anisotropic dilepton spectrum induced by chiral anomaly in strong magnetic fields
DESCRIPTION
Anisotropic dilepton spectrum induced by chiral anomaly in strong magnetic fields. In collaboration with Kaz . Itakura and Sho Ozak i. Koichi Hattori ( Yonsei Univ.) NFQCD@YITP, 12 th Dec. 2013. Possible signature of the early-time dynamics. Key ingredient 1: Strong fields . - PowerPoint PPT PresentationTRANSCRIPT
Anisotropic dilepton spectrum induced by chiral anomaly in strong magnetic fields
Koichi Hattori (Yonsei Univ.)NFQCD@YITP, 12th Dec. 2013
In collaboration with
Kaz. Itakura and Sho Ozaki
Key ingredient 1: Strong fields
Chromo electromagnetic fields Magnetic fields (QED)
Key ingredients 2: EM probes
Possible signature of the early-time dynamics
Penetrating probes porters carrying information of the early-time dynamics.
Possible effects of strong magnetic fields on 1. neutral pions related to dilepton spectra KH, K.Itakura, S.Ozaki, 20132. direct-photon propagations (vacuum polarization tensor) KH, K. Itakura (I) (II) 2013
Challenging on both theoretical and experimental sides!
Violation of axial current conservation
Absence of radiative correction Adler & Bardeen, 1960Triangle diagram gives the exact result in the all-order perturbation theory
Adler, Bell, Jackiw, 1959
Dominant (98.798 % in the vacuum)
99.996 %
``Dalitz decay ‘’ (1.198 % in the vacuum)
NLO contribution to the total decay rate Only corrections to external legs are possible
LO contribution to the total decay rate
Effects of external magnetic fields
Decay mode possible only in external field
“Bee decay” can be comparable to Dalitz decay and even π0 2γ, depending on B.
Replacement of a photon line by an external field
Decay width of “Bee decay”
WZW effective vertexπ0γ
Dalitz decay
Bee decay
Decay widths
Mean lifetime
femtometer
Branching ratios
Analytical modeling of colliding nuclei, Kharzeev, McLerran, Warringa, NPA (2008)
Pre-equilibrium
QGP
Strong magnetic fields in UrHIC
Event-by-event analysis, Deng, Huang (2012)
Au-Au 200AGeV b=10fm
Lifetime of B-field is shorter than the lifetime of neutral pions.
No chance to observe the new decay mode in the heavy-ion collisions.
Neutral-pion production from prompt γ* in strong B-fieldsPrompt γ* are produced in hard parton scatterings.
Gluon compton scattering in LO annihilation in LO
Without B-fields, mostly converted into dileptons.
+ Prompt photons are produced at the impacts of AA (pp, pA) collisions, so that converted into π0 in B-fields (and π0 decays outside B-fields).
Rapidly decaying B-field
π0γ*
Dilepton-production from γ* are suppressed.
A new neutral-pion production mechanism.
Given amount of γ*
Conversions of prompt γ* to pions in strong B-fieldsπ0 (only in B-fields)
Dileptons
Negative v2 of dileptons
Strong time-dependence of B-fields Energy transfer from B-fieldsLienard-Wiechert potentials Fourier componentTime-dependence
Dilepton yield in the presence of B-field Elliptically anisotropic pion productions
Summary in part 1
We investigated conversions between neutral pions and virtual photons in external magnetic fields.
+ A new decay channel “Bee decay” becomes possible, and becomes even the dominant decay mode in strong B-fields. Can be important in macroscopic systems such as the magnetars (neutron stars).
+ Oriented pion production from prompt virtual photon gives rise to a negative v2 of dileptons (and a positive v2 of neutral pions).
Photon propagations in strong magnetic fields
“Vacuum birefringence” and “real-photon decay”
What is “Birefringence” ?
Doubled image due to a ray-splitting in birefringent substances
Polarization 1Polarization 2
Incident light“Calcite” (方解石 )
Two polarization modes of a propagating photon have different refractive indices.
How about the vacuum with external magnetic fields ?
+ Lorentz & Gauge symmetries n ≠ 1 in general
+ Oriented response of the Dirac sea Vacuum birefringence
Modifications of photon propagations in strong B-fields
Magnetic field
QGP
Refraction of photon in the vacuum with B-fieldswithout medium effects
Real photon decay Dilepton emissions from real photon decay, as well as virtual photon conversions (γ* e+e- )
Could be important in pre-equilibrium stage,
and in QGP additively to medium effects
Photon vacuum polarization tensor:
Modified Maxwell eq. :
Dressed propagators in Furry’s picture
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 Furry’s picture
In heavy ion collisions, B/Bc ~ O(104) >> 1
Resummation w.r.t. external legs by “proper-time method“ Schwinger
Nonlinear to strong external fields
Schwinger, Adler, Shabad, Urrutia, Tsai and Eber, Dittrich and Gies
Exponentiated trig-functions generate strongly oscillating behavior witharbitrarily high frequency.
Integrands having strong oscillations
Photon propagation in a constant external magnetic fieldLorentz and gauge symmetries lead to a tensor structure,
θ: angle btw B-field and photon propagation
B
Summary of relevant scales and preceding calculations
Ultrarelativistic heavy-ion collisions
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
Decomposition into a double infinite sum
Analytic results of integrals without any approximation
Polarization tensor acquires an imaginary part above
Every term results in either of three simple integrals.
Summary of relevant scales revisited- An infinite number of the Landau levels
(Photon momentum) Narrowly spaced Landau levels
Renormalization
+= ・・・+ +
Log divergence
Subtraction term-by-term
Ishikawa, Kimura, Shigaki, Tsuji (2013)
Taken from Ishikawa, et al. (2013)
Finite
Re Im
Complex refractive indices
The Lowest Landau Level (ℓ=n=0)
Dielectric constant at the LLL
Polarization excites only along the magnetic field``Vacuum birefringence’’
Solutions of Maxwell eq. with the vacuum polarization tensor
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 in RHIC and LHC
Angle dependence of the refractive indexReal part
No imaginary part
Imaginary part
Summary in 2nd part
We obtained the general analytic form of the resummed 1-loop polarization tensor in magnetic fields as the summation w.r.t. the Landau levels.
+ Confirmed to reproduce the preceding approximate calculations. Ishikawa, Kimura, Shigaki, Tsuji
+ We obtained the complex refractive indices (photon dispersions) by solving the modified Maxwell Eq.
+ Neutral pions and dileptonsClose look at phenomenology including competing effects.
+ Real photonsApplications of photon propagation to phenomenologies in the heavy-ion collisions and the magnetars (neutron stars).
Prospects
Branching of virtual prompt photon
q q2 Im
2 Im q q
Anisotropic on-shell pion production
Fourier component of an external field Anisotropic pion production
Isotropic dilepton production
Effective coupling between π0 and 2γ
(Rest frame)
Neutral pion decay into dilepton
Bext = (0,0,B), Eext = 0
EM current
q q
Neutral pion decay into dilepton (continued)
Decay rates in three modes Mean lifetime
Energy dependence of the decay rates
Field-strength dependence of the branching ratio
Angle dependence of the branching ratio Angle dependence of the lifetime
Primakoff effect
Recent measurement in JLab (2011)(PrimEX collaboration)
Prompt photon from hard parton scatterings
+ Prompt photons are produced at the moment of AA (pp, pA) collisions, so that they have much chance to interact with B-field.
Gluon compton scattering in LO annihilation in LO
Profiles of time-dependence magnetic fields
Time-dependence Fourier component
q0
π0
kq=q0+k
γ
Number of neutral pions increaseNumber of dilepton decrease
Elliptically anisotropic pion productions
Positive v2 of neutral pionsNegative v2 of dileptons
Neutral-pion production from prompt γ* in strong B-fields
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
Analytic representation of Pmn(q,B)
• Infinite summation w.r.t. n and l = summation over two Landau levels• Numerically confirmed by Ishikawa, et al. arXiv:1304.3655 [hep-ph]• couldn’t find the same results starting from propagators with Landau level decomposition
Dielectric constant at the lowest-Landau-level
Dielectric constant at the LLL
Polarization excites only along the magnetic field
ArcTan : source of an imaginary part above the lowest threshold
Angle dependence of the refractive index
Direction of arrow : direction of photon propagation
Norm of arrow : magnitude of the refraction index
Magnetic field
Shown as a deviation from unit circle
Complex refractive index
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