Peter Bosted (Jefferson Lab and Peter Bosted (Jefferson Lab and William and Mary)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 photondue 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 0.9383 GeV. Also want

high Q2

Photon has energy and “mass2” Q2

(from D. Day)

Electron scattering versus , Q2(from D. Day)

(scattering probability)

x=Q2/2M

What was learned at SLAC using high and Q2 (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=Q2/2M via the process of gluon radiation.

What was learned at SLAC using high and Q2 (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=Q2/2M via the process of gluon radiation.

What was learned at SLAC using high and Q2 (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=Q2/2M via the process of gluon radiation.

What was learned at SLAC using high and Q2 (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=Q2/2M via the process of gluon radiation.

What was learned at SLAC using high and Q2 (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=Q2/2M 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=Q2/2M 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 Q2

(F1 is sum of u(x) and d(x) weighted by charge squared)

Polarization of quarksQuarks 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 Pt 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 g1

Gluons and Sea Quarks

• Gluon polarization poorly known (just that not maximal, probably positive)..

• Sea quark knowledge will improve with SIDISstudies in future.

Polarized DIS Theoretically cleanest was to learn about polarized gluons is through pQCD evolution in deep inelastic scattering (DIS)Q2-dependence at fixed x influenced by gluon radiation [log(Q2)]. Wilson coefficients calculated to NLO in pQCD.

Largest sensitivity at low Q2 where s largest (but need to account for power law higher twist)

Why deuteron best for G(x)?

• The q3 terms from p and n, about twice size of q8 and erms, cancels in deuteron.• Relative gluon contributions largest in deuteron: relevant as experimental errors dominated by syst. scale factors.

q3

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 NH3, ND3

Polarized SIDIS at JLAB using CLAS

Took data in 2009:4 months on NH3

1.5 months on ND3

Many improvementscompared 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 PB about 0.8• Target polarization 0.7 (p), 0.3 (d)• Dilution factor f about 0.2• Depolarization factor DLL(y) about 0.3• Net result: need to run long time!

Determination of g1/F1 (approximately A1):proportional to quark polarizations

++−+

++−+

+−

≈NN

NN

)y(fDPPA

LLTB

p 11

Very preliminary g1/F1 for proton

Very preliminary g1/F1 for deuteron

Significant improvement in G(x) and neutron HT

Projected Impact in LSS framework

without

With newresults

Error on G(x)HT coefficients

Status of inclusive g1/F1

• 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 quarkThis 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 quarkThis 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 quarkThis 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)

Mx2 = W2 = M2 + Q2 (1/x – 1)

Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z)

z = Em/

(For Mm small, pm collinear with , and Q2/2 << 1)

SIDIS – LO Picture

Leading-orderPicture: hit one

Quark

Want large Q2 to keep Mx big

(e,e’)

(e,e’m)

Mx2 = W2 = M2 + Q2 (1/x – 1)

Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z)

z = Em/

(For Mm small, pm collinear with , and Q2/2 << 1)

SIDIS – LO Picture

Leading-orderPicture: 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 Q2, , 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: Q2 dependence (QCD evolution, higher twist sensitive to correlations), and both PDFs and FFs likely depend on pt.

Main ideas of SIDIS

•Hit a quark hard (high Q2, , 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: Q2 dependence (QCD evolution, higher twist sensitive to correlations), and both PDFs and FFs likely depend on pt.

Main ideas of SIDIS

•Hit a quark hard (high Q2, , 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: Q2 dependence (QCD evolution, higher twist sensitive to

correlations), and both PDFs and FFs likely depend on pt.

Main ideas of SIDIS

SIDIS kinematic plane and relevant variables

Ey /=

)/(sinEEQ ' 24 22 θ=

MQx 2/2=

'EE−=

/Ez h=

Pt is transverse momentum relative to virtual photon

Mx2=M2+Q2(1/x-1) is invariant mass of

total hadronic final state

pion

MX

kT-dependent SIDIS

pt = Pt – z kt + O(kt

2/Q2)

Assume Pt of observed pion is 3D vector sum of quark kt and a fragmentation that generates extra vector pt.

Very priminary ratio of average u/d versus kt from Lattic QCD by Bernhard

Musch (arXiv:0908.1283)

Equivalent ratio of Gaussian kt widths is 0.97: compatible with our fit

Lattic QCD calculation shows HUGEdependence 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 proportionalto quark polarization

(alignment with proton)

z-depenence of kt averaged SIDIS g1/F1

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 use0.3<z<0.7

50

x-depenence of kt-averaged SIDIS proton g1/F1

W>2 GeV, Q2>1.1 GeV2, 0.4<z<0.7Good agreement with predictions

based on inclusive scattering.

Negative pion smaller due to

greater incluence of d quarks.

pt-depenence of SIDIS proton A1 = g1/F1

CLAS Preliminary

M.Anselmino et al hep-ph/0608048

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

02=0.25GeV2

D2=0.2GeV2

Trends less pronounced if put highercut on z (pion momenta)

Need more data to study depenence on all kinematic variables

New Experiment: eg1-dvcsData in previous plots from 2001In 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 pt 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, 14N, …) Sensitivity to cuts “Target fragmentation” contributions, resonances, … Also study rich physics in target polarization single-spin asymmetry

Summary and OutlookPicture 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 OutlookPicture 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 OutlookPicture 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

Q Q Q D

D

D

e

pion

e

6 GeV

1.7 GeV

0.5-7.4 GeV/c

H, D targets

superconducting magnets,quadrupole: focussing/defocussing

collimator

detectorsystem

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” Mx: 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, Q2=2.5 GeV2, W=2.5 GeV

?

Jlab Hall C

Is SIDIS framework OK at low Mx?

Neglect sea quarks and assume no pt 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 pt

[p(+) - p(-)]/[d(+) - d(-)]

= [4u(x) - d(x)]/[3(u(x) + d(x))]

independent of z and pt,

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 & CTEQ,@ LO or NLO

(recall, z = 0.65 ~ Mx

2 = 2.5 GeV2)

And, the Q22-dependence seems flat and in agrreement with LO model

too, for Q2>2 GeV2

Transverse momentum dependence of SIDIS

All slopes similar, but subtle difference seem to exist.

Transverse momentum dependence of SIDIS

Fit to data of previous slideWith severn parameter fit: important four are:(u)2 ~ Gaussian width of u(x,kt)

(d)2 ~ Gaussian width of d(x,kt)(+)2 ~ Gaussian width of D+

(z,pt) ()2 ~ Gaussian width of D-

(z,pt)

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,Q2) = q+ (x,Q2) + q- (x,Q2)

G(x,Q2) = G+ (x,Q2) + G- (x,Q2)

Define spin-dependent structure parton distribution functions:

q(x,Q2) = q+ (x,Q2) + q- (x,Q2)

G(x,Q2) = G+ (x,Q2) - G- (x,Q2)

Spin Structure Functions

F1=q

g1=q