Out-of-this-World Physics: From Particles to Black Holes Greg Landsberg L.G.Landsberg Symposium December 19, 2005

Outline A Word on Hierarchies Standard Model: Beauty and the Beast How to Make Gravity Strong? Looking for Extra Dimensions… Production of Black Holes at Colliders December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

N.B. Large Hierarchies Tend to Collapse... December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Hierarchy of the Standard Model Beauty … vev MGUT MPl Gravitational Force E [GeV] EM/Hypercharge Weak Force Strong Force Inverse Strength RGE evolution 1016 102 1019 and the Beast Extra dimensions might get rid of the beast while preserving the beauty! December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

But Keep in Mind… Fine tuning (required to keep a large hierarchy stable) exists in Nature: Solar eclipse: angular size of the sun is the same as the angular size of the moon within 2.5% (pure coincidence!) Politics: Florida recount, 2,913,321/2,913,144 = 1.000061 Numerology: 987654321/123456789 = 8.000000073 (HW Assignment: is it really numerology?) But: beware the anthropic principle Properties of the universe are special because we exist in it Don’t give up science for philosophy: so far we have been able to explain how the universe works entirely by science December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Math Meets Physics Math physics: some dimensionalities are quite special Example: Laplace equation in two dimensions has a logarithmic solution; for any higher number of dimensions it obeys the power law Some of these peculiarities exhibit themselves in condensed matter physics, e.g. diffusion equation solution allows for long-range correlations in 2D-systems (cf. flocking) Modern view in topology: one dimension is trivial; two and three spatial dimensions are special (properties are defined by the topology); any higher number is not Do we live in a special space, or only believe that we are special? December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

The ADD Model SM fields are localized on the (3+1)-brane; gravity is the only force that “feels” the bulk space What about Newton’s law? Ruled out for infinite extra dimensions, but does not apply for sufficiently small compact ones Gravity is fundamentally strong force, bit we do not feel that as it is diluted by the volume of the bulk G’N = 1/MD2; MD  1 TeV More precisely, from Gauss’s law: Amazing as it is, but no one has tested Newton’s law to distances less than  1mm (as of 1998) Thus, the fundamental Planck scale could be as low as 1 TeV for n > 1 December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Longitudinal ED Simultaneously, another idea has appeared: Explore modification of the RGE in (4+n)-dimensions to achieve low-energy unification of the gauge forces [Dienes, Dudas, Gherghetta, PL B436, 55 (1998)] To achieve that, allow gauge bosons (g, g, W, and Z) to propagate in an extra dimension, which is “longitudinal” to the SM brane and compactified on a “natural” EW scale: R ~ 1 TeV-1 MZ MGUT MPl=1/GN MS M’GUT Gravitational Force logE EM/Hypercharge Weak Force Strong Force Real GUT Scale Virtual Image Inverse Strength M’Pl L ~ 1 TeV December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Randall-Sundrum Scenario Randall-Sundrum (RS) scenario [PRL 83, 3370 (1999); PRL 83, 4690 (1999)] + brane – no low energy effects +– branes – TeV Kaluza-Klein modes of graviton Low energy effects on SM brane are given by Lp; for krc ~ 10, Lp ~ 1 TeV and the hierarchy problem is solved naturally x5 SM brane G AdS Planck brane r Planck brane (f = 0) SM brane (f = p) AdS5 f k: AdS curvature Reduced Planck mass: December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Differences Between the Models TeV-1 Scenario: Pro: Lowers GUT scale by changing running of the couplings Only gauge bosons (g/g/W/Z) “live” in ED’s Size of ED’s ~1 TeV-1 or ~10-19 m Con: Gravity is not in the picture ADD Model: Pro: “Eliminates” the hierarchy problem by stating that physics ends at a TeV scale Only gravity lives in the “bulk” space Size of ED’s (n=2-7) between ~100 mm and ~1 fm Black holes at the LHC and in the interactions of UHE cosmic rays Con: Doesn’t explain why ED are so large RS Model: Pro: A rigorous solution to the hierarchy problem via localization of gravity Gravitons (and possibly other particles) propagate in a single ED, w/ special metric Con: Size of ED as small as ~1/MPl or ~10-35 m G Planck brane x5 SM brane December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Kaluza-Klein Spectrum ADD Model: Winding modes with energy spacing ~1/r, i.e. 1 meV – 100 MeV Can’t resolve these modes – they appear as continuous spectrum TeV-1 Scenario: Winding modes with nearly equal energy spacing ~1/r, i.e. ~TeV Can excite individual modes at colliders or look for indirect effects RS Model: “Particle in a box” with a special metric Energy eigenvalues are given by zeroes of Bessel function J1 Light modes might be accessible at colliders Gravitational coupling per mode; many modes E E E ~1 TeV ~MGUT ~MPl GN for zero-mode; ~1/Lp for others ge … … Mi Mi M1 M0 M0 December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Using the ED Paradigm EWSB from extra dimensions: Hall, Kolda [PL B459, 213 (1999)] (lifted Higgs mass constraints) Antoniadis, Benakli, Quiros [NP B583, 35 (2000)] (EWSB from strings in ED) Cheng, Dobrescu, Hill [NP B589, 249 (2000)] (strong dynamics from ED) Mirabelli, Schmaltz [PR D61, 113011 (2000)] (Yukawa couplings from split left- and right-handed fermions in ED) Barbieri, Hall, Namura [hep-ph/0011311] (radiative EWSB via t-quark in the bulk) Flavor/CP physics from ED: Arkani-Hamed, Hall, Smith, Weiner [PRD 61, 116003 (2000)] (flavor/CP breaking fields on distant branes in ED) Huang, Li, Wei, Yan [hep-ph/0101002] (CP-violating phases from moduli fields in ED) Neutrino masses and oscillations from ED: Arkani-Hamed, Dimopoulos, Dvali, March-Russell [hep-ph/9811448] (light Dirac neutrinos from right-handed neutrinos in the bulk or light Majorana neutrinos from lepton number breaking on distant branes) Dienes, Dudas, Gherghetta [NP B557, 25 (1999)] (light neutrinos from right-handed neutrinos in ED or ED see-saw mechanism) Dienes, Sarcevic [PL B500, 133 (2001)] (neutrino oscillations w/o mixing via couplings to bulk fields) Many other topics from Higgs to dark matter December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

ED and Flavor Physics bulk SM bulk gauge fields via gravity ED models offer a powerful paradigm for explaining flavor sector and CP-violation New amplitudes and phases could be transmitted to our world via gravity (or other bulk fields), thus naturally introducing small parameters needed for description of CP-violation, flavor physics, etc. Some realizations of this class of models give realistic CKM matrix (e.g., Arkani-Hamed, Hall, Smith, Weiner [PRD 61, 116003 (2000)]) The idea of “shining” mentioned in the original ADD papers could explain why these effects were stronger in early universe “shining” bulk “CP-brane” SM big bang December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Flavor Physics from Geometry Arkani-Hamed/Schmaltz [Phys. Rev. D61, 033005 (2000)] – split fermions embedded in a “fat” brane Wave-functions of different families of quarks and leptons are spatially offset, thus the overlap areas are reduced exponentially A fruitful paradigm to build models of flavor and mixing with automatically suppressed FCNC and stable proton Possible to construct realistic CKM matrices via geometry of extra brane Similar attempts in Randall-Sundrum class of models In some of these models LFV decays of kaons are predicted and could be sought Huber [NP 666, 269 (2003)] Quark doublets of 3 generations Quark singlets of 3 generations Branco/de Gouvea/Rebelo [Phys. Lett. B506, 115 (2001)] December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Tabletop Gravity Experiments Sub-millimeter gravity measurements could probe only n=2 case only within the ADD model The best sensitivity so far have been achieved in the U of Washington torsion balance experiment – a high-tech “remake” of the 1798 Cavendish experiment R < 0.16 mm (MD > 1.7 TeV) Sensitivity vanishes quickly with the distance – can’t push limits further down significantly Started restricting ADD with 2 extra dimensions; can’t probe any higher number Ultimately push the sensitivity by a factor of two in terms of the distance No sensitivity to the TeV-1 and RS models [J. Long, J. Price, hep-ph/0303057] E.Adelberger et al. PRL 86, 1418 (2001) ~ ~ December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Astrophysical and Cosmological Constraints Supernova cooling due to graviton emission – an alternative cooling mechanism that would decrease the dominant cooling via neutrino emission Tightest limits on any additional cooling sources come from the measurement of the SN1987A neutrino flux by the Kamiokande and IMB Application to the ADD scenario [Cullen and Perelstein, PRL 83, 268 (1999); Hanhart, Phillips, Reddy, and Savage, Nucl. Phys. B595, 335 (2001)]: MD > 25-30 TeV (n=2) MD > 2-4 TeV (n=3) Distortion of the cosmic diffuse gamma radiation (CDG) spectrum due to the GKK  gg decays [Hall and Smith, PRD 60, 085008 (1999)]: MD > 100 TeV (n=2) MD > 5 TeV (n=3) Overclosure of the universe, matter dominance in the early universe [Fairbairn, Phys. Lett. B508, 335 (2001); Fairbairn, Griffiths, JHEP 0202, 024 (2002)] MD > 86 TeV (n=2) MD > 7.4 TeV (n=3) Neutron star g-emission from radiative decays of the gravitons trapped during the supernova collapse [Hannestad and Raffelt, PRL 88, 071301 (2002)]: MD > 1700 TeV (n=2) MD > 60 TeV (n=3) Caveat: there are many known (and unknown!) uncertainties, so the cosmological bounds are reliable only as an order of magnitude estimate Still, n=2 is largely disfavored December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Collider Signatures for Large ED Kaluza-Klein gravitons couple to the energy-momentum tensor, and therefore contribute to most of the SM processes For Feynman rules for GKK see: [Han, Lykken, Zhang, PRD 59, 105006 (1999)] [Giudice, Rattazzi, Wells, NP B544, 3 (1999)] Since graviton can propagate in the bulk, energy and momentum are not conserved in the GKK emission from the point of view of our 3+1 space-time Depending on whether the GKK leaves our world or remains virtual, the collider signatures include single photons/Z/jets with missing ET or fermion/vector boson pair production Graviton emission: direct sensitivity to the fundamental Planck scale MD Virtual effects: sensitive to the ultraviolet cutoff MS, expected to be ~MD (and likely < MD) The two processes are complementary Real Graviton Emission Monojets at hadron colliders GKK g q Single VB at hadron or e+e- colliders GKK V Virtual Graviton Effects Fermion or VB pairs at hadron or e+e- colliders V GKK f December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Virtual Graviton Exchange L’EPilogue (Large ED) e+e-  gG e+e-  ZG Experiment n=2 n=3 n=4 n=5 n=6 ALEPH 1.28 0.97 0.78 0.66 0.57 0.35 0.22 0.17 0.14 0.12 DELPHI 1.38 1.02 0.84 0.68 0.58 L3 0.81 0.67 0.51 0.60 0.38 0.29 0.24 0.21 OPAL 1.09 0.86 0.71 0.61 0.53 Color coding 184 GeV 189 GeV >200 GeV l=-1 l=+1 GL All limits are in TeV Virtual Graviton Exchange Experiment e+e- m+m- t+t- qq f f gg WW ZZ Combined ALEPH 1.04 0.81 0.65 0.67 0.60 0.62 0.53/0.57 0.46/0.46 (bb) 1.05 0.84 0.81 0.82 0.75/1.00 (<189) DELPHI 0.59 0.73 0.56 0.65 0.60 0.76 0.83 0.91 0.60/0.76 (ff) (<202) L3 0.98 1.06 0.56 0.69 0.58 0.54 0.49 0.49 0.84 1.00 0.99 0.84 0.68 0.79 1.0/1.1 (<202) OPAL 1.15 1.00 0.62 0.66 0.62 0.66 0.89 0.83 0.63 0.74 1.17/1.03 (<209) December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes LEP Combined: 1.2/1.1 TeV

Colliders: Graviton Emission 85 pb-1 ee  g + GKK at LEP g + MET final state MP > 1.4-0.5 TeV (ADLO), for n=2…7 qq/gg  q/g + GKK at the Tevatron jets + MET final state Z(nn)+jets is irreducible background Challenging signature due to large instrumental backgrounds from jet mismeasurement, cosmics, etc. DØ pioneered this search and set limits [PRL, 90 251802 (2003)] MP > 1.0-0.6 TeV for n=2…7 Later, CDF achieved slightly better limits Expected reach for Run II/LHC: Theory: [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] [Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)] [PRL 90, 251802 (2003)] GKK g q n MD reach, Run I MD reach, Run II MD reach, LHC 100 fb-1 2 1100 GeV 1400 GeV 8.5 TeV 3 950 GeV 1150 GeV 6.8 TeV 4 850 GeV 1000 GeV 5.8 TeV 5 700 GeV 900 GeV 5.0 TeV December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Tevatron: Virtual Graviton Effects GKK f Expect an interference with the SM fermion or boson pair production High-mass, low |cosq*| tail is a characteristic signature of LED [Cheung, GL, PRD 62 076003 (2000)] Best limits on the effective Planck scale come from new DØ Run II data: MPl > 1.1-1.6 TeV (n=2-7) Combined with the Run I DØ result: MPl > 1.1-1.7 TeV – tightest to date Sensitivity in Run II and at the LHC: Run II, 200 pb-1 December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Interesting Candidate Events While the DØ data are consistent with the SM, the two highest-mass candidates have anomalously low value of cosq* typical of ED signal: Event Callas: Mee = 475 GeV, cosh* = 0.01 Event Farrar: Mgg = 436 GeV, cosh* = 0.03 December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Antoniadis, Benaklis, Quiros [PL B460, 176 (1999)] TeV-1 Extra Dimensions Intermediate-size extra dimensions with TeV-1 radius Introduced by Antoniadis [PL B246, 377 (1990)] in the string theory context; used by Dienes, Dudas, Gherghetta [PL B436, 55 (1998)] to allow for low-energy unification Expect ZKK, WKK, gKK resonances at the LHC energies At lower energies, can study effects of virtual exchange of the Kaluza-Klein modes of vector bosons Current indirect constraints come from precision EW measurements: 1/r ~ 6 TeV No dedicated experimental searches at colliders to date Antoniadis, Benaklis, Quiros [PL B460, 176 (1999)] ZKK December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

First Dedicated Search for TeV-1 Extra Dimensions While the Tevatron sensitivity is inferior to indirect limits, it explores the effects of virtual KK modes at higher energies, i.e. complementary to those in the EW data DØ has performed the first dedicated search of this kind in the dielectron channel based on 200 pb-1 of Run II data (ZKK, gKK  e+e-) The 2D-technique similar to the search for ADD effects in the virtual exchange yields the best sensitivity in the DY production [Cheung, GL, PRD 65, 076003 (2002)] Data agree with the SM predictions, which resulted in the following limit: 1/R > 1.12 TeV @ 95% CL R < 1.75 x 10-19 m 200 pb-1, e+e- Event Callas Interference effect 1/R = 0.8 TeV December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Randall-Sundrum Model Observables Need only two parameters to define the model: k and rc Equivalent set of parameters: The mass of the first KK mode, M1 Dimensionless coupling To avoid fine-tuning and non-perturbative regime, coupling can’t be too large or too small 0.01 ≤ ≤ 0.10 is the expected range Gravitons are narrow Expected Run II sensitivity in DY Drell-Yan at the LHC M1 Davoudiasl, Hewett, Rizzo [PRD 63, 075004 (2001)] December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

First Search for RS Gravitons Already better limits than sensitivity for Run II, as predicted by phenomenologists! [PRL 95, 091801 (2005)] Assume fixed K-factor of 1.3 for the signal The tightest limits on RS gravitons to date December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Black Holes on Demand NYT, 9/11/01 December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Theoretical Framework Based on the work done with Dimopoulos a few years ago [PRL 87, 161602 (2001)] and a related study by Giddings/Thomas [PRD 65, 056010 (2002)] Extends previous theoretical studies by Argyres/Dimopoulos/March-Russell [PL B441, 96 (1998)], Banks/Fischler [JHEP, 9906, 014 (1999)], Emparan/Horowitz/Myers [PRL 85, 499 (2000)] to collider phenomenology Big surprise: BH production is not an exotic remote possibility, but the dominant effect! Main idea: when the c.o.m. energy reaches the fundamental Planck scale, a BH is formed; cross section is given by the black disk approximation: Geometrical cross section approximation was argued in early follow-up work by Voloshin [PL B518, 137 (2001) and PL B524, 376 (2002)] More detailed studies showed that the criticism does not hold: Dimopoulos/Emparan – string theory calculations [PL B526, 393 (2002)] Eardley/Giddings – full GR calculations for high-energy collisions with an impact parameter [PRD 66, 044011 (2002)]; extends earlier d’Eath and Payne work Yoshino/Nambu - further generalization of the above work [PRD 66, 065004 (2002); PRD 67, 024009 (2003)] Hsu – path integral approach w/ quantum corrections [PL B555, 29 (2003)] Jevicki/Thaler – Gibbons-Hawking action used in Voloshin’s paper is incorrect, as the black hole is not formed yet! Correct Hamiltonian was derived: H = p(r2 – M)  ~ p(r2 – H), which leads to a logarithmic, and not a power-law divergence in the action integral. Hence, there is no exponential suppression [PRD 66, 024041 (2002)] RS parton M2 = s ^ s ~ pRS2 ~ 1 TeV -2 ~ 10-38 m2 ~ 100 pb December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Assumptions and Approximation Fundamental limitation: our lack of knowledge of quantum gravity effects close to the Planck scale Consequently, no attempts for partial improvement of the results, e.g.: Grey body factors BH spin, charge, color hair Relativistic effects and time-dependence The underlying assumptions rely on two simple qualitative properties: The absence of small couplings; The “democratic” nature of BH decays We expect these features to survive for light BH Use semi-classical approach strictly valid only for MBH » MP; only consider MBH > MP Clearly, these are important limitations, but there is no way around them without the knowledge of QG December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Black Hole Production LHC n=4 Schwarzschild radius is given by Argyres et al., hep-th/9808138 [after Myers/Perry, Ann. Phys. 172 (1986) 304]; it leads to: Hadron colliders: use parton luminosity w/ MRSD-’ PDF (valid up to the VLHC energies) Note: at c.o.m. energies ~1 TeV the dominant contribution is from qq’ interactions stot = 0.5 nb (MP = 2 TeV, n=7) LHC n=4 stot = 120 fb (MP = 6 TeV, n=3) [Dimopoulos, GL, PRL 87, 161602 (2001)] December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Black Hole Decay Hawking temperature: RSTH = (n+1)/4p (in natural units  = c = k = 1) BH radiates mainly on the brane [Emparan/Horowitz/Myers, hep-th/0003118] l ~ 2p/TH > RS; hence, the BH is a point radiator, producing s-waves, which depends only on the radial component The decay into a particle on the brane and in the bulk is thus the same Since there are much more particles on the brane, than in the bulk, decay into gravitons is largely suppressed Democratic couplings to ~120 SM d.o.f. yield probability of Hawking evaporation into g, l±, and n ~2%, 10%, and 5% respectively Averaging over the BB spectrum gives average multiplicity of decay products: Note that the formula for N is strictly valid only for N » 1 due to the kinematic cutoff E < MBH/2; If taken into account, it increases multiplicity at low N [Dimopoulos, GL, PRL 87, 161602 (2001)] Stefan’s law: t ~ 10-26 s December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Black Hole Factory Black-Hole Factory [Dimopoulos, GL, PRL 87, 161602 (2001)] Black-Hole Factory n=2 n=7 g+X Drell-Yan Spectrum of BH produced at the LHC with subsequent decay into final states tagged with an electron or a photon December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Shape of Gravity at the LHC [Dimopoulos, GL, PRL 87, 161602 (2001)] Relationship between logTH and logMBH allows to find the number of ED, This result is independent of their shape! This approach drastically differs from analyzing other collider signatures and would constitute a “smoking cannon” signature for a TeV Planck scale December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Black Hole Events First studies already initiated by ATLAS and CMS ATLAS –CHARYBDIS HERWIG-based generator with more elaborated decay model [Harris/Richardson/Webber] CMS – TRUENOIR [GL] Simulated black hole event in the ATLAS detector [from ATLAS-Japan Group] Simulated black hole event in the CMS detector [A. de Roeck & S. Wynhoff] December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

Conclusions If you still think that gravity is weak force, you may be spending too much time in the lab! Stay tuned – next generation of collider experiments has a good chance to solve the mystery of large extra dimensions! If large extra dimensions are realized in nature, black hole production at future colliders is likely to be the first signature for quantum gravity at a TeV Many other exciting consequences from effects on precision measurements to detailed studies of quantum gravity If any of these new ideas is correct, we might see a true “Grand Unification” – that of particle physics, astrophysics and cosmology – in just a few years from now! December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black Holes