Nonperturbative calculations and open problems of QED in ...€¦ · Ritus-Narozhnyconjecture a 0...

Intro. Pair production Mass Infra-red High χ Conclusions

Nonperturbative calculations and open problems ofQED in strong external fields

Anton Ilderton

SLAC NPQED 2019

Ilderton, PRD 99 (2019) 085002 [arXiv:1901.00317]Ilderton, to appear


Outline

1. Ritus-Narozhny conjecture

2. Constant fields and beyond: three examples

Sauter-Schwinger effect

Ritus mass

Infra-red emission

3. Ritus-Narozhny conjecture beyond constant fields


Ritus-Narozhny conjecture

Furry expansion:QED coupling α runs, but typically small.

Treat perturbatively

Coupling to background: a0 “eE

mω

a0 ą 1: treat exactly

+ +

Furry expansion is a vital tool for theory and expt.

Ñ SLAC E144, recent & planned expt, all PIC codes, etc.

Conjecture: Furry expansion breaks down.Narozhnyi, JETP 28 (1969) 371; Ritus, JETP 30 (1970) 1181


Ritus-Narozhny conjecture

a0 “eE

mωØ intensity b “

ω

mγ Ø energy χ “ a0b

Review: Fedotov J.Phys.: Conf.Ser. 826 (2017)

Constant crossed field E.B “ 0 “ E2 ´B2

Loops: power law scaling with αχ2{3

Ñ Furry breakdown as αχ2{3 Ñ 1 (χÑ 1600)

How to calculate? Physics unknown. (Need to resum all loops)

Quantum effects: χ ą 0.01. Recently: χ » 0.1 . . . 1.Cole et al PRX 8 (2018), Poder et al PRX 8 (2018)


Non-perturbative pair production

A sufficiently strong electric field E can collapse into pairs:

PV T

„ peEq2 exp

„

´ πm2

eE

Non-perturbative effect. See talk by Gerald Dunne

Exponential supression below ES :“ m2{e

Assumes a constant & homogeneous field.

Schwinger effect: how to go beyond constant fields?


Sauter-Schwinger effect in non-constant fields

Locally Constant Field Approximation?

Ppairs „ V TE2 exp”

´πESE

ı

?ÝÑ

ż

d4xE2pxq exp”

´πESEpxq

ı

Q. When does this work?

A1. Often a good approximation. Schneider et al PRD 98 (2018)

A2. Not exact in general. Nikishov NPB 21 (1970)Narozhnyi & Nikishov Sov.J.Nucl.Phys. 11 (1970), Dunne et al PRD73 (2006)

A3. Only exact for E “ Ept` zq.Tomaras et al PRD 62 (2000)

Ilderton JHEP 1409 (2014)


Semiclassical approximation

Semiclassical approx: P „ exp”

´ iSpxclqı

Instanton: periodic classical path. Complex-valued1.

m:xµcl “ eFµνpxclq 9xνcl

Example:

E ” E0 sech2pωqq with q “ λ t`?1´ λ2 z

Interpolating spacetime dependence

´iSpxclq „

¿

dq 9q 9q2 “ λ` a20 tanh2pωqq

Contour integral over the instanton in the complex plane.

1Lavrelashvili et al NPB 329 (1990), Kim & Page PRD 75 (2007), Bender et al PRL 104 (2010), Dumlu& Dunne PRD 84 (2011), Ilderton Torgrimsson Wårdh PRD 92 (2015)


Semiclassical approximation

Semiclassical approx: P „ exp”

´ iSpxclqı

Instanton: periodic classical path. Complex-valued1.

m:xµcl “ eFµνpxclq 9xνcl

Example: E ” E0 sech2pωqq with q “ λ t`?1´ λ2 z

Interpolating spacetime dependence

´iSpxclq „

¿

dq 9q 9q2 “ λ` a20 tanh2pωqq

Contour integral over the instanton in the complex plane.

1Lavrelashvili et al NPB 329 (1990), Kim & Page PRD 75 (2007), Bender et al PRL 104 (2010), Dumlu& Dunne PRD 84 (2011), Ilderton Torgrimsson Wårdh PRD 92 (2015)


Interpolating instantons

Complex qpτq plane E ” Epqq , q “ t` 0z

-1 1

- Π2

Π2 Time-dependent.

Instanton circles a branch.

Extended / nonlocal.

Exact results in Eptq:not LCFA.



Complex qpτq plane E ” Epqq, q “ 0.9t` 0.4z

-1 1

- Π2

Π2

Time & space dependent.

Branch points move closer.

Extended / nonlocal



Complex qpτq plane E ” Epqq , q “ 0.7pt` zq

-1 1

- Π2

Π2

q: lightfront time.Brodsky et al Phys.Rept. 301 (1998)

Branch cut Ñ pole.

Instantons Ñ points (Cauchy)Ilderton Torgrimsson Wårdh PRD 92 (2015)

Localisation when LCFA exact.

LCFA: exception, not rule.


Field-dependent mass shift

“Mass operator” (elastic scattering) in constant E.Ritus, ZhETF 75 (1978) & 76 (1979)

F0 = iF1 = N0 =`F0 = iF1 = N0 =„ m

ˆ

1´α

2

E

ES

˙

m “ renormalised. Field-dependent mass correction.

Classical! – survives ~Ñ 0 limit..

Two-loop effective action; ImÑ pair productionLebedev & Ritus, Sov.Phys.JETP 59 (1984)

P „ e2E2 exp”

´ πm2

eE

ı´

1` απ¯2

Conjecture: loops exponentiate? Beyond constant fields?


Field-dependent mass shift

“Mass operator” (elastic scattering) in constant E.Ritus, ZhETF 75 (1978) & 76 (1979)

F0 = iF1 = N0 =`F0 = iF1 = N0 =„ m

ˆ

1´α

2

E

ES

˙

m “ renormalised. Field-dependent mass correction.

Classical! – survives ~Ñ 0 limit..

Two-loop effective action; ImÑ pair productionLebedev & Ritus, Sov.Phys.JETP 59 (1984)

P „ e2E2 exp”

´ π1

eEm2

´

1´α

2

E

ES

¯2ı

Conjecture: loops exponentiate ùñ same mass appears.? Beyond constant fields?


The infra-red in the LCFA

Bremsstrahlung: σ „

ż

ωIR

dk

k„ logωIR

Constant crossed fields: σ „

ż

ωIR

dk

k2{3„ 0

F 0=

iF1

=N

0=

k

E.B “ 0 “ E2 ´B2

Softening of IR divergence: feature or bug?

Same behaviour in PIC codes using LCFA.Harvey Ilderton King PRA 91 (2015), DiPiazza et al PRA 98 (2018)

Exact plane wave calculation: Ą crossed field as limit.


The infra-red in plane waves

Photon emission in plane wave IR divergent ðñ Ep0q “ 0

e.g. constant for finite duration

σ „ Ep0q logωIRloooooomoooooon

` finite termsloooooomoooooon

contains CCF limit

Missed if assumed constant from the start.Ò

Dinu et al, PRD 86 (2012)

CCF result does not generalise: no softening of IR.Ilderton Torgrimsson PRD 87 (2013)

LCFA at odds with QED in the IR.


A closer look at high χ behaviour.

All for constant crossed fields.

E.B “ 0 “ E2 ´B2

Look at pulsed plane waves.

Depends only on χ

Processes depend on a0 & b

χ “ a0b compositeDifferent ways to reach high χ

Expect logs. Why 2{3? Ñ Airy

No Airy functions?Airy reappears in LCFA

Ritus, J.Russ.Laser Res. 6 (1995) 497

No exact results. . . see below. . .




E.B “ 0 “ E2 ´B2 Look at pulsed plane waves.

Depends only on χ

Processes depend on a0 & b









E.B “ 0 “ E2 ´B2 Look at pulsed plane waves.

Depends only on χProcesses depend on a0 & b







Same χ, different high.

Look at existing pulse (plane wave) calculations.

π 2π 3π 4π

Emax

π 2π 3π 4π

Emax

Different ways to reach the same high χ “ a0b.

Behaviour of physical processes is not universal.Baier & Katkov Sov.Phys.JETP 26 (1968), Khokonov TPL 31 (2005)

Dinu, Harvey, Ilderton, Marklund, Torgrimsson PRL 116 (2016)

Compare high-χ behaviour as a0 Ñ8 or bÑ8.

Podszus & DiPiazza PRD 99 (2019)

Ilderton PRD 99 (2019)


Summary: nonlinear Compton & spin flip

F0 = iF1 = N0 = andF0 = iF1 = N0 =

High intensity, a0 Ñ8 gap High energy, bÑ8

P „αa

2{30

b1{3

„αχ2{3

bP „

αa20b

log b „ αa30χlogχ

(χ „ a0 Ñ8) (χ „ bÑ8)

‚ Same from LCFA ‚ High χ (energy) scaling: log.

‚ Cannot reproduce bÑ8



F0 = iF1 = N0 = andF0 = iF1 = N0 =


P „αa

2{30

b1{3„αχ2{3

b

P „αa20b


(χ „ a0 Ñ8)

(χ „ bÑ8)

‚ Same from LCFA

‚ High χ (energy) scaling: log.




F0 = iF1 = N0 = andF0 = iF1 = N0 =


P „αa

2{30

b1{3„αχ2{3

bP „

αa20b

log b

„ αa30χlogχ

(χ „ a0 Ñ8)

(χ „ bÑ8)

‚ Same from LCFA

‚ High χ (energy) scaling: log.




F0 = iF1 = N0 = andF0 = iF1 = N0 =


P „αa

2{30

b1{3„αχ2{3

bP „

αa20b


(χ „ a0 Ñ8) (χ „ bÑ8)

‚ Same from LCFA ‚ High χ (energy) scaling: log.



Summary: photon helicity flip at high χ

ϵ′µ ϵµ

detector


P „α2χ4{3

b2P „ α2 a

60

χ2

`

1`# logχ˘

pχ „ a0 Ñ8q pχ „ bÑ8q

LCFA cannot reproduce high-energy behaviour.

Taking a0 Ñ8 precludes taking bÑ8.


Discussion: high energy

1. “High χ” can be reached by high energy.

2. High χ-energy behaviour; logs as usual.

3. High energy limit not recovered from constant field / LCFA.(e.g. impossible to obtain log terms)

4. Corollary: LCFA (& PIC!) has wrong high energy behaviour.(But tough to reach this regime.)


Discussion: high intensity

1. αχ2{3 scaling appears to persist in pulses.

2. R-N conjecture applies beyond constant fields.. . . if LCFA holds . . .

3. What if LCFA does not hold?

-2 -1 1 2ϕ

-2 -1 1 2ϕ

a0

sech2 plane wave Ñ delta function in limit.Ilderton, to appear


Ultra-short pulses

Exact, closed form results for pair production, γ emission,& related one-loop processes

High-intensity behaviour: Ilderton, to appear

Ppair „4

3

α

πlog a0 , PNLC „

12α

πlog2 a0

(Leading-log only.)

No power law! Slow log increase instead.

Scaling different when LCFA does not hold.

Difference in behaviour: comes from the infra-red...


Conclusions

New physical effects in strong background fields.

Ritus-Narozhny conjecture: uncharted strong field regime?

Many open questions re RN conjecture.

High χ not universal: not at high energy or in short pulse.

LCFA? (Fails in the IR and the UV).

If there: effects to improve Furry expansion?

Resummation? Inclusion of back-reaction? Depletion?For the future!

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