2. University of Wisconsin-Milwaukee
Spacetime foam at TeV
Luis Anchordoqui
University of Wisconsin-Milwaukee

3. Bounds on Quantum Gravity from limits on proton lifetime
Probability of 2 bound quarks being within of one another
Proton size
Fundamental Planck length
Probability that 2 quarks pass within within
Heisenberg uncertainty lifetime of a black hole
Lower limit on proton lifetime
Super- Kamiokande Collaboration, Phys. Rev. Lett. 83 (1999) 1529
Adams, Kane, Mbonye & Perry, Int. J. Mod. Phys. A 16 (2001) 2399

4. Split fermions
Arkani –Hamed & Schmaltz, Phys. Rev. D 61 (2000)

5. Gravity-induced decoherence in the electroweak sector
Consider two neutrino generations
Basis of mass eigenstates and with masses and
Flavor eigenstates and represented by 2 x 2 matrices
Interactions with foamy reservoir described by generalized Liouville equation
Dissipative operator

6. Gravity-induced decoherence in the electroweak sector
Using the identity and the Pauli matrices
Energy conservation
Complete positivity
Increase of the von-Neumann entropy
Dissipation as perturbation on standard oscillations
Decoherence effects vanish in the weak gravitional limit

7. Gravity-induced decoherence in the electroweak sector
Initial condition

8. best fit oscillations + decoherence
Bounds on quantum decoherence from Super-Kamiokande data
zenith angle distribution shows deficit of upward-going muon neutrinos
well explain by oscillations
Super Kamiokande Collaboration, Phys. Rev. Lett. 81 (1998) 1562
best fit oscillations + decoherence
@ 90 % CL
Lisi, Marrone & Montanino Phys. Rev. Lett. 85 (2000) 1166

9. Lower limit on the UV cutoff well beyond the electroweak scale
Bounds on quantum decoherence from Super-Kamiokande data
@ 90 % CL
Naturalness expectation
Lower limit on the UV cutoff
well beyond the electroweak scale

10. Bounds on quantum decoherence from CCFR detector
CCFR/NuTeV Collaboration
Phys. Rev. Lett. 78 (1997) 2912
Phys. Rev. D 59 (1999)
@ 99% CL
Gago, Santos, Tevez & Zukanovich Funchal, Phys. Rev. D 63 (2001)
Bounds on quantum decoherence in the quark sector
Persistence of coherence in oscillations
@ 90% CL
Ellis , Hagelin, Nanopoulos & Srednicki. Nucl. Phys. B 241 (1984) 381

11. LAA, Goldberg, Gonzalez García, Halzen, Hooper, Sarker & Weiler
Conclusions
If M QG = 1 TeV interactions with virtual black holes non dissipative
Non-disipative interactions gravity embedded in String Theory -
S-matrix description B-violating ql and B-conserving qq outgoing channels may not have same probability
Future prospects
90% (99%) CL
LAA, Goldberg, Gonzalez García, Halzen, Hooper, Sarker & Weiler
Phys. Rev. D 72 (2005)