind quarks together Proton Constituents: Quarks and Gluons quarks and gluons are confined in proton and their properties define characteristics of the proton, like its mass and the spin (angular momentum intrinsic to a body)

q(x) - Probability to find a quark with a fraction x=Q 2 /2M of proton longitudinal momentum P (in direction of collision with electron) 3 non-interacting quarks Longitudinal quark distribution functions Interacting quarks

With newer data from e-p collider HERA, QCD gluon radiation confirmed over huge range in x and Q 2 (F 1 is sum of u(x) and d(x) weighted by charge squared)

Polarization of quarks Quarks have spin, which can be aligned or anti aligned with proton spin Anti-parallel electron & proton spins Parallel electron & proton spins Experiment: compare:

Averaged over P t and x, u quark spins are about 50% aligned with proton, d quark spins about 40% anti-aligned (from SLAC, Jlab inelusive electron scattering) u d

Spin Structure of the Nucleon  Spin sum rule: total spin 1/2 formed by quarks (small), gluons, and orbital angular momentum (sum of these must be big).  How much carried by gluons?: major focus of large experimental program worldwide (RHIC, DESY, CERN, JLab…).  How big is quark and gluon orbital angular momentum (focus of new programs at Jlab…)

Valence Quarks  Pretty well known now, primarily from measurements of proton and neutron g 1

Gluons and Sea Quarks Gluon polarization poorly known (just that not maximal, probably positive).. Sea quark knowledge will improve with SIDIS studies in future.

Polarized DIS  Theoretically cleanest was to learn about polarized gluons is through pQCD evolution in deep inelastic scattering (DIS)  Q 2 -dependence at fixed x influenced by gluon radiation [log(Q 2 )]. Wilson coefficients calculated to NLO in pQCD.  Largest sensitivity at low Q 2 where  s largest (but need to account for power law higher twist)

 Why deuteron best for  G(x)? The  q 3 terms from p and n, about twice size of  q 8 and  erms, cancels in deuteron. Relative gluon contributions largest in deuteron: relevant as experimental errors dominated by syst. scale factors. q3q3 q8q8 

Physics Impact Adding the 2001 CLAS data to the analysis of the LSS group (NLO plus Higher Twist) had a major impact on error band of  G(x) Without CLAS With CLAS With 12 GeV

C.E.B.A.F. at Jefferson Lab in Newport News 6 GeV continuous beams now: 12 GeV in 2013 or so.

Scattering of 5.9 GeV polarized electrons off polarized NH 3, ND 3 Polarized SIDIS at JLAB using CLAS Took data in 2009: 4 months on NH3 1.5 months on ND3 Many improvements compared to 2001: equivalent to 30x more events

Polarized Target 5 T1 K

Purple beads are ammonia (NH3); only the protons are polarized, the nitrogen makes for (big) background

Beam polarization P B about 0.8 Target polarization 0.7 (p), 0.3 (d) Dilution factor f about 0.2 Depolarization factor D LL (y) about 0.3 Net result: need to run long time! Determination of g 1 /F 1 (approximately A 1 ): proportional to quark polarizations

Very preliminary g 1 /F 1 for proton

Very preliminary g 1 /F 1 for deuteron

Significant improvement in  G(x) and neutron HT Projected Impact in LSS framework without With new results Error on  G(x) HT coefficients

Status of inclusive g 1 /F 1 Big reduction in statistical errors. Need to finalize results (radiative corrections, normalization uncertainties) Can then input into global PDF fits Higher twist and resonance region contributions important to take into account.

How to go further and learn more then just the structure transverse to the motion or spin of the nucleon?  One way is to also detect “knocked- out” quark: measure it’s direction relative to the virtual photon probe, and also what type of quark  This is called Semi-Inclusive Deep Inelastic Scattering (SIDIS)  Need electron accelerator with “continuous” beam instead of the short intensive bursts of SLAC (which quark with which electron?).

How to go further and learn more then just the structure transverse to the motion or spin of the nucleon?  One way is to also detect “knocked-out” quark: measure it’s direction relative to the virtual photon probe, and also what type of quark  This is called Semi-Inclusive Deep Inelastic Scattering (SIDIS)  Need electron accelerator with “continuous” beam instead of the short intensive bursts of SLAC (which quark with which electron?).

How to go further and learn more then just the structure transverse to the motion or spin of the nucleon?  One way is to also detect “knocked-out” quark: measure it’s direction relative to the virtual photon probe, and also what type of quark  This is called Semi-Inclusive Deep Inelastic Scattering (SIDIS)  Need electron accelerator with “continuous” beam instead of the short intensive bursts of SLAC (which quark with which electron?).

(e,e’) (e,e’m) M x 2 = W 2 = M 2 + Q 2 (1/x – 1) M x 2 = W’ 2 = M 2 + Q 2 (1/x – 1)(1 - z) z = E m / (For M m small, p m collinear with , and Q 2 / 2 << 1) SIDIS – LO Picture Leading-order Picture: hit one Quark Want large Q 2 to keep M x big

(e,e’) (e,e’m) M x 2 = W 2 = M 2 + Q 2 (1/x – 1) M x 2 = W’ 2 = M 2 + Q 2 (1/x – 1)(1 - z) z = E m / (For M m small, p m collinear with , and Q 2 / 2 << 1) SIDIS – LO Picture Leading-order Picture: hit one Quark But also want large z, so pion not from “X”

Asymptotic freedom strong force is arbitrarily weak at ever shorter distances. Hadronization is the process of the formation of hadrons (like pions) out of quarks and gluons. Confinement when the force between quarks increases as the distance between them increases, so no quarks can be found individually as the strong interaction forces them to form pairs or triplets. QCD introduces complications!

Asymptotic freedom strong force is arbitrarily weak at ever shorter distancess. Hadronization is the process of the formation of hadrons (like pions) out of quarks and gluons. Confinement: the force between quarks increases as the distance between them increases, so no quarks can be found individually. The strong interaction forces them to form pairs or triplets. QCD introduces complications!

Asymptotic freedom strong force is arbitrarily weak at ever shorter distancess. Hadronization is the process of the formation of hadrons (like pions) out of quarks and gluons. Confinement when the force between quarks increases as the distance between them increases, so no quarks can be found individually as the strong interaction forces them to form pairs or triplets. QCD introduces complications!

Hit a quark hard (high Q 2,, W) and it flies away from target remanents and fragments into pions. “Current fragmentation”. Controlled by PDFs (u(x), d(x),  u(x),  d(x)…) Leading (highest z) pion will tend to select out which quark was hit (  + from u,  - from d). Controlled by fragmentation functions (FF) D + (z) (favored) and D - (z) (unfavored) Real life: Q 2 dependence (QCD evolution, higher twist sensitive to correlations), and both PDFs and FFs likely depend on p t. Main ideas of SIDIS

Hit a quark hard (high Q 2,, W) and it flies away from target remanents and fragments into pions. “Current fragmentation”. Controlled by PDFs (u(x), d(x),  u(x),  d(x)…) Leading (highest z) pion will tend to select out which quark was hit (  + from u,  - from d). Controlled by fragmentation functions (FF) D + (z) (favored) and D - (z) (unfavored) Real life: Q 2 dependence (QCD evolution, higher twist sensitive to correlations), and both PDFs and FFs likely depend on p t. Main ideas of SIDIS

Hit a quark hard (high Q 2,, W) and it flies away from target remanents and fragments into pions. “Current fragmentation”. Controlled by PDFs (u(x), d(x),  u(x),  d(x)…) Leading (highest z) pion will tend to select out which quark was hit (  + from u,  - from d). Controlled by fragmentation functions (FF) D + (z) (favored) and D - (z) (unfavored) Real life: Q 2 dependence (QCD evolution, higher twist sensitive to correlations), and both PDFs and FFs likely depend on p t. Main ideas of SIDIS

SIDIS kinematic plane and relevant variables P t is transverse momentum relative to virtual photon M x 2 =M 2 +Q 2 (1/x-1) is invariant mass of total hadronic final state pion MXMX

k T -dependent SIDIS p t = P t – z k t + O(k t 2 /Q 2 ) Assume P t of observed pion is 3D vector sum of quark k t and a fragmentation that generates extra vector p t.

Very priminary ratio of average u/d versus kt from Lattic QCD by Bernhard Musch (arXiv: ) Equivalent ratio of Gaussian k t widths is 0.97: compatible with our fit

Lattic QCD calculation shows HUGE dependence of average u quark polarization on transverse momentum (new!) Bernhard Mush (very preliminary) On this plot, ratio of 5 means 66% polaraization (1 means 0%)

Diquark model Jakob, Mulders, Rodrigues, Nucl. Phys. A 1997 A.Bacchetta (JLab-07) Also predicts big dependence g1/f1 is proportional to quark polarization (alignment with proton)

z-depenence of k t averaged SIDIS g 1 /F 1 CLAS 5.7 GeV PRELIMINARY Good agreement with predictions based on inclusive scattering. Negative pion smaller due to greater incluence of d quarks. For rest of talk, will use 0.3<z<0.7

50 x-depenence of k t -averaged SIDIS proton g 1 /F 1 W>2 GeV, Q 2 >1.1 GeV 2, 0.4<z<0.7 Good agreement with predictions based on inclusive scattering. Negative pion smaller due to greater incluence of d quarks.

p t -depenence of SIDIS proton A 1 = g 1 /F 1 CLAS Preliminary M.Anselmino et al hep-ph/ From  + results, maybe u-quarks less polarized at high Pt, as predicted by Lattice QCD and diquark model. But,  - disagrees diquark model. Waiting for Lattice for d-quark  0 2 =0.25GeV 2  D 2 =0.2GeV 2

Trends less pronounced if put higher cut on z (pion momenta) Need more data to study depenence on all kinematic variables

New Experiment: eg1-dvcs  Data in previous plots from 2001  In 2009 took about 30x more data.  Added new detector (IC) so could emphasize  0, which has smaller corrections than  + or  -  Higher statistics also allow studies of single-spin asymmetries involving target polarization (not ready to show yet).

Very preliminary results for g1/F1 versus pt in 4 x bins (no radiative corrections!) z>0.3  +  0  -

Very preliminary results for g1/F1 versus pt in 4 x bins (no radiative corrections!)  +  0  - z>0.4

Are  0 results compatible with no p t dependence? Answer: 3 bins: yes; high-x bin, maybe not…

Eg1-dvcs “to do” list  Radiative corrections  Systematics (R=sigma_L/sigma_T, g2 contributions, 14 N, …)  Sensitivity to cuts  “Target fragmentation” contributions, resonances, …  Also study rich physics in target polarization single-spin asymmetry

Summary and Outlook  Picture of internal structure of proton and neutron still pretty fuzzy, especially regarding transverse motion of quarks, and internal orbital angular momentum.  New experiments using SIDIS are helping to sharpen the picture: Jefferson Lab is playing a big role.  Upgrade of Jlab to 12 GeV, and a future even higher energy electron-proton collider, will be needed to get a really crisp picture.

Summary and Outlook  Picture of internal structure of proton and neutron still pretty fuzzy, especially regarding transverse motion of quarks, and internal orbital angular momentum.  New experiments using DIS and SIDIS are helping to sharpen the picture: JLab is playing a big role.  Upgrade of Jlab to 12 GeV, and a future even higher energy electron-proton collider, will be needed to get a really crisp picture.

Summary and Outlook  Picture of internal structure of proton and neutron still pretty fuzzy, especially regarding transverse motion of quarks, and internal orbital angular momentum.  New experiments using SIDIS are helping to sharpen the picture: Jefferson Lab is playing a big role.  Upgrade of Jlab to 12 GeV, and a future even higher energy electron- proton collider, will be needed to get a really crisp picture.

Backup slides

HMS SOS QQQ D D D e pion e 6 GeV 1.7 GeV GeV/c H, D targets superconducting magnets, quadrupole: focussing/defocussing collimator detector system detector system iron magnets First studies of SIDIS at JLab in Hall C

The High Momentum Spectrometer in Hall C

Electron beam with E=5.5 GeV Proton and Deuteron targets SIDIS measurements of both  + and  - Electrons scattered at 24 to 36 degrees into SOS Pions detected in the HMS spectrometer Hall C experiment E00-108

Rather low “mass” of final state: W: 2<W<3 GeV Rather low of “target remenant mass” M x : will description in terms of scattering of single quarks hold? Hall C experiment E00-108

z-Dependence of cross sections at Pt=0 Good agreement with prediction using PDFs and fragmentation functions from other experiments, except for z>0.7, or Mx>1.4 GeV. x=0.3, Q 2 =2.5 GeV 2, W=2.5 GeV  ? Jlab Hall C

Is SIDIS framework OK at low M x ? Neglect sea quarks and assume no p t dependence to parton distribution functions (for now):  [  p (  + ) +  p (  - )]/[  d (  + ) +  d (  - )] = [4u(x) + d(x)]/[5(u(x) + d(x))] ~  p /  d independent of z and p t [  p (  + ) -  p (  - )]/[  d (  + ) -  d (  - )] = [4u(x) - d(x)]/[3(u(x) + d(x))] independent of z and p t, but more sensitive to assumptions

Yes, These two ratios make sense more or less Even though only a few pions being produced “Works” better “Works” worse Closed (open) symbols reflect data after (before) events from coherent  production are subtracted GRV & LO or NLO (recall, z = 0.65 ~ M x 2 = 2.5 GeV 2 )

2 And, the Q 2 -dependence seems flat and in agrreement with LO model too, for Q 2 >2 GeV 2

Transverse momentum dependence of SIDIS All slopes similar, but subtle difference seem to exist.

Transverse momentum dependence of SIDIS Fit to data of previous slide With severn parameter fit: important four are: (  u ) 2 ~ Gaussian width of u(x,k t ) (  d ) 2 ~ Gaussian width of d(x,k t ) (  + ) 2 ~ Gaussian width of D + (z,p t ) (   ) 2 ~ Gaussian width of D - (z,p t )

 Factorization valid  Fragmentation functions do not depend on quark flavor (type)  Widths Gaussian and can be added in quadrature  Sea quarks are negligible  Particular function form for the Cahn effect (kinematic shifting)  No additional higher twist effects  NLO corrections can be ignored Assumptions:

Ellipses are fits with different systematic assumptions Black dot is from a particular di-quark model Dashed lines have equal (u,d) or (+,-) widths Fit results

Results compatible with no difference, as well as possibly d width smaller u width Focus on d-quark transverse width (vertical) versus u-quark width (horizonontal)

 Longitudinal parton distributions can be defined in terms of two components: spin of quark(gluon) aligned (+) or anti-aligned (-) with nucleon spin: ie q(x,Q 2 ) = q + (x,Q 2 ) + q - (x,Q 2 ) G(x,Q 2 ) = G + (x,Q 2 ) + G - (x,Q 2 )  Define spin-dependent structure parton distribution functions:  q(x,Q 2 ) = q + (x,Q 2 ) + q - (x,Q 2 )  G(x,Q 2 ) = G + (x,Q 2 ) - G - (x,Q 2 ) Spin Structure Functions F1=qF1=q g1=qg1=q