strange quark contribution to the proton spin, from elastic ep and n p scattering

Strange Quark Contribution to the Proton Spin, from Elastic ep and p

Scattering

Stephen Pate

New Mexico State University

SPIN 2006

Kyoto, Japan, 3-October-2006

A combined analysis of HAPPEx, G0, and BNL E734 data

Outline• Initial indication of significant negative strange quark contribution to the proton spin came from SU(3)-based analysis of inclusive polarized DIS data from CERN (EMC);

• Similar experiments at SLAC and CERN supported this finding;

• An attempt to confirm this using neutrino-proton elastic scattering (BNL E734) was inconclusive;

• HERMES made first significant measurement of strange quark polarized p.d.f., using semi-inclusive DIS, for 0.03 < x < 0.2; suggests strange quark contribution to the proton spin is essentially zero!

• A combined analysis of BNL E734 p data with very recent HAPPEX and G0 forward-scattering ep data show the Q2-dependence of the strange axial form factor for 0.45 < Q2 < 1.0 GeV2; suggests the strange quark contribution is negative…

• What to do now?

s from polarized inclusive DISPlan: Measure values of g1(x,Q2), extrapolated to x=0 and x=1, and combine with axial charges from hyperon beta-decay data to extract a flavor decomposition of the quark axial charges.

[E.g. see B.W. Filippone and X. Ji, Adv. Nucl. Phys. 26 (2001) 1 and references therein…]

Surprise #1: Quarks contribute only about 20% of the proton spin.

Surprise #2: Strange quarks make a negative contribution: s ~ 0.15

Problems:

Need SU(3) flavor symmetry to bring in the hyperon data.

Extrapolation to x=0 problematic.

=> Unknown theoretical uncertainties.

s from p elastic scatteringPlan: Measure absolute cross section for p elastic scattering, and extract the strange contribution to the proton axial form factor. Extrapolate to Q2=0 to obtain the strange quark axial charge.

€

s = GAs (Q2 = 0) = Δs(x,Q2 = ∞)dx

0

1

∫

Note: Elastic p scattering and inclusive DIS both measure the sum of strange quark and strange anti-quark contributions.

€

s + Δs

BNL E734 measured this cross section for both neutrinos and anti-neutrinos, but result for s was inconclusive.

Large uncertainty in cross sections.

Lowest Q2 point (0.45 GeV2) not really low enough.

Subsequent reanalyses (Garvey et al, Alberico et al.) came to similar non-conclusion.

s from polarized semi-inclusive DISPlan: Measure tagged structure function g1

h(x,Q2) by observing leading hadrons in coincidence with scattered lepton. Use leading-order analysis to extract separated polarized quark distributions q(x). Integrate observed portion of q(x) to get estimates of axial charges.

[See HERMES PRD 71 (2005) 012003 and talk by Hal Jackson a few minutes ago…]

Result:

Advantages: No SU(3) assumption. No extrapolations to x=0. Can separate quark and anti-quark contributions.

Disadvantages: Leading-order analysis. Some folks question validity of factorization at relatively low Q2.

Result contradicts SU(3)-based analysis of inclusive DIS data.

€

s(x)dx0.02

1

∫ = 0 within errors

s from combination of ep and p elastic scattering data

[finally we come to the main point of this talk…]

Plan: Combine existing p data from BNL E734 with recent parity-violating ep scattering data from HAPPEx and G0. Extract the strangeness contribution to the proton electromagnetic and axial form factors point-by-point. Observe Q2-dependence of these form factors for the very first time.

[See SP, PRL 92 (2004) 082002, and SP et al., hep-ex/0512032]

Advantages: No SU(3) assumption. Get total integral over x by using elastic scattering. Neutrino scattering is very sensitive to the axial form factor.

Features of parity-violating forward-scattering ep data

• measures linear combination of form factors of interest

• axial terms are doubly suppressed

(1 4sin2W) ~ 0.075

kinematic factor ”' ~ 0 at forward angles

• significant radiative corrections exist, especially in the axial term

parity-violating data at forward angles are mostly sensitive to the strange electric and magnetic form factors

€

For a hydrogen target, the asymmetry as a linear combination of GEs , GM

s , GACC and GA

s is :

A p = A0p + AE

pGEs + AM

p GMs + AAIV

p GACC + AA

pGAs

where A0p = −K p

1− 4sin2 θW( ) 1+ RVp

( ) εGEp 2

+ τGMp 2 ⎛

⎝ ⎜

⎞ ⎠ ⎟

− 1+ RVn

( ) εGEpGE

n + τGMp GM

n( )

− ′ ε GMp 1− 4sin2 θW( ) 3RA

T = 0GA8

[ ]

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

⎫

⎬

⎪ ⎪

⎭

⎪ ⎪

AEp = K p εGE

p 1+ RV0

( ){ }

AMp = K p τGM

p 1+ RV0

( ){ }

AAIVp = K p ′ ε GM

p 1− 4sin2 θW( ) 1+ RAT =1

( ){ }

AAp = K p ′ ε GM

p 1− 4sin2 θW( ) 1+ RA0

( ){ }

K p =GFQ2

4π 2α

1

εGEp 2

+ τGMp 2

Full Expression for the PV ep Asymmetry

Note suppression of axial terms by ( sinW and ”'

€

τ = Q2

4M 2

ε = 1+ 2(1+ τ )tan2 θ /2( )[ ]−1

′ ε = (1−ε 2)τ (1+ τ )

Things known and unknown in the PV ep Asymmetry

€

GACC =

gA

1+ Q2 M A2

( )2

GA8 =

1

2 3

3F − D( )

1+ Q2 M A2

( )2

M A =1.001± 0.020 GeV Budd, Bodek and Arrington : hep - ex/0308005 and 0410055[ ]

gA =1.2695 ± 0.0029 Particle Data Group 2005[ ]

3F − D = 0.585 ± 0.025 Goto et al. PRD 62 (2000) 034017[ ]

use of 3F − D implies use of flavor - SU(3), but GA8 is suppressed by ′ ε and 1− 4sin2 θW( )[ ]

€

The R's are radiative corrections calculated at Q2 = 0 in the formalism of

Zhu et al. PRD 62 (2000) 033008[ ]. The Q2 - dependence is unknown,

and so we have assigned a 100% uncertainty to the values.

RVp = −0.045 RV

n = −0.012 RV0 = −0.012

RAT =1 = −0.173 RA

T =0 = −0.253 RA0 = −0.552

from evaluation of Arvieux et al., to be published[ ]

€

GE ,Mp,n = Kelly parametrization PRC 70 (2004) 068202[ ]

with G0 uncertainties http : //www.npl.uiuc.edu/exp/G0/Forward[ ]

Features of elastic p data

• measures quadratic combination of form factors of interest

• axial terms are dominant at low Q2

€

dσ

dQ2νp →νp( ) Q2 →0

⏐ → ⏐ ⏐ GF2

128π

M p2

Eν2

−GAu + GA

d + GAs

( )2

+ 1− 4sin2 θW( )2 ⎡

⎣ ⎢ ⎤ ⎦ ⎥

• radiative corrections are insignificant

[Marciano and Sirlin, PRD 22 (1980) 2695]

neutrino data are mostly sensitive to the strange axial form factor

Elastic NC neutrino-proton cross sections

€

dσ

dQ2νp →νp( ) =

GF2

2π

Q2

Eν2

A ± BW + CW 2( )

+ ν

− ν

W = 4 Eν M p − τ( ) τ = Q2 4M p2

A =1

4GA

Z( )

21+ τ( ) − F1

Z( )

2− τ F2

Z( )

2 ⎛ ⎝ ⎜

⎞ ⎠ ⎟1− τ( ) + 4τF1

Z F2Z ⎡

⎣ ⎢ ⎤

⎦ ⎥

B = −1

4GA

Z F1Z + F2

Z( )

C =1

64τGA

Z( )

2+ F1

Z( )

2+ τ F2

Z( )

2 ⎡ ⎣ ⎢

⎤ ⎦ ⎥

Dependence on strange form factors is buried in the weak (Z) form factors.

The BNL E734 Experiment

• performed in mid-1980’s

• measured neutrino- and antineutrino-proton elastic scattering

• used wide band neutrino and anti-neutrino beams of <E>=1.25 GeV

• covered the range 0.45 < Q2 < 1.05 GeV2

• large liquid-scintillator target-detector system

• still the only elastic neutrino-proton cross section data available

Q2 (GeV)2

d/dQ2(p) (fm/GeV)2

d/dQ2(p) (fm/GeV)2

correlation coefficient

0.45 0.165 0.033 0.0756 0.0164 0.134

0.55 0.109 0.017 0.0426 0.0062 0.256

0.65 0.0803 0.0120 0.0283 0.0037 0.294

0.75 0.0657 0.0098 0.0184 0.0027 0.261

0.85 0.0447 0.0092 0.0129 0.0022 0.163

0.95 0.0294 0.0074 0.0108 0.0022 0.116

1.05 0.0205 0.0062 0.0101 0.0027 0.071

Uncertainties shown are total (stat and sys).

Correlation coefficient arises from systematic errors.

E734 Results

Combination of the ep and p data sets

We use PV ep data in the same range of Q2 as the E734 experiment.

• The original HAPPEx measurement: Q2 = 0.477 GeV2 [PLB 509 (2001) 211 and PRC 69 (2004) 065501]

• The recent G0 data covering the range 0.1 < Q2 < 1.0 GeV2 [PRL 95 (2005) 092001]

E734 Q2 range

Combination of the ep and p data setsSince the neutrino data are quadratic in the form factors, then there will be in general two solutions when these data sets are combined.

Fortunately, the two solutions are very distinct from each other, and other available data can select the correct physical solution.

Intersections between electron and neutrino data.

1

2Q2 = 0.5 GeV2

General Features of the two Solutions

There are three strong reasons to prefer Solution 1:

• GAs in Solution 2 is inconsistent with all DIS estimates for s

• GMs in Solution 2 is inconsistent with the recent HAPPEx result of GM

s ~ 0 at Q2 = 0.1 GeV2

• GEs in Solution 2 is inconsistent with the idea that GE

s should be small, and conflicts with expectation from recent G0 data that GE

s may be negative near Q2 = 0.3 GeV2

GEs Consistent with zero

(with large uncertainty)Large and positive

GMs Consistent with zero

(with large uncertainty)Large and negative

GAs Small and negative Large and positive

Solution 1 Solution 2

I only present Solution 1 hereafter.

HAPPEx & E734 [SP, PRL 92 (2004) 082002]

G0 & E734 [SP et al., hep-ex/0512032]

First determination of the strange axial form factor.

€

GAs

€

GMs

€

GEs

HAPPEx & E734 [SP, PRL 92 (2004) 082002]

G0 & E734 [SP et al., hep-ex/0512032]

Q2-dependence suggests s < 0 !

€

GAs

Strange Axial Form Factor from ep and p Elastic Scattering Data

E734 data quality and Q2 range again prevent a definitive conclusion, but the trend clearly suggests a negative strange quark contribution.

€

Δs(x)dx0.02

1

∫ = 0 within errors (HERMES)

and also Δs(x)dx0

1

∫ ≈ −0.1 (form factors and inclusive DIS)

What if….?

If these two results are both true, then the average value of s(x) in the range x < 0.02 must be ~ 5. That’s not impossible, as s(x) is ~20-300 in the range x~10-2 to 10-3 (CTEQ6). But we would need a mechanism that would “turn on” the strange quark polarization suddenly at these low x values.

Another more exotic possibility exists…

A topological “x0” contribution to the singlet axial charge?

€

gA(0) = Δq

q

∑ − 3α s

2πΔg

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟partons

g A(0)

DIS

1 2 4 4 4 3 4 4 4

+ C∞

Accessible in a form factor measurement

“subtraction at infinity” term from dispersion relation integration [Steven Bass, hep-ph/0411005]

Accessible in deep-inelastic measurements

€

The C∞ term would correspond to a zero - momentum

"polarized condensate" contribution to the proton spin,

observable as a difference between the DIS and form

factor measurements.

What to do?

• The E734 data have insufficient precision and too narrow a Q2 range to determine the strange quark contribution to the proton spin. Better neutrino data is needed, with smaller uncertainties and points nearer Q2 = 0. A detailed understanding of the Q2-dependence of these form factors will not be possible until a more dense set of resolved data points are available.

• The semi-inclusive DIS data need to be extended to lower x and higher Q2 to determine which of the two proposed explanations is correct, or perhaps to reveal some other explanation. A NLO analysis would also be a good idea.

We need to approach the problem from the point of view of both kinds of data.

Better p elastic scattering data

• FINeSSE (B. Fleming and R. Tayloe) at BNL or FNAL

€

Measure ratio of NC to CC neutrino scattering from nucleons:

RNC/CC =σ νp → νp( )

σ νn → μ− p( )

⇒ Numerator is sensitive to GAs (denominator not)

⇒ Both processes have unique charged particle

final state signatures

⇒ Ratio largely eliminates uncertainties in neutrino flux,

detector efficiency, and (we expect) nuclear target effects

• A measurement of p elastic scattering is being considered for JPARC (NeuSpin, see talk by Y. Miyachi).

Better semi-inclusive DIS data

• Electron Ion Collider (EIC)

The problem of the strange quark contribution to the proton spin is an explicit part of the physics program at this new facility.

Improved version of HERMES semi-inclusive measurement will explore the quark polarizations to lower x and higher Q2.

[Figure is a simulation from Kinney and Stoesslein, AIP Conf. Proc. 588 (2001) 171.]

HERMES

Conclusion

Strange quark contribution to the proton spin remains a mystery.

HERMES semi-inclusive DIS data suggests zero contribution.

Inclusive DIS data with SU(3)-based analysis, and independent data from form factor measurements, suggest a negative contribution.

None of these measurements are definitive.

Better neutrino data are needed to improve the form factor picture for a clean determination of s. => FINeSSE/NeuSpin

Better semi-inclusive DIS data are needed to explore the low-x region to better understand the s(x) distribution. => EIC

[This work supported by the US DOE.]

strange quark contribution to the proton spin, from elastic ep and n p scattering

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