Strong-field physics
in heavy-ion collisions
Hidetoshi Taya( RIKEN )PlanInteraction b/w heavy-ion & strong-field communities must be useful !
(1) Heavy-ion coll. can be used as a tool to study strong-field QED(2) The knowledge of strong-field QED can be used to understand heavy-ion coll.

1. One-page introduction of heavy-ion collisions
2. Creation of strong EM field in heavy-ion coll.
・ Different creation mechanisms at high and low energies
・ “Non-perturbativeness” of the EM field⇒ Non-perturbative regime can be accessed by low-energy collisions[Nishimura (Osaka), Ohnishi (Kyoto), HT, in preparation]

3. Open question in HIC, related to strong color physics
・ Non-equilibrium dynamics of QGP formation[HT, Ph. D thesis]

1. One-page introduction of heavy-ion collisions
2. Creation of strong EM field in heavy-ion coll.
3. Open question in HIC, related to strong color physics
4. Summary

What is heavy-ion collisions ?

Animation stolen from Internet✔ Accelerator experiments at RHIC @ Brookhaven (2000~) & LHC @ CERN (2010~)✔ The goal: Understand the origin of matter(1) Reproduce an extremely high temperature & dense state just after the Big Bang(2) Understand properties of matter under extreme conditions, i.e., quark-gluon plasma (QGP)(3) Better understand the fundamental theory of matter, i.e., quantum chromodynamics (QCD)✔ Current status:
Energy regime of 𝐸𝐸CM = 𝑂𝑂 100 GeV − 5 TeV per nucleon has been studied experimentally

・ Many successful results (e.g., realization of 𝑇𝑇 = 𝑂𝑂 1012 K , QGP found to be perfect liquid , … )・ But still remain various theoretical problems (e.g., non-equilibrium dynamics of QGP formation)
・ Future plan: go to higher 𝑂𝑂 40 TeV (e.g., FCC＠CERN) or lower energies 𝑂𝑂 1 GeV (FAIR@GSI, NICA@JINR, …)

1. One-page introduction of heavy-ion collisions
2. Creation of strong EM field in heavy-ion coll.
3. Open question in HIC, related to strong color physics
4. Summary

Strong B field in heavy-ion coll. at high energies
JbJB∝J✔ Strong magnetic field is created (∵ large 𝑍𝑍 ∼ 80, large velocity 𝑣𝑣 ≈ 𝑐𝑐 or 𝛾𝛾 ∼ 102−3 ⇒ large 𝐽𝐽)

Strong B field in heavy-ion coll. at high energies[Deng, Huang (2012)]
See also [Bzdak, Skokov (2012)] [Hattori, Huang (2016)]✔ Strong magnetic field is created (∵ large 𝑍𝑍 ∼ 80, large velocity 𝑣𝑣 ≈ 𝑐𝑐 or 𝛾𝛾 ∼ 102−3 ⇒ large 𝐽𝐽)
Pro: Super strong 𝑒𝑒𝑒𝑒 = 𝑂𝑂 1 GeV 2 ≈ 𝑂𝑂(1042 W/cm2 )(Strongest in the Universe !)Cons: Extremely short-lived 𝜏𝜏 ≪ 1 fm⁄𝑐𝑐 = 𝑂𝑂(10−24 sec)
⇒ Affects “non-perturbativeness” of physics

Shorter lifetime ⇒ more perturbative✔ Intuition: No time for multiple interactions
𝑭𝑭𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

…

𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

Shorter lifetime ⇒ more perturbative✔ Intuition: No time for multiple interactions
𝑭𝑭𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

…

𝑭𝑭

𝑭𝑭

𝑭𝑭

✔ “Phase diagram” of strong-field physics

Non-pert.

・ Three dimensionful parameters in the system: e𝐸𝐸, 𝜏𝜏, 𝑚𝑚

High-energy HIC⇒ Two dim.-less parameters determine the physics𝑒𝑒𝑒𝑒 𝜏𝜏𝜈𝜈 ==1/𝜏𝜏(Typical energy)(Work by field)(Work by field)(Photon energy)

𝑭𝑭[HT, Fujiii, Itakura (2014)][HT, Fujimori, Misumi, Nitta, Sakai (2021)]

As example: Vacuum particle prod. by E field w/ finite lifetime𝑚𝑚𝛾𝛾 ==𝑒𝑒𝑒𝑒 𝜏𝜏𝑭𝑭Non-linear⇒ Characterize the magnitude of work

⇒ Characterize the number of photons

Pert.

(LO is enough)・ 𝛄𝛄 ≪ 𝟏𝟏 , 𝝂𝝂 ≫ 𝟏𝟏 ⇒ Non-perturbative, 𝛄𝛄 ≫ 𝟏𝟏 , 𝝂𝝂 ≪ 𝟏𝟏 ⇒ perturbative・ High-energy HIC: 𝑒𝑒𝑒𝑒 ∼ 1 GeV 2 , 𝜏𝜏 ∼ 0.1 fm⁄𝑐𝑐 ⇒ γ ∼ 10−5 , 𝜈𝜈 ∼ 0.1 (for QED 𝑚𝑚 = 𝑚𝑚𝑒𝑒 )Shorter lifetime ⇒ more perturbative✔ Intuition: No time for multiple interactions
𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭…

𝑭𝑭𝑭𝑭𝑭𝑭✔ “Phase diagram” of strong-field physics

Non-pert.

・ Three dimensionful parameters in the system: e𝐸𝐸, 𝜏𝜏, 𝑚𝑚

High-energy HIC⇒ Two dim.-less parameters determine the physics𝑒𝑒𝑒𝑒 𝜏𝜏𝜈𝜈 ==1/𝜏𝜏(Typical energy)(Work by field)(Work by field)(Photon energy)

𝑭𝑭[HT, Fujiii, Itakura (2014)][HT, Fujimori, Misumi, Nitta, Sakai (2021)]

As example: Vacuum particle prod. by E field w/ finite lifetime𝑚𝑚𝛾𝛾 ==𝑒𝑒𝑒𝑒 𝜏𝜏𝑭𝑭Non-linear⇒ Characterize the magnitude of work

⇒ Characterize the number of photonsPert.

(LO is enough)・ 𝛄𝛄 ≪ 𝟏𝟏 , 𝝂𝝂 ≫ 𝟏𝟏 ⇒ Non-perturbative, 𝛄𝛄 ≫ 𝟏𝟏 , 𝝂𝝂 ≪ 𝟏𝟏 ⇒ perturbative・ High-energy HIC: 𝑒𝑒𝑒𝑒 ∼ 1 GeV 2 , 𝜏𝜏 ∼ 0.1 fm⁄𝑐𝑐 ⇒ γ ∼ 10−5 , 𝜈𝜈 ∼ 0.1 (for QED 𝑚𝑚 = 𝑚𝑚𝑒𝑒 )⇒ High-energy heavy-ion coll. is meaningless for strong-field physics ?
⇒ Not necessarily. Still a good chance to study non-linear effects

Experimental results✔ Very first observation of high-order QED processes(Prior to any other experiments; e.g., high-power laser)ex. 1) Light-by-light scattering[ATLAS (2016)]

ex. 2) Breit-Wheeler process[STAR (2019)]

But, that’s all in HIC. Your input for more interesting observables needed !

Experimental results✔ Very first observation of high-order QED processes(Prior to any other experiments; e.g., high-power laser)ex. 1) Light-by-light scatteringex. 2) Breit-Wheeler process[ATLAS (2016)][STAR (2019)]

But, that’s all in HIC. Your input for more interesting observables needed !

✔ But, what we really want is something non-pert. !

...

So, heavy-ion is useless ??? ⇒ can be useful at low energies ！

Strong E field in heavy-ion coll. at low energies✔ Different mechanism due to nuclear stopping (Landau picture)
Low energy

High energy⇒≈

penetrate with each othermerge at the center⇒ current ⇒ B⇒ charge ⇒ E✔ The E field would be strong and long-lived
Rough idea: large atomic number 𝑍𝑍tot = 𝑍𝑍1 + 𝑍𝑍2 = 𝑂𝑂 150 ≳ 1/𝛼𝛼

⇒ Strong Coulomb field 𝑒𝑒𝐸𝐸 =𝛼𝛼𝑍𝑍tot𝑟𝑟 2≳ 𝑚𝑚𝑒𝑒2 over the Compton wavelength 𝑉𝑉 ≳ 𝑚𝑚𝑒𝑒−3

Estimation with hadron trans. model (JAM) (1/2)[Nishimura (Osaka), Ohnishi (Kyoto), HT, in progress]y✔ Time evolution of EM field (central coll. b=0) @ z=0・ Lorentz inv. 𝐹𝐹 ≔ 𝐸𝐸 2 − 𝐵𝐵2 (F>0: Electric, F<0: Magnetic)
ECM = 2.0 GeV

3.0 GeVx

4.0 GeV

6.3 GeVz
7.7 GeV50 MeV 450 MeV 450 MeV 450 MeV 450 MeV 40 MeV 40 MeV 40 MeV 40 MeV 40 MeV 4− 50 MeV 4− 50 MeV 4− 50 MeV 4− 50 MeV 4− 50 MeV 4・ Field strength can be strong as 𝑒𝑒 2 𝐹𝐹 ~ 𝑒𝑒𝐸𝐸 2 = 𝑂𝑂 50 MeV 4⇒ Very strong for QED (𝒎𝒎𝒆𝒆 = 𝟎𝟎. 𝟓𝟓𝟓𝟓𝟓𝟓 𝐌𝐌𝐌𝐌𝐌𝐌)

Estimation with hadron trans. model (JAM) (2/2)[Nishimura (Osaka), Ohnishi (Kyoto), HT, in progress]✔ Spacetime volume of EM field

Volume for𝑒𝑒 2 𝐹𝐹 = |𝑒𝑒𝑬𝑬|2 − 𝑒𝑒𝑩𝑩 2 > 30 MeV 4

Low energy HIC・ Strong E field with 𝑒𝑒 𝐹𝐹 ~ 𝑒𝑒𝑒𝑒 ~ 30 MeV ,lifetime 𝜏𝜏 ≳ 20 fm⁄𝑐𝑐 , volume 𝑉𝑉 ≳ 15 fm 3222

⇒ Non-perturbative !
∵γ=𝑚𝑚𝑚𝑚
or= 𝑂𝑂(0.1), 𝜈𝜈 = 𝑒𝑒𝑒𝑒𝜏𝜏 2 or 𝑒𝑒𝑒𝑒𝑙𝑙 2 = 𝑂𝑂(10)𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

Non-linearPert.

(LO is enough)Non-pert.

1. One-page introduction of heavy-ion collisions
2. Creation of strong EM field in heavy-ion coll.
3. Open question in HIC, related to strong color physics
4. Summary

Unsolved problem in HIC: Formation process of QGP

QGP

before coll.

coll.

QGP

hadron gas> 0 fm/c

0 fm/c~ 1 fm/c~ 10 fm/c

Unsolved problem in HIC: Formation process of QGP

QGP

before coll.

coll.

QGP

hadron gas> 0 fm/c

0 fm/c~ 1 fm/c~ 10 fm/c

Unsolved problem in HIC: Formation process of QGP

QGP

before coll.

coll.

QGPhadron gas> 0 fm/c

0 fm/c~ 1 fm/c~ 10 fm/c■ ⇒ Exp: Deep inelastic scattering
Theory: pQCD (or color glass condensate)■ ⇒ Exp: Many observables, e.g., collective flow, thermal photon, …
Theory: Relativistic hydrodynamics (with tiny viscosity)

Unsolved problem in HIC: Formation process of QGP？

QGP

before coll.

coll.

QGP

hadron gas> 0 fm/c

0 fm/c~ 1 fm/c~ 10 fm/c■ ⇒ Exp: Deep inelastic scattering
Theory: pQCD (or color glass condensate)■ ⇒ Exp: Many observables, e.g., collective flow, thermal photon, …
Theory: Relativistic hydrodynamics (with tiny viscosity)■ ⇒ Understood neither experimentally nor theoreticallyKey: Strong-field physics✔ The formation process of QGP= How does strong color EM field decay into a hydro. matter ?
Understand-ableわかるknown

Key: Strong-field physics✔ The formation process of QGP= How does strong color EM field decay into a hydro. matter ?
Understand-ableわかるknown

DIS @ HERA

High-energy heavy ions＝(valence) quarks

Super dense gluon state≃densitygluons(high) energy(low)“color charged plate”
with huge color charge density(𝜎𝜎 ∼ 𝑄𝑄𝑠𝑠2 ∼ 𝑂𝑂 1 GeV 2 )Key: Strong-field physics✔ The formation process of QGP= How does strong color EM field decay into a hydro. matter ?
Understand-ableわかるknown⇒“color capacitor”(w/ 𝜎𝜎 ∼ 𝑄𝑄𝑠𝑠2 ∼ 𝑂𝑂 1 GeV 2 )Generation ofstrong color EM field(𝑔𝑔𝑔𝑔, 𝑔𝑔𝑔𝑔 = 𝑂𝑂 1 GeV 2 )[Low, Nussinov, Casher, Neuberger (1970s)][McLerran, Lappi, Kovner, Weigert (2005)][Lappi (2006)]

× 1 GeV 4 ∼ 1042 W⁄cm≃

2 2

Just after a collision𝑠𝑠 𝜏𝜏−1× 1 𝑄𝑄GeVApplication of strong-field QED ideas✔ Borrowed ideas from strong-field QED・ Plasma instability (e.g., Weibel)
・ Schwinger effect

Review: [Mrowczynski (2006)](but not very successful at the moment …)[Kerman, Matsui, Gatoff (1987)] [Tanji (2008)] [HT (2017)]✔ I don’t explain today, but …
New ideas & techniques have been developed in HIC,
possibly useful in strong-field QED・ non-equil. attractor, non-equil. universality, hydrodynamization,
validity of classical/quantum description, …
・ 2PI formalism, classical statistical simulation, chiral kinetic theory,realtime lattice technique, …

Application of QED theory of Schwinger to HIC/QCD
QED: [Kluger, Eisenberg, Svetitsky, Cooper, Mottola (1990s)]✔ Mean-field treatment of the backreaction problem� 𝜈𝜈 𝜓𝜓
𝜕𝜕𝜇𝜇 𝐹𝐹𝜇𝜇𝜇𝜇 = 𝜓𝜓𝛾𝛾

Maxwell eq.
Dirac eq.

i𝜕𝜕 − 𝑒𝑒𝑒𝑒 − 𝑚𝑚 𝜓𝜓 = 0

Maxwell eq. for 𝐴𝐴̅

Split the total EM field 𝐴𝐴 into strong 𝐴𝐴̅ = 𝐴𝐴and quantum fluctuation 𝑎𝑎 as 𝐴𝐴 = 𝐴𝐴̅ + 𝑎𝑎

� 𝜈𝜈 𝜓𝜓𝜕𝜕𝜇𝜇 𝐹𝐹�𝜇𝜇𝜇𝜇 = 𝜓𝜓𝛾𝛾� 𝜈𝜈 𝜓𝜓 − 𝜓𝜓𝛾𝛾� 𝜈𝜈 𝜓𝜓𝜕𝜕𝜇𝜇 𝑓𝑓𝜇𝜇𝜇𝜇 = 𝜓𝜓𝛾𝛾i𝜕𝜕 − 𝑒𝑒𝐴𝐴̅ − 𝑚𝑚 𝜓𝜓 = 𝑒𝑒𝑒𝑒𝜓𝜓Maxwell eq. for 𝑎𝑎
Dirac eq.

QCD: [HT, Ph. D thesis (2017)]

annoying…

Mean-field approximation RHS → RHS

Maxwell eq. for 𝐴𝐴̅
Maxwell eq. for 𝑎𝑎
Dirac eq.

� 𝜈𝜈 𝜓𝜓
𝜕𝜕𝜇𝜇 𝐹𝐹�𝜇𝜇𝜇𝜇 = 𝜓𝜓𝛾𝛾
𝜕𝜕𝜇𝜇 𝑓𝑓𝜇𝜇𝜇𝜇=0i𝜕𝜕 − 𝑒𝑒𝐴𝐴̅ − 𝑚𝑚 𝜓𝜓 = 0

Solvable !
(numerically)Result: Particle distribution
𝐝𝐝𝟔𝟔 𝑵𝑵
Longtidinal distribution 𝟐𝟐
at 𝒑𝒑𝑻𝑻 ∼ 𝟎𝟎
𝐝𝐝𝒙𝒙𝑻𝑻 𝐝𝐝𝜼𝜼 𝐝𝐝𝒑𝒑𝟐𝟐𝑻𝑻 𝐝𝐝𝒑𝒑𝜼𝜼

GluonQuark✔ Plasma oscillation + Pauli blocking & Bose enhancement + Redshift by expansion✔ Particle yield after momentum integration ~ 1000 particles/rapidity⇒ consistent with exp. ⇒ ・ Schwinger effect is the mechanism of the particle prod. in HIC
・ QED technique is actually useful✔ But, not the end: mean-field theory does not explain thermalization⇒ need to go beyond mean-field ⇒ needs your inputs !

1. One-page introduction of heavy-ion collisions
2. Creation of strong EM field in heavy-ion coll.
3. Open question in HIC, related to strong color physics
4. Summary

PlanInteraction b/w heavy-ion & strong-field communities must be useful !
(1) Heavy-ion coll. can be used as a tool to study strong-field QED(2) The knowledge of strong-field QED can be used to understand heavy-ion coll.

1. One-page introduction of heavy-ion collisions
2. Creation mechanism of strong EM field in heavy-ion coll.

High energy
E = O(100 - 1000 GeV)

Different creation mechanisms at high and low energies⇒ strong B field at high energy, strong E field at low energy

3. Open question in HIC,
related to strong color physics

Low energy
E = O(1-10 GeV)
HIC

Non-pert.

Non-equilibrium dynamics of QGP formation⇒ Schwinger effect nicely explains
the particle-production process in HIC
but needs more to describe
the thermalization/hydrodynamization processPert.

(LO is enough)Non-linear