1 De-Chang Dai ( 戴德昌 ) SUNY at Buffalo Black holes and extra dimensions Dec. 10, 2009 NTHU Dec. 10, 2009 NTHU

Brane world models → large extra dimensions Extra dimensions seem to be necessary in an ultimate theory of high energy physics Black holes are the most interesting and intriguing solutions of Einstein's equation Motivation Higher dim. black holes as classical solutions Black holes in accelerators!

doomsday

Black Max: event generator Black Max: event generator

5 Laplace named them “Dark Stars” Laplace named them “Dark Stars” Black Holes in Newton’s physics Black Holes in Newton’s physics Laplace, 18 century, Newton’s mechanics: Black Holes in Newton’s gravity: Solid, compact objects whose escape velocity is greater then C Black Holes in Newton’s gravity: Solid, compact objects whose escape velocity is greater then C

Karl Schwarzschild Albert Einstein 1915: General Relativity, Einstein’s Theory of Gravity 1916: Schwarzschild’s Discovery of BHs in GR 1916: Schwarzschild’s Discovery of BHs in GR 1915: General Relativity, Einstein’s Theory of Gravity 1916: Schwarzschild’s Discovery of BHs in GR 1916: Schwarzschild’s Discovery of BHs in GR

7 First use of the term “Black Hole” – Wheeler, 1967

The need for physics beyond the standard model Validity of SM is probably limited to energies up to 1 TeV Hierarchy Problem If, Hope SUSY ? Extra dimensions? …

9 Arkani-Hamed, Dimopoulos and Dvali, Phys. Lett. B 429, 263 (1998) Antoniadis, Arkani-Hamed, Dimopoulos and Dvali, Phys. Lett. B 436,257 (1998) Arkani-Hamed, Dimopoulos and Dvali, Phys. Lett. B 429, 263 (1998) Antoniadis, Arkani-Hamed, Dimopoulos and Dvali, Phys. Lett. B 436,257 (1998) Strong gravity: ADD model Our universe consists of: Our universe consists of: 3+n space-like dimensions (bulk) 3+n space-like dimensions (bulk) n dimensions compactified to radius R n dimensions compactified to radius R Our universe consists of: Our universe consists of: 3+n space-like dimensions (bulk) 3+n space-like dimensions (bulk) n dimensions compactified to radius R n dimensions compactified to radius R Only gravitons are allowed to propagate in all dimensions Only gravitons are allowed to propagate in all dimensions SM particles are bound to 3-dim submanifold (brane) SM particles are bound to 3-dim submanifold (brane) Only gravitons are allowed to propagate in all dimensions Only gravitons are allowed to propagate in all dimensions SM particles are bound to 3-dim submanifold (brane) SM particles are bound to 3-dim submanifold (brane)

10 In this framework: Gravity is as strong as the other interactions Gravity is as strong as the other interactions But gravitational force is diluted due to the presence of extra dimensions But gravitational force is diluted due to the presence of extra dimensions Gravity is as strong as the other interactions Gravity is as strong as the other interactions But gravitational force is diluted due to the presence of extra dimensions But gravitational force is diluted due to the presence of extra dimensions Weak gravity is only an illusion for an observer located on the brane Fundamental gravity can be as strong as the electroweak force

Gaussian surface Close: Far:

12. If an impact parameter b is smaller than 2R H for a given E c Black holes in accelerators

The total black hole production cross section in pp collison is: The sum runs over all partons in the proton The sum runs over all partons in the proton is the proton-proton COM energy is the proton-proton COM energy are the parton distribution functions are the parton distribution functions is the momentum fraction carried by an i-th parton is the momentum fraction carried by an i-th parton is the momentum transfer is the momentum transfer is the minimal energy needed to form a black hole is the minimal energy needed to form a black hole

14 Large Hadron Collider → CERN (?) Numerical estimates : LHC - black hole factory! 10 7 black holes per year if M * =1 TeV LHC: E c =14 TeV

15 BH event may have a distinct signature in accelerators! BH event may have a distinct signature in accelerators! Number of particles emitted equal to black hole entropy: Number of particles emitted equal to black hole entropy: e.g. 5 TeV black hole emits of the order of 30 particles e.g. 5 TeV black hole emits of the order of 30 particles Number of particles emitted equal to black hole entropy: Number of particles emitted equal to black hole entropy: e.g. 5 TeV black hole emits of the order of 30 particles e.g. 5 TeV black hole emits of the order of 30 particles Life-time of a small black hole very short : Life-time of a small black hole very short : TeV black hole lives seconds TeV black hole lives seconds → disappears almost instantaneously → disappears almost instantaneously Life-time of a small black hole very short : Life-time of a small black hole very short : TeV black hole lives seconds TeV black hole lives seconds → disappears almost instantaneously → disappears almost instantaneously

16 Schwarzschild-like solution (non-rotating) Schwarzschild-like solution (non-rotating) Higher dimensional black hole solutions Higher dimensional black hole solutions Kerr-like solution (rotating): 5D Kerr-like solution (rotating): 5D

17 Number of degrees of freedom much larger on the brane ? (60 SM particles vs. 1 graviton) Number of degrees of freedom much larger on the brane ? (60 SM particles vs. 1 graviton) R. Emparan, G. Horowitz, R. Myers, Phys. Rev. Lett (2000) “Black holes radiate mostly on the brane” R. Emparan, G. Horowitz, R. Myers, Phys. Rev. Lett (2000) “Black holes radiate mostly on the brane” Where do black holes mostly radiate? Brane or Bulk?

# of degrees of freedom of gravitons in the N+1-dimensional space-time is: # of degrees of freedom of gravitons in the N+1-dimensional space-time is: Objection 1: Objection 1: Objection 2: Objection 2: V. Frolov, D. Stojkovic, Phys. Rev. Lett. 89: (2002) Black holes radiate mostly OFF the brane ! Black holes radiate mostly OFF the brane ! At least as long as they are rotating fast

19 Any particle emitted in the bulk can cause a recoil of the black hole from the brane Any particle emitted in the bulk can cause a recoil of the black hole from the brane V. Frolov, D. Stojkovic, Phys. Rev. Lett. 89: (2002) Recoil due to Hawking radiation can be very significant for small black holes (energy of emitted particles comparable to the mass of the black hole) Recoil due to Hawking radiation can be very significant for small black holes (energy of emitted particles comparable to the mass of the black hole) Consequences: Consequences: i) black hole radiation would be suddenly terminated i) black hole radiation would be suddenly terminated ii) observer located on the brane would register apparent ii) observer located on the brane would register apparent energy non-conservation energy non-conservation Consequences: Consequences: i) black hole radiation would be suddenly terminated i) black hole radiation would be suddenly terminated ii) observer located on the brane would register apparent ii) observer located on the brane would register apparent energy non-conservation energy non-conservation Recoil Effect

20 ® = ¼ = 2 _ J = 0 _ J = ¼¾ar H cos 2 ® Evaporation of a black hole off of a tense brane D. Dai, N. Kaloper, G. Starkman, D. Stojkovic, Phys.Rev.D75:024043,2007 6D black hole on a co-dimension 2 brane deficit angle horizon radius

21 J. Feng, A. Shapere, Phys. Rev. Lett. 88: (2002 ) Black Holes from Cosmic Rays Black Holes from Cosmic Rays Cosmic rays are Nature's free collider Observed events produce COM energy of 100 TeV If M * ≈1TeV (quantum gravity energy scale), then small black holes can be produced in the atmosphere Proposed mechanism: - neutrino-nucleon scattering deep in the atmosphere Cosmic rays are Nature's free collider Observed events produce COM energy of 100 TeV If M * ≈1TeV (quantum gravity energy scale), then small black holes can be produced in the atmosphere Proposed mechanism: - neutrino-nucleon scattering deep in the atmosphere

22 Cosmic neutrinos Cosmic protons scatter off the cosmic microwave background to create ultra-high energy neutrinos These neutrinos enter Earth's atmosphere They have very weak SM interactions Dominant interaction: Cosmic neutrinos Cosmic protons scatter off the cosmic microwave background to create ultra-high energy neutrinos These neutrinos enter Earth's atmosphere They have very weak SM interactions Dominant interaction:

The total black hole production cross section in neutrino-nucleon scattering is: The sum runs over all partons in the nucleon The sum runs over all partons in the nucleon are the parton distribution functions are the parton distribution functions is momentum transfer is momentum transfer The cross section for black hole production is found to be several orders of The cross section for black hole production is found to be several orders of magnitude higher than the SM cross section for magnitude higher than the SM cross section for if M* ≈1-10TeV if M* ≈1-10TeV

24 Best current setup for cosmic ray studies Located in Argentina (Pampa Amarillas) Best current setup for cosmic ray studies Located in Argentina (Pampa Amarillas) 1600 Water Cerenkov ground arrays 4 air fluorescence telescopes spread over 3000 km Water Cerenkov ground arrays 4 air fluorescence telescopes spread over 3000 km 2 Pierre Auger Auger Observatory Auger Observatory

25 Numerical estimates: Numerical estimates: - Auger can detect ~ 100 black holes in 3 years (i.e. BEFORE the LHC data become available) (i.e. BEFORE the LHC data become available) This could be the first window into extra dimensions This could be the first window into extra dimensions USA Today version: USA Today version: "Dozens of tiny black holes may be forming right over our heads... A new observatory might start spotting signs of the tiny terrors, A new observatory might start spotting signs of the tiny terrors, say physicists Feng and Shapere. They're harmless and pose no say physicists Feng and Shapere. They're harmless and pose no threat to humans." threat to humans." Numerical estimates: Numerical estimates: - Auger can detect ~ 100 black holes in 3 years (i.e. BEFORE the LHC data become available) (i.e. BEFORE the LHC data become available) This could be the first window into extra dimensions This could be the first window into extra dimensions USA Today version: USA Today version: "Dozens of tiny black holes may be forming right over our heads... A new observatory might start spotting signs of the tiny terrors, A new observatory might start spotting signs of the tiny terrors, say physicists Feng and Shapere. They're harmless and pose no say physicists Feng and Shapere. They're harmless and pose no threat to humans." threat to humans."

Auger has reported some interesting results but NO black hole events! Auger has reported some interesting results but NO black hole events! 26 Six years after… Are TeV scale gravity models already excluded? 26 Some things have their natural habitat in the "grand desert“ that is destroyed by a low scale gravity Like proton stability, neutrino masses... Low scale quantum gravity implies very fast proton decay! Some things have their natural habitat in the "grand desert“ that is destroyed by a low scale gravity Like proton stability, neutrino masses... Low scale quantum gravity implies very fast proton decay! The other problem:

Model Building Model Building Life always can find its way., and so do the theories.

28 An alternative: Split Fermions An alternative: Split Fermions N. Arkani-Hamed, M. Schmaltz, Phys. Rev. D 61: (2000) In order to suppress a direct QQQL coupling we must separate quarks form leptons Quarks and leptons are localized at different points on a thick brane Or alternatively, on different branes The model yields exponentially small coupling (wave function overlap) between quarks and leptons Dangerous QQQL interaction is suppressed An alternative: Split Fermions An alternative: Split Fermions N. Arkani-Hamed, M. Schmaltz, Phys. Rev. D 61: (2000) In order to suppress a direct QQQL coupling we must separate quarks form leptons Quarks and leptons are localized at different points on a thick brane Or alternatively, on different branes The model yields exponentially small coupling (wave function overlap) between quarks and leptons Dangerous QQQL interaction is suppressed

29 Consequences: the price we to have pay Consequences: the price we to have pay Spatial separation between the quark and lepton wave functions Spatial separation between the quark and lepton wave functions successfully suppresses proton decay successfully suppresses proton decay However, this implies strong consequences for cosmic ray However, this implies strong consequences for cosmic ray neutrino scattering off the atmosphere neutrino scattering off the atmosphere The correct black hole production cross section in collisions of The correct black hole production cross section in collisions of neutrinos with each quark in a nucleon is not neutrinos with each quark in a nucleon is not The correct cross section is divided by the large suppression factor of The correct cross section is divided by the large suppression factor of Consequences: the price we to have pay Consequences: the price we to have pay Spatial separation between the quark and lepton wave functions Spatial separation between the quark and lepton wave functions successfully suppresses proton decay successfully suppresses proton decay However, this implies strong consequences for cosmic ray However, this implies strong consequences for cosmic ray neutrino scattering off the atmosphere neutrino scattering off the atmosphere The correct black hole production cross section in collisions of The correct black hole production cross section in collisions of neutrinos with each quark in a nucleon is not neutrinos with each quark in a nucleon is not The correct cross section is divided by the large suppression factor of The correct cross section is divided by the large suppression factor of

30 Large suppression factors enter the total production cross section and render the corresponding probability for the black hole production by cosmic neutrinos completely uninteresting for the Auger Observatory! Non-observation of BH events at the Auger likely has no implications for the LHC Non-observation of BH events at the Auger likely has no implications for the LHC

31 Neutron-antineutron oscillations are described by uddudd operator Limits on oscillations require splitting between u and d quarks Consequences Consequences As the separation between quarks increases, the maximum 3+1-dim impact parameter that results in black hole creation decreases the production cross section goes down the production cross section goes down the bulk component of angular momentum grows the bulk component of angular momentum grows Neutron-antineutron oscillations are described by uddudd operator Limits on oscillations require splitting between u and d quarks Consequences Consequences As the separation between quarks increases, the maximum 3+1-dim impact parameter that results in black hole creation decreases the production cross section goes down the production cross section goes down the bulk component of angular momentum grows the bulk component of angular momentum grows D. Dai, D. Stojkovic, G. Starkman, D. Dai, D. Stojkovic, G. Starkman, Phys.Rev.D73:104037,2006 Implications of split fermions for the LHC

32 Implications of split fermions for the LHC

33 Black Max Black Max “BlackMax: A black-hole event generator with rotation, recoil, split branes, and brane tension” D. Dai, G. Starkman, D. Stojkovic, C. Issever, E. Rizvi, J. Tseng Phys.Rev.D77:076007,2008 D. DaiG. StarkmanD. StojkovicC. IsseverE. RizviJ. Tseng “BlackMax: A black-hole event generator with rotation, recoil, split branes, and brane tension” D. Dai, G. Starkman, D. Stojkovic, C. Issever, E. Rizvi, J. Tseng Phys.Rev.D77:076007,2008 D. DaiG. StarkmanD. StojkovicC. IsseverE. RizviJ. Tseng

34 Black Max procedure

35 BlackMax: A black-hole event generator with rotation, recoil, split branes, and brane tension. D. Dai, G. Starkman, D. Stojkovic, C. Issever, E. Rizvi, J. Tseng Phys.Rev.D77:076007,2008 D. DaiG. StarkmanD. StojkovicC. IsseverE. RizviJ. Tseng BlackMax: A black-hole event generator with rotation, recoil, split branes, and brane tension. D. Dai, G. Starkman, D. Stojkovic, C. Issever, E. Rizvi, J. Tseng Phys.Rev.D77:076007,2008 D. DaiG. StarkmanD. StojkovicC. IsseverE. RizviJ. Tseng Black Max output Black Max output

Conclusions Conclusions If gravity is strong, mini black holes may be produced in the LHC. No black holes in Auger does not imply that no black holes in the LHC. There are still several difficulties to overcome to fully understand the black hole signals.

THANK YOU THANK YOU