towards a combined analysis of inclusive/exclusive ......rpp!3 a. n. hiller blin ghp workshop...

Towards a combined analysis of inclusive/exclusive electroproduction

Astrid N. Hiller Blin Johannes Gutenberg University Mainz

in collaboration with M. Vanderhaeghen and Hall B

CLAS/CLAS12 physics program

GHP Workshop Denver, CO 2019-04-12

P CJ A

Interest in inclusive electron scattering

• CLAS(12) inclusive F2 data:Will reach 0.05 GeV2 < Q2 < 12 GeV2

and W up to 4 GeV

• Resonance regime well covered:towards parton distributions at large x

• Combining high and low-energy models: tests on quark-hadron duality

• Enables description of observables integrated over range of energies:Cottingham formula, subtraction function in VVCS

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10F 2

W [GeV]

Q2=1.0 GeV2

CLAS dataHigh-energy model (DL)Low-energy model (BC)

BC: Christy and Bosted, PRC 86 (2010) 055213DL: Donnachie and Landshoff, PLB 595 (2004) 393

CLAS data: http://clas.sinp.msu.ru/strfun/

X

p

e−

!2A. N. Hiller Blin GHP Workshop 2019-04-12

Exclusive electron scattering

• Connection with CLAS(12) exclusive electrocouplings

• Longitudinal and transverse couplings of separate resonances available

• Allows to separate the resonant and non-resonant contributions

N*

p

e−

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Δ(1232)3/2+

Fit error estimateFit central curve

CLASHall CMAMI

MIT/BatesHall A

Hall A 2007RPP


Exclusive to inclusive electron scatteringPrecise low-energy CLAS(12) data on inclusive electron scattering

F1(⌫, q2) / �T (⌫, q

2)<latexit sha1_base64="5voc8r5X1+mSJqPrMpn2xS2ifu8=">AAACDHicbVDLSsNAFJ3UV62vqEs3wSpUkJIUQd0VBXFZobGFJobJdNIOnczEmYlQQn/Ajb/ixoWKWz/AnX/jtA2i1QMXDufcy733hAklUtn2p1GYm19YXCoul1ZW19Y3zM2ta8lTgbCLOOWiHUKJKWHYVURR3E4EhnFIcSscnI/91h0WknDWVMME+zHsMRIRBJWWAnPvInAqHksPb29qB14ieKK4J0kvhkHzWw/Msl21J7D+EicnZZCjEZgfXpejNMZMIQql7Dh2ovwMCkUQxaOSl0qcQDSAPdzRlMEYSz+bfDOy9rXStSIudDFlTdSfExmMpRzGoe6MoerLWW8s/ud1UhWd+BlhSaowQ9NFUUotxa1xNFaXCIwUHWoCkSD6Vgv1oYBI6QBLOgRn9uW/xK1VT6vO1VG5fpanUQQ7YBdUgAOOQR1cggZwAQL34BE8gxfjwXgyXo23aWvByGe2wS8Y71/QRJpX</latexit><latexit sha1_base64="5voc8r5X1+mSJqPrMpn2xS2ifu8=">AAACDHicbVDLSsNAFJ3UV62vqEs3wSpUkJIUQd0VBXFZobGFJobJdNIOnczEmYlQQn/Ajb/ixoWKWz/AnX/jtA2i1QMXDufcy733hAklUtn2p1GYm19YXCoul1ZW19Y3zM2ta8lTgbCLOOWiHUKJKWHYVURR3E4EhnFIcSscnI/91h0WknDWVMME+zHsMRIRBJWWAnPvInAqHksPb29qB14ieKK4J0kvhkHzWw/Msl21J7D+EicnZZCjEZgfXpejNMZMIQql7Dh2ovwMCkUQxaOSl0qcQDSAPdzRlMEYSz+bfDOy9rXStSIudDFlTdSfExmMpRzGoe6MoerLWW8s/ud1UhWd+BlhSaowQ9NFUUotxa1xNFaXCIwUHWoCkSD6Vgv1oYBI6QBLOgRn9uW/xK1VT6vO1VG5fpanUQQ7YBdUgAOOQR1cggZwAQL34BE8gxfjwXgyXo23aWvByGe2wS8Y71/QRJpX</latexit><latexit sha1_base64="5voc8r5X1+mSJqPrMpn2xS2ifu8=">AAACDHicbVDLSsNAFJ3UV62vqEs3wSpUkJIUQd0VBXFZobGFJobJdNIOnczEmYlQQn/Ajb/ixoWKWz/AnX/jtA2i1QMXDufcy733hAklUtn2p1GYm19YXCoul1ZW19Y3zM2ta8lTgbCLOOWiHUKJKWHYVURR3E4EhnFIcSscnI/91h0WknDWVMME+zHsMRIRBJWWAnPvInAqHksPb29qB14ieKK4J0kvhkHzWw/Msl21J7D+EicnZZCjEZgfXpejNMZMIQql7Dh2ovwMCkUQxaOSl0qcQDSAPdzRlMEYSz+bfDOy9rXStSIudDFlTdSfExmMpRzGoe6MoerLWW8s/ud1UhWd+BlhSaowQ9NFUUotxa1xNFaXCIwUHWoCkSD6Vgv1oYBI6QBLOgRn9uW/xK1VT6vO1VG5fpanUQQ7YBdUgAOOQR1cggZwAQL34BE8gxfjwXgyXo23aWvByGe2wS8Y71/QRJpX</latexit><latexit sha1_base64="5voc8r5X1+mSJqPrMpn2xS2ifu8=">AAACDHicbVDLSsNAFJ3UV62vqEs3wSpUkJIUQd0VBXFZobGFJobJdNIOnczEmYlQQn/Ajb/ixoWKWz/AnX/jtA2i1QMXDufcy733hAklUtn2p1GYm19YXCoul1ZW19Y3zM2ta8lTgbCLOOWiHUKJKWHYVURR3E4EhnFIcSscnI/91h0WknDWVMME+zHsMRIRBJWWAnPvInAqHksPb29qB14ieKK4J0kvhkHzWw/Msl21J7D+EicnZZCjEZgfXpejNMZMIQql7Dh2ovwMCkUQxaOSl0qcQDSAPdzRlMEYSz+bfDOy9rXStSIudDFlTdSfExmMpRzGoe6MoerLWW8s/ud1UhWd+BlhSaowQ9NFUUotxa1xNFaXCIwUHWoCkSD6Vgv1oYBI6QBLOgRn9uW/xK1VT6vO1VG5fpanUQQ7YBdUgAOOQR1cggZwAQL34BE8gxfjwXgyXo23aWvByGe2wS8Y71/QRJpX</latexit>

F2(⌫, q2) / �T (⌫, q

2) + �L(⌫, q2)

<latexit sha1_base64="SZ5DpE8YoHOLe+BRfmRBxlbz8hQ=">AAACHnicbZDLSsNAFIYn9VbrLerSTbAIFaUkRbzsioK4cFGhtYUmhsl00g6dzMSZiVBK38SNr+LGhYrgSt/GaRuKtv4w8POdczhz/iCmRCrb/jYyc/MLi0vZ5dzK6tr6hrm5dSt5IhCuIU65aARQYkoYrimiKG7EAsMooLgedC+G9foDFpJwVlW9GHsRbDMSEgSVRr55fOmXCi5LDu/vSvtuLHisuCtJO4J+dcIPUnI9Ib6Zt4v2SNascVKTB6kqvvnptjhKIswUolDKpmPHyutDoQiieJBzE4ljiLqwjZvaMhhh6fVH9w2sPU1aVsiFfkxZI/p7og8jKXtRoDsjqDpyujaE/9WaiQpPvT5hcaIwQ+NFYUItxa1hWFaLCIwU7WkDkSD6rxbqQAGR0pHmdAjO9MmzplYqnhWdm6N8+TxNIwt2wC4oAAecgDK4AhVQAwg8gmfwCt6MJ+PFeDc+xq0ZI53ZBn9kfP0AmmuhDA==</latexit><latexit sha1_base64="SZ5DpE8YoHOLe+BRfmRBxlbz8hQ=">AAACHnicbZDLSsNAFIYn9VbrLerSTbAIFaUkRbzsioK4cFGhtYUmhsl00g6dzMSZiVBK38SNr+LGhYrgSt/GaRuKtv4w8POdczhz/iCmRCrb/jYyc/MLi0vZ5dzK6tr6hrm5dSt5IhCuIU65aARQYkoYrimiKG7EAsMooLgedC+G9foDFpJwVlW9GHsRbDMSEgSVRr55fOmXCi5LDu/vSvtuLHisuCtJO4J+dcIPUnI9Ib6Zt4v2SNascVKTB6kqvvnptjhKIswUolDKpmPHyutDoQiieJBzE4ljiLqwjZvaMhhh6fVH9w2sPU1aVsiFfkxZI/p7og8jKXtRoDsjqDpyujaE/9WaiQpPvT5hcaIwQ+NFYUItxa1hWFaLCIwU7WkDkSD6rxbqQAGR0pHmdAjO9MmzplYqnhWdm6N8+TxNIwt2wC4oAAecgDK4AhVQAwg8gmfwCt6MJ+PFeDc+xq0ZI53ZBn9kfP0AmmuhDA==</latexit><latexit sha1_base64="SZ5DpE8YoHOLe+BRfmRBxlbz8hQ=">AAACHnicbZDLSsNAFIYn9VbrLerSTbAIFaUkRbzsioK4cFGhtYUmhsl00g6dzMSZiVBK38SNr+LGhYrgSt/GaRuKtv4w8POdczhz/iCmRCrb/jYyc/MLi0vZ5dzK6tr6hrm5dSt5IhCuIU65aARQYkoYrimiKG7EAsMooLgedC+G9foDFpJwVlW9GHsRbDMSEgSVRr55fOmXCi5LDu/vSvtuLHisuCtJO4J+dcIPUnI9Ib6Zt4v2SNascVKTB6kqvvnptjhKIswUolDKpmPHyutDoQiieJBzE4ljiLqwjZvaMhhh6fVH9w2sPU1aVsiFfkxZI/p7og8jKXtRoDsjqDpyujaE/9WaiQpPvT5hcaIwQ+NFYUItxa1hWFaLCIwU7WkDkSD6rxbqQAGR0pHmdAjO9MmzplYqnhWdm6N8+TxNIwt2wC4oAAecgDK4AhVQAwg8gmfwCt6MJ+PFeDc+xq0ZI53ZBn9kfP0AmmuhDA==</latexit><latexit sha1_base64="SZ5DpE8YoHOLe+BRfmRBxlbz8hQ=">AAACHnicbZDLSsNAFIYn9VbrLerSTbAIFaUkRbzsioK4cFGhtYUmhsl00g6dzMSZiVBK38SNr+LGhYrgSt/GaRuKtv4w8POdczhz/iCmRCrb/jYyc/MLi0vZ5dzK6tr6hrm5dSt5IhCuIU65aARQYkoYrimiKG7EAsMooLgedC+G9foDFpJwVlW9GHsRbDMSEgSVRr55fOmXCi5LDu/vSvtuLHisuCtJO4J+dcIPUnI9Ib6Zt4v2SNascVKTB6kqvvnptjhKIswUolDKpmPHyutDoQiieJBzE4ljiLqwjZvaMhhh6fVH9w2sPU1aVsiFfkxZI/p7og8jKXtRoDsjqDpyujaE/9WaiQpPvT5hcaIwQ+NFYUItxa1hWFaLCIwU7WkDkSD6rxbqQAGR0pHmdAjO9MmzplYqnhWdm6N8+TxNIwt2wC4oAAecgDK4AhVQAwg8gmfwCt6MJ+PFeDc+xq0ZI53ZBn9kfP0AmmuhDA==</latexit>

σRU(W, Q2) = σR

T (W, Q2) + ϵTσRL (W, Q2)

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σU

[µb]

W [GeV]

Q2 = 2 GeV2

1σ bandResonant

Data interpolation


�T,L(W,Q2) = �RT,L(W,Q2) + �NR

T,L(W,Q2)


F1(⌫, q2) / �T (⌫, q


F2(⌫, q2) / �T (⌫, q

2) + �L(⌫, q2)


σRU(W, Q2) = σR


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σU

[µb]

W [GeV]

Q2 = 2 GeV2

1σ bandResonant

Data interpolation


Breit-Wigner resonance model

σRT,L(W, Q2) =

πq2

γ ∑N*,Δ*

(2Jr + 1)M2

r Γtot(W )ΓT,Lγ (Mr)

(M2r − W2)2 + M2

r Γ2tot(W )

�T,L(W,Q2) = �RT,L(W,Q2) + �NR

T,L(W,Q2)

Mokeev et al., PRC 86 (2012) 035203


F1(⌫, q2) / �T (⌫, q


F2(⌫, q2) / �T (⌫, q

2) + �L(⌫, q2)


σRU(W, Q2) = σR


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σU

[µb]

W [GeV]

Q2 = 2 GeV2

1σ bandResonant

Data interpolation


Electrocouplings for resonance contribution

σRT,L(W, Q2) =

πq2

γ ∑N*,Δ*

(2Jr + 1)M2


(M2r − W2)2 + M2

r Γ2tot(W )



σRT,L(W, Q2) =

πq2

γ ∑N*,Δ*

(2Jr + 1)M2


(M2r − W2)2 + M2

r Γ2tot(W )

Electrocouplings from CLAS(12) exclusive datahttps://userweb.jlab.org/∼isupov/couplings/https://userweb.jlab.org/~mokeev/resonance_electrocouplings/ ΓL

γ (Mr, Q2) ∼ S1/2(Q2)2

ΓTγ (Mr, Q2) ∼ A1/2(Q2)

2+ A3/2(Q2)

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Q2[GeV2]

Δ(1232)3/2+


CLASHall CMAMI

MIT/BatesHall A

Hall A 2007RPP



σRT,L(W, Q2) =

πq2

γ ∑N*,Δ*

(2Jr + 1)M2


(M2r − W2)2 + M2

r Γ2tot(W )

Electrocouplings from CLAS(12) exclusive datahttps://userweb.jlab.org/∼isupov/couplings/https://userweb.jlab.org/~mokeev/resonance_electrocouplings/

Allows to determine the resonant contributions from exclusive data to inclusive scattering

ΓLγ (Mr, Q2) ∼ S1/2(Q2)

2

ΓTγ (Mr, Q2) ∼ A1/2(Q2)

2+ A3/2(Q2)

2

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0 1 2 3 4 5 6

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1/2

[GeV

-1/2

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Q2[GeV2]

Δ(1232)3/2+


CLASHall CMAMI

MIT/BatesHall A

Hall A 2007RPP 0

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σU

[µb]

W [GeV]

Q2 = 1 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total


Electrocoupling data input: examples

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Δ(1232)3/2+


CLASHall CMAMI

MIT/BatesHall A

Hall A 2007RPP

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eV-1

/2]

Q2[GeV2]

N(1440)1/2+


CLASHall A

RPP

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103 A

1/2

[GeV

-1/2

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Q2[GeV2]

N(1535)1/2-


CLASE94014

Hall ARPP

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103 S

1/2

[GeV

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Q2 [GeV2]

N(1680)5/2+


CLASMAIDHall A

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1/2

[GeV

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Q2 [GeV2]

Δ(1620)1/2-


CLAS-40

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1/2

[GeV

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Q2 [GeV2]

N(1720)3/2+


CLAS

https://userweb.jlab.org/~mokeev/resonance_electrocouplings/

Interpolation functions with error bars estimated from data uncertaintieshttps://userweb.jlab.org/∼isupov/couplings/


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σU

[µb]

W [GeV]

Q2 = 4 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

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σU

[µb]

W [GeV]

Q2 = 1 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

Resonance contribution to inclusive scattering

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σU

[µb]

W [GeV]

Q2 = 0.5 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

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σU

[µb]

W [GeV]

Q2 = 3 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total


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σU

[µb]

W [GeV]

Q2 = 4 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

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120

140

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σU

[µb]

W [GeV]

Q2 = 1 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

Resonance contribution to inclusive scattering

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300

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σU

[µb]

W [GeV]

Q2 = 0.5 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

Tails of resonances give substrantial contributions to neighboring regions!

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σU

[µb]

W [GeV]

Q2 = 3 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total


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σU

[µb]

W [GeV]

Q2 = 5 GeV2

1σ bandResonant

Data extrapolation

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σU

[µb]

W [GeV]

Q2 = 2 GeV2

1σ bandResonant

Data interpolation 0

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25

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σU

[µb]

W [GeV]

Q2 = 3 GeV2

1σ bandResonant

Data interpolation

Inclusive unpolarized cross sections

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σU

[µb]

W [GeV]

Q2 = 4 GeV2

1σ bandResonant

Data interpolation

https://clasweb.jlab.org/physicsdb/Golubenko et al., 1902.02900 [hep-ex]


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σU

[µb]

W [GeV]

Q2 = 5 GeV2

1σ bandResonant

Data extrapolation

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σU

[µb]

W [GeV]

Q2 = 2 GeV2

1σ bandResonant

Data interpolation 0

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σU

[µb]

W [GeV]

Q2 = 3 GeV2

1σ bandResonant

Data interpolation

Inclusive unpolarized cross sections

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12

14

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

σU

[µb]

W [GeV]

Q2 = 4 GeV2

1σ bandResonant

Data interpolation

https://clasweb.jlab.org/physicsdb/Golubenko et al., 1902.02900 [hep-ex]

Second resonance region decreases less with Q2


0

0.05

0.1

0.15

0.2

0.25

0.3

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

π+π- N η N

π N(1520) 3/2-

ρ N ω N

π N(1680) 5/2+

F 2

W [GeV]

Q2=1.5 GeV2

Data - resonancesBC NR

0

0.05

0.1

0.15

0.2

0.25

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

π+π- N η N

π N(1520) 3/2-

ρ N ω N

π N(1680) 5/2+

F 2

W [GeV]

Q2=2.0 GeV2


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

π+π- N η N

π N(1520) 3/2-

ρ N ω N

π N(1680) 5/2+

F 2

W [GeV]

Q2=3.0 GeV2


0

0.02

0.04

0.06

0.08

0.1

0.12

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

π+π- N η N

π N(1520) 3/2-

ρ N ω N

π N(1680) 5/2+

F 2

W [GeV]

Q2=4.0 GeV2


First estimates to backgroundBC: Christy and Bosted, PRC 86 (2010) 055213


Background continuation to high energies

�T,L(W,Q2) = �RT,L(W,Q2) + �NR

T,L(W,Q2)

Regge background


Donnachie and Landshoff, PLB 595 (2004) 393

HERA data


F2(x,Q2) = fh(Q

2)x�✏h + fs(Q2)x�✏s + fr(Q

2)x�✏r<latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit><latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit><latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit><latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">AAACO3icbZBLS8NAFIUn9VXrK+rSTbAoFbUkRVAXQlEQly1aW+gjTKaTZujkwcxEWkJ+mBt/hDtXblyouHXvpM1CGw8MHL57L3fusQJKuND1FyU3N7+wuJRfLqysrq1vqJtb99wPGcIN5FOftSzIMSUebggiKG4FDEPXorhpDa+SevMBM058706MA9x14cAjNkFQSGSqt9dmpTQ6qvcqB/sXtumUEjfqRccdHHBCZYsTH9omz3KecJblLDbVol7WJ9KyxkhNEaSqmepzp++j0MWeQBRy3jb0QHQjyARBFMeFTshxANEQDnBbWg+6mHejyfGxtidJX7N9Jp8ntAn9PRFBl/Oxa8lOFwqHz9YS+F+tHQr7rBsRLwgF9tB0kR1STfhakqTWJwwjQcfSQMSI/KuGHMggEjLvggzBmD05axqV8nnZqJ8Uq5dpGnmwA3ZBCRjgFFTBDaiBBkDgEbyCd/ChPClvyqfyNW3NKenMNvgj5fsHNDmssg==</latexit>

x =Q2

2MN⌫<latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit><latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit><latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit><latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit>

Fit to data at high energies

�T,L(W,Q2) = �RT,L(W,Q2) + �NR

T,L(W,Q2)

Regge background


Donnachie and Landshoff, PLB 595 (2004) 393

HERA data


F2(x,Q2) = fh(Q

2)x�✏h + fs(Q2)x�✏s + fr(Q

2)x�✏r<latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit><latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit><latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit><latexit sha1_base64="pYsokocCw6NzZgsxgLQZpzoYzBU=">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</latexit>

x =Q2

2MN⌫<latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit><latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit><latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit><latexit sha1_base64="GSZliZRZ5RSyNx5ReWsWxcS8sGI=">AAAB/XicbVBNS8NAEN3Ur1q/ouLJy2IRPJWkCOpBKHrxorRgbKGJYbPdtEs3m7C7EUsI+Fe8eFDx6v/w5r9x2+agrQ8GHu/NMDMvSBiVyrK+jdLC4tLySnm1sra+sbllbu/cyTgVmDg4ZrHoBEgSRjlxFFWMdBJBUBQw0g6Gl2O//UCEpDG/VaOEeBHqcxpSjJSWfHPv8dwNBcJZ676eZ/Vr/8blae6bVatmTQDniV2QKijQ9M0vtxfjNCJcYYak7NpWorwMCUUxI3nFTSVJEB6iPulqylFEpJdNzs/hoVZ6MIyFLq7gRP09kaFIylEU6M4IqYGc9cbif143VeGpl1GepIpwPF0UpgyqGI6zgD0qCFZspAnCgupbIR4gnYbSiVV0CPbsy/PEqdfOanbruNq4KNIog31wAI6ADU5AA1yBJnAABhl4Bq/gzXgyXox342PaWjKKmV3wB8bnDz8jlTo=</latexit>

Hard pomeron

Soft pomeron

Meson exchange✏h = ↵h � 1 = 0.452

<latexit sha1_base64="bbnm2LlDx2qzqMmMRKBnsAusDRc=">AAACA3icbZDNSsNAFIUn9a/Wv6jLboJFcGNISkVdFIpuXFYwttCEMJlOm6GTyTAzEUrowo2v4saFiltfwp1v47TNQlsPDHycey937ok4JVI5zrdRWlldW98ob1a2tnd298z9g3uZZgJhD6U0Fd0ISkwJw54iiuIuFxgmEcWdaHQ9rXcesJAkZXdqzHGQwCEjA4Kg0lZoVn3MJaEa46YPKY9hGJ+6TcdunNVDs+bYzkzWMrgF1EChdmh++f0UZQlmClEoZc91uApyKBRBFE8qfiYxh2gEh7inkcEEyyCfHTGxjrXTtwap0I8pa+b+nshhIuU4iXRnAlUsF2tT879aL1ODiyAnjGcKMzRfNMiopVJrmojVJwIjRccaIBJE/9VCMRQQKZ1bRYfgLp68DF7dvrTd20atdVWkUQZVcAROgAvOQQvcgDbwAAKP4Bm8gjfjyXgx3o2PeWvJKGYOwR8Znz8elJak</latexit><latexit sha1_base64="bbnm2LlDx2qzqMmMRKBnsAusDRc=">AAACA3icbZDNSsNAFIUn9a/Wv6jLboJFcGNISkVdFIpuXFYwttCEMJlOm6GTyTAzEUrowo2v4saFiltfwp1v47TNQlsPDHycey937ok4JVI5zrdRWlldW98ob1a2tnd298z9g3uZZgJhD6U0Fd0ISkwJw54iiuIuFxgmEcWdaHQ9rXcesJAkZXdqzHGQwCEjA4Kg0lZoVn3MJaEa46YPKY9hGJ+6TcdunNVDs+bYzkzWMrgF1EChdmh++f0UZQlmClEoZc91uApyKBRBFE8qfiYxh2gEh7inkcEEyyCfHTGxjrXTtwap0I8pa+b+nshhIuU4iXRnAlUsF2tT879aL1ODiyAnjGcKMzRfNMiopVJrmojVJwIjRccaIBJE/9VCMRQQKZ1bRYfgLp68DF7dvrTd20atdVWkUQZVcAROgAvOQQvcgDbwAAKP4Bm8gjfjyXgx3o2PeWvJKGYOwR8Znz8elJak</latexit><latexit sha1_base64="bbnm2LlDx2qzqMmMRKBnsAusDRc=">AAACA3icbZDNSsNAFIUn9a/Wv6jLboJFcGNISkVdFIpuXFYwttCEMJlOm6GTyTAzEUrowo2v4saFiltfwp1v47TNQlsPDHycey937ok4JVI5zrdRWlldW98ob1a2tnd298z9g3uZZgJhD6U0Fd0ISkwJw54iiuIuFxgmEcWdaHQ9rXcesJAkZXdqzHGQwCEjA4Kg0lZoVn3MJaEa46YPKY9hGJ+6TcdunNVDs+bYzkzWMrgF1EChdmh++f0UZQlmClEoZc91uApyKBRBFE8qfiYxh2gEh7inkcEEyyCfHTGxjrXTtwap0I8pa+b+nshhIuU4iXRnAlUsF2tT879aL1ODiyAnjGcKMzRfNMiopVJrmojVJwIjRccaIBJE/9VCMRQQKZ1bRYfgLp68DF7dvrTd20atdVWkUQZVcAROgAvOQQvcgDbwAAKP4Bm8gjfjyXgx3o2PeWvJKGYOwR8Znz8elJak</latexit><latexit sha1_base64="bbnm2LlDx2qzqMmMRKBnsAusDRc=">AAACA3icbZDNSsNAFIUn9a/Wv6jLboJFcGNISkVdFIpuXFYwttCEMJlOm6GTyTAzEUrowo2v4saFiltfwp1v47TNQlsPDHycey937ok4JVI5zrdRWlldW98ob1a2tnd298z9g3uZZgJhD6U0Fd0ISkwJw54iiuIuFxgmEcWdaHQ9rXcesJAkZXdqzHGQwCEjA4Kg0lZoVn3MJaEa46YPKY9hGJ+6TcdunNVDs+bYzkzWMrgF1EChdmh++f0UZQlmClEoZc91uApyKBRBFE8qfiYxh2gEh7inkcEEyyCfHTGxjrXTtwap0I8pa+b+nshhIuU4iXRnAlUsF2tT879aL1ODiyAnjGcKMzRfNMiopVJrmojVJwIjRccaIBJE/9VCMRQQKZ1bRYfgLp68DF7dvrTd20atdVWkUQZVcAROgAvOQQvcgDbwAAKP4Bm8gjfjyXgx3o2PeWvJKGYOwR8Znz8elJak</latexit>

✏s = ↵s � 1 = 0.0667<latexit sha1_base64="pooiVbT9GsBtOH7cEAUdvze01hw=">AAACBHicbZDNSgMxFIUz9a/Wv1GXuggWwY1lRqTVRaHoxmUFxxY6w5BJM21oJhOSjFBKN258FTcuVNz6EO58G9N2Ftp6IPBx7r3c3BMJRpV2nG+rsLS8srpWXC9tbG5t79i7e/cqzSQmHk5ZKtsRUoRRTjxNNSNtIQlKIkZa0eB6Um89EKloyu/0UJAgQT1OY4qRNlZoH/pEKMoMqrqPmOijUJ26dafiVKu10C4bmAougptDGeRqhvaX301xlhCuMUNKdVxH6GCEpKaYkXHJzxQRCA9Qj3QMcpQQFYymV4zhsXG6ME6leVzDqft7YoQSpYZJZDoTpPtqvjYx/6t1Mh1fBCPKRaYJx7NFccagTuEkEtilkmDNhgYQltT8FeI+kghrE1zJhODOn7wI3lnlsuLenpcbV3kaRXAAjsAJcEENNMANaAIPYPAInsEreLOerBfr3fqYtRasfGYf/JH1+QPD7pb8</latexit><latexit sha1_base64="pooiVbT9GsBtOH7cEAUdvze01hw=">AAACBHicbZDNSgMxFIUz9a/Wv1GXuggWwY1lRqTVRaHoxmUFxxY6w5BJM21oJhOSjFBKN258FTcuVNz6EO58G9N2Ftp6IPBx7r3c3BMJRpV2nG+rsLS8srpWXC9tbG5t79i7e/cqzSQmHk5ZKtsRUoRRTjxNNSNtIQlKIkZa0eB6Um89EKloyu/0UJAgQT1OY4qRNlZoH/pEKMoMqrqPmOijUJ26dafiVKu10C4bmAougptDGeRqhvaX301xlhCuMUNKdVxH6GCEpKaYkXHJzxQRCA9Qj3QMcpQQFYymV4zhsXG6ME6leVzDqft7YoQSpYZJZDoTpPtqvjYx/6t1Mh1fBCPKRaYJx7NFccagTuEkEtilkmDNhgYQltT8FeI+kghrE1zJhODOn7wI3lnlsuLenpcbV3kaRXAAjsAJcEENNMANaAIPYPAInsEreLOerBfr3fqYtRasfGYf/JH1+QPD7pb8</latexit><latexit sha1_base64="pooiVbT9GsBtOH7cEAUdvze01hw=">AAACBHicbZDNSgMxFIUz9a/Wv1GXuggWwY1lRqTVRaHoxmUFxxY6w5BJM21oJhOSjFBKN258FTcuVNz6EO58G9N2Ftp6IPBx7r3c3BMJRpV2nG+rsLS8srpWXC9tbG5t79i7e/cqzSQmHk5ZKtsRUoRRTjxNNSNtIQlKIkZa0eB6Um89EKloyu/0UJAgQT1OY4qRNlZoH/pEKMoMqrqPmOijUJ26dafiVKu10C4bmAougptDGeRqhvaX301xlhCuMUNKdVxH6GCEpKaYkXHJzxQRCA9Qj3QMcpQQFYymV4zhsXG6ME6leVzDqft7YoQSpYZJZDoTpPtqvjYx/6t1Mh1fBCPKRaYJx7NFccagTuEkEtilkmDNhgYQltT8FeI+kghrE1zJhODOn7wI3lnlsuLenpcbV3kaRXAAjsAJcEENNMANaAIPYPAInsEreLOerBfr3fqYtRasfGYf/JH1+QPD7pb8</latexit><latexit sha1_base64="pooiVbT9GsBtOH7cEAUdvze01hw=">AAACBHicbZDNSgMxFIUz9a/Wv1GXuggWwY1lRqTVRaHoxmUFxxY6w5BJM21oJhOSjFBKN258FTcuVNz6EO58G9N2Ftp6IPBx7r3c3BMJRpV2nG+rsLS8srpWXC9tbG5t79i7e/cqzSQmHk5ZKtsRUoRRTjxNNSNtIQlKIkZa0eB6Um89EKloyu/0UJAgQT1OY4qRNlZoH/pEKMoMqrqPmOijUJ26dafiVKu10C4bmAougptDGeRqhvaX301xlhCuMUNKdVxH6GCEpKaYkXHJzxQRCA9Qj3QMcpQQFYymV4zhsXG6ME6leVzDqft7YoQSpYZJZDoTpPtqvjYx/6t1Mh1fBCPKRaYJx7NFccagTuEkEtilkmDNhgYQltT8FeI+kghrE1zJhODOn7wI3lnlsuLenpcbV3kaRXAAjsAJcEENNMANaAIPYPAInsEreLOerBfr3fqYtRasfGYf/JH1+QPD7pb8</latexit>

✏r = ↵r � 1 = �0.476<latexit sha1_base64="45L9XV96A8BVvDBv/w2RfykPLms=">AAACBHicbZDNSsNAFIUn9a/Wv6hLXQwWwU1DIsXqolB047KCsUITwmQ6aYdOJmFmIpTQjRtfxY0LFbc+hDvfxmmbhbYeGPg4917u3BOmjEpl299GaWl5ZXWtvF7Z2Nza3jF39+5kkglMXJywRNyHSBJGOXEVVYzcp4KgOGSkEw6vJvXOAxGSJvxWjVLix6jPaUQxUtoKzEOPpJIyjaLpIZYOUCBqTrNmW/XGWWBWbcueCi6CU0AVFGoH5pfXS3AWE64wQ1J2HTtVfo6EopiRccXLJEkRHqI+6WrkKCbSz6dXjOGxdnowSoR+XMGp+3siR7GUozjUnTFSAzlfm5j/1bqZis79nPI0U4Tj2aIoY1AlcBIJ7FFBsGIjDQgLqv8K8QAJhJUOrqJDcOZPXgT31LqwnJt6tXVZpFEGB+AInAAHNEALXIM2cAEGj+AZvII348l4Md6Nj1lryShm9sEfGZ8/uS6W9Q==</latexit><latexit sha1_base64="45L9XV96A8BVvDBv/w2RfykPLms=">AAACBHicbZDNSsNAFIUn9a/Wv6hLXQwWwU1DIsXqolB047KCsUITwmQ6aYdOJmFmIpTQjRtfxY0LFbc+hDvfxmmbhbYeGPg4917u3BOmjEpl299GaWl5ZXWtvF7Z2Nza3jF39+5kkglMXJywRNyHSBJGOXEVVYzcp4KgOGSkEw6vJvXOAxGSJvxWjVLix6jPaUQxUtoKzEOPpJIyjaLpIZYOUCBqTrNmW/XGWWBWbcueCi6CU0AVFGoH5pfXS3AWE64wQ1J2HTtVfo6EopiRccXLJEkRHqI+6WrkKCbSz6dXjOGxdnowSoR+XMGp+3siR7GUozjUnTFSAzlfm5j/1bqZis79nPI0U4Tj2aIoY1AlcBIJ7FFBsGIjDQgLqv8K8QAJhJUOrqJDcOZPXgT31LqwnJt6tXVZpFEGB+AInAAHNEALXIM2cAEGj+AZvII348l4Md6Nj1lryShm9sEfGZ8/uS6W9Q==</latexit><latexit sha1_base64="45L9XV96A8BVvDBv/w2RfykPLms=">AAACBHicbZDNSsNAFIUn9a/Wv6hLXQwWwU1DIsXqolB047KCsUITwmQ6aYdOJmFmIpTQjRtfxY0LFbc+hDvfxmmbhbYeGPg4917u3BOmjEpl299GaWl5ZXWtvF7Z2Nza3jF39+5kkglMXJywRNyHSBJGOXEVVYzcp4KgOGSkEw6vJvXOAxGSJvxWjVLix6jPaUQxUtoKzEOPpJIyjaLpIZYOUCBqTrNmW/XGWWBWbcueCi6CU0AVFGoH5pfXS3AWE64wQ1J2HTtVfo6EopiRccXLJEkRHqI+6WrkKCbSz6dXjOGxdnowSoR+XMGp+3siR7GUozjUnTFSAzlfm5j/1bqZis79nPI0U4Tj2aIoY1AlcBIJ7FFBsGIjDQgLqv8K8QAJhJUOrqJDcOZPXgT31LqwnJt6tXVZpFEGB+AInAAHNEALXIM2cAEGj+AZvII348l4Md6Nj1lryShm9sEfGZ8/uS6W9Q==</latexit><latexit sha1_base64="45L9XV96A8BVvDBv/w2RfykPLms=">AAACBHicbZDNSsNAFIUn9a/Wv6hLXQwWwU1DIsXqolB047KCsUITwmQ6aYdOJmFmIpTQjRtfxY0LFbc+hDvfxmmbhbYeGPg4917u3BOmjEpl299GaWl5ZXWtvF7Z2Nza3jF39+5kkglMXJywRNyHSBJGOXEVVYzcp4KgOGSkEw6vJvXOAxGSJvxWjVLix6jPaUQxUtoKzEOPpJIyjaLpIZYOUCBqTrNmW/XGWWBWbcueCi6CU0AVFGoH5pfXS3AWE64wQ1J2HTtVfo6EopiRccXLJEkRHqI+6WrkKCbSz6dXjOGxdnowSoR+XMGp+3siR7GUozjUnTFSAzlfm5j/1bqZis79nPI0U4Tj2aIoY1AlcBIJ7FFBsGIjDQgLqv8K8QAJhJUOrqJDcOZPXgT31LqwnJt6tXVZpFEGB+AInAAHNEALXIM2cAEGj+AZvII348l4Md6Nj1lryShm9sEfGZ8/uS6W9Q==</latexit>

Fit to data at high energies

�T,L(W,Q2) = �RT,L(W,Q2) + �NR

T,L(W,Q2)

Regge background


High and low energies: previous works

At low Q2: high- and low-energy theories compatible in overlap region At slightly higher Q2: huge gap between high and low-energy models

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10

F 2

W [GeV]

Q2=0.23 GeV2


BC: Christy and Bosted, PRC 86 (2010) 055213 DL: Donnachie and Landshoff, PLB 595 (2004) 393 CLAS data: http://clas.sinp.msu.ru/strfun/

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10F 2

W [GeV]

Q2=1.0 GeV2



Updated parametrization: fit to dataF2(ν, Q2) = Fres

2 (ν, Q2) + (1 −νthr

ν )a(Q2)

(1 +νthr

ν )b(Q2) 2

∑i=0

fi(Q2)( 2MN

Q2(ν − νthr))

ϵi

• Recovers Regge behaviour at larger energies

• Implements threshold and resonant behaviour


Updated parametrization: fit to data

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

10

F 2

W [GeV]

Q2=1.0 GeV2


BC: Christy and Bosted, PRC 86 (2010) 055213DL: Donnachie and Landshoff, PLB 595 (2004) 393CLAS data: http://clas.sinp.msu.ru/strfun/

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 100

F 2

W [GeV]

Q2 = 0.9 GeV2

Fit resultResonant

Non-resonantHERA data

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 100

F 2

W [GeV]

Q2 = 0.975 GeV2

Fit resultResonant

Non-resonantCLAS data

Preliminary

First combined model for low and high energies!

F2(ν, Q2) = Fres2 (ν, Q2) + (1 −

νthr

ν )a(Q2)

(1 +νthr

ν )b(Q2) 2

∑i=0

fi(Q2)( 2MN

Q2(ν − νthr))

ϵi

• Recovers Regge behaviour at larger energies

• Implements threshold and resonant behaviour


Summary

• New resonance model: N* electrocouplings from CLAS(12) allow separation into longitudinal and transverse resonant cross sections

• No fits needed for description of the resonant contributions toinclusive electron-scattering cross sections

• Intricate behaviour with W and Q2 in the resonance regime

• First estimates for the background behaviour

A. N. Hiller Blin GHP Workshop 2019-04-12 !13

Outlook

• Transition between low and high x (or energies)

• Important for VVCS subtraction function, Cottingham formula, …

• High-energy data described well by Regge models:update with threshold parameters and resonance contributions

• Updates on inclusive and exclusive electron scattering CLAS12:coming soon!


-60

-40

-20

0

20

40

60

80

100

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

N(1720)3/2+


CLASRPP

-5

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

N(1710)1/2+


CLASRPP

-55-50-45-40-35-30-25-20-15-10

-5 0

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

N(1680)5/2+


CLASMAIDHall A

RPP-5

0

5

10

15

20

25

30

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

N(1675)5/2-


CLASRPP

0 5

10 15 20 25 30 35 40 45 50

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

Δ(1620)1/2-


CLASRPP

-110-100-90-80-70-60-50-40-30-20-10

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

N(1520)3/2-


CLASHall A

RPP

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

Δ(1700)3/2-


CLASRPP

-10

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

N(1650)1/2-


CLASRPP

A1/2

-50-45-40-35-30-25-20-15-10

-5 0 5

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

N(1720)3/2+


CLASRPP

-10

-5

0

5

10

15

20

25

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

N(1675)5/2-


CLASRPP

-20

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

N(1680)5/2+


CLASMAIDHall A

RPP

-20 0

20 40 60 80

100 120 140 160 180

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

N(1520)3/2-


CLASHall A

RPP

-300

-250

-200

-150

-100

-50

0

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

Δ(1232)3/2+


CLASHall CMAMI

MIT/BatesHall A

Hall A 2007RPP

0

20

40

60

80

100

120

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

Δ(1700)3/2-


CLASRPP

A3/2

-11-10

-9-8-7-6-5-4-3-2-1 0

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

N(1710)1/2+


CLAS

-20

-15

-10

-5

0

5

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

N(1675)5/2-


CLAS

-10

0

10

20

30

40

50

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

N(1440)1/2+


CLASHall A

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

Δ(1232)3/2+


CLASHall CMAMI

MIT/BatesHall A

Hall A 2007

-50

-40

-30

-20

-10

0

10

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

N(1520)3/2-


CLASHall A

-60

-50

-40

-30

-20

-10

0

10

20

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

N(1535)1/2-


CLASHall A

-20-18-16-14-12-10

-8-6-4-2 0

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

N(1650)1/2-


CLAS

6 8

10 12 14 16 18 20 22 24 26

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

Δ(1700)3/2-


CLAS

S1/2

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6

103 A

1/2

[GeV

-1/2

]

Q2[GeV2]

New N(1720)3/2+


CLAS

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 1 2 3 4 5 6

103 A

3/2

[GeV

-1/2

]

Q2 [GeV2]

New N(1720)3/2+


CLAS 0

10

20

30

40

50

60

0 1 2 3 4 5 6

103 S

1/2

[GeV

-1/2

]

Q2 [GeV2]

New N(1720)3/2+


CLAS

New resonance

0

20

40

60

80

100

120

140

0.8 1 1.2 1.4 1.6 1.8

σT

[µb]

W [GeV]

Q2 = 1 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

0

1

2

3

4

5

6

7

8

0.8 1 1.2 1.4 1.6 1.8

σT

[µb]

W [GeV]

Q2 = 4 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

0

50

100

150

200

250

300

0.8 1 1.2 1.4 1.6 1.8

σT

[µb]

W [GeV]

Q2 = 0.5 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

0

2

4

6

8

10

12

14

16

0.8 1 1.2 1.4 1.6 1.8

σT

[µb]

W [GeV]

Q2 = 3 GeV2

N(1440) 1/2+

N(1520) 3/2-

N(1535) 1/2-

N(1650) 1/2-

N(1675) 5/2-

N(1680) 5/2+

N(1710) 1/2+

N(1720) 3/2+

Δ(1232) 3/2+

Δ(1620) 1/2-

Δ(1700) 3/2-

N’(1720) 3/2+Total

towards a combined analysis of inclusive/exclusive ......rpp!3 a. n. hiller blin ghp workshop...

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