Study of strange quark in the nucleon with neutrino scattering

T.-A. Shibata a

a Tokyo Institute of Technology, Oookayama 2-12-1, Meguro, Tokyo, 152-8551, Japan

Spin structure of the nucleon is one of the current topics of particle physics. It provides a test of QCD whichis a part of standard model. Contribution of the strange quark spin to the nucleon spin can be studied withneutrino scattering at medium energies.

1. Introduction

Spin of hadrons and leptons played importantroles in the history of physics. For example, po-larized nucleon, nuclei and leptons had been usedto study the parity violation. The magnetic mo-ment of lepton is being used to test QED.

The nucleon is not an elementary particle butis made of partons. Spin of the nucleon should re-flect the dynamical characteristics of the partonsinside the nucleon. Spin of the nucleon, therefore,provides a test of our present understanding ofQCD(Quantum ChromoDynamics) which is thetheory of strong interaction. QCD is a part ofthe standard model of particle physics of today.

In the static model of the constituent quark,the expectation value of u quark spin in the pro-ton is + 2

3 , and that of d quark is − 16 . The sum is

+ 12 as the assumption here is that the proton spin

is completely carried by quarks as shown in Fig-ure 1. These values are obtained with the quarkwave function of the proton:

|p ↑>=

√23|u ↑ u ↑ d ↓> −

√16|u ↑ u ↓ d ↑>

−√

16|u ↓ u ↑ d ↑> (1)

The quarks in the proton are antisymmetric ifspace, flavor, spin and color degrees of freedomare considered.

The ratio of the magnetic moments of the pro-ton and neutron µn

µp= −0.685 is consistent with

what is obtained from the quark wave function− 2

3 .

Figure 1. A sketch of the proton where spins ofthree quarks compose the proton spin 1

2

2. EMC and deep inelastic scattering

The ‘proton spin problem’ was discovered bydeep inelastic scattering with high energy leptonbeam. EMC experiment at CERN reported in1988[1] that the quark spin contribution to theproton spin is small:12 ± 9 ± 14%, contrary tothe simple picture in the previous chapter. In thefollowing measurements by SMC and at SLAC,the result was confirmed with the neutron, too.

Nuclear Physics B (Proc. Suppl.) 149 (2005) 242–244

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The world data now show that the quark spincontribution to the nucleon spin is 20-30%.

The nucleon spin is composed of quark spin,gluon spin and orbital angular momenta of quarksand gluons:

12

=12Σ + ∆G + Lq + Lg (2)

Σ = ∆u + ∆d + ∆s + ∆u + ∆d + ∆s (3)

Σ is the quark spin contribution to the nucleon.∆u, for example, denotes the helicity differenceu→(x) − u←(x) integrated over the full range ofBjorken x. Flavor separation of the quark spinis studied by HERMES using identification ofhadrons produced in deep inelastic electron scat-tering[2]. The u and d quarks in the proton havebeen rather well measured. The key point to beexplored is the contribution of the strange quarkor sea quarks in general. In the EMC result, thestrange quark contribution was slightly negative:strange quark is oppositely polarized with respectto the proton spin. This needs to be studied as afunction of Bjorken x.

Up to now the unpolarized parton distributionsin the nucleon have been measured with muon,electron and neutrino scattering. The spin struc-ture of the nucleon has been studied with muonand electron scattering. Now we have a new pos-sibility to study the nucleon spin with neutrinobeam which is the subject of this paper. In par-ticular, the spin contribution of the strange quarkcan be measured with neutrino beams. Polar-ized proton-proton collision at BNL is anotherappoach to the proton spin problem.

3. Neutrino scattering

Cross section for neutrino-nucleon elastic scat-tering was measured by E734 experiment at BNLand strange quark spin ∆s in the proton was stud-ied[4]. The neutrino beam energy was 1.3 GeV onaverage. Both neutrino beam and anti-neutrinobeam were used.

The cross section for charged current interac-tion is expressed as

dσ

dQ2=

G2F

2π

E2ν

Q2[A ± BW ± CW 2], (4)

W = 4(Eν

Mp− τ), τ =

Q2

4M2p

(5)

A =14[G2

1(1+τ)−(F 21 −τF 2

2 )(1−τ)+4τF1F2],(6)

B = −14[G1(F1 + τF2)], (7)

C =116

M2p

Q2[G2

1 + F 21 + τF 2

2 ] (8)

G1(Q2) =−0.631

(1 + Q2

M2A

)2+

Gs1(Q2)2

(9)

Here, ± sign in Eq.4 is for ν and ν. TheQ2 dependence of the cross section contains afew form factors, one of which is the strangeform factor Gs

1(Q2). At Q2 → 0, it becomes∆s: Gs

1(Q2 → 0) = ∆s. The cross section for

proton is needed to be extracted. The combina-tion of measurements with liquid scintillators ofdifferent hydrogen fraction will be used for thispurpose. The strange form factor and the axial-vector dipole mass MA are the parameters to befitted. The neutrino beam at J-PARC with highintensity is suited for this experiment. There is aplan at FNAL and BNL, which is called FINeSSE,to measure ∆s.

4. Impact of strange quark spin

The quark spin contribution to the nucleonspin, in particular, the contribution of sea quarksis crucial to understand the nucleon spin in termsof quark-parton model.

Furthermore, strange spin has a connectionwith neutron electric dipole moment (EDM) sinceneutron EDM is theoretically predicted to beproportional to the spin of quarks[3]: mu∆u +md∆d + ms∆s. The strange quark contributionis expected to be large as ms is large. Dark mat-ter reaction is also sensitive to ∆s.

5. Polarized beam and polarized targets

In a longer time range, a very attractive fea-ture of the neutrino beam is its full polarization.This is made use of, if the polarized target canbe used. When the beam diameter is reduced

T.-A. Shibata / Nuclear Physics B (Proc. Suppl.) 149 (2005) 242–244 243

to about 10 cm, the polarized targets of presentday technique can be used. Because of the lep-ton number conservation, neutrino reacts on thequark with specific charge in charged current in-teraction:

ν + d → µ− + u (10)

ν + u → µ+ + d (11)

with some mixture of s and c contributions.Therefore, the polarized scattering provides se-lective and unique informations. The data canbe analysed together with the data from chargedlepton scattering. Flavor separation of the quarkspin will then reach a new stage of precision.

6. Summary

The neutrino beam at J-PARC energy is apromising tool to explore the spin structure ofthe nucleon. The neutrino beam is in particularuseful to study the strange quark contribution tothe nucleon spin. In a longer time range, the fullpolarization of the neutrino beam can be madeuse of, when polarized targets are used together.

REFERENCES

1. J. Ashman et al., Phys. Lett. B 206 364(1988),J. Ashman et al. Nucl. Phys. B 328 1 (1989).

2. A. Airapetian et al, Phys. Rev. Lett. 92012005 (2004).

3. J. Ellis and R.A. Flores, Phys. Lett. B 37783 (1996).

4. L.A. Ahrens et al., Phys. Rev. D 35 785(1987), G.T. Garvey et al.. Phys. Rev. C 48761 (1993).

T.-A. Shibata / Nuclear Physics B (Proc. Suppl.) 149 (2005) 242–244244