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Structure Functions In-Medium and the EMC Effect
Stephen Tronchin
The University of Adelaide
CSSM, Cairns, July 2017
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 1 / 29
Overview
The EMC effect
Free Structure Functions
In-Medium Structure Functions
Results
Summary
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The EMC Effect
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The EMC Effect
What is the EMC Effect?
First measured in 1983 by the European Muon Collaboration (EMC) throughDeep Inelastic Scattering of muons off Deuteron and IronThe EMC effect is the result when you take the ratio of the In-Medium toFree Structure Function of the proton: F ∗2 (x)/F2(x)
J. Ashman et al., Z. Phys. C57, 211 (1993)J. Gomez et al., Phys. Rev. D49, 4348 (1994)
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The EMC Effect
The EMC results surprised the nuclear physics community and raised manyquestions 0 o ...
Contemplations of the EMC effect:
Is the proton an immutable object or does the internal structure change whenimmersed in a medium such as an atomic nucleus?
What is it that alters the quark momentum inside a bound nucleon?
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 5 / 29
The EMC Effect
The EMC results surprised the nuclear physics community and raised manyquestions 0 o ...
Contemplations of the EMC effect:
Is the proton an immutable object or does the internal structure change whenimmersed in a medium such as an atomic nucleus?
What is it that alters the quark momentum inside a bound nucleon?
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 5 / 29
Free Structure Functions
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Free Structure Functions
Take the course of the Operator Product Expansion (OPE) with the MIT BagModel to determine quark distributions.
2-quark intermediate state
4-quark intermediate states
Processess contributing to the twist-2 matrix elements[1]
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Free Structure Functions
The MIT Bag
Essentially put three non-interactingquarks inside a volume (or bag)
It is a valence quark picture of thenucleon
The effect of the one-gluonexchange is incorporated throughdiquark mass splitting
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Free Structure Functions
Calculating the Free Quark Distributions
Start with the two-quark intermediate state
2-quark intermediate state
The lowest energy MIT bag wave function is:
Ψm(x) =
j0(
Ω|x|R
)χm
iσ· x j1(
Ω|x|R
)χm
(1)
with Ω = 2.04
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Free Structure Functions
Calculating the Free Quark Distributions
Now we can calculate the quark distribution of the free nucleon[1]:
q↑↓N(2)(x) =M
(2π)2
∑m
〈µ|Pf ,m|µ〉∫ ∞
[M2(1−x)2−M2n ]
2M(1−x)
pndpn|φ2(pn)|2
|φ3(0)|2|Ψ↑↓m (pn)|2 (2)
From this the Structure Functions of the proton can be determined:
F2(x) = x∑f
e2f qf (x) = x
[(2
3
)2
u(x) +
(1
3
)2
d(x)
](3)
g1(x) =1
2
∑f
e2f ∆qf (x) =
1
2
[(2
3
)2
∆u(x) +
(1
3
)2
∆d(x)
](4)
[1]A. W. Schreiber, A. I. Signal, and A. W. Thomas, Phys. Rev. D44(9),2653-2661 (1991)
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Free Structure Functions
Calculating the Free Quark Distributions
Including the four-quarkintermediate states
The four-quark term isapproximated by C (1− x)7, and isincluded to satisfy normalizationrequirements∫ 1
0
dx(u↑(x) + u↓(x)
)= 2 (5)∫ 1
0
dx(d↑(x) + d↓(x)
)= 1 (6)
4-quark intermediate states
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Free Structure Functions
Quark Distributions of the free proton
Valence quark distributions in the Bag model.Distributions are at the model scale.
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Free Structure Functions
Quark Distributions in the Bag model and Nambu-Jona-Lasinio (NJL) model
Bag Model: Polarized u distribution NJL Model: Polarized u distribution[2]
[2]I. C. Cloet, W. Bentz and A. W. Thomas, Nuclear Physics B, 141, 225-232(2005)
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In-Medium Structure Functions
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In-Medium Structure Functions
In-Medium effects to be considered
Fermi motion of the nucleon
Nucleon Nucleon interaction
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In-Medium Structure Functions
Fermi motion
This is a well explored effects and is incorporated through a convolution withthe Fermi smearing function
f0(yA) =3
4
(EF
pF
)3[(
pF
EF
)2
− (1− yA)2
](7)
where EF and pF are the proton Fermi energy and Fermi momentum.
Fermi motion of a nucleon in a nucleus
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In-Medium Structure Functions
Nucleons interact through meson exchange
Scalar σ-meson: Responsible for the intermediate range attraction
Vector ω-meson: Responsible for the short range repulsion
The importance of QCD
For the nucleon as a whole, the Lorentz scalar mean field and Lorentz vectormean field cancel to give approximately 8 MeV of binding energy
However: Once we consider the internal structure of the nucleon, these twoeffects are totally different
We need a way to include these interactions into the calculations at thequark level!
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 17 / 29
In-Medium Structure Functions
Nucleons interact through meson exchange
Scalar σ-meson: Responsible for the intermediate range attraction
Vector ω-meson: Responsible for the short range repulsion
The importance of QCD
For the nucleon as a whole, the Lorentz scalar mean field and Lorentz vectormean field cancel to give approximately 8 MeV of binding energy
However: Once we consider the internal structure of the nucleon, these twoeffects are totally different
We need a way to include these interactions into the calculations at thequark level!
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 17 / 29
In-Medium Structure Functions
Quark Meson Coupling (QMC) Model
QMC: The mesons couple to the quarks rather than the nucleon as a whole:Discussd earlier this week by Kay Martinez and Tony Thomas
In the context of QCD, the difference of the two components of the nuclear meanfield becomes crucial
The vector field has the effect of simply shifting the definition of the energy, butthe scalar field alters the quark wave function
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In-Medium Structure Functions
Quark Meson Coupling (QMC) Model
QMC: The mesons couple to the quarks rather than the nucleon as a whole:Discussd earlier this week by Kay Martinez and Tony Thomas
In the context of QCD, the difference of the two components of the nuclear meanfield becomes crucial
The vector field has the effect of simply shifting the definition of the energy, butthe scalar field alters the quark wave function
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 18 / 29
In-Medium Structure Functions
Quark Meson Coupling (QMC) Model
QMC: The mesons couple to the quarks rather than the nucleon as a whole:Discussd earlier this week by Kay Martinez and Tony Thomas
In the context of QCD, the difference of the two components of the nuclear meanfield becomes crucial
The vector field has the effect of simply shifting the definition of the energy, butthe scalar field alters the quark wave function
Stephen Tronchin (UofA) EMC Effect CSSM, 2017 18 / 29
In-Medium Structure Functions
Including the effect of the mean Scalar Field generated by the σ-meson
Scalar field coupling to the quark gives the quark and nucleon an effectivemass
m∗q = mq − gqσ σ ≈ −138 MeV (8)
M∗ = M −[
gσσ −d
2(gσσ)2
]≈ 750 MeV (9)
This alters the eigenfrequency of the wave function appearing in qN(x)
Ψ∗m(x) =
j0(
Ω∗|x|R
)χm
iσ· x b j1(
Ω∗|x|R
)χm
(10)
with Ω∗ ≈ 1.70
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In-Medium Structure Functions
Including the effect of the mean Vector Field generated by the ω-meson
Vector field incorporated through scaling the quark distribution and shiftingthe Bjorken variable x [3]
qA(xA) =εFEF
qA0
(εFEF
xA −V0
EF
)(11)
where
εF = EF + 3V0, (12)
and V0 is the repulsive Vector potential felt by the quark
[3]I. C. Cloet, W. Bentz and A. W. Thomas, Nuclear Physics B, 141, 225-232(2005)
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In-Medium Structure Functions
Combine effects to obtain In-Medium Quark Distributions
Include Scalar field effects through effective quark and nucleon mass
qN0(x) =M∗
(2π)2
∑m
〈µ|Pf ,m|µ〉∫ ∞
[M∗2(1−x)2−M∗2n ]
2M∗(1−x)
pndpn|φ∗2(pn)|2
|φ∗3(0)|2|Ψ∗m(pn)|2
(13)
Include Fermi motion through a convolution with Fermi smearing functionf0(yA)
qA0(xA) =
∫dyA
1
yAqN0
(xAyA
)f0(yA) (14)
Include Vector field effects by scaling the quark distribution and shifting x
qA(xA) =εFEF
qA0
(xA =
εFEF
xA −V0
EF
)(15)
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Results
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Results
Unpolarized In-Medium over Free Structure Function of the Proton
EMC data from I. Sick and D. Day, Phys. Lett. B 274, 16 (1992)
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Results
Unpolarized In-Medium over Free Structure Function of the Proton
Blue solid line: Unpolarized EMC ratio F ∗2 (x)/F2(x)
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Results
Polarized In-Medium over Free Structure Function of the Proton
Blue solid line: Unpolarized EMC ratio F ∗2 (x)/F2(x).
Magenta solid line: Polarized EMC ratio g∗1 (x)/g1(x).
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Results
Exciting times for the Polarized EMC effect
With the 12 GeV upgrade at JLab there will hopefully be a measurement ofthe polarized EMC effect
Any EMC effect for the polarized case would be a major discovery
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Summary
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Summary
What have we just learned?
The intermediate range attraction between nucleons is a strong Lorentz scalar
The internal structure of a bound nucleon is altered by this scalar field
Starting from the quark level, using the QMC and MIT bag model, thegeneral shape of the observed unpolarized EMC effect is reproduced to agood degree
This plays a crucial role in understanding atomic nuclei, as the nucleons thatoccupy nuclear shell orbits are not free nucleons
Measurements of the polarized EMC effect will help further develop ourunderstanding of the nucleon and nuclear structure
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The End
Thank you,and have a safe journey home ,
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