Nucleon polarizabilities theory and experiments
Download
1 / 41

Nucleon Polarizabilities: Theory and Experiments - PowerPoint PPT Presentation


  • 114 Views
  • Uploaded on

Nucleon Polarizabilities: Theory and Experiments. Chung-Wen Kao Chung-Yuan Christian University. 2007.3 .30. NTU. Lattice QCD Journal Club. What is Polarizability?. Excited states. Electric Polarizability. Magnetic Polarizability.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Nucleon Polarizabilities: Theory and Experiments' - vilina


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Nucleon polarizabilities theory and experiments

Nucleon Polarizabilities:Theory and Experiments

Chung-Wen Kao

Chung-Yuan Christian University

2007.3 .30. NTU. Lattice QCD Journal Club


What is polarizability
What is Polarizability?

Excited states

Electric Polarizability

Magnetic Polarizability

Polarizability is a measures of rigidity of a system and deeply relates with the excited spectrum.


Chiral dynamics and nucleon polarizabilities
Chiral dynamics and Nucleon Polarizabilities


Real compton scattering
Real Compton Scattering

Spin-independent

Spin-dependent


Ragusa polarizabilities
Ragusa Polarizabilities

Forward spin polarizability

Backward spin polarizability

LO are determined by e, M κ

NLO are determined by

4 spin polarizabilities, first defined by Ragusa


Physical meaning of ragusa polarizabilities
Physical meaning of Ragusa Polarizabilities



Dispersion relation
Dispersion Relation

Relate the real part amplitudes to the imaginary part

By Optical Theorem :

Therefore one gets following dispersion relations:


Derivation of sum rules
Derivation of Sum rules

Expanded by incoming photon energy ν:

Comparing with the low energy expansion of forward amplitudes:


Generalize to virtual photon
Generalize to virtual photon

Forward virtual virtual Compton scattering (VVCS) amplitudes

h=±1/2 helicity of electron


Dispersion relation of vvcs
Dispersion relation of VVCS

The elastic contribution can be calculated from

the Born diagrams with Electromagnetic vertex


Sum rules for vvcs
Sum rules for VVCS

Expanded by incoming photon energy ν

Combine low energy expansion and dispersion relation one gets 4 sum rules

On spin-dependent vvcs amplitudes:

Generalized GDH sum rule

Generalized spin polarizability sum rule


Theory vs experiment
Theory vs Experiment

  • Theorists can calculate Compton scattering amplitudes and extract polarizabilities.

  • On the other hand, experimentalists have to

    measure the cross sections of Compton scattering to extract polarizabilities.

  • Experimentalists can also use sum rules to get the values of certain combinations of polarizabilities.


Chiral symmetry of qcd if m q 0
Chiral Symmetry of QCD if mq=0

Left-hand and right-hand quark:

QCD Lagrangian is invariant if

Massless QCD Lagrangian has SU(2)LxSU(2)Rchiral symmetry.


Quark mass effect

If mq≠0

QCD Lagrangian is invariant if θR=θL.

Therefore SU(2)LXSU(2)R →SU(2)V, ,if mu=md

SU(2)A is broken by the quark mass


Spontaneous symmetry breaking
Spontaneous symmetry breaking

Spontaneous symmetry breaking:

a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. The system no longer appears to behave in a symmetric manner.

Example:

V(φ)=aφ2+bφ4, a<0, b>0.

Spontaneous symmetry

Mexican hat potential

U(1) symmetry is lost if one expands around the degenerated vacuum!

Furthermore it costs no energy to rum around the orbit →massless mode exists!! (Goldstone boson).


An analogy ferromagnetism
An analogy: Ferromagnetism

Above Tc

Below Tc

<M>=0

<M>≠0


Pion as goldstone boson
Pion as Goldstone boson

  • π is the lightest hadron. Therefore it plays a dominant the long-distance physics.

  • More important is the fact that soft π interacts each other weakly because they must couple derivatively!

  • Actually if their momenta go to zero, π must decouple with any particles, including itself.

Start point of an EFT for pions.

~t/(4πF)2


Chiral perturbation theory
Chiral Perturbation Theory

  • Chiral perturbation theory (ChPT) is

    an EFT for pions.

  • The light scale is p and mπ.

  • The heavy scale isΛ~4πF~1 GeV,

    F=93 MeVisthe pion decay constant.

  • Pion coupling must be derivative so

    Lagrangian start fromL(2).


Set up a power counting scheme
Set up a power counting scheme

  • kn for a vertex with n powers of p or mπ.

  • k-2 for each pion propagator:

  • k4 for each loop:∫d4k

  • The chiral power :ν=2L+1+Σ(d-1) Nd

  • Since d≧2 therefore νincreases with the

    number of loop.





Theoretical predictions of and
Theoretical predictions of α and β

LO HBChPT (Bernard, Kaiser and Meissner , 1991)

NLO HBChPT

LO HBChPT including Δ(1232)


Extraction of and
Extraction of α and β

Linearly polarized incoming photon+ unpolarized target:

Small energy, small cross section;

Large energy, large higher order terms contributes


Extraction of and1
Extraction of α and β



MAID

Estimate

Bianchi Estimate


Theoretical predictions of 0 q 2 and q 2
Theoretical predictions of γ0(Q2) and δ(Q2)

LO+NLO HBChPT (Kao, Vanderhaeghen, 2002)

LO+NLO Manifest Lorentz invariant ChPT (Bernard, Hemmert Meissner

2002)

MAID

Lo

Lo

Lo Δ

LO+NLO


Data of spin forward polarizabilities
Data of spin forward polarizabilities

LO+NLO HBChPT

LO+NLO MLI ChPT

MAID



Longitudinal and perpendicular asymmetry
Longitudinal and perpendicularasymmetry

Plan experiments by HIGS, TUNL.




Polarizabilities on the lattice
Polarizabilities on the lattice

Detmold, Tiburzi, Walker-Loud, 2003

Background field method:


Polarizabilities on the lattice

Two-point correlation function

Constant electric field at X1 direction

Example:


Summary and outlook
Summary and Outlook

  • Polarizabilities are important quantites relating with inner structure of hadron

  • Tremendous efforts have contributed to

    Polarizabilities, both theory and experiment.

  • We hope our lattice friend can help us to clarify some issues, in particular, neutron polarizabilities.


ad