Structure Functions In-Medium and the EMC Effect€¦ · Structure Functions In-Medium and the EMC E ect ... Free Structure Functions In-Medium Structure Functions Results ... q A(x

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


The EMC Effect


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)


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?


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?





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]



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



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




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)




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



Quark Distributions of the free proton

Valence quark distributions in the Bag model.Distributions are at the model scale.



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)





In-Medium effects to be considered

Fermi motion of the nucleon

Nucleon Nucleon interaction



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



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!



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!



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















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



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)



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)


Results


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)


Results

Unpolarized In-Medium over Free Structure Function of the Proton

Blue solid line: Unpolarized EMC ratio F ∗2 (x)/F2(x)


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).


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


Summary


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


The End

Thank you,and have a safe journey home ,


Documents

Structure Functions In-Medium and the EMC Effect€¦ · Structure Functions In-Medium and the EMC E ect ... Free Structure Functions In-Medium Structure Functions Results ... q A(x