ATLAS measurement of light-by-light scattering provides Constraint on Born-Infeld Theory from Light-by-Light Scattering at the LHC ATLAS measurement of light-by-light scattering provides first significant constraint on nonlinear extension of QED (suggested by string theory) John Ellis JE, Mavromatos & You, arXiv:1703.08450

Light-by-Light Scattering in QED Electron (charged particle) loops induce light-by-light scattering: γγγγ First calculations:

2-Loop calculation in QED + QCD Displaying fermion thresholds Bern, de Freitas, Dixon, Ghinculov & Wong, hep-ph/0109079

Opportunity at the LHC Cross-section at the LHC: D’Enterria & da Silveira, arXiv:1305.7142 Cross-section at the LHC: After experimental cuts:

Born-Infeld Theory Original Born-Infeld modification of QED: Based on “unitarian” idea of maximum electromagnetic field, cf, velocity of light Limit on Coulomb potential

Born-Infeld & String Theory Original Born-Infeld modification of QED: Derived from string theory: in D dimensions: 4 dimensions: Limiting gauge field  brane velocity = light Mass scale M = √β 1/distance between branes, ≥ TeV? Born & Infeld 1934 Fradkin & Tseytlin 1985 Bachas, hep-th/9511043

Constraints on Born-Infeld Theory? Strongest constraint from electronic and muonic atom spectra: ? But derivation criticized Other probes of nonlinearities in light insensitive to Born-Infeld photon splitting in atomic fields Magnetic birefringence New constraint from observation of light-by-light scattering in heavy-ions: Soff, Rafelski & Greiner 1973 Carley & Kiessling, math-ph/0506069 Akhmadaliev et al., hep-ex/0111084 PVLAS Collaboration JE, Mavromatos & You, arXiv:1703.08450

Constraints on Nonlinearities Heisenberg-Euler: c0,2 = 7 c2,0  Born-Infeld: c0,2 = 4 c2,0 Birefringence experiments constrain Heisenberg-Euler, not Born-Infeld Fouché, Battesti & Rizzo, arXiv:1605.04102

Best Previous Constraint on Born-Infeld? Energy levels in atomic physics: ? BUT: spectral results invalid Carley & Kiesslingl, math-ph/0506069

First Measurement of Light-by-Light Scattering Peripheral heavy-ion collisions at the LHC: γγγγ Expected in ordinary QED from fermion loops ATLAS measurement agrees with QED Can be used to constrain nonlinearities in Born-Infeld ATLAS Heisenberg & Euler 1936 JE, Mavromatos & You: arXiv:1703.08450

Light-by-Light Scattering: QED vs Born-Infeld JE, Mavromatos & You, arXiv:1703.08450 Characteristic angular distributions Born-Infeld more isotropic, larger γγ masses γ angle

Light-by-Light Scattering: QED vs Born-Infeld JE, Mavromatos & You, arXiv:1703.08450 Characteristic mass distributions Born-Infeld larger γγ masses Conservative approach: use total # of ATLAS events Plausible approach: cut mγγ > 25 GeV (no events) Heisenberg & Euler 1936 Born & Infeld 1934 Invariant γγ mass

Constraint on Born-Infeld Scale JE, Mavromatos & You, arXiv:1703.08450 ATLAS constraint on σ(γγγγ) constrains M = √β All events with mγγ ≤ M: limit M ≈ 100, 210 GeV Assume σ = mγγ2 at higher masses: M ≈ 190, 330 GeV Entering range of low-scale brane models All ATLAS events mγγ > 25 GeV

Implications for Monopoles JE, Mavromatos & You, arXiv:1703.08450 So far have discussed Born-Infeld extension of QED Could also consider Born-Infeld extension of SM Born-Infeld extension of U(1)Y has an electroweak monopole, mass: Our result implies mass > 11 TeV  LHC, but  FCC-hh @ 100 TeV? Arunasalam & Kobakhidze, arXiv:1702.04068

Prospects Sensitivity to Born-Infeld in : γγγγ will increase with future LHC data Also FCC-hh Greatest γγγγ sensitivity at CLIC? benefiting from e+e- centre-of-mass energy of 3 TeV Cross-section grows as E8! Estimate sensitivity to Born-Infeld scale > 1 TeV Born-Infeld extension of Standard Model? Could also consider constraints on “mixed” Born-Infeld nonlinearities in : γγZZ, : γγgg JE, Mavromatos, Roloff & You, in preparation