1. 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:

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

3. 2-Loop calculation in QED + QCD
Displaying fermion thresholds
Bern, de Freitas, Dixon, Ghinculov & Wong, hep-ph/

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

5. 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

6. 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/

7. 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/
Akhmadaliev et al., hep-ex/
PVLAS Collaboration
JE, Mavromatos & You, arXiv:

8. 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:

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

10. 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:

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

12. Light-by-Light Scattering: QED vs Born-Infeld
JE, Mavromatos & You, arXiv:
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

13. Constraint on Born-Infeld Scale
JE, Mavromatos & You, arXiv:
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

14. Implications for Monopoles
JE, Mavromatos & You, arXiv:
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  100 TeV?
Arunasalam & Kobakhidze, arXiv:

15. 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