FFlavor Decomposition of Nucleon Form Factors
Bogdan Wojtsekhowski Thomas Jefferson National Accelerator FacilityNewport News, Virginia 23606 USA (Dated: January 8, 2020)The nucleon form factors provide fundamental knowledge about the strong interaction. We reviewthe flavor composition of the nucleon form factors and focus on an analysis of the possible impactof the s -quark contribution. A future experiment is presented to measure the strange form factorat large momentum transfer. PACS numbers: PACS numbers:14.20.Dh, 13.40.Gp
High Q nucleon form factor experiments Nucleon structure investigation using high energy electron scattering has been a successful field where many dis-coveries have been made since the 1955 observation of the proton size [1]. The status of current knowledge of thenucleon electromagnetic form factors is reviewed in Ref. [2]. To a large extent, this success is due to the dominanceof the one-photon exchange mechanism of electron scattering as proposed in the original theory [3].The most decisive studies of the partonic structure of the nucleon could be performed when the dominant part of thewave function is a 3-quark Fock state. This requires large momentum transfer, Q > , when the contributionof the pion cloud is suppressed. By the early 90s, the data sets at large Q for the proton and the neutron have beenfound to be in agreement in the Dipole fit, G Dipole = (1 + Q / . GeV ]) − , see Ref. [4]. The SLAC experimentaldata [5] on the proton Dirac form factor F p at Q above 10 GeV have been found to be in fair agreement withthe scaling prediction [6] based on perturbative QCD: F p ∝ Q − , where Q is the negative four-momentum transfersquared.New development began with a precision experiment [7] which made a very productive realization of a doublepolarization method suggested in Refs. [8]. The double polarization method has large sensitivity to the typically smallelectric form factor due to the interference nature of the double polarization asymmetry. It is also less insensitive tothe two-photon exchange contributions, which complicates the Rosenbluth method.The experimental results from Jefferson Laboratory [9] are shown in Fig. 1 (left). The ratio of the proton Pauli formfactor F p and the Dirac form factor F p have been found to be in disagreement with the scaling law F p /F p ∝ /Q (which requires the G p E to be proportional to G p M for large momentum transfer, τ >>
1) suggested in Ref. [6]. ] [GeV Q p M / G p E G p m -0.50.00.51.0 GEp(1)GEp(2)GEp(3)GEp / SBS
VMD - E. Lomon (2002)VMD - Bijker and Iachello (2004)RCQM - G. Miller (2002)DSE - I. Cloet (2009) = 300 MeV L , )/Q L / (Q ln (cid:181) /F F [GeV ] Q u 1 / F d 1 F -0.4-0.3-0.2-0.100.10.20.30.40.50.6 ) D (cid:40) pE Kelly Fit (GKelly FitCLAS data
SLAC data
GMn/SBS projected
FIG. 1: Left: Existing data and projected data accuracy for the ratio of the µ p G p E / G p M . Right: Ratio of the d - and u -quarkcontributions to the proton form factor F p from measurement of the G n M / G p M (see more in the text). The data for µ p G p E / G p M revealed an unexpected reduction with Q , which also means that F p and Q × F p for theproton have different Q dependencies. The origin of the scaling prediction violation has been attributed to an effectof the quark orbital momentum (so-called “logarithmic scaling”) which provides a very efficient fit of the data for aproton in a wide range of the momentum transfer above 1 GeV [10]. a r X i v : . [ nu c l - e x ] J a n The measurement of the proton to the neutron cross section ratio in the quasi-elastic nucleon knockout from thedeuteron was used in JLab’s precision experiment of the neutron magnetic form factor for Q up to 4 GeV [11].With the latest JLab experiment on the neutron electric form factor [12], the data on all four nucleon form factorshave become available in the Q region of 3-quark dominance.The first analysis of these new data for the flavor contributions to the nucleon form factors was reported in Ref. [13].The Q F /F for individual flavors as a function of Q shown in Fig. 2 (left) does not have any sign of the saturationexpected in the case of approaching the pQCD regime. Analysis shows a large unexpected reduction in the relativesize of the d -quark contribution to the F p form factor, which drops by a factor of 3 when Q increases from 1 to3.4 GeV . A similar result was found in an advanced analysis [14] with the GPD-based fits of the form factors, seeFig. 2 (right). / F F S = Q p S n S BJY - pQCD (2003) ] [GeV Q d S- u S1 2 3 4 5 6 7 8024 q 2 F Q q - k u quark d quark Q [GeV ] q 1 F Q u quark 2.0 · d quark FIG. 2: The flavor decomposition of proton form factors per Refs. [13, 14].
The 0bserved reduction of the d -quark contribution to F p naturally explains the JLab result for the momentumdependence of F p / F p without the effect of the quark orbital momentum (at least at Q below 3.4 GeV ). The originof the observed F d / F u reduction with the increase of Q is a subject of significant interest as it could be the mostdirect evidence of the di-quark correlations in a nucleon as proposed in Ref. [20].The flavor decomposition leads to two simple conclusions: • The contributions of the u -quarks and d -quark to the magnetic and electric form factors of the proton all havedifferent Q dependencies. • The contribution of the d -quark to the F p form factor at Q =3.4 GeV is three times less than the contributionof the u -quarks (corrected for the number of quarks and their charge).The second observation suggests that the probability of proton survival after the absorption of a massive virtualphoton is much higher when the photon interacts with a u -quark, which is doubly represented in the proton. This maybe interpreted as an indication of an important role of the u - u correlation. It is well known that the correlation usuallyenhances the high momentum component and the interaction cross section. The relatively weak d -quark contributionto the F p indicates a suppression of the u - d correlation or a mutual cancellation of different types of u - d correlations. The SBS nucleon form factor program
A set of experiments was proposed with the Super BigBite Spectrometer whose large angular acceptance allows usto advance very significantly the measurements of the G p E , G n M , and G n E (see Table I).The first measurement for the neutron magnetic form factor ( G n M ) is under preparation for data taking in 2021.Fig. 1 (right) shows the projected accuracy for the ratio F u / F d obtained from G n M / G p M with systematic uncertaintiesdominated by the uncertainty of the G p E / G p M ratio. Form factor Reference Q range, GeV ∆ G/G
Dipole (stat/syst) at max Q G p E [23] 5-12 0.08 / 0.02 G n E [25] 1.5-10.2 0.23 / 0.07 G n M [24] 3.5-13.5 0.06 / 0.03TABLE I: Upcoming measurements of the nucleon form factors in JLab Hall A with SBS (approved experiments). Projectedrange of Q and accuracy relative to the Dipole form factor at max. value of Q . New experiment for measurement of the strangeness form factor at high Q In this section we present the physics motivation and specific ideas for a new experiment for the measurementof the F ps by using SBS equipment. In the original flavor decomposition study [13] we decided to omit the heavierquark contribution motivated by the fact that all experimental data on the strangeness form factor of a proton F ps areconsistent with zero [15, 17] (in agreement with the lattice calculations). However, all known experiments wereperformed for Q below 1 GeV . At the same time, the relative role of the s ¯ s in the elastic electron-nucleon scatteringcould be higher at the momentum transfer of 3 GeV [18]. The recent analysis of the possible value for the strangeform factor performed by T. Hobbs, M. Alberg, and J. Miller suggests that F ps could be as high as a G Dipole (whichis 0.03 at Q =3.4 GeV ) or even larger, see Fig. 3 from Refs. [18, 19]. Q , GeV -0.100.10.20.3 G E ss + η G M ss G0, 2005 PVA4 HAPPEX-III HAPPEX-I, -II
FIG. 3: The strange form factor vs. momentum transfer data and projections per Refs. [18, 19].
In the one-photon exchange approximation, the amplitude for electron-nucleon elastic scattering can be written as M nuc = − (4 πα/Q ) l µ J nuc µ , where α is the fine structure constant, l µ = eγ µ e is the leptonic vector current, and J nuc µ = (cid:104) p ( n ) | ( uγ µ u + − dγ µ d ) + − sγ µ s ) | p ( n ) (cid:105) (1)is the hadronic matrix element of the electromagnetic current operators for the proton (neutron).The corresponding nucleon form factors for the virtual photon have three contributions: G γ E , M = G u E,M + − G d E,M + − G s E,M (2)The Z boson exchange between an electron and a nucleon leads to a similar structure of the current. The contributionof G Z E,M could be observed thanks to the significant interference term in the matrix element of the scattering. Themeasurement of the asymmetry of the longitudinally polarized electrons scattering from a proton (left vs. right) allowsus to find G s E,M , see Refs. [15, 16] and complete flavor decomposition of the nucleon form factors (assuming isospinsymmetry).It is easy to see that the uncertainty in G s E,M (and F , ) contributes linearly to the uncertainty of u - and d -quarkcontributions. At Q =3.4 GeV for the ∆ G s = G Dipole the corresponding uncertainty ∆( Q F d ) ∼ .
35, which is muchlarger than the contribution from the uncertainty of the G n E [12], see Fig. 2.The interest in high Q measurement of F ps is also motivated by the expectation that F ps has a maximum at amomentum transfer much larger than the location of the G n E maximum due to the heavier mass of the s -quark. Suchan expectation is supported by the small radius of a φ meson which could be obtained from the form factor in the φ decay to π ◦ e + e − [27].There are two experimental difficulties in doing the F ps measurement at large Q : the reduced counting rate and largebackground from inelastic electron-proton scattering. The reduction of the counting rate, which is due to reductionof the σ Mott G Dipole , is partly compensated for by a linear increase of the asymmetry for high Q . For suppression ofthe inelastic events we proposed to use the tight time and the angular correlations between the scattered electron andrecoiled proton (as well as the energy deposited in the detectors), as it was considered in Ref. [28].The solid angle of the apparatus should cover a suitable range of the momentum transfer ∆ Q /Q ∼ . FIG. 4: Left: Side view of the apparatus. The electron beam goes from right to left. The proton detector is shown in greenand the electron detector in purple; the liquid hydrogen target is shown in blue. Right: Front view of the apparatus. Theblocks in orange get signals from the electron and the proton whose directions are shown in red.
The proposed detector configuration has an electron arm with a solid angle of 0.1 sr at a scattering angle of 18 ± F ps of 0.002. Such a measurement will provide the first experimentallimit on F ps at large momentum transfer of 3 GeV (or discover its non-zero value) and reduce the current uncertaintyfrom the strangeness contribution in the flavor separated proton form factors such as F d by six times. Acknowledgments
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