Recent progress in hadron physics -From hadrons to quark and gluon- 2013 Feb. 18-22, Yonsei...
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Transcript of Recent progress in hadron physics -From hadrons to quark and gluon- 2013 Feb. 18-22, Yonsei...
Recent progress in hadron physics -From hadrons to quark and gluon- 2013Feb. 18-22, Yonsei University
1. Photon propagation in strong magnetic field: “Vacuum birefringence”,
KH and K. Itakura, Ann. Phys. 330 (2013) 23-54.
KH and K. Itakura, arXiv: 1212.1897 [hep-ph].
Koichi Hattori (Yonsei Univ.)
Effects of strong magnetic fields
2. Pion reactions in strong magnetic field,
KH, K. Itakura, S. Ozaki, in preparation
What is “Birefringence ( 複屈折 )” ?
Doubled image by a ray splitting in birefringent material
Polarization 1Polarization 2
Incident light“Calcite” ( 方解石 )
Two polarization modes of a propagating photon have different refractive indices.
+ Strong magnetic fields in heavy-ion collisions
+ Our analytic calculation of the photon vacuum polarization tensor Refractive indices (“Vacuum birefringence”)
+ Some features of the obtained refractive index
Table of contents of 1st part
How is in the vacuum with external magnetic field ?
+ Lorentz & Gauge symmetries n ≠ 1 in general
+ Oriented response of the Dirac sea Vacuum birefringence
induced by strongly accelerated heavy nucleiExtremely strong magnetic fields in peripheral collisions
vN > 0.9999 c Z = 79 (Au), 82 (Pb)
t = 0.1 fm/c 0.5 fm/c 1 fm/c 2 fm/c
Superposition of circulating magnetic fields in the transverse plane
Geometry in peripheral collisions
Lienard-Wiechert potential
From Itakura-san’s talk in “International conference on physics in intense field 2010 @ KEK”
Strong magnetic fields in nature and laboratories
Magnet in Lab.
Magnetar
Heavy ion collisions
2nd PIF, 9-11, July, 2013, @DESY
Analytical modeling of colliding nuclei, Kharzeev, McLerran, Warringa, NPA (2008)
Pre-equilibrium
QGP
Time evolution of the magnetic field after collisions
Simple estimates by Lienard-Wiechert potential
Still a few orders stronger than the “critical field”
Time evolution of the matter “QGP” after the collision
Strong magnetic field
EM probe
Hadronic probe
QGP Hadronization Hadron gas
Pre-equilibrium
QGP
CollisionIncidenceLorentz construction
Magnetic field
QGP
Photon splitting: γ+B 2γ, avoiding Furry’s theorem
Refraction of photon, without Lorentz symmetry
Dilepton emission from real photon decay, as well as virtual photon γ* e+e-
Modifications of photon propagations by nonlinear QED effects
Photon vacuum polarization tensor with the dressed fermion propagators:
Modified Maxwell eq. :
EM probes would carry away info of initial stage.
Break-down of naïve perturbation in strong magnetic 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 heavy ion collisions, B/Bc ~ O(104) >> 1
Resummation w.r.t external legs by “proper-time method “Schwinger
Nonlinear to the external field
Photon propagation in a constant external magnetic fieldLorentz and gauge symmetries lead to a tensor structure,
B
θ: angle btw B-field and photon propagation
Eigen-equations from the modified Maxwell eq.
Following from the tensor structure, we obtain distinct eigenmodes!!
“Vacuum birefringence”
with eigenvectors,
Melrose and Stoneham
Scalar coefficient functions χ by the proper-time method
Schwinger, Adler, Shabad, Urrutia, Tsai and Eber, Dittrich and Gies
Given by a double integral wrt proper time variablesassociated with two fermion lines
Vacuum birefringence has been led by the tensor structure.
What dynamics is encoded in the scalar functions, χi ?
Decomposition into a double infinite sum
Analytic integration without any approximation
Polarization tensor has an imaginary part above
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)
Summary of relevant scales and available calculations for χ’s
(Photon momentum)
With a great contribution of Ishikawa-san (Hiroshima Univ.), complete photon propagator in strong B-field is now available.
Dielectric constant / refractive index by self-consistent treatment
Close look at the lowest Landau level
Vacuum polarization tensor from the LLL
Dielectric constant at the LLL
Polarization excites only along the magnetic field
Comparison with numerical result
LLL approx. agrees with numerical result in strong field limit
Kohri & Yamada
Modified photon dispersion relation from the vacuum polarization tensor
Modified Maxwell eq. :
Dispersion relation of q
Consistent solution wrt the real and imag. parts
Air ( 1atm, 0℃ ): n=1.0003Water (20℃) : n=1.333Calcite: no=1.6584, ne=1.4864
Complex refractive index from the lowest-Landau-level
Re[n] on unstable branchRe[n] on stable branch
Br = (50,100,500,1000,5000,10000, 50000)
Relation btw. real and imaginary partson unstable branchIm[n] on unstable branch
Dependence on magnetic-field strength
Angle dependence of the refractive index
Photon decay length in strong magnetic field
Propagating EM field:
Intensity of the field:
Photon decay length:
Direction of arrow : direction of photon propagation
Norm of arrow : magnitude of the refraction index
Magnetic field
Angle dependence of the refractive indexShown as a deviation from unit circle
Angle dependence at various photon energies
Real part
No imaginary part
Imaginary part
Implications in heavy-ion collisions
Strong BQGP
quark
gluons
photons
Synchrotron radiation of photon/gluon from quark
K.Tuchin, PRC (2010), [hep-ph/1209.0799] (2012)
Magnetic field induced photon/gluon emissions
Effects on photon HBT interferometry
Modified refractive index induces a distorted HBT image
K.Itakura and KH (2011)
Decay of real photon induces negative contribution to photon’s v2
Decay of real photon induces positive contribution to dilepton’s v2
Also, there would be effects on the higher harmonics
Effects on anisotropic flow
Needs systematic studies in HIC.
Summary of 1st part
- We analytically evaluated the photon vacuum polarization tensor in external magnetic fields.
- We inspected the complex dielectric constant/refraction index around the lowest-Landau-level threshold with a self-consistent treatment.
Prospects- Application to EM probe in heavy-ion collisions and magnetar. Polarization dependence, Energy and angle dependences…
Competition/interplay between birefringence and splitting
Pion reactions in strong magnetic fields
is coming soon.
Scalar coefficient functions χ in the proper-time method
Schwinger, Adler, Shabad, Urrutia, Tsai and Eber, Dittrich and Gies
Given by a double integral wrt proper time variablesassociated with two fermion lines
Dimesionless variables
Exponentiated trig-functions generate strongly oscillating behavior witharbitrarily high frequency.
Integrands having strong oscillation
Vacuum birefringence has been led by the tensor structure.
What dynamics is encoded in the scalar functions, χi ?
Analytic calculation of the double integral
Any term reduces to either of elementary integrals.
Two important relations
Associated Laguerre polynomial
★
★
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
Extremely strong magnetic field in the direction of the out-of-reaction plane
Geometry of the peripheral collision and strong B-field
b
Finite impact parameter
Lorentz - contracted nuclei
Primordial and thermalized matter
An extremely strong magnetic field in Ultrarelativistic Heavy-Ion Collision
Direct photon from initial stage in UrHIC
Space (z)
Time Various hadron emissions& photon from hadron decay, π0 2γ
Intermediate and hard regime :emission from primordial matter
Direct photon spectrum
Low Pt regime: dominant emission in hadron phase
Initial and background photons
Directly accessible to the initial stage and QGP
Thermalization
Interaction with B-field
?
Detecting photon from the initial stage⇔ Detecting effects of B-field
Polarization in dielectric medium : a classical argument
Incident light
Schematic picture of the birefringence
Dissipation Linear bound force
Anisotropic constants result in an anisotropic response.
What happens with the anisotropic (discretized) spectrum by the Landau-levels ?
Incident light field
Lorentz-type dispersion :
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
Photon decay channel opens at every Landau level
Analytic results!Applicable to any momentum regime and field strength !
Combination of known functions
Applicable to both on-shell and off-shell photon!
Sum wrt Landau levels