qcd workshop on chirality, vorticity and magnetic field in heavy ion collisions @ucla, jan. 21-23,...
TRANSCRIPT
![Page 1: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/1.jpg)
QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015
Photon Propagation in Magnetic Fields in Strong Magnetic Fields
KH, K. Itakura (KEK), Ann. Phys. 330 (2013); Ann. Phys. 334 (2013)
Koichi HattoriRIKEN-BNL Research Center
![Page 2: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/2.jpg)
RHIC@BNL
LHC@CERN
Phase diagram of QCD matter
Asymptotic freedomQuark-gluon plasma
Light-meson spectra in B-fields Hidaka and A.Yamamoto
Quark and gluon condensates at zero and finite temperatures Bali et al.
Results from lattice QCD in magnetic fields
![Page 3: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/3.jpg)
Extremely strong magnetic fieldsUrHIC NS/Magnetar
Lienard-Wiechert potential
Z = 79(Au), 82(Pb)
Lighthouse in the sky
PSR0329+54
c.f.) Possible mechanism of strong B from “chiral instability”: the conversion of μ5
generated in electron captures.
Ohnishi and Yamamoto, Akamatsu and Yamamoto
![Page 4: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/4.jpg)
Strong magnetic fields in nature and laboratories
Magnet in Lab.
Magnetar
Heavy ion collisions
![Page 5: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/5.jpg)
Polarization 1Polarization 2
Incident light“Calcite” (方解石 )
“Birefringence”: Polarization-dependent refractive indices.
Response of electrons to incident lights Anisotropic responses of electrons result in polarization-dependent and anisotropic photon spectra.
Photon propagations in substances
![Page 6: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/6.jpg)
+ Lorentz & Gauge symmetries n ≠ 1 in general
+ Oriented response of the Dirac sea ``Vacuum birefringence”
How about the vacuum with external magnetic fields ?- The Landau-levels
B
![Page 7: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/7.jpg)
Modifications of photon propagations in strong B-fields- Old but unsolved problems
Quantum effects in magnetic fields
Photon vacuum polarization tensor:
Modified Maxwell eq. :
Dressed propagators in Furry’s picture
・・・
・・・
Should be suppressed in the ordinary perturbation theory, but not in strong B-fields.
eBeB eB
![Page 8: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/8.jpg)
Break-down of naïve perturbation in strong B-fields
Naïve perturbation breaks down when B > Bc
Need to take into account all-order diagrams
Critical field strengthBc = me
2 / e
Dressed fermion propagator in Furry’s picture
Resummation w.r.t. external legs by “proper-time method“ Schwinger
Nonlinear to strong external fields
![Page 9: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/9.jpg)
Photon propagation in a constant external magnetic field
Vanishing B limit:
θ: angle btw B-field and photon propagation
BGauge symmetries lead to a tensor structure,
Schwinger, Adler, Shabad, Urrutia, Tsai and Eber, Dittrich and Gies
Exponentiated trig-functions generate strongly oscillating behavior witharbitrarily high frequency.
Integrands with strong oscillations
![Page 10: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/10.jpg)
Summary of relevant scales and preceding calculations
Strong field limit: the lowest-Landau-level approximation(Tsai and Eber, Shabad, Fukushima )
Numerical computation below the first threshold(Kohri and Yamada) Weak field & soft photon limit
(Adler)
?Untouched so far
General analytic expression
Euler-Heisenberg LagrangianIn soft photon limit
![Page 11: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/11.jpg)
2nd step: Getting Laguerre polynomials
Associated Laguerre polynomial
Decomposing exponential factors
Linear w.r.t. τ in exp.
1st step: “Partial wave decomposition”
Linear w.r.t. τ in exp.
Linear w.r.t. τ in exp.
![Page 12: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/12.jpg)
By the decomposition of the integrand, any term reduces to either of three elementary integrals.
Transverse dynamics: Wave functions for the Landau levels given by the associated Laguerre polynomials
![Page 13: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/13.jpg)
UrHIC
Prompt photon ~ GeV2
Thermal photon ~ 3002 MeV2 ~ 105 MeV2
Untouched so far
Strong field limit (LLL approx.)(Tsai and Eber, Shabad, Fukushima )
Soft photon & weak field limit(Adler)
Numerical integration(Kohri, Yamada)
External photon momentum
Analytic result of integrals- An infinite number of the Landau levels
KH, K.Itakura (I)
⇔Polarization tensor acquires an imaginary part when
Lowest Landau level
Narrowly spaced Landau levels
![Page 14: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/14.jpg)
Complex refractive indices
Solutions of Maxwell eq. with the vacuum polarization tensor
The Lowest Landau Level (ℓ=n=0)
Refractive indices at the LLL
Polarization excites only along the magnetic field``Vacuum birefringence’’
KH, K. Itakura (II)
![Page 15: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/15.jpg)
Self-consistent solutions of the modified Maxwell Eq.
Photon dispersion relation is strongly modified when strongly coupled to excitations (cf: exciton-polariton, etc)
cf: air n = 1.0003, water n = 1.333
𝜔2/4𝑚2
≈ Magnetar << UrHIC
𝜔2/4𝑚2
![Page 16: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/16.jpg)
Angle dependence of the refractive indexReal part
No imaginary part
Imaginary part
![Page 17: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/17.jpg)
“Mean-free-path” of photons in B-fields
λ (fm)
When the refractive index has an imaginary part,
![Page 18: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/18.jpg)
Summary for Photon propagation+ We obtained an analytic form of the polarization tensor in magnetic fields as the summation w.r.t. the Landau levels.
+ We obtained the complex refractive indices (photon dispersions) by solving the modified Maxwell Eq. self-consistently. Photons decay within a microscopic spatial scale.
Neutron stars = Pulsars Possibly “QED cascade” in strong B-fields
What is the mechanism of radiation?
We got precise descriptions of vertices: Dependences on magnitudes of B-fields, photon energy, propagation angle and polarizations.
Prospects: Microscopic mechanism of the pulsation
“Photon Splitting”Softening of photons
![Page 19: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/19.jpg)
![Page 20: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/20.jpg)
Analytical modeling of colliding nuclei, Kharzeev, McLerran, Warringa, NPA (2008)
Pre-equilibrium
QGP
Strong magnetic fields induced by UrHIC
![Page 21: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/21.jpg)
Dimesionless variables Schwinger, Adler, Shabad, Urrutia, Tsai and Eber, Dittrich and Gies
1st step: Use a series expansion known as partial wave decomposition Baier and Katkov
Exponentiated trig-functions generate strongly oscillating behavior by arbitrarily high frequency.
![Page 22: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/22.jpg)
After 1st step:
2nd step:
Associated Laguerre polynomial
Then, any term reduces to either of three elementary integrals.
![Page 23: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/23.jpg)
1st step: Use a series expansion known as partial wave decomposition Baier and Katkov
2nd step:
Associated Laguerre polynomial
Then, any term reduces to either of three elementary integrals.
![Page 24: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/24.jpg)
Close look at the integrals
What dynamics is encoded in the scalar functions ?
An imaginary part representing a real photon decay
⇔
⇔Invariant mass of a fermion-pair in the Landau levels
![Page 25: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/25.jpg)
Analytic results of integrals without any approximation
Polarization tensor acquires an imaginary part above
Every term results in either of three simple integrals.
A double infinite sum
KH, K. Itakura (I)
![Page 26: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/26.jpg)
Renormalization
+= ・・・+ +
Log divergence
Term-by-term subtraction
Ishikawa, Kimura, Shigaki, Tsuji (2013)
Taken from Ishikawa, et al. (2013)
Finite
Re Im
![Page 27: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/27.jpg)
Br = (50,100,500,1000,5000,10000, 50000)
Real part of n on stable branch
Imaginary part of n on unstable branch
Real part of n on unstable branch
Relation btw real and imaginary partson unstable branch
![Page 28: QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions @UCLA, Jan. 21-23, 2015 Photon Propagation in Magnetic Fields in Strong](https://reader030.vdocuments.us/reader030/viewer/2022032802/56649e0e5503460f94af8cde/html5/thumbnails/28.jpg)
Br = (50,100,500,1000,5000,10000, 50000)
Real part of ε on stable branch
Imaginary part of ε on unstable branch
Real part of ε on unstable branch
Relation btw real and imaginary partson unstable branch