Insight into nucleon structure from generalized parton distributions

a r

X i v :h e p -l a t /0309060v 1 15 S e p 2003

1

Insight into nucleon structure from generalized parton distributions

LHPC and SESAM Collaborations ?:

J.W.Negele a ,R.C.Brower b ,P.Dreher a ,R.Edwards c ,G.Fleming c ,Ph.H¨a gler a ,Th.Lippert d ,A.V.Pochinsky a ,D.B.Renner a ,D.Richards c ,K.Schilling d ,and W.Schroers a

a Center for Theoretical Physics,Massachusetts Institute of Technology,Cambridge,MA 02139,USA

b Department of Physics,Boston University,Boston,MA 02215,USA

c

Thomas Je?erson National Accelerator Facility,Newport News,VA 23606,USA d

Department of Physics,University of Wuppertal,D-42097Wuppertal,Germany

The lowest three moments of generalized parton distributions are calculated in full QCD and provide new insight into the behavior of nucleon electromagnetic form factors,the origin of the nucleon spin,and the transverse structure of the nucleon.

1.INTRODUCTION

Matrix elements of the light cone operator

O (x )= dλ2

)n P e

?ig

λ/2

?λ/2

dαn ·A (αn )ψ(

λn

ψq γ{μ1i D μ2...i D μn }ψq

provide a wealth of precise information about the quark and gluon structure of the nucleon.The di-agonal nucleon matrix element P |O (x )|P mea-sures the light cone momentum distribution,q (x ),

and P |O {μ1μ2...μn }

q |P speci?es the

(n ?1)th mo-ment of this distribution, dx x n ?1q (x ).O?-diagonal matrix elements of O (x )measure the generalized parton distributions[1]H (x,ξ,t )and E (x,ξ,t ):

P ′|O (x )|P = γ H (x,ξ,t )+

i?

?Supported

by DOE contracts DE-FC02-94ER40818,DE-FG02-91ER40676,and DE-AC05-84ER40150.Ph.H.and

W.S.are Feodor-Lynen Fellows

these generalized parton distributions,and this work considers the generalized form factors A n 0(t )≡ dxx n ?1H (x,0,t )and B n 0(t )≡

dxx n ?1E (x,0,t ).

Two special cases are important for the present work.The zeroth moments correspond to the familiar electromagnetic form factors (weighted with appropriate quark charges),A 10(t )=F 1(t )and B 10(t )=F 2(t ).The ?rst moments yield the total quark angular momentum,J q =1

2Σ

=

1

(2π)2

H (x,0,??2⊥)e

?ib ⊥?⊥

,where q (x,b ⊥)is the probability of ?nding a quark with longitudinal momentum fraction x and transverse position (or impact parameter)b ⊥,and ?⊥is the transverse momentum transfer.Physically,we expect the transverse size of the nucleon to decrease signi?cantly as x increases.As x →1,a single parton carries all the mo-

Figure 1.Electromagnetic form factor ratio Q2F2(Q2)

2m

σμ1α ?αB10(t), P′|O{μ1μ2}|P =ˉP{μ1 γμ2} A20(t)

+i

m

?{μ1?μ2}C2(t), P′|O{μ1μ2μ3}|P =ˉP{μ1ˉPμ2 γμ3} A30(t) +i

2m

?{μ1?μ2 σμ3}α ?αB32(t),

whereˉPμ=(Pμ+P′μ)/2.

We calculated connected diagram contributions

F

(

t

)

|t| [GeV2]

Figure2.Generalized form factors A u+d

20

(t)and

B u+d

20

(t),with dipole?ts denoted by dashed curves.

using～200SESAM[4]full QCD con?gurations with Wilson fermions atβ=5.6on163×32lat-tices at each of three quark masses,κ=0.1570, 0.1565,and0.1560,corresponding to pion masses de?ned by r0of744,831,and897MeV respec-tively.

Figure1shows our result for the electromag-netic form factor ratio F2/F1divided by the next to leading order light cone wave function result[5] log2(Q2/Λ2)/Q2withΛ=0.3GeV.The Q2de-pendence is in excellent agreement with the recent JLab data[6]plotted in Ref.[5],but the overall ra-tio is a factor of four too high in the heavy quark world in which mπ～700-900MeV.

The total quark contribution to the nucleon spin is given by the extrapolation to t=0of

A u+d

20

(t)and B u+d

20

(t)shown in Figure2.Since

A u+d

20

(t)is calculated directly at t=0and B u+d

20

(t) is well?t by a constant that is measured to be nearly zero with small errors,the connected con-tribution to the angular momentum is measured to within a few https://www.360docs.net/doc/b211855240.html,bined with the re-sults ofΣfrom reference[7],we obtain the con-nected diagram contributions to the decomposi-tion of nucleon spin shown in Table1.Simi-lar results have been obtained in refs.[8,9].To the extent that the disconnected diagrams do not change the qualitative behavior,we conclude that of the order of70%of the spin of the nucleon arises from the quark spin and a negligible frac-

3 0.15700.1560

0.67±.040.68±.02

0.06±.050.00±.03

0.73±.040.68±.03