Strong field physics in high-energy heavy-ion collisions

Kazunori Itakura

(Theory Center, KEK) Heavy Ion Meeting July 18 th 2013 @ Orsay

Plan

• • • •

Introduction

what is strong field physics? why relevant for HIC? strong magnetic field in heavy-ion collisions

Photons in strong B

Hattori-Itakura AP 330, 334 (2013) vacuum birefringence and decay into e+e- pair photon’s HBT interferometry in HIC

Neutral pions in strong B

Hattori-Itakura-Ozaki, arXiv:1305.7224

new decay mode : p 0 +B  photon conversion into p 0 e+e- “Bee decay” in strong B

Summary

•

What

is strong field physics?

Characteristic phenomena that occur under strong gauge fields

(EM fields and Yang-Mills fields) •

Typically, weak-coupling but non-perturbative

ex) electron propagator in a strong magnetic field •

eB c



m e

2 1 

O

  

eB m e

2    

O

      

eB m e

2    2    

eE c

~

m e

2 Schwinger’s critical field must be resummed when B >> B

c



“Nonlinear QED effects”

A new interdisciplinary field:

involving high-intensity LASER physics, hadron physics (heavy-ion physics), condensed matter physics (exciton), astrophysics (neutron stars, magnetars, early universe)

•

Physics in Intense Fields @ DESY

Second meeting on strong field physics (successor of the previous meeting PIF2010 held in KEK)

•

Discussed various topics including

- Double Compton scattering - Vacuum birefringence - Schwinger mech. and real threshold?

dynamically assisted Schwinger mechanism - QED cascading, etc

All of these topics will be important also in heavy-ion collisions.

After a finite short time,

Quark-Gluon Plasma (QGP)

is created as a local equilibrium state

Little Bang

``Early thermalization” problem

How is it possible to thermalize in such a short period??

What happens in early time stages??

Original figure by P. Sorensen arXiv:0905.0174

Why

is it important in HIC?

•

Strong EM/YM fields appear in the very early time of heavy-ion collisions. In other words, the fields are strongest in the early time stages.

•

Indispensable for understanding the early-time dynamics in heavy-ion collisions

strong YM fields (glasma)  thermalization (not for today) strong EM fields  probe of early-time dynamics “Strong field physics” occurs only under strong fields. It must carry the information of the early time stages!!!

Strong magnetic fields in HICs

• Non-central HICs at RHIC and LHC provide STRONGEST magnetic fields.

10 4



eB max

Event-by-event analysis, Deng, Huang (2012) Strong

~ 1 – 10 m

p

Au-Au 200AGeV

>> m

e

140MeV 0.5MeV

eB/m e

2

b eB/m u

2 ~ O(10 5 ) t =0, O(10 2 3 ) t ~0.6fm

~ O(10 3 ) t =0, O(10 0 1 ) t ~0.6fm

for u quark

m u

~ 2MeV • Decay very fast: Strong field physics will be most prominent in very early time!

(though the fields are still strong enough even at QGP formation time)

We discuss

• •

Novel properties of photons and neutral pions strong magnetic fields in Possible observable effects in HICs

• •

HICs create many photons and neutral pions.

Both are charge neutral . But can be affected through fermion (quark or electron) one loop.

Photons in strong B

z

B q

Dressed fermion in external B • •

Properties of a photon propagating in a magnetic field

 vacuum polarization tensor P mn (

q

,

B

)

Old but new problem

[Weisskopf 1936, Baier-Breitenlohner 1967, Narozhnyi 1968, Adler 1971] - Polarization tensor P mn (

q

,

B

) has been known in integral form - Analytic representation obtained very recently [Hattori-Itakura 2013]

Magnetic vacuum as a media

Propagating photon in strong magnetic field

= probing magnetic vacuum “polarized” by external fields ~ photon couples to virtual excitation of vacuum (cf: exciton-polariton)

B dependent anisotropic response of a fermion

(Landau levels) - discretized transverse vs unchanged longitudinal motion  Two different refractive indices :

VACUUM BIREFRINGENCE

- energy conservation gets modified  Pol. Tensor can have imaginary part :

PHOTON DECAY INTO e+e- PAIR

(lots of astrophysical applications) T II parallel to B transverse to B present only in external fields  || mn  mn  

diag

( 1 , 0 , 0 , 1 ) 

diag

( 0 , 1 , 1 , 0 )

•

Vacuum birefringence

Maxwell eq. with the polarization tensor :

•

Dispersion relation of two physical modes gets modified



Two refractive indices : “Birefringence”

z

n

2  |

q

 2 | 2

B

1. Compute c 0 , c 1 , c 2 analytically at the one-loop level Hattori-Itakura Ann.Phys.330 (2013) 2. Solve them self-consistently w.r.t

n in LLL approx.

Hattori-Itakura Ann.Phys.334 (2013) g

q

m

x

Analytic representation of

P mn

(

q

,

B

)

Representation in double integral w.r.t. proper times corresponding to two propagators

Indeed, a recent review says,,,, arXiv: 1111.5984

Analytic representation of

P mn

(

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

B/B c

Refractive index

• Need to self-consistently solve the equation (effects of back-reaction) • Use LLL solution for simplicity  c 0  c 2  0 , c 1  0 𝜔 2 /4𝑚 2

n

|| 2

n

2   1  1  c 1 c 1 cos 2 q  1 , c 1  c 1 (

q

|| 2 ,

q

2  ,

B

) q

B q

|| 2   2 -

q z

2   2 ( 1 -

n

|| 2 cos 2 q ) = 500 (magnetar) | 2   2

n

|| 2 sin 2 q

q

2   |

q

 𝜔 2 /4𝑚 2 • • Refractive index n || deviates from 1 and increases with increasing  cf: air n = 1.0003, water n = 1.333

New branch at high energy is accompanied by an imaginary part  decay into an e+e- pair

Decay length

Amplitude of an incident photon decays exponentially characterized by the decay length Surviving length ~ life time Very short length  relevant for magnetars 𝜔 2 /4𝑚 2

B

Real part

Angle dependence

Photon mom.

direction Real part of n

Imaginary part

No imaginary part

• •

Consequences in HIC

Generates elliptic flow (v 2 ) and higher harmonics (v n )

(at low momentum region)

Distorted photon ``HBT image”

• •

Based on a simple toy model with moderate modification

Hattori & KI, arXiv:1206.3022

Photons emitted at early time will be affected Magnification (lensing) and distortion

Neutral pion decay

•

Chiral anomaly

induces p 0 decay through triangle diagram Dominant (98.798 % in vacuum) 99.996 % Dalitz decay (1.198 % in vacuum) NLO contribution •

Adler-Bardeen’s theorem

There is no radiative correction to the triangle diagram Triangle diagram gives the exact result in all-order perturbation theory  only two photons can couple to p 0

•

Neutral pions in strong B

Hattori , KI, Ozaki, arXiv:1305.7224[hep-ph] There is only one diagram for a constant external field to be attached e + p 0 g * e cf: axion (very light, but small coupling)

O

 

e

2

eB m

p 2  

B

p 0 +

B

 e + e “Bee” decay • Also implies -- conversion into g with space-time varying B -- Primakoff process* ( g * + B -- mixing of p 0 and g  p 0 ): important in HIC * observed in nuclear Coulomb field

Decay rates of three modes

Solid : “Bee” decay Dashed: 2 g decay Dotted : Dalitz decay

Mean lifetime

Magnetar Heavy Ion Collision

B

p

=B/m

p

2

t

life

  1

total

  2 g 1  

Dalitz

 

Bee

 Picometer  femtometer Energetic pions created in cosmic ray reactions will be affected

g

conversion into

p

0

in HICs

HICs create many high energy g s as well as g *s (decaying into dileptons) nucleus g / g * g / g * nucleus Gluon Compton scattering in LO

q

annihilation in LO Some of g * will convert into p 0 in strong B, inducing reduction of dilepton yield Conversion rate is strongest in perpendicular direction to B mostly dileptons  negative elliptic flow of dileptons B Reaction zone some of them convert into p 0 (less dileptons) • • p 0 will get positive v2 but difficult to see Depends on time profile of B fields LHC RHIC

Summary

• • • • •

Strong field physics can in principle provide useful information on early-time dynamics of HIC. Photons and neutral pions strong magnetic fields.

exhibit interesting phenomena in Photons show birefringence and can decay into e+e- pairs. We obtained analytic representation computed refractive indices. of the polarization tensor and Chiral anomaly suggests that neutral pions can decay into e+e without an accompanying photon, which becomes the dominant decay mode in strong magnetic fields. Conversion of a virtual photon into a neutral pion is also possible and can be seen as negative elliptic flow of dileptons in heavy-ion collisions.

1 Tesla = 10 4 Gauss

How strong?

10 17 —10 18 Gauss

 eB ~ 1 – 10 m p

: Noncentral heavy-ion coll. at RHIC and LHC 10 15 Gauss : Also strong Yang-Mills fields

 gB ~ 1– a few GeV

Magnetars 4x10 13 Gauss : “Critical” magnetic field of electrons



eB

c = m

e

= 0.5

MeV 45 Tesla : strongest steady magnetic field (High Mag. Field. Lab. In Florida)

10 8

Tesla=10 12 Gauss: Typical neutron star Super critical magnetic surface field may have existed in 8.3 Tesla : very early Universe. Superconducting Maybe after EW phase magnets in LHC transition? (cf: Vachaspati ’91)