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S(p)−1 = Z2 (iγ · p+mbm) + Z1

∫ Λ

q

g2Dµν(p− q)λa

2γµS(q)Γa

ν(q, p)d4q

(2π)4,

! Y<#

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q

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S(p) = −iγ · p σV (p2, ζ2) + σS(p2, ζ2) =1

iγ · pA(p2, ζ2) +B(p2, ζ2)=

Z(p2, ζ2)

iγ · p +M(p2)

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0 2 4 6 8 10Q

2 [GeV2]

0

0.5

1

µ p GEp/ G

Mp

r1+ = 0.0 fm

r1+ = 0.4 fm

r1+ = 0.8 fm

r1+ = 1.2 fm

SLAC globalQattan (2005)Punjabi (2005)Gayou (2002)

0 2 4 6 8 10 12

Q2 [GeV

2]

-0.1

0

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µ n GE

n / G

Mn

Data parametrisationMadey, et al., nucl-ex/0308007r1

+ = 0.4 fm

r1+ = 0.8 fm

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F2p(Q

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0 2 4 6 8 10

Q2 (GeV2)

F bare2p

(Q2)

F vmd2p

(Q2)

2p(Q2)

F vmd+π

2p(Q2)

Empirical

0 1 2 3 4 5

Q2/M

2

0

0.04

0.08

0.12

0.16

F2: D

SE

- K

elly

proton

neutron

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�bcQ2 ≈ 2M2

N

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β� ��GICIfw[UdutLC%�-duC bFE�HK[UdufDGIsgEMHDN�[et

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β� ��GVCIf�[edgtLCO? `�tLCÊ[UZA�Üb:tLHUEMH\J [e�IZDtLH\J dgCVmIdgfDE�[UZ�cS[U�FE�[2[e�IdgcS[eHUEMCVcedu[edgtLC

�:tLGICImFE�HKJ�sudgZDc©E�[p2 ∼ 0.6

}&Z¹R 2 ?Ü^vduCIfDZ{E�bIHKtL�_Z�%Xc�duCIbIGV[G�Üt/�ÜZDCÊ[UG�� Qdgc&bVHedgCVfDdgbIEMsgsÕJücK�FEMHKZDm

ZA��GFE�sgsuJ�E�� tMC��LcK[�[e�IZ=mIHeZ�ceceZ�mv� ��GFE�HeY�c©dgC�E2[UHeEMCIcedÕ[UdutLC�bIHet�fDZ�cecDNF[e�IZDCüZ]EMf@�üf]EMCü�_Z�fDtMCIcedumIZDHKZDmäE�cEM�IcKtLHe�VdgC��=E@� t�� Z�C�[eG�� ��HeEMf�[edgtLC

Q/3?�����GIc×dgC2tLHKmIZDHn[Ut�f�tº�MZDH¸[U�IZ"mIt��íEMduC

p2 ∈ [0.5, 1.0]}&Z¹R 2

tLCIZ�HKZA��GIdgHKZDcQ2 ∈ [5, 10]

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�ÜZDCÊ[qduCÊ[Ut�EÜbIHetM�_Z,t���[U�VZ'mIHKZDcecKZDmv� ��GFEMHeYU� EMcec ��GICIf�[edgtLC�?����IZSZ�._tLH\[q�FE�c�� EMCÊJ7��EMfDZw[Uc©E�CImî[U�VZ�FHKcK[°f]EMsufDGIsgE�[UdutLCIc�E�HeZ&�:ZDdgC��Üb:ZDH6��tLH4�ÜZDm�E�["suZ]EMmVdgC����¹tLHemVZDHaduC�[U�IZ=�&^Vl [eHeGICVf]E�[edgtLCO?�qEÃ[UGIHeEMsgsÕJLN�E,HKZ���Z�HeZDCVfDZ©fDEMsgf�GIs~E�[edgtLC2duc¬CVZDZDmVZDmONItMCIZ°[e�FE�[¬mIt�ZDc�CVtM[�duCIfDtMHeb:tLHUE�[eZ�[U�IZ6HeGICICVdgC��,t��

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NOceduCIfDZSZ�� bVdgHeduf]EMsusuJGM(Q2 = 0) = 3

?&���Iduc©f]E�sgfDGVs~E�[edgtLCI�SGIcK[©�_Z2E�CFEMsuJ�B�ZDm EMCImä[e�IZ

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0

0.5

1.0

1.5

2.0

GM

(Q2)

0 2 4 6 8 10

Q2 (GeV2)

GbareM

(Q2)

GvmdM

(Q2)

M(Q2)

Gvmd+π

M(Q2)

� O)!"�E_2� ÇV¤²µX³´Ú"·UËM­KÏ]ª�� ����S��,S�dS�Q���40�V rz��:T������$%�T2�T��o��X�� � 5$%(c)d���S�'n�o;n5��c 0���'fc)8,�

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∆bIHetMb_Z�HK[UduZDc�N o"dusgs��_ZÜEMbIbVsgdgZ�mä[Ut�[U�VZ

N → ∆[eHUEMCVcedu[edgtLC�?a���IZ'c\[UHKtLC����Üt/�ÜZDCÊ[UG�� mIZDb:ZDCImVZDCIf�ZSt���[e�IZ'mIHKZDcKceZDm�� ��GFEMHKYI� EMcec2��GICIfw[UdutLC

dgc�EMC{dgCÊ[UZ��LHUEMsvbFEMH\[nt��:[U�Iduc ��HUE��ÜZ�o¬tLHKY:?����IZDHKZ���tLHKZMN�dgCS[e�Idgcnc\[UGImvJSdu[-o"dgsgsv�_Z�b_tLcKcedu�IsgZ�NÊZM? �I?uNL[et©��EMHKJEMH\[Ud��IfDd~E�sgsuJ2[e�IZ�b_tMcedu[edgtLCít���[e�IZG�íE�HeYMZ�mümVHetLb�dgC�[e�IZ�mIHeZ�ceceZ�mv� ��GFE�HeY7� EMcecF��GICVf�[UdutLC�EMCIm�[U�IZ�HeZ���JdgmVZDCÊ[Ud �´J�Z-,vb:ZDHed�� Z�CÊ[@EMs×ced��LCFE�[eGIHeZ�c>��tLH�dÕ[Uc=bIHeZ�ceZDCVfDZ�EMCVm sgt�f]EÃ[UdgtMCO?í���Iduc,c\[UGImvJ|o¬tLGIsum �:ZA�LduC|duC�Üdgmv� ��3�3LSE�CIm��_Z�fDt�� bIsuZ�[eZDm��ÊJ�[U�IZ��:ZA�LduCICIduC��2t��� ��0Y��V?

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N → ∆[UHUE�CIcedÕ[UdgtMCO?-���IZ°[Ud�� Z"HeZ���GIdgHKZDmí[etSfDt/�ÜbIsuZ�[UZ"[U�Vdgc×Z�._tLHK[¬dgc×GICIf�ZDHK[UEMdgC�N

�LdÕ�LZDC [e�FE�[2dÕ[SduC��MtLsu�MZDc{E��n�F� cK[eGImIZ�C�[{o"�It�ducSCIt²o/CIZ]E�HedgC���fDt/�ÜbIsgZw[UdutLC t��"�VdgcSHKZDceZDEMHef@��N¬�IGv[EMcKceG��ÜdgC��{[U�IE�[©EÜCIZ�o�c\[UGImVZDCÊ[&dgc ��tLGVCImätLH°E b:tLc\[UmIt�f�[etLHUEMs ��Z�sgsgt²oæf]EMCîEMcecKG�� Z,HeZ�ceb:tLCIcedu�Idgsudu[�JMNhEHeZDEMcetMCFEM�IsuZ&ZDcK[edE� E�[UZ&ducF��tLH�fDt�� bIsuZ�[edgtLC��ÊJ7�Üdgmv� ��0Y��v?->¹[°ce�ItMGIsgm��:Z=Z�� bV�FEMceduBDZ�mONF�It²o�Zw�LZ�HDNh[U�FE�[��tLH'[eZDf@�ICVdgf]E�saHeZDEMcetLCVcS[U�IducSZ�._tLHK[Sf]EMC tLCIsÕJÛbIHet�mIGIf�Z"��tLH4� ��EMf�[etLHec2tMGV[S[Ut��Üt�mIZDc\[ � t�� Z�C�[eG��[UHeEMCIc6��ZDH �I��duBM?ÕN

Q2 ∼ 2M2N

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uβ∆(p′)

{

HM(q2)KMβµ(q2) +HE(q2)KE

βµ(q2) +HC(q2)KC

βµ(q2)

}

nµup(p)!(l #

>�C Z��h? lîEM�:tº�MZMNuβ

∆(p′)duc,Eük6E�Hedu[UEÃ�\^�f@��o"duC��LZ�H=cKbIdgCVtLH>��tMH�[e�IZ

∆NKM,E,C

βµ

EMHeZ{[U�VZífDt²��EMHKd~EMCÊ[UcmIZ-�FCIZDm duC & :+(�N

nµ duc'E�sgd��L�Ê[K��f�tLCIZ2�LZ�f�[etLH'CItMH4� EMsgduBDZDm cKGIf@� [U�FEÃ[n2 = 0

EMCImnµPµ = 1

?����IZHeZ�s~E�[edgtLCVce�Idub��_Zw[�o�Z�ZDCü[e��� ��tMH4�S��E�f�[UtMHec"EMCIm�[U�VZ'}��¸�qc"dgca[e�IZDC

2G∗M(t) =

dxHM(t, x, ξ), 2G∗E(t) =

dxHE(t, x, ξ) and 2G∗C(t) =

dxHC(t, x, ξ).

���IZ2�FHec\[�bVHUEMfw[UdgfDEMshEMbIbVsgdgfDE�[UdutLC2t���}=�¸�qc¸[Ut=HeZ�cetLCFE�CIfDZ�c�o�Z�HeZ6HeZDb:tLH\[UZDmÜdgCI& e�( ��tLHn[U�IZN → ∆

[UHeEMCIcKdu[UdutLCO?{>¹[=oaEMc=ce�Vtºo"C|[U�FE�[�[e�IZíE�CIt/� EMsgtLGVcesuJüHUE�bIdgmL��EMsgsut�.|t���[e�IZG∗

M

fDEMCÛ�_ZÜmIdgHKZDfw[UsuJäHeZw�s~EÃ[UZDmÜ[Ut�[U�IZ6GICIZ0,Vb:ZDfw[UZ�mIsuJ HUEMbVdgm'��E�sgsgt�.�t��O[e�IZqZ�s~EMc\[Uduf°�VZDsgdufDdÕ[�J IFdgb

F2

N�o"�Iduf@���FEMm �_Z�ZDC�HeZ�fDZ�C�[esuJmIducefDt²�MZDHeZ�mON:��J�f�tLCIc\[UHUE�dgCIduC��2[U�IZ

N → ∆}��×�ï�ÊJ�[U�IZ�dgcKt²�LZDfw[UtLH°bFEMH\[°t��-[e�IZ�ZDs~E�cK[Uduf�cef]EÃ[e[UZ�HeduC��

��tLHM� ��EMf�[etLHec�?��-d��LGIHeZbY'�ÜcK�It²o"c&E��ÜtLHKZ=HKZDf�ZDCÊ[ & x<( �I[°[UtG∗

M

Nho"�Vdgf@�üo�EMc°tL�V[UEMdgCIZ�mU��HKt/�8}��×�6cfDtMCIcK[eHUEMduCIZDm���Het/� ZDsgEMcK[edgf&cefDE�[e[eZDHKdgC��ÜGIceduC��ÜE k"ZA���LZ�sgdgY�Z&bFEMHeE�� Zw[UZ�HedgBDE�[UdutLCO?����IZ?�FtLGVHedgZ�Ha[UHeEMCIc\���tLHM� t�� [e�IZ�}��×� �LdÕ�LZ�ca[U�IZ©mVdgcK[eHedu�IGV[UdutLCít��[e�IZ&dE�ÜbFEMfw[abFE�HUE��ÜZ�[eZDH & ;�(OduC�[U�IZ©[eHUEMCVcK�LZ�HecKZ=bVs~EMCIZ��cD?n[U�VZ=sutLC��LdÕ[UGImVdgCFEMs �Üt/� Z�CÊ[UG�� ��HUEMfw[UdgtMCONId�?jZM?

HM(~b⊥, x)NIEMsgcKtÜcK�It²o"CîduC���dE�I?]Y���?

HM(x,~b⊥) =

d2(~q⊥)

2π2ei(~b⊥·~q⊥)HM(−~q2

⊥, x, 0).

���IZqEMbIbIsudgf]EÃ[UdgtMCÜt��O[U�IZ©}=�¸� ��tMH4� EMsgduc4�ßEMCIm�C�GIf�sgZDtMC�Z-,vfDdÕ[@E�[edgtLCÜdgcD�ÜtLcK[¬HeZDEMmIdgsÕJ2ceZ�ZDC�duC [U�VZ

J = 1/2 → 1/2[UHeEMCIcKdu[UdutLCIc�cKGIf@�äEMc�[e�IZ

N → P11(1440)tLHa[U�IZ

S11(1535)?

��� �N → P11 ���������� �

^vduCIfDZ&[U�VZN → P11(1440)

dgc"E1/2+ → 1/2+ [eHUEMCIcKdu[edgtLCONvdu[ec°f�GIHeHKZDCÊ[6cK[UHKGIf�[eGIHeZ=dgc�cKdE�ÜdgsgEMH¬[et

3x

Page 29: ;69 /0 1 &< 25 ( 2= /> @?A2) CB+2=2D FE( (< HGI /J K % 2D ...boson.physics.sc.edu/~gothe/research/pub/white-paper-09.pdfo"dgsus×bVHet² dgmIZ CVZ o dgC tLH M íEÃ[UdgtMCÛtMC

��OH!���<DA��y\���B��yb8,��'n�oT�6�5�')X ��'n����'n�o;n��SVcn;"c)8,� 0 ��')z 0*%�6�cn��'G∗

M

��/�ce%(dS,�oT�/V� ��_{�b5,;)dS�Q^% Wh��QEQ ���d1 ��$%('e%(z���cn��')d�{%(c)d���S �0-c)8,������%�;nc)d�6�d�;n�{X �o6�cn��' 0 ��')z 0�%�6�cn��'�%(�����d��oT cn��c)8,�

N → ∆c)'e%(S,;)dc)d���SB� t���c)cn��zG�

yb8,�&TAd�;)c)')d/�5�c)d���S^�0 c)8,��c)'e%(S,;nX ��'n;n��dz��$%�6�c-�$%('e%(z���cn��' ~b⊥%(S,Tr����S�QEdc)5,TAdS$%(� dz���z���SVc)5�zG�

ZDsgEMcK[edgf&cKf]E�[K[UZDHKdgC��VNId�?jZM?

ΓµP11 =

F P111 (q2)

M2N

(

q2γµ− 6 qqµ)

+F P11

2 (q2)

2MN

iσµνqν

o"�Iduf@��dE��� Z�mId~E�[eZDsÕJ�sgZDEMmIc°[Ut�E�}��¸� cK[UHKGIf�[eGIHeZSEMCIm�HeZ�s~E�[eZDm3��tMH4� ��EMf�[etLHec6Z-,VEMfw[UsuJîEMc©duCîZ�s~EMc\[UdgfcefDE�[e[eZDHKdgC��Iû

P+

dy−eixP+y− 〈P11(p′)| ψP11 (−y/2) γνnνψ (y/2) |N(p)〉

y+=~y⊥=0

=

HP11u(p′)

(q2γµ− 6 qqµ)nµ

M2N

u(p) + EP11u(p′)iσµν nµqν

2MN

u(p)! :�#

�;

Page 30: ;69 /0 1 &< 25 ( 2= /> @?A2) CB+2=2D FE( (< HGI /J K % 2D ...boson.physics.sc.edu/~gothe/research/pub/white-paper-09.pdfo"dgsus×bVHet² dgmIZ CVZ o dgC tLH M íEÃ[UdgtMCÛtMC

F q1P11

(t) =

HqP11

(x, ξ, t)dx F q2P11

(t) =

EqP11

(x, ξ, t)dx

y9"&2�� → _11

����������� ���IZS11(1535)

�FE�cJπ = 1/2−

EMCIméducÜ[e�IZäf@�IduHUEMs"CIZ��ÊE�[edu�LZübFEMHKdu[�JbFEMH\[UCIZ�H"t���[e�IZ�C�GIfDsuZDtLCO?¸���IZ�f�GIHeHKZDCÊ[qc\[UHKGIf�[eGIHeZ��FEMc°EMC�Z-,�[eHUE

γ5

EMCVmüfDEMCü�:Z&o"HedÕ[e[UZ�C

ΓµS11 =

F S111 (q2)

M2N

(

q2γµ− 6 qqµ)

γ5 +F S11

2 (q2)

2MNiσµνqνγ5

o"�Iduf@�üsuZ]EMmIca[et

P+

dy−eixP+y− 〈S11(p′)| ψS11 (−y/2) γνnνψ (y/2) |N(p)〉

y+=~y⊥=0

=

HS11u(p′)

(q2γµ− 6 qqµ)nν

M2N

γ5u(p) + ES11u(p′)iσµνγ5

qνnν

2MN

u(p)!1e/#

o"du[e�

F q1S11

(t) =

HqS11

(x, ξ, t)dx F q2S11

(t) =

EqS11

(x, ξ, t)dx

y9"&2 � → Λ � Σ� �6EMHem Z-,vfDsuGIcedÕ�LZîbVHet�fDZDcKceZ�cío"du[e� cK[eHUEMC��LZDCIZ�cec�bIHKtvmVGIf�[edgtLC oaE�c [UHKZ]E�[eZDméduC

k"Z���cD? & k+(:EMCIm & l�(�N�dgC2o"�Iduf@�íZ�._ZDfw[Uc¬HeZDsgE�[UZ�mÜ[etSU(3)

IFE²�MtLH×cKJ �'�ÜZ�[eHKJÊ���VHeZ]E�Y�duC��,EMHeZ°mIducefDGVceceZ�mO?���IZ{}��¸�qc©f�tLHeHKZDceb:tLCImä[et [e�IZSbIHKtvf�ZDcec6o"�IZDHKZ2EíCItLC���cK[eHUEMC��LZ ��GFEMHKYüduc°[UEMYMZ�C�tLGV[qt��n[U�IZ,dgCIdÕ[UdgEMsC�GIfDsuZDtLC{EÃ[-[U�VZacebFE�fDZw��[Ud�� Z¬b_tLduCÊ[

y/2NMEMCIm'[e�IZDCÜEqc\[UHeEMC��LZF��GFE�HeY=dgc�bIGv[n�FEMf@Y=Z-,vfDdÕ[UduC��&Eq�ÊJ�b_Z�HetLC

E�[©[e�IZ2cebIEMfDZ��¹[Ud�� Z'b_tLduCÊ[ |y/2 ?��FtLsusgt²o"dgC��ík"Z��Í? & k�(�[U�IZ2c\[UHUE�C��LZDCVZDcec=f@�FEMC��LdgC���mVdgcK[eHedu�IGV[UdutLCIc ��tLH

N → Σ,Λ[UHeEMCIcedÕ[UdutLCIcDû

P+

dy−eixP+y− 〈Y (p′)| ψ (−y/2) as (−y/2) γνnνaq (y/2)ψ (y/2) |N(p)〉∣

y+=~y⊥=0

=

HN→Y u(p′)

(q2γµ− 6 qqµ)nν

M2N

γ5u(p) + EN→Y u(p′)iσµνγ5

qνnν

2MN

u(p)! x�#

o"�IZ�HeZas

dgcq[e�IZ2fDHKZ]E�[edgtLC�tMb_Z�HUE�[etLH©t��¬E�cK[eHUEMC��LZ ��GFEMHeYäEMCImaq

[U�IZÜEMCVCIdg�Idus~E�[edgtLC�tLb:ZDHeE�[UtLH6t���ECItLC���cK[eHUEMC��LZG��GIEMHeYhN

utMHdNFE�[ −y/2 EMCIm y/2 NVHKZDceb:ZDfw[UdÕ�LZDsÕJL?

.;�(<�"��[6#����2N_��- `[��E�2D% � .{6H_I` �

�L

Page 31: ;69 /0 1 &< 25 ( 2= /> @?A2) CB+2=2D FE( (< HGI /J K % 2D ...boson.physics.sc.edu/~gothe/research/pub/white-paper-09.pdfo"dgsus×bVHet² dgmIZ CVZ o dgC tLH M íEÃ[UdgtMCÛtMC

���IZ{��dE�M��[\�\`�tLCVZ{^vG�� k"GIsuZ�!��`�^VkH#©EMbIbIHKtÊEMf@�ÛEMsusgt²o"c©tLCIZS[et�f]EMsufDGIsgE�[UZ*��tLH4� ��EMf�[etLHec8!�EMCImONb:tM[UZ�C�[ed~EMsusuJMNIEMsucet }=�¸�qcC#"GVcedgC��'�SGVf@�I�ÜtLHeZ�sudE�Üdu[UZ�m�dgC���tLH4� E�[UdutLCíf�t/�ÜbFEMHeZ�m�[etÜ[e�IZ@��GIsgs�CVtLCIb:ZDH\�[UGVHe�FE�[edu�MZ©oaE]�LZG��GICIfw[UdutLCIcDNIEMsg�:ZDdÕ[ao"du[e��cet/�ÜZ�EMcecKG��ÜbV[UdutLCIcD?n���VZ>�MHetLGICVmVo�tMHeY�t��[U�VZ@� Zw[U�It�m�t���`�^Vk"c=o�EMc'sgEMdgm duC & L�(�?U�FtLsusgt²o"dgC���[e�IZ{o�tLHKY9& Y��<(×mIZ��MtM[UZ�m [UtüZDsgZ�f�[eHet/� E��LCIZw[Uduf2C�GVfDsgZ�tLCB��tMH4���EMfw[UtLHKc�[U�IZ

Nγ∆[UHUE�CIcedÕ[UdgtMCIc-o¬ZDHeZ°fDtMCIcedumIZDHKZDmÜdgCU& Y�Y�(:EMCIm2[e�IZ

N → S11[eHUEMCIcKdu[edgtLCIc-dgCU& Y� �NVY�k+(�?

�`�^Vk"c°�IE²�MZ'E�sgcet{�:ZDZ�CîEMbVbIsgduZDm�[Ut{[U�VHeZDcK�ItLsum�bVdgtLC�ZDsuZDfw[UHetMbIHet�mIGIfw[UdgtMCL& Y'lVNY�:<(�?�FtLHaZ0,IE�� bIsuZMNIduC�tLHemIZ�H�[Ut{f]EMsufDGIsgE�[UZ6[U�IZ&[UHeEMCIcKdu[UdutLC�E��ÜbIsgdÕ[UGImVZ

NS11 (P ′)∣

∣jemµ

∣N (P )⟩

= NS11 (P ′)

(

F S111 (q2)

(q2γµ− 6 qqµ)

M2N

F S112 (q2)iσµν

2MN

)

γ5N (P )! ; #

tLCIZ�f�tLCIcedumIZDHKc�[U�IZ�fDtMHeHeZ�s~E�[edgtLC"��GVCIf�[edgtLC

dx e−iqx〈S11(P ′)|T{η(0)jemµ (x)}|0〉

dgCüo"�Idgf@�ηdgc©E ceGIdÕ[@EM�IsuZ'tMb_Z�HUE�[etLH6o"dÕ[U�äC�GIf�sgZDtMC ��GFE�C�[eG��<C�G��'�_Z�HecD?&A b_tLbVGIs~EMH6f@�ItLdufDZSducDN ��tMH

Z-,VE��ÜbIsuZ

η(0) = εijk(uiCγµuj)(0)γ5γµdk(0)

!1L/#

o"�IZ�HeZui,j(0)

EMCImdk(0)

EMHKZ6Gv� ��GFEMHeYÜEMCVmímv� ��GIEMHeY��FZ�sgm tLb_Z�HUE�[etLHec�Ni, j, k = 1, . . . , 3

dgc¸[U�IZ6fDtLsutLHdgCVmIZ-, �

Cduca[U�IZ�f@�FEMHM�LZ�fDtLC � G��ÊE�[edgtLC�� E�[UHKd ,_?����IZ�ZDsuZDfw[UHet��íE��MCIZ�[edgf©f�GIHeHKZDCÊ[qduc

jemµ (x) = euu(x)γµu(x) + edd(x)γµd(x) + ess(x)γµs(x)

! Y��/#

zîEMY�duC��SGIcKZ©t���[U�VZ©mIGFEMsudu[�JÜt�����`a����GFEMHKYÊ� �LsgGVtLC�EMCImí�FEMmIHKtLCIdgf6mIZA�MHeZDZ�c�t�� ��HeZ�ZDmIt�� [U�VHetLG��M�mIduceb:ZDHecKdgtLCüHeZ�s~E�[edgtLCIc°tLCIZ,f]EMCäo"HKdu[eZSE HKZDbIHKZDcKZDCÊ[@E�[edgtLC���tMH6[U�VZ*��tLHM� ��E�f�[UtMHec©E�bIb_ZDEMHeduC��íduCR! ; #°duC[UZ�H4�ÜcSt��"[U�VZ�mIdgc\[UHedu�IGV[edgtLC E�� bVsgdu[eGImIZ�c"!��"A6c$#St��"[U�VZ

S11

HeZDcKtLCFEMCVfDZM?|���IZDcKZ��"A6c{fDtLHKHeZDcKb_tMCIm[Ut�[e�IZ � t�� Z�C�[eG�� ��HUEMfw[UdgtMC�mIdgc\[UHedu�IGV[edgtLCIc6t��¸[U�IZ2[e�IHeZ�Z ��GIEMHeY�c�dgCä[e�IZ

S11EÃ[�c4� EMsgs [UHeEMCIcK�MZDHKceZ

ceZ�bFEMHeE�[UdutLCIcD?IO6CVsgdgY�Z [e�IZS11

o�E]�LZ"��GICVf�[UdutLCIc=[U�IZ�� cKZDsu�MZDc�N�[U�IZí�"A6cSf]E�C �_ZíEMfDf�ZDcKceZDm [U�VHetLG��M�s~EÃ[e[UdufDZ©fDEMsgf�GIs~EÃ[UdgtMCIcD?

���IZ sgZDEMmIduC�� [�o"dgc\[K� k C�GIf�sgZ�tLCJ!�bIHet�[UtLC #���A f]E�C �:Z mIZ��ICIZDmæEMc�ER�íE�[eHed ,éZ�sgZA�ÜZDCÊ[�t��=[U�VZCItLCVsgt�f]EMs_sgdE�M��[\��HeE²JÜtLb:ZDHeE�[UtMH�[U�FEÃ[�dgCÊ�LtMsu�LZ�c2��GIEMHeY��FZDsumIc�t�� �Ldu�MZDC��IZ�sgdgf�du[�J

q↑(↓) = (1/2)(1± γ5)q

k3�

Page 32: ;69 /0 1 &< 25 ( 2= /> @?A2) CB+2=2D FE( (< HGI /J K % 2D ...boson.physics.sc.edu/~gothe/research/pub/white-paper-09.pdfo"dgsus×bVHet² dgmIZ CVZ o dgC tLH M íEÃ[UdgtMCÛtMC

〈0|εijk(

u↑i (a1n)C 6nu↓j(a2n))

6nd↑k(a3n)|N(P )〉 =

= −1

2fN pn 6nu↑N(P )

[dx] e−ipnP

xiai ϕN(xi) .! Y3Y<#

�6Z�HeZPµ

NP 2 = m2

N

N�dgc¸[U�IZ6bIHet�[UtLC'� t/�ÜZDCÊ[eG��üNuN(P )

dgc¬[e�IZqGVceGFEMs_�qduHUEMf°cebIduCItLH×dgC HeZDsgE�[UdÕ��dgcK[edgfCItLHM�íE�sgdgBDE�[UdutLCON

EMC|EMHe�IdÕ[UHeEMHKJ�sudE�L�Ê[\��sgduYMZ'�MZDfw[UtLH�o"du[e�n2 = 0

N-EMc=mIZ-�FCIZDm EM�_t²�MZMN�E�CImC[e�IZ

f@�FEMHM�LZw�¹fDtLC � G��ÊE�[edgtLC�íE�[eHed ,�?����VZü��EMHedgEM�IsuZDcx1, x2, x3

�IE²�MZî[U�VZ3�ÜZ]EMCIduC�� t��©[U�IZI� t�� Z�C�[eG����HUE�f�[UdutLCIc�fDEMHeHKdgZDm �ÊJ�[U�IZ�[e�IHeZ�ZÛ��EMsuZDCIf�Z ��GFE�HeY�cîE�CIm [e�IZÛdgCÊ[UZ��LHUE�[edgtLC �ÜZ]E�ceGIHKZÛduc�mIZ��FCVZDm*E�c∫

[dx] =∫ 1

0dx1dx2dx3δ(

xi−1)?-���VZ�� dgsucetLC=sgduCIZDc�[U�IE�[-Z�CIceGVHeZF�ÊE�G��LZ×dgCÊ��EMHedgEMCIfDZ×EMHKZ¬duCIceZ�HK[eZDm

�:Z�[�o¬ZDZDCü[U�IZG��GFEMHKY�c&�I[U�IZwJ�EMHeZ&CVtM[°ce�It²o"CI��tMH��IHeZw�vdÕ[�JL?���IZ�mIZ-�FCIdu[edgtLC�duCB! Y3Y<#�duc�ZA��GIdÕ�ME�sgZDCÊ[�[etÜ[e�IZ@��tLsgsutºo"duC��*��tMH4��t��[U�VZ���EMsuZDCIf�Z&bIHet�[UtLC�cK[UE�[UZ

|p, ↑〉 = fN

[dx]ϕN(xi)

2√

24x1x2x3

{

|u↑(x1)u↓(x2)d

↑(x3)〉 − |u↑(x1)d↓(x2)u

↑(x3)〉}

,! Y� /#

o"�IZ�HeZS[U�VZ2EMHeHKt²o"c&dgCImIduf]E�[eZ=[e�IZS�IZ�sgdufDdu[edgZ�cqEMCVmä[U�IZSc\[@EMCVmFEMHem�HKZDsgE�[UdÕ�vducK[edgf=CItLH4� EMsudgB]EÃ[UdgtMC���tMH6[U�VZcK[UE�[UZ�c°EMCImü�qdgHeEMf&cebIduCItLHKc°duc�dE�ÜbIsgduZDmO?

���IZ�CItMCIsgt�f]EMs×tLb:ZDHeE�[UtLHSEMbIb:Z]EMHKdgC��ätMC [e�IZ�s�?j�O?jcD?Ût�� ! Y3Y #,mIt�ZDc2CItM[S�FE]�LZ�EämIZ��ICIdu[eZ�bFEMHedÕ[�JL?����GIcí[e�IZîceE�� Z�tLb:ZDHeE�[UtLHÜfDtMGIbIsgZ�cíE�sgcetÛ[Ut

N∗(1535)EMCImétLCVZüfDEMCémIZ-�FCIZî[e�IZîf�tLHeHKZDceb:tLCImVdgC��

sgZDEMmIduC����¹[�o"ducK["��AïEMc

〈0|εijk(

u↑i (a1n)C 6nu↓j(a2n))

6nd↑k(a3n)|NS11(P )〉 =

=1

2fN∗ pn 6nu↑S11(P )

[dx] e−ipnP

xiai ϕS11(xi)! Y�k #

o"�IZ�HeZMNvt���f�tLGIHecKZMNP 2 = m2

N∗

?n���IZqCItMH4� EMsgduB]E�[edgtLCSf�tLCIc\[@EMCÊ[UcfN

NfN∗

EMHKZ6mVZ��FCIZ�m�ceGIf@� [U�FE�[×[U�VZ��Aqc6EMHeZ&CVtLH4� EMsgduBDZ�m�[Ut{GICIdÕ["dgCÊ[UZ��LHUEMs�û

[dx] ϕ(xi) = 1 .! Y'l #

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