Strange Nucleon Form Factors from $ep$ and $nu p$ Elastic Scattering

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Strange Nucleon Form Factors from ep and νp Elastic Scattering Stephen Pate ?Physics Department,New Mexico State University,Las Cruces NM 88003,USA Abstract The recent parity-violating ep forward-scattering elastic asymmetry data from Je?erson Lab (HAPPEx and G0),when combined with the νp elastic cross section data from Brookhaven (E734),permit an extraction of the strangeness contribution to the vector and axial nucleon form factors for momentum transfers in the range 0.45

I.INTRODUCTION

Ever since the discovery of the?rst“strange”particles in cosmic ray experiments[1] and the subsequent formulation of the3-quark model of baryons[2],nuclear and particle physicists have sought to understand the role the strange quark plays in“non-strange”par-ticles like the proton.Traditionally these investigations have taken place in the context of deep-inelastic scattering.However,a strong e?ort has been made to measure the strange quark contribution to the elastic form factors of the proton,in particular the vector(electric and magnetic)form factors.These experiments[3,4,5,6,7,8,9,10,11,12]exploit an interference between theγ-exchange and Z-exchange amplitudes in order to measure weak

elastic form factors G Z,p

E and G Z,p

M

which are the weak-interaction analogs of the more tra-

ditional electromagnetic elastic form factors Gγ,p

E and Gγ,p

M

for which copious experimental

data are available.The interference term is observable as a parity-violating asymmetry in elastic e p scattering,with the electron longitudinally polarized.By combining the electro-magnetic form factors of the proton and neutron with the weak form factors of the proton, one may separate the up,down,and strange quark contributions;for example,the electric form factors may be written as follows:

Gγ,p

E =

2

3

G d E?

1

3

G d E?

1

3

G s E

G Z,p

E

= 1?83sin2θW G d E+ ?1+4

2 ?G u A+G d A+G s A .

The u?d portion of this form factor is well-known from neutronβ-decay and other charged-current(CC)weak interaction processes likeνμ+n→p+μ?:

G CC A=G u A?G d A=

g A

where g A=1.2695±0.0029is the axial coupling constant[13]and M A=1.001±0.020 is the so-called“axial mass”which is a very successful?tting parameter for the data on this form factor[14].The strange quark portion,G s A,is essentially unknown,except for some contradictory indications from polarized deep-inelastic scattering,which we discuss in more detail below.In elastic ep scattering,the axial form factor does not appear as a pure weak-interaction process;there are signi?cant radiative corrections which carry non-trivial theoretical uncertainties.The result is that,while the measurement of parity-violating asymmetries in e p elastic scattering is well suited to a measurement of G s E and G s M,these experiments cannot cleanly extract G s A.The strange axial form factor is of great interest, however,because of the role it plays in the understanding of the spin structure of the proton.

II.STRANGE QUARKS AND THE SPIN OF THE PROTON

The strange quark contribution to the proton spin has been a subject of investigation ever since the?rst polarized inclusive deep-inelastic measurements of the spin-dependent structure function g1(x)by EMC[15]demonstrated that the Ellis-Ja?e sum rule[16,17]did not hold true.Subsequent measurements at CERN and SLAC supported the initial EMC measurements,and a global analysis[18]of these data suggested?s≈?0.15.This analysis carries with it an unknown theoretical uncertainty because the deep-inelastic data must be extrapolated to x=0and an assumption of SU(3)-?avor symmetry must be invoked.

In the meantime,the E734experiment[19]at Brookhaven measured theνp andˉνp elastic scattering cross sections in the momentum-transfer range0.45

The HERMES experiment[22]measured the helicity distribution of strange quarks,?s(x),using polarized semi-inclusive deep-inelastic scattering and a leading order“purity”analysis,and found?s(x)≈0in the range0.03

the analysis of the inclusive deep-inelastic data.This disagreement could be due to a failure of one or more of the assumptions made in the analysis of the inclusive and/or the semi-inclusive data,or it could be due to a more exotic physics mechanism such as a“polarized condensate”at x=0not observable in deep-inelastic scattering[23].

https://www.360docs.net/doc/7219145259.html,BINING ep ANDνp ELASTIC DATA

On account of the apparent discrepancy between the analyses of the two di?ernt kinds of deep-inelastic data,another method is needed to shed light on the strange quark contribution to the proton spin.Recently[24]it has become possible to determine the strange vector and axial form factors of the proton by combining data from elastic parity-violating e p scattering experiments at Je?erson Lab with theνp andˉνp elastic scattering data from E734.The parity-violating e p data place constraints on the strange vector form factors that were not available for previous analyses of E734data.

Several experiments have now produced data on forward parity-violating e p elastic scat-tering[3,4,5,6,7,8].Of most interest here are measurements that lie in the same Q2 range as the BNL E734experiment,which are the original HAPPEx measurement[3]at Q2=0.477GeV2and four points in the recent G0data[6].These forward scattering data are most sensitive to G s E,somewhat less sensitive to G s M,and almost completely insensi-tive to the axial form factors due to supression by both the weak vector electron charge (1?4sin2θW)and by a kinematic factor that approaches0at forward angles.

The basic technique for combining the e p,νp,andˉνp data sets has already been de-scribed[24]and the details of the present analysis will be published[25].The results are displayed in Figure1.The uncertainties in all three form factors are dominated by the large uncertainties in the neutrino cross section data.Since those data are somewhat insensitive to G s E and G s M then the uncertainties in those two form factors are generally very large. However the results for the strange axial form factor are of su?cient precision to give a hint of the Q2-dependence of this important form factor for the very?rst time.There is a strong indication from this Q2-dependence that?s<0,i.e.that the strange quark contribution to the proton spin is negative.However the data are not of su?cient quality to permit an extrapolation to Q2=0,so no quantitative evaluation of?s from these data can be made at this time.

https://www.360docs.net/doc/7219145259.html,PARISON TO MODEL CALCULATIONS

It is interesting to compare these results with models that can calculate a Q2-dependence for these form factors.Silva,Kim,Urbano and Goeke[26,27,28]have used the chiral quark soliton model(χQSM)to calculate G s E,M,A(Q2)in the range0.0

V.FUTURE EXPERIMENTS

To provide a useful determination of?s,better data are needed for both the form factors and the polarized parton distribution functions.Two new experiments have been proposed to provide improved neutrino data for the determination of the strange axial form factor. FINeSSE[33]proposes to measure the ratio of the neutral-current to the charged-current νN andˉνN processes.A measurement of R NC/CC=σ(νp→νp)/σ(νn→μ?p)and ˉR

=σ(ˉνp→ˉνp)/σ(ˉνp→μ+n)combined with the world’s data on forward-scattering NC/CC

PV ep data can produce a dense set of data points for G s A in the range0.25

the determination of the polarized strange quark distribution?s(x)can be improved.A measurement of this type is envisioned[35,36]for the proposed electron-ion collider facility. At the same time,a future electron-ion collider could provide an improved measurement of the integral 10g p1(x)dx,which can be combined with aνp elastic scattering measurement of the proton’s weak axial charge and a recently developed axial charge sum rule[23,37]to provide an additional determination of?s and perhaps evidence for a“polarized condensate”at x=0[23].It is only with these improved data sets that we will be able to arrive at an understanding of the strange quark contribution to the proton spin.

VI.NUCLEAR EFFECTS IN A(ν,p)X

FINeSSE and NeuSpin will make use of nuclear targets,like carbon or argon perhaps, in order to bring NCνN→νN and CCνN→μN count rates up to a level needed for timely completion of the experiments.In order to reach the level of precision in G s A needed for an extraction of?s then a good understanding of initial and?nal state nuclear e?ects is needed.A number of theoretical e?orts have been made in the last few years in this direction.There is no space here for any detailed discussion of these calculations but some summary remarks are in order.Maieron et al.[38,39]studied quasi-elasticνμN scattering in16O and12C using a relativistic shell model and treating?nal state e?ects in a distorted wave impulse approximation(DWIA).Meucci et al.[40,41]used a relativistic DWIA model with a relativistic mean-?eld model of the nucleus to study the same processes in12C and also studying?nal state e?ects.Martinez et al.[42]studied these processes in12C and56Fe using a relativistic description of the nucleus and the scattering process;signi?cantly,they argue that nuclear transparencies measured in A(e,e′p)experiments can be applied to?nal state e?ects in A(ν,p)processes.The work of van der Ventel and Piekarewicz[43,44]centers on the calculation of a set of nuclear structure functions(describing the neutrino-nucleus scattering)via a relativistic plane wave impulse approximation.Finally,the work of Leitner et al.[45,46]uses a fully relativistic formalism including the quasielastic and resonance scattering channels,and taking into account a variety of nuclear and?nal state e?ects.The results of several of these studies imply that the ratios R NC/CC andˉR NC/CC to be measured in FINeSSE are relativly insentive to many e?ects of the nucleus and?nal state interactions.

Acknowledgments

The author is grateful to S.D.Bass,H.E.Jackson,D.O.Riska,and A.W.Thomas for useful discussions.This work was supported by the US Department of Energy.

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2-0.2

-0.1

00.1

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00.20.40.6

0.81G Q s E 2[(GeV)2]r

r r r r r r r r r r r r r r r r r r r r 2

G s M -0.4

-0.2

0.2

0.4

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-0.1

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G s A FIG.1:Results of this analysis for the strange vector and axial form factors of the proton.Open circles are from a combination of HAPPEx and E734data,while the closed circles are from a combination of G 0and E734data.[Open squares are from Ref.[8]and involve parity-violating e p data only.]The theoretical curves are from Ref.[26,27,28](solid line),Ref.[31](small-dotted line),and Ref.[32](big-dotted line).There is not any calculation of G s A from Ref.[32].