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)
JE, Mavromatos & You, arXiv:1703.08450
John Ellis
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
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: Born & Infeld 1934
• Derived from string theory:
in D dimensions:
Fradkin & Tseytlin 1985
4 dimensions:
• Limiting gauge field  brane velocity = light
Bachas, hep-th/9511043
• Mass scale M = √β 1/distance between branes,
≥ TeV?
Constraints on Born-Infeld Theory?
• Strongest constraint from electronic and muonic
atom spectra:
?
Soff, Rafelski & Greiner 1973
– But derivation criticized
Carley & Kiessling, math-ph/0506069
• Other probes of nonlinearities in light
insensitive to Born-Infeld
– photon splitting in atomic fields
– Magnetic birefringence
Akhmadaliev et al., hep-ex/0111084
PVLAS Collaboration
• New constraint from observation of light-bylight scattering in heavy-ions:
JE, Mavromatos & You, arXiv:1703.08450
Constraints on Nonlinearities
• Heisenberg-Euler: c0,2 = 7 c2,0 
• Born-Infeld: c0,2 = 4 c2,0
Fouché, Battesti & Rizzo, arXiv:1605.04102
Birefringence experiments constrain
Heisenberg-Euler, not Born-Infeld
Best Previous Constraint on Born-Infeld?
• Energy levels in atomic physics:
?
Carley & Kiesslingl, math-ph/0506069
First Measurement of Light-by-Light Scattering
• Peripheral heavy-ion collisions at the LHC: γγγγ
ATLAS
• Expected in ordinary QED from fermion loops
Heisenberg & Euler 1936
• ATLAS measurement agrees with QED
• Can be used to constrain nonlinearities in Born-Infeld
JE, Mavromatos & You: arXiv:1703.08450
Light-by-Light Scattering: QED vs Born-Infeld
JE, Mavromatos & You, arXiv:1703.08450
• Characteristic angular distributions
γ angle
• Born-Infeld more isotropic, larger γγ masses
Light-by-Light Scattering: QED vs Born-Infeld
JE, Mavromatos & You, arXiv:1703.08450
• Characteristic mass distributions
Heisenberg & Euler 1936
Born & Infeld 1934
Invariant γγ mass
• Born-Infeld larger γγ masses
• Conservative approach: use total # of ATLAS events
• Plausible approach: cut mγγ > 25 GeV (no events)
Constraint on Born-Infeld Scale
JE, Mavromatos & You, arXiv:1703.08450
• ATLAS constraint on σ(γγγγ) constrains M = √β
All ATLAS events
mγγ > 25 GeV
• 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
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:
Arunasalam & Kobakhidze, arXiv:1702.04068
• Our result implies mass > 11 TeV
•  LHC, but  FCC-hh @ 100 TeV?
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!
JE, Mavromatos, Roloff & You, in preparation
• 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