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 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 Vacuum polarisation At Schwinger critical field strength, vacuum decays into real pairs Strong External Field New phenomenology results - odd − − vertex diagrams, resonant + + − − + − propagators, different manifestations − + − − + + of IR divergences + + + − − + e− − + + − + − − − + Careful studies will allow planned + + − + + + + − + − experiments that test strong field + − − + − − + theory − − Virtual dipole screen Need to investigate experimental signatures within reach using today’s Bare/Dressed charge 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 � ∞ � x � x � 1 / 3 � 1 / 3 ∆ µ α 2 π dx µ 0 = Gi (1 + x ) 3 2 π Υ Υ 0 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 A ext µ and quantum A µ parts L Int QED = ¯ ∂ − m ) ψ − 1 4 ( F µν ) 2 − e ¯ A ext + / ψ ( i/ ψ ( / A ) ψ A ext − m ) ψ FP − 1 4 ( F µν ) 2 − e ¯ ψ FP / L FP QED = ¯ ψ FP ( i/ A ψ FP ∂ − e / Euler-Lagrange equation → new equations of motion requires exact (w.r.t. A ext ) solutions ψ FP A ext − m ) ψ FP =0 ( i/ ∂ − e / 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)] x u p , � � ψ FP = E p e − ip 2( k · p ) ( e / 1 A ext / k + i 2 e ( A e · p ) − ie 2 A ext 2 ) · E p =exp − A. Hartin Strong field QED effects
Motivation/theory 1st and 2nd order Furry picture processes p k f f 1st order intense field process: High Intensity Compton Scattering (HICS) x p i + nk → p f + k f intense laser field included to all orders p Volkov E p functions ”dress the vertex” i p k 2nd order intense field processes: f f Stimulated Compton Scattering (SCS) y p i + k i + nk → p f + k f p extra propagator poles leading to physically accessible resonances x related to energy level structure of vacuum p k i i ALL processes are in effect ”strong field” processes A. Hartin Strong field QED effects
Motivation/theory Unstable Strong field particles & resonant transitions Electrons decay in strong field Furry picture p k f f Background field renders vacuum a dispersive medium x new effects: Lamb shift, vacuum birefringence, resonant transitions electron has a finite lifetime, Γ and p probability of radiation, W i 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 p k f f x 2 d 4 p p + m G FP = / E p ( x ′ ) e ip · ( y − x ) p 2 − m 2 ¯ � (2 π )4 E p ( x ) p pole condition: ( p i + k i + nk ) 2 = m 2 x 1 p k i i • Resonance conditions: Energy ω i 1 + β + ω (1 − cos θ i ) /γ n=3 ω = n 1 + β cos θ i + a 2 0 (1 − cos θ i ) / 2 γ 2 (1 + β ) n=2 n = 0 = ⇒ ω i = 0 ”normal” IR divergence • interpretation in terms of Zeldovich quasi-energy levels n=1 • The IR divergence is the base energy level 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) Intense laser � u r e m 2 ρ ω 2+2 u + u 2 � � dW du 4 ∞ n ξ J 2 (1 + u ) ( J 2 n -1 +J 2 2 J 2 Radiated n ) ∆ t = � n − n +1 − photon Scattered (1 + u ) 2 ωǫ i 0 electron n =1 � 2 n k · p ξ u u � � u n = and Bessel function arguments, z =2 n 1 − m 2 (1 + ξ ) 1+ ξ u n u n e− beam 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, ω f nγ 2 (1 + β ) 2 ω f = ω γ 2 (1 + β )(1 − β cos θ f ) + ( ξ/ 2 + nωγ (1 + β ))(1 + cos θ f ) A. Hartin Strong field QED effects
Motivation/theory One and two step trident processes 2step: HICS + One photon pair production: Initial state produced by photon radiation p p _ pprod onset is 4 nωω i + ≥ 2 m 2 ∗ m 2 x k i + nk → p + + p − Observed with 46.6 GeV primary electrons (SLAC, E144) k i Studies underway by LUXE theory team! p Trident process: i p One step process, virtual particle exchange l p i + nk → p f + p + + p − y x Resonant propagator poles/Breit-Wigner cut q resonances due to bound states p f Res diff x-section can exceed that of 1st order process by orders of magnitude A. Hartin Strong field QED effects
Motivation/theory SCS resonances in probe laser angle scan Intense Probe laser 2 eV, intense laser 1 eV laser electrons 10 MeV, detector at 160 o 10000 v2=0 v2=0.2 v2=0.5 v2=2.0 di ff x-sect /( α 2 /32m 2 ) Scattered 1000 photon Scattered electron 100 10 1 88 88.5 89 89.5 90 90.5 91 91.5 92 incoming photon angle Probe laser Probe laser 4 eV, intense laser 1 eV e− beam electrons 40 MeV, detector at 175 o 10000 v2=0 v2=0.2 v2=0.5 ω i v2=2.0 di ff x-sect /( α 2 /32m 2 ) key ratio for resonance is ω ∈ Z v2=5.0 1000 resonances broadened by larger 100 a 0 ( ξ ) resonances smeared out by short 10 115 116 117 118 119 120 121 122 123 124 125 laser pulses incoming photon angle A. Hartin Strong field QED effects
Motivation/theory Stimulated photon splitting rate at resonance At resonance, photon propagator on-shell, p k multiply differential rates of separate i 1 processes a y l 1 b d W P S = d W HICS Γ 2 d Π (3) FP x z c Assume N= 10 10 electrons per bunch, 50 keV (split) photons p k 2 f d W P S ≈ 1 event per 2 bunch collisions Intense laser • Order of magnitude estimate Split photon Scattered • Without resonance, electron 1 event per 10 4 bunches • Doable at resonance? experimental considerations • Need detailed calculation e− beam A. Hartin Strong field QED effects
Motivation/theory Resonant Dark Photon/Axion searches BSM mechanisms to explain dark matter Dark photon - spontaneously broken U(1) Dark photon, A’ Vector Axion - spontaneously broken Peccei-Quinn Dark Standard Sector Model PseudoScalar L = g ′ e ¯ ψγψA ′ Axion, a 1 ψγγ 5 ψ∂ µ a ¯ L = f a p i Strong field QFT allows resonant production of p _ dark bosons. Rate is increased by order of 1/ Γ 2 ≈ 1 /α 2 ≈ 10 4 at resonant peak A’ a, γ 1 d W = d W HICS Γ 2 d W PPROD p + p Resonant peaks shift with mass of virtual f particle - a potentially good discriminator for axion/dark photon exchange A. Hartin Strong field QED effects
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