Modification of nucleon spectral function in the nuclear medium from QCD sum rules Collaborators: Philipp Gubler(ECT*), Makoto Oka Tokyo Institute of Technology

Modification of nucleon spectral function in the nuclear medium from QCD sum rules

Collaborators: Philipp Gubler(ECT*), Makoto Oka

Tokyo Institute of Technology 　 Keisuke Ohtani

Outline

•Nucleon QCD sum rule in vacuum

•Summary

•QCD sum rules

•Nucleon QCD sum rule in nuclear matter

•Introduction

Introduction

・ Hadron properties in the nuclear medium

N

N

N

N

N N

N

N

NN

N

Probe hadron

Nuclear matter

The properties of the hadron are modified in the medium.

Partial restoration of the chiral symmetry

Interaction with the nucleons in the nuclear matter

We focus on the nucleon ground state and its negative parity excited state.

IntroductionMass spectrum of the nucleons

p, n

N(1440)

N(1535)

N(1650)

Positive parity Negative parity


p, n

N(1440)

N(1535)

N(1650)

Positive parity

• It is predicted that Chiral symmetry breaking cause these difference.

Negative parity

• The mass difference between nucleon ground state and N(1535) is about 600 MeV.


p, n

N(1440)

N(1535)

N(1650)

Positive parity

• It is predicted that Chiral symmetry breaking cause these difference.

Negative parity


To investigate these properties from QCD, non perturbative method is needed.

When chiral symmetry is restored, the mass spectrum will change.

Analysis of QCD sum rule in nuclear matter


?In the nuclear matter

is calculated by the operator product expansion (OPE)

Non perturbative contributions are expressed by some Condensates.

QCD sum rulesHadronic spectral function

, ・・・

An order parameter of chiral symmetry

Application of the analyses in the nuclear matter.

QCD sum rulesVacuum Nuclear matter

N

N

N

N

N N

N

N

NN

N

Probe hadron

In nuclear matterIn vacuum

Probe hadron： Ground state of nuclear matter

Nuclear matter

N

N

N

N

N N

N

N

NN

N


Probe hadron

Modification:

Chiral condensate ：

New condensate:

Probe hadron

： Ground state of nuclear matter

QCD sum rulesVacuum

QCD sum rules

τ 、 s: parameterOPE side

Gaussian sum rule

Vacuum Nuclear matter

is calculated by OPETransformation

We extract the information on the spectral function with maximum entropy method (MEM).

contains the term

Nucleon QCD sum rule in vacuumThe behavior of the OPE data in the vacuum

The difference between positive parity and negative parity is mainly caused by chiral condensate term.

Positive parity OPENegative parity OPE

term

Parity: + Parity: -

Mass spectrum of the nucleons

930MeV


1550 MeV

In both positive and negative parity, the peaks are found.In the negative parity state, the peak correspond to the N(1535) or (and) N(1650).

Nucleon QCD sum rule in vacuum

The behavior of the OPE data in the nuclear matter


N

N

N

N

N N

N

N

NN

N

Probe nucleon


Probe hadron

： Ground state of nuclear matter

Nucleon QCD sum rule in nuclear matter

Positive parity OPE Negative parity OPE

term

term

ρN: nuclear matter density



Parity: + Parity: -

Mass spectrum of the nucleonsVacuum


contain the terms

Positive parity: OPE data decreases.

Negative parity: OPE data slightly increases.

ρ ＝ 0.25ρNPositive parity OPE Negative parity OPE

term

term



Parity: + Parity: -

？Mass spectrum of the nucleons

contains the term



term

term



Parity: + Parity: -

？Mass spectrum of the nucleonsρ ＝ 0.5ρN

contain the terms

contains the term





term

term



Parity: + Parity: -


contain the terms

contains the term





term

term



Parity: + Parity: -


contain the terms

contains the term




Positive parity OPE dataNegative parity OPE data

term

term

: n=n0

: ρ=0.75ρ0

: ρ=0.5ρ0

: ρ=0.25ρ0

: Vacuum


ρN : nuclear matter density

Vacuum


ρ ＝ 0.25ρN Positive parity OPE dataNegative parity OPE data

term

term

: n=n0

: ρ=0.75ρ0

: ρ=0.5ρ0

: ρ=0.25ρN

: Vacuum





term

term

: n=n0

: ρ=0.75ρ0

: ρ=0.5ρN

: ρ=0.25ρN

: Vacuum





term

term

: n=n0

: ρ=0.75ρN

: ρ=0.5ρN

: ρ=0.25ρN

: VacuumPositive parity Negative parity


: ρ=1.0ρ0




term

term

: n=n0

: ρ=0.75ρN

: ρ=0.5ρN

: ρ=0.25ρN

: VacuumPositive parity Negative parity


: ρ=1.0ρN


The values of the energies are obtained.



N N

N

N

N

N

N N

N

Probe nucleon

Propagator: Propagator:

N

NN

N

Pole of positive energy state:

Effective mass:

Pole of negative energy state:


　　　　　　　　　Investigation of effective masses and vector self energies

210 q

210 q

u

By fitting the phenomenological side and OPE side, we can investigate the self energies.

+ (contribution of negative parity states)

are calculated by OPE are expressed by the propagators in physical energy region




Vacuum ρ=0.25 ρN ρ=0.5 ρN ρ=0.75 ρN ρ=1.0 ρN

810

120

151040

660

270

1460

80

490

430

1430

110

290

640

1410

130

1550

930

0

0

•We analyze the nucleon spectral function by using QCD sum rules with MEM

Summary

• The information of not only the ground state but also the negative parity excited state is extracted

• We find that the difference between the positive and negative parity spectral function is mainly caused by the chiral condensate.

•We apply this method to the analyses in nuclear medium and investigate the effective masses and the vector self-energies.

•As the density increases, the effective masses decrease and the vector self-energies increase.

Documents

Modification of nucleon spectral function in the nuclear medium from QCD sum rules Collaborators: Philipp Gubler(ECT*), Makoto Oka Tokyo Institute of Technology