Strong field QED effects in the quantum vacuum generated by - - PowerPoint PPT Presentation

Motivation/theory

Strong field QED effects in the quantum vacuum generated by laser-electron interactions

• A. Hartin

Universit¨ at Hamburg/DESY (UCL from 1st Jan)

LUXE meeting, DESY December 7th, 2017

• A. Hartin

Strong field QED effects

Motivation/theory

Motivation - physics in strong background fields

Vacuum polarisation

+ − + − + − + − + − + − + − + − + − + + − − + − + + + + + + − − − + − + + + + + − − − − − − − −

Strong External Field Virtual dipole screen

e−

Bare/Dressed charge

Heisenberg uncertainty, Casimir force

• virtual particles are real!

Strong background field polarises the vacuum The screening charge is rearranged, leading to possibly large effects even at modest field strengths At Schwinger critical field strength, vacuum decays into real pairs New phenomenology results - odd vertex diagrams, resonant propagators, different manifestations

• f IR divergences

Careful studies will allow planned experiments that test strong field theory Need to investigate experimental signatures within reach using today’s and upcoming technology

• A. Hartin

Strong field QED effects

Motivation/theory

Loop corrections in an external field

anomalous magnetic moment (one-loop) in a charge bunch field

∆µ µ0 = α 2π

∞

2π dx (1 + x)3

x

Υ

1/3 Gi x

Υ

1/3

ILC 1TeV CLIC 3TeV

Non perturbative QFT wrt background field changes the vacuum Even for small field strength, there is a predicted correction to the AMM Experimental tests.. see V. G. Baryshevsky and A. O. Grubich, Sov. J. Nucl.

• Phys. 44, 721 (1986)
• A. Hartin

Strong field QED effects

Motivation/theory

(W.H.) Furry Picture

Separate gauge field into external Aext

µ and

quantum Aµ parts

LInt

QED= ¯

ψ(i/ ∂−m)ψ− 1

4 (Fµν)2−e ¯

ψ( / Aext+ / A) ψ LFP

QED= ¯

ψFP(i/ ∂−e / Aext−m)ψFP− 1

4 (Fµν)2−e ¯

ψFP / A ψFP

Euler-Lagrange equation → new equations of motion requires exact (w.r.t. Aext) solutions ψFP

(i/ ∂− e / Aext− m)ψFP=0

For certain classes of external fields (plane waves, Coloumb fields and combinations) exact solutions exist [Volkov Z Physik 94 250 (1935), Bagrov and

Gitman, Exact solutions of relativistic wave equations (1990)]

ψFP=Ep e−ip

· x up,

Ep=exp

• −

1 2(k·p) (e /

Aext/ k+i2e(Ae·p)−ie2Aext2)

• A. Hartin

Strong field QED effects

Motivation/theory

1st and 2nd order Furry picture processes

x k p

f f

p

i

f

k

f

p

i

p p

i

k

x y

1st order intense field process:

High Intensity Compton Scattering (HICS) pi + nk → pf + kf intense laser field included to all orders Volkov Ep functions ”dress the vertex”

2nd order intense field processes:

Stimulated Compton Scattering (SCS) pi + ki + nk → pf + kf extra propagator poles leading to physically accessible resonances related to energy level structure of vacuum

ALL processes are in effect ”strong field” processes

• A. Hartin

Strong field QED effects

Motivation/theory

Unstable Strong field particles & resonant transitions

x k p

f f

p

i

Electrons decay in strong field Furry picture

Background field renders vacuum a dispersive medium new effects: Lamb shift, vacuum birefringence, resonant transitions electron has a finite lifetime, Γ and probability of radiation, W

Resonant transitions in propagator

required by S-matrix analyticity Optical theorem W = Im(Σ) extra propagator poles leading to physically accessible resonances related to energy level structure of vacuum

Similar decay (one photon pair production) and lifetime for photons

• A. Hartin

Strong field QED effects

Motivation/theory

Furry picture propagator & it’s pole structure

propagator poles have a new structure due to contributions from the strong field nk

GFP=

• d4p

(2π)4 Ep(x) / p+m p2−m2 ¯

Ep(x′) eip·(y−x) pole condition: (pi+ki+nk)2=m2

f

k

f

p

i

p

1

x

p

i

k

2

x

• Resonance conditions:

ωi ω = n 1 + β + ω(1 − cos θi)/γ 1 + β cos θi + a2

0(1 − cos θi)/2γ2(1 + β)

n = 0 = ⇒ ωi = 0 ”normal” IR divergence

• interpretation in terms of Zeldovich quasi-energy levels
• The IR divergence is the base energy level

n=1 n=2 n=3

Energy

• 1. Calculate the width of the energy levels (avoids poles)
• 2. Include other processes with same pole structure

We need to calculate Furry Picture loop diagrams

• A. Hartin

Strong field QED effects

Motivation/theory

Multiphoton/nonlinear radiation (HICS process)

dW ∆t = rem2ρω ωǫi

∞

• n=1

u

n

du (1 + u)2

• 4

ξ J2

n−

2+2u+u2 (1 + u) (J2

n-1+J2 n+1−

2 J2

n)

• un=

2n k·p m2(1 + ξ) and Bessel function arguments, z=2 n

• ξ

1+ξ u un

• 1−

u un

• photon

electron Scattered e− beam laser Intense Radiated

Multiphoton events from a single vertex Mass shift: Compton edge shifts with strong laser intensity Onset of nonlinear effects at ξ > 0.1 Intensity dependent radiated photon energy, ωf ωf = ω

nγ2(1 + β)2 γ2(1 + β)(1 − β cos θf) + (ξ/2 + nωγ(1 + β))(1 + cos θf)

• A. Hartin

Strong field QED effects

Motivation/theory

One and two step trident processes

x ki p

+

p

_

f

p p

i x y

p q l

cut

2step: HICS + One photon pair production:

Initial state produced by photon radiation pprod onset is 4nωωi

m2

≥ 2m2

∗

ki + nk → p+ + p− Observed with 46.6 GeV primary electrons (SLAC, E144) Studies underway by LUXE theory team!

Trident process:

One step process, virtual particle exchange pi + nk → pf + p+ + p− Resonant propagator poles/Breit-Wigner resonances due to bound states Res diff x-section can exceed that of 1st

• rder process by orders of magnitude
• A. Hartin

Strong field QED effects

Motivation/theory

SCS resonances in probe laser angle scan

Scattered photon electron Scattered e− beam laser Intense Probe laser

key ratio for resonance is

ωi ω ∈ Z

resonances broadened by larger a0(ξ) resonances smeared out by short laser pulses Probe laser 2 eV, intense laser 1 eV electrons 10 MeV, detector at 160o

1 10 100 1000 10000 88 88.5 89 89.5 90 90.5 91 91.5 92

diff x-sect /(α2/32m2) incoming photon angle

v2=0 v2=0.2 v2=0.5 v2=2.0

Probe laser 4 eV, intense laser 1 eV electrons 40 MeV, detector at 175o

10 100 1000 10000 115 116 117 118 119 120 121 122 123 124 125

diff x-sect /(α2/32m2) incoming photon angle

v2=0 v2=0.2 v2=0.5 v2=2.0 v2=5.0

• A. Hartin

Strong field QED effects

Motivation/theory

Stimulated photon splitting rate at resonance

k

1

k2

y x z

a b c

l

f

p p

i

electron Scattered e− beam Intense laser Split photon

At resonance, photon propagator on-shell, multiply differential rates of separate processes dWPS = dW HICS

1 Γ2 dΠ(3)FP

Assume N=1010 electrons per bunch, 50 keV (split) photons dWPS ≈ 1 event per 2 bunch collisions

• Order of magnitude estimate
• Without resonance,

1 event per 104 bunches

• Doable at resonance?

experimental considerations

• Need detailed calculation
• A. Hartin

Strong field QED effects

Motivation/theory

Resonant Dark Photon/Axion searches

Vector PseudoScalar

Dark Sector Standard Model

Axion, a Dark photon, A’

f

p p

i

p+ p

_

A’

γ

a,

BSM mechanisms to explain dark matter Dark photon - spontaneously broken U(1) Axion - spontaneously broken Peccei-Quinn L = g′e ¯ ψγψA′ L =

1 fa

¯ ψγγ5ψ∂µa Strong field QFT allows resonant production of dark bosons. Rate is increased by order of 1/Γ2 ≈ 1/α2 ≈ 104 at resonant peak dW = dW HICS

1 Γ2 dW PPROD

Resonant peaks shift with mass of virtual particle - a potentially good discriminator for axion/dark photon exchange

• A. Hartin

Strong field QED effects