Strong-field physics
in(low-energy) heavy-ion collisions
Hidetoshi TAYA
(RIKEN iTHEMS)

Purpose

ContentsLow-energy HIC might be useful to study strong-(electric-)field phys.
・ Review strong-field physics at HIC・ Not to advertise my works, but to stimulate discussions (hopefully…)
・ Discuss (or introduce or speculate) implications to low-energy HIC(・ Comments and/or criticisms are very welcome)

1. Review of strong-field physics
・ Why is strong-field physics interesting and can be relevant to hadron/QCD ?

2. Strong-field physics in high-energy HIC
3. Strong-field physics in low-energy HIC・ Vacuum (dielectric) polarization
・ Electric-field induced birefringence1. Review of strong-field physics
2. Strong-field physics in high-energy HIC
3. Strong-field physics in low-energy HIC
4. Summary

New extreme condition: Strong EM fieldNew extreme condition: Strong EM field

VacuumNew extreme condition: Strong EM field

𝑭𝑭Vacuum

Weak fields (𝒆𝒆𝒆𝒆⁄𝒎𝒎𝟐𝟐 ≪ 𝟏𝟏)
Perturbative physics⇒ Very well understoodin both exp.& theor.

ex.) electron anomalous magnetic moment
𝛼𝛼 −1 theor. = 137.03599914 …
= 137.03599899 …
𝛼𝛼 −1 exp.

[Aoyama, Kinoshta, Nio (2017)]

high-energy processes in accelerator exp.

New extreme condition: Strong EM field

𝑭𝑭𝑭𝑭Vacuum

Weak fields (𝒆𝒆𝒆𝒆⁄𝒎𝒎𝟐𝟐 ≪ 𝟏𝟏)

𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭…

Strong fields (𝒆𝒆𝑭𝑭⁄𝒎𝒎𝟐𝟐 ≫ 𝟏𝟏)

Perturbative physics

Non-perturbative physics⇒ Very well understoodin both exp.& theor.

⇒ Unexplored in both exp. & theor.

ex.) electron anomalous magnetic moment
𝛼𝛼 −1 theor. = 137.03599914 …
= 137.03599899 …
𝛼𝛼 −1 exp.

[Aoyama, Kinoshta, Nio (2017)]

high-energy processes in accelerator exp.

Strong-field phenomena✔ Novel QED processes

Review: [Fedotov, Ilderton, Karbstein, King, Seipt, HT, Torgrimsson (2022)]ex.) Schwinger mechanism, Photon splitting, Vacuum birefringence, …
(= polarization dep. reflective index)～

vacuumStrong-field phenomena✔ Novel QED processes

Review: [Fedotov, Ilderton, Karbstein, King, Seipt, HT, Torgrimsson (2022)]ex.) Schwinger mechanism, Photon splitting, Vacuum birefringence, …
(= polarization dep. reflective index)～

vacuum

✔ Impacts on hadron physics and QCD[HT (2015)]

ex. 1) Hadron properties:⇒ masses, charge dist.,
decay modes, polarization, …
See also recent review [Iwasaki, Oka, Suzuki (2021)]

ex. 2) Phase diagram and transition:[D’Elia et al. (2022)]⇒ (Inverse) magnetic catalysis, Inhomogeneous phase, …
See also Hattori’s talk on Sat.

ex. 3) Others: Anomalous transport phenomena, Glasma, chirality prod., …
Many reviews, e.g., [Kharzeev, Liao, Voloshin, Wang (2016)][Hattori, Huang (2017)] …

See Yang’s talk on Sat.

Strong-field phenomena✔ Novel QED processes

Review: [Fedotov, Ilderton, Karbstein, King, Seipt, HT, Torgrimsson (2022)]ex.) Schwinger mechanism, Photon splitting, Vacuum birefringence, …
(= polarization dep. reflective index)～vacuum✔ Impacts on hadron physics and QCD[HT (2015)]

ex. 1) Hadron properties:⇒ masses, charge dist.,
decay modes, polarization, …
See also recent review [Iwasaki, Oka, Suzuki (2021)]

ex. 2) Phase diagram and transition:[D’Elia et al. (2022)]⇒ (Inverse) magnetic catalysis, Inhomogeneous phase, …
See also Hattori’s talk on Sat.

ex. 3) Others: Anomalous transport phenomena, Glasma, chirality prod., …
Many reviews, e.g., [Kharzeev, Liao, Voloshin, Wang (2016)][Hattori, Huang (2017)] …

See Yang’s talk on Sat.

✔ Experimentally, however (almost) NONE of them has been verified

Development of intense laser✔ Experimental progress is mainly lead by laser physics
Adapted from [Mourou, Tajima, Bulanov (2006)]

𝒆𝒆𝒆𝒆, 𝒆𝒆𝒆𝒆~ 𝟓𝟓𝟓𝟓𝟓𝟓 𝐤𝐤𝐤𝐤𝐤𝐤 𝟐𝟐𝟏𝟏𝟏𝟏𝟐𝟐𝟐𝟐

Strong-field regime

Current strongest laser
𝐼𝐼 > 1017 eV 4CoReLS @ Korea

𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

Laser intensity 𝐼𝐼 𝐞𝐞𝐞𝐞 𝟒𝟒

Critical field for electrons[Yoon et al., (2021)]

𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

Birth of laser

Near-future laser
𝐼𝐼 > 1018 eV 4e.g., ELI @ Europe

Invention ofCPA technique𝟏𝟏𝟏𝟏𝟗𝟗𝟏𝟏𝟏𝟏𝟒𝟒1960 ’70‘80’90 2000 ’10‘20𝐼𝐼 ∼ 1016 eV 4
HERUCLES @ USA[Yanovsky et al., (2008)]

Development of intense laser✔ Experimental progress is mainly lead by laser physics
Adapted from [Mourou, Tajima, Bulanov (2006)]

𝒆𝒆𝒆𝒆, 𝒆𝒆𝒆𝒆~ 𝟓𝟓𝟓𝟓𝟓𝟓 𝐤𝐤𝐤𝐤𝐤𝐤 𝟐𝟐𝟏𝟏𝟏𝟏𝟐𝟐𝟐𝟐

Strong-field regime

Current strongest laser
𝐼𝐼 > 1017 eV 4CoReLS @ Korea

𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏Laser intensity 𝐼𝐼 𝐞𝐞𝐞𝐞 𝟒𝟒

Critical field for electrons[Yoon et al., (2021)]

𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

Birth of laser

Near-future laser
𝐼𝐼 > 1018 eV 4e.g., ELI @ Europe

Invention ofCPA technique𝟏𝟏𝟏𝟏𝟗𝟗𝟏𝟏𝟏𝟏𝟒𝟒1960 ’70‘80’90 2000 ’10‘20

𝐼𝐼 ∼ 1016 eV 4
HERUCLES @ USA[Yanovsky et al., (2008)]✔ However, still weaker even than QED scale⇒ Any physical systems where strong fields are available ? ⇒ HIC !

1. Review of strong-field physics
2. Strong-field physics in high-energy HIC
3. Strong-field physics in low-energy HIC
4. Summary

Strong fields in high-energy HIC
B∝JJb

JAnimation stolen from Internet✔ Strong magnetic fields are created in high-energy HIC(also strong vorticity
cf. talks by Niida, Huang,Yi, Xin-Li, Liao)Strong fields in high-energy HIC[Deng, Huang (2012)]
See also [Bzdak, Skokov (2012)] [Hattori, Huang (2016)]✔ Strong magnetic fields are created in high-energy HIC(also strong vorticity
cf. talks by Niida, Huang,Yi, Xin-Li, Liao)

Pros: Extremely strong (strongest in the current Universe) (𝑒𝑒𝑒𝑒 ≫ Λ2QCD )Cons: Extremely short-lived (𝜏𝜏 ≪ 1 fm/𝑐𝑐 )⇒ Affects “non-perturbativeness” of strong-field processes

Shorter lifetime, less non-perturbative✔ If lifetime is short, no time for multiple interactions
𝑭𝑭𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

…

𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

Shorter lifetime, less non-perturbative✔ If lifetime is short, no time for multiple interactions
𝑭𝑭𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

𝑭𝑭

…

✔ “Phase diagram” (for the pair production from the vacuum by E field)
・ Three dim. para. characterize the system 𝑒𝑒𝑒𝑒, 𝜏𝜏, 𝑚𝑚⇒ Two dim.-less para. control the interplay
𝛾𝛾 =𝑚𝑚=𝑒𝑒𝑒𝑒 𝜏𝜏𝑒𝑒𝑒𝑒 𝜏𝜏
𝜈𝜈 ==1/𝜏𝜏(rest mass of particle)(work done by field)(work done by field)(photon energy)= (“strength” of the work)= (# of photons involved)

・ Non-perturbative for 𝜸𝜸 ≪ 𝟏𝟏 , 𝝂𝝂 ≫ 𝟏𝟏
・ For high-energy HIC: 𝑒𝑒𝑒𝑒 ∼ 1 GeV

2𝑭𝑭𝑭𝑭

𝑭𝑭𝑭𝑭

[HT, Fujiii, Itakura (2014)]

Non-perturbative
High-energy HIC(for 𝒎𝒎~𝚲𝚲𝐐𝐐𝐐𝐐𝐐𝐐 )Perturbative(LO pert. is enough)10−3 𝑚𝑚 = Λ QCD, 𝜏𝜏 ∼ 0.1 fm⁄𝑐𝑐 ⇒ 𝛾𝛾 ∼ � −5, 𝜈𝜈 ∼ 0.1
10𝑚𝑚 = 𝑚𝑚e

Shorter lifetime, less non-perturbative✔ If lifetime is short, no time for multiple interactions
𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭𝑭…

𝑭𝑭𝑭𝑭✔ “Phase diagram” (for the pair production from the vacuum by E field)

Non-perturbative⇒ Two dim.-less para. control the interplay
𝑚𝑚=𝑒𝑒𝑒𝑒 𝜏𝜏𝑒𝑒𝑒𝑒 𝜏𝜏𝜈𝜈 ==1/𝜏𝜏(rest mass of particle)(work done by field)(work done by field)(photon energy)= (“strength” of the work)= (# of photons involved)

・ Non-perturbative for 𝜸𝜸 ≪ 𝟏𝟏 , 𝝂𝝂 ≫ 𝟏𝟏・ For high-energy HIC: 𝑒𝑒𝑒𝑒 ∼ 1 GeV

2𝑭𝑭[HT, Fujiii, Itakura (2014)]

・ Three dim. para. characterize the system 𝑒𝑒𝑒𝑒, 𝜏𝜏, 𝑚𝑚𝛾𝛾 =𝑭𝑭High-energy HIC(for 𝒎𝒎~𝚲𝚲𝐐𝐐𝐐𝐐𝐐𝐐 )Perturbative(LO pert. is enough)10−3 𝑚𝑚 = Λ QCD, 𝜏𝜏 ∼ 0.1 fm⁄𝑐𝑐 ⇒ 𝛾𝛾 ∼ � −5, 𝜈𝜈 ∼ 0.1
10𝑚𝑚 = 𝑚𝑚e✔ High-energy HIC is useless for strong-field physics ?

⇒ Not necessarily useless. Still useful to study higher order QED processes

Experimental progress✔ Strong-magnetic-field induced processes are explored✔ First observations of higher-order QED processes(= prior to intense laser and any other experiments !)ex. 1) Light-by-light scattering[ATLAS (2016)]

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

Experimental progress✔ Strong-magnetic-field induced processes are explored✔ First observations of higher-order QED processes(= prior to intense laser and any other experiments !)ex. 1) Light-by-light scattering[ATLAS (2016)]

ex. 2) Breit-Wheeler process[STAR (2019)]✔ No evidence for QCD x strong B field phenomena[STAR (2021)]ex. ) Negative result for chiral magnetic effect at isobar collisions at RHIC

Experimental progress✔ Strong-magnetic-field induced processes are explored✔ First observations of higher-order QED processes(= prior to intense laser and any other experiments !)ex. 1) Light-by-light scattering[ATLAS (2016)]

ex. 2) Breit-Wheeler process[STAR (2019)]✔ No evidence for QCD x strong B field phenomena[STAR (2021)]ex. ) Negative result for chiral magnetic effect at isobar collisions at RHIC
✔ Nice experimental progress, but our goal was to study NON-pert. stuffs…
⇒ Any ways to study non-perturbative QED and/or QCD x QED phenomena ?
⇒ LOW-energy HIC may be useful1. Review of strong-field physics
2. Strong-field physics in high-energy HIC
3. Strong-field physics in low-energy HIC
4. Summary

Strong fields in low-energy HIC✔ Low energy ⇒ Landau’s stopping picture
・ Net proton rapidity dist. dN/dy[Esumi (2007)]AGS

・ Time evolution at middle/low-energy HIC
O(10 AGeV)O(10 AMeV)

Collision
EnergySPS
RHIC 62[Nara (1999; proc)]

RHIC 200
LHC 5500[Maruyama, Bonasera, Papa, Chiba (2002)]⇒ Dense matter is formed for not-short-time 𝑶𝑶(𝟏𝟏𝟏𝟏 − 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝐟𝐟𝐟𝐟/𝒄𝒄)

Strong fields in low-energy HIC✔ Low energy ⇒ Landau’s stopping picture
・ Net proton rapidity dist. dN/dy[Esumi (2007)]AGS

・ Time evolution at middle/low-energy HIC
O(10 AGeV)O(10 AMeV)

Collision
EnergySPS
RHIC 62[Nara (1999; proc)]

RHIC 200
LHC 5500[Maruyama, Bonasera, Papa, Chiba (2002)]⇒ Dense matter is formed for not-short-time 𝑶𝑶(𝟏𝟏𝟏𝟏 − 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝐟𝐟𝐟𝐟/𝒄𝒄)✔ Strong electric field is created via formation of “High Z atom” s.t. 𝒁𝒁 > 𝟏𝟏/𝜶𝜶・ No electric current ⇒ Negligible magnetic fields
𝑍𝑍𝑍𝑍・ Rough estimate of electric-field strength: 𝑒𝑒𝑒𝑒 ∼ 𝑟𝑟 2 ∼ Λ2QCD ∼ 100 MeV 210−1𝑚𝑚⇒ 𝛾𝛾 =<�𝑒𝑒𝑒𝑒𝑒𝑒 ∼ 10−4𝑚𝑚 = Λ QCD∼ 0.1, 𝜈𝜈 = 𝑒𝑒𝑒𝑒𝜏𝜏 2 > 10 ⇒ Non-pert. �𝜸𝜸 ≪ 𝟏𝟏 for QED & QCD !
∼𝝂𝝂 ≫ 𝟏𝟏𝑚𝑚 = 𝑚𝑚e

Possible strong-field phenomena ?
✔ Low-energy HIC might be useful to study strong-electric-field physics✔ As example, I introduce two possible QED phenomena(no one has ever observed those strong-field phenomena, so it is very impactful if we could observe them with HIC)

・ Vacuum (dielectric) polarization

Pioneering works [Pieper, Greiner (1969)][Gershtein, Zeldovich (1970)]
Recent review [Rafelski, Kirsch, Muller, Greiner (2016)]
Recent attempts [Maltsev et al. (2019)] [Popov et el. (2020)]- An old but unsolved problem that is worthwhile to be re-investigated now
・ Electric-field induced birefringence(・ QCD x strong E field phenomena could also occur, but I don’t discuss here)(e.g., chiral symmetry restoration, anomalous transports such as CESE, …)[Suganuma, Tatsumi (1993)][Huang, Liao (2013)]

Vacuum (dielectric) polarization (1/2)✔ At high energy, B was important, but at low energy E may be important
Magnetic B field ⇒ System is stable ↔ Electric E field ⇒ UNstable

Vacuum (dielectric) polarization (1/2)✔ At high energy, B was important, but at low energy E may be important
Magnetic B field ⇒ System is stable ↔ Electric E field ⇒ UNstable✔ Spontaneous pair production and vacuum （dielectric) polarization
・ For constant field ⇒ Schwinger mechanism
Energypositive energy states
gap
Dirac sea
x=0xConst E

[Schwinger (1951)]

𝑉𝑉 = −𝑒𝑒𝑒𝑒𝑒𝑒tunnelingVacuum (dielectric) polarization (1/2)✔ At high energy, B was important, but at low energy E may be important
Magnetic B field ⇒ System is stable ↔ Electric E field ⇒ UNstable✔ Spontaneous pair production and vacuum （dielectric) polarization
・ For constant field ⇒ Schwinger mechanism[Schwinger (1951)]

𝑉𝑉 = −𝑒𝑒𝑒𝑒𝑒𝑒

Energypositive energy states
gap

Const E

tunneling

Dirac sea
x=0

Energyxcontinuum+mdiscrete

𝑉𝑉 = −-m𝑍𝑍𝑍𝑍
𝑟𝑟

・ Similar for Coulomb field- Difference: energy is discretized below 𝐸𝐸 < +𝑚𝑚

r=0r⇒ Tunneling occurs only if there’re levels at 𝐸𝐸 < −𝑚𝑚 ⇐ Satisfied for 𝑍𝑍 > 𝛼𝛼 −1[Pieper, Greiner (1969)] [Gershtein, Zeldovich (1970)]- Tunneling ⇒ positron is emitted & the vacuum is (electrically) polarizedVacuum (dielectric) polarization (2/2)✔ Theoretical expectation:

Non-trivial positron spectrum at low energies

Vacuum (dielectric) polarization (2/2)✔ Theoretical expectation:

Non-trivial positron spectrum at low energies
subcritical✔ Experimental status[Wang et al. (2013)]

・Analogous phenomenon
was observed with graphene

supercritical

Vacuum (dielectric) polarization (2/2)✔ Theoretical expectation:

Non-trivial positron spectrum at low energies
subcritical✔ Experimental status[Wang et al. (2013)]

・Analogous phenomenon
was observed with graphene

supercritical・ Should observe something similar in HIC, but …
Low-energy HIC exp. O(10 MeV/u) were done in 80-90’s but were inconclusive[Cowan et al. (EPOS coll.) (1985)]⇒ couldn’t eliminate contaminations from nuclear excitations[Heinz et al. (ORANGE coll.) (2000)]⇒ Conclusion: more detailed exp. & theor. studies are needed
Theor.: Realistic EM field, realtime dynamics, …

cf. [Maltsev et al. (2019)][Popov et el. (2020)]

Exp: Energy/Z/angular dependencies, precision, …

Vacuum birefringence by E-field (1/2)✔ “Tilting” of the vacuum also affects the propagation of photons⇐ Electrons in the Dirac sea has “distributions” due to quantum reflection
E field

𝑉𝑉 = −𝑒𝑒𝑒𝑒𝑒𝑒

in-coming
Reflected
out-going

positive energy statesDistribution of electrons
EnergyDirac seaxgap

Vacuum birefringence by E-field (1/2)✔ “Tilting” of the vacuum also affects the propagation of photons⇐ Electrons in the Dirac sea has “distributions” due to quantum reflection
E field

𝑉𝑉 = −𝑒𝑒𝑒𝑒𝑒𝑒

in-coming
Reflected
out-going

positive energy states

Distribution of electrons
EnergyDirac seagapx✔ Interactions b/w photon and the Dirac sea modifies the prop. of photon(1) Photon decay and refraction reflects the Dirac-sea structure(2) E field has direction, so the refractive index have preferred direction⇒ BirefringenceVacuum birefringence by E-field (2/2)
E field

E fieldℰ ∝ e−i𝜔𝜔𝜔𝜔

E field✔ A very preliminary result for const E-field + electric wave

𝒟𝒟 = 𝜀𝜀ℰ = 𝑛𝑛2 ℰ = 1 + 𝜒𝜒 ℰ

Vacuum birefringence by E-field (2/2)
E field

E fieldℰ ∝ e−i𝜔𝜔𝜔𝜔

E field✔ A very preliminary result for const E-field + electric wave

𝒟𝒟 = 𝜀𝜀ℰ = 𝑛𝑛2 ℰ = 1 + 𝜒𝜒 ℰ

✔ Change of imaginary & real parts of electric permittivity 𝜺𝜺Im 𝜀𝜀 𝐸𝐸 − 𝜀𝜀 0 /𝑒𝑒 2(non-linear Breit-Wheeler)

𝑒𝑒𝐸𝐸 ⁄𝑚𝑚2 = 0.25

Optical thm.
(Kramers-Kronig rel.)Real part ⇒ photon birefringenceRe 𝜀𝜀 𝐸𝐸 − 𝜀𝜀 0 /𝑒𝑒 2Imaginary part ⇒ photon decay[HT, Ironside, in prep]

𝑒𝑒𝐸𝐸 ⁄𝑚𝑚2 = 0.25

・ Oscillating behavior
larger prob. density ⇒ affects more
⇐ Oscillating distributions of electrons in the Dirac sea
・ Polarization dependent⇒ Measure photon polarization and angular dist.

1. Review of strong-field physics
2. Strong-field physics in high-energy HIC
3. Strong-field physics in low-energy HIC
4. Summary

Message

Summary

Low-energy HIC might be useful to study strong-(electric-)field phys

1. Review of strong-field physics
・ Interesting: Novel chance to explorer the non-pert. regime of QED & QCD

2. Strong-field physics in high-energy HIC・ Strongest magnetic field is created⇒ leading to the first observations of higher-order QED processes(e.g., Breit-Wheeler pair production, light-by-light scattering)・ But is short-lived, affecting the “non-perturbativeness” of the strong-field processes

3. Strong-field physics in low-energy HIC・ Strong electric field with relatively long lifetime would be created

・ Vacuum (dielectric) polarization & electric-field induced birefringence⇒ May affect the low-energy positron/photon spectrum・ Less investigated and so interesting to explorer strong QED & QCD x QEDprocesses in low-energy HIC