Out-of-this-World Physics: Black Holes at

Future Colliders

Greg Landsberg

Space Telescope Science Institute Spring Symposium

April 23, 2007

22STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

OutlineOutline

Astroparticle Connections

The Hierarchy Problem

Some Solutions

Production of Black Holes at Future Colliders

Conclusions

33STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

Astro-Particle PhysicsAstro-Particle PhysicsLast decade emphasized remarkable connection between the astrophysics and particle physics: Searches for dark matter QFT connections to early universe and inflation Black hole thermodynamics The landscape

The more we study these seemingly different subjects, the more connections we discover Physics at the very large distances may be inherently connected to the

physics at the shortest ones

More similarities: Microscopes vs. telescopes Large international collaborations Complicated detectors

We are (hopefully!) doing the things via two complementary means

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Microscopes vs. TelescopesMicroscopes vs. Telescopes

r ~ 1/E

= 1.22 /D

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Beautiful InstrumentsBeautiful Instruments

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Spectacular LaunchesSpectacular Launches

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Deep FieldsDeep Fields

Quantum vacuum texture

Hubble Deep Field Survey

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Mass and GravityMass and GravityIsaac Newton: the force that makes the apple fall is the same force that keeps the moon going around the Earth!

2R

MmGF N

mM

R

F

Charles Coulomb: opposite electric charges attract!

+Q qF

2R

QqGF C

R

Mass is similar to electric charge?!

But gravity is 1038=100,000,000,000,000,000,000,000,000,000,000,000,000(hundred billion billion billion billions) times WEAKER than electricity! Why?

The hierarchy problem (MPl = GN-½ = 1016 TeV » MEW ~ 1 TeV ~ 1000 Mp)

Isaac Newton

Charles Coulomb

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N.B. Large Hierarchies Tend to N.B. Large Hierarchies Tend to Collapse...Collapse...

The eighties

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Gravitational Hierarchy CollapseGravitational Hierarchy Collapse

Human Castles in Catalonia

With thanks to Chris Quigg and the B44 restaurant in San Francisco

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More Large HierarchiesMore Large Hierarchies

Collapse of the Soviet Union

The nineties…

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Note: Some Hierarchies are Note: Some Hierarchies are Surprisingly Stable…Surprisingly Stable…

The 2000-ies

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And Bear in Mind…And Bear 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 (!!!)

(Food for thought: is it really numerology?)

1414STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

Solutions to the Hierarchy ProblemSolutions to the Hierarchy Problem

Several classes of solutions exist in particle physics: Introduction of intermediate energy scales with new particles

and interactions (e.g., Technicolor) Introduction of new symmetries, which guarantee high

degree of cancellation of various effects, thus providing fine-tuning by the means of symmetry (e.g., SUSY)

Ignorance or not the right question (e.g., anthropic principle)

New class of solutions was found in the late 90-ies, requiring modification of space itself to make gravity fundamentally strong force (MPl ~ 1 TeV), which only appears weak at low energies Two such models: large and warped extra dimensions

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Large Extra DimensionsLarge Extra DimensionsArkani-Hamed, Dimopoulos, Dvali (ADD) [PLB 429, 263(1998)]SM fields are localized on the (3+1)-brane; gravity is the only force that “feels” the bulk spaceWhat about Newton’s law?

Ruled out for infinite extra dimensions, but does not apply for sufficiently small compact ones

1

2123

212

11

nnn

PlPl r

mm

Mr

mm

MrV

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)

Current limits: n = 2 nearly ruled out; for n > 2 limits are: MD > 1.4 TeV

nPl

nD RMM 22

4106

33

270

1108

2

1

12

12

2

nm

nnm

nmm

nm

M

M

MR

n

D

Pl

D

,

,

, .

,/

231 ][/ nPlM

Rr

rR

mm

MrV

nnnPl

for 21

23

1

~

1616STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

Randall-Sundrum ModelRandall-Sundrum ModelRandall-Sundrum (RS) model [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 ; for kRC ~ 10, ~ 1 TeV and the hierarchy problem is solved naturally

G

Planck branex5

SM brane

22C

kR22 dRdxdxeds C

8PlPl MM

Rc

Planck brane ( = 0)

SM brane()

AdS5

k – AdS curvature

kr

PleM

Reduced Planck mass:

AdS

Anti-deSitter space-time metric:

1717STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

Examples of Compact Examples of Compact DimensionsDimensions

M.C.Escher, Mobius Strip II (1963) M.C.Escher, Relativity (1953)

[All M.C. Escher works and texts copyright © Cordon Art B.V., P.O. Box 101, 3740 AC The Netherlands. Used by permission.]

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The Large Hadron ColliderThe Large Hadron ColliderLHC- the new energy frontier proton-proton collider being built at the border of France and Switzerland, near GenevaProton-proton collisions at the c.o.m. of 14 TeVLuminosity (event rate) of 1034 cm-2s-1 = 0.01 Hz/pbTwo general-purpose experiments: ATLAS and CMSScheduled to start operating at full energy in Spring 2008

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Black Holes on DemandBlack Holes on Demand

NYT, 9/11/01

N.B. Also possible in the Randall-Sundrum model

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Black Holes in General RelativityBlack Holes in General Relativity

Black holes (BH) are direct prediction of Einstein’s General Relativity (GR) It’s somewhat ironical that

Einstein himself never believed in BH!

Schwarzschild showed (1916) that the space-time metric for a massive body has a singularity at r = RS 2MGN/c2

r and t essentially swap places for r < RS

Hence, if the mass M is enclosed within its Schwarzschild radius RS, a “black hole” is formed

Naїvely, a black hole would only grow once it’s formedIn 1975 Hawking showed that this is not true [Commun. Math. Phys. 43, 199 (1975)], as the black hole can evaporate by emitting virtual pairs at the event horizon, with one particle of the pair escaping the BHThese particles have a black-body spectrum at the Hawking temperature:

In natural units ( = c = k = 1), one has: RSTH = (4)

If TH is high enough, massive particles can also be produced in the process of evaporation

SH kRcT 4

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Note, that Rs can be derived from Newtonian gravity by taking the escape velocity, vesc = (2GNM/RS)1/2 to be equal to c – first noticed by Pierre-Simon Laplace in his famous 1796’s “Exposition du Systeme du Monde”

A few years earlier (1783) John Michell presented similar qualitative idea (“dark star”) to the Royal Society: “If the semi-diameter of a sphere of the same density with the

Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it, would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to the vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity”

The name, “Black Hole,” was coined only half-a-century after Schwarzschild by John Wheeler (in 1967)

Previously these objects were often referred to as “frozen stars” due to the time dilation at the event horizon

Brief History of HolesBrief History of HolesBrief History of HolesBrief History of Holes

Pierre Laplace

John Wheeler

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Looking for Black HolesLooking for Black HolesThe most straightforward evidence, Hawking radiation, is not likely to ever be observed for astronomical black holes (TH ~ 100 nK, ~ 100 km, P ~ 10-27 W: ~1014 years for a single to reach us!)LIGO/VIRGO/LISA hope to observe gravitational waves from black hole collisions (cf. Joan Centrella’s talk)

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Black Hole EvaporationBlack Hole EvaporationAs the BH evaporates, its mass becomes smaller, RS decreases, and Hawking temperature increasesConsequently, as the BH evolves, the radiation spectrum becomes harder and harder, until the BH evaporates completely in a giant flash of lightErgo, the BH spends most of its time at the lowest temperature, when the radiation is soft (cf. Gary Horowitz’s talk)

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Black Holes at CollidersBlack Holes at CollidersBased on 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, more formal 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 phenomenologyBig 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!

Black hole

p p

RS

quark

quark

M2 = s

~ RS ~ 1 TeV ~ 10 m ~ 100 pb

Corresponds to ~1 Hz BH rate!

Cross section is given by a black disk approximation:

Artist’s view:

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Assumptions and ApproximationAssumptions and ApproximationFundamental limitation: our lack of knowledge of quantum gravity (QG) effects close to the Planck scaleConsequently, 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 BHUse semi-classical approach strictly valid only for MBH » MPl; only consider MBH > MPl

Clearly, these are important limitations, but there is no way around them without detailed knowledge of QG features

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Black Hole ProductionBlack Hole ProductionSchwarzschild 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

1

2

222

22

38

1

n

P

BH

PSBH n

n

M

M

MRMs )ˆ(

a

BHbaa

bas

M a

aBH

BH

MsBHBH

sx

Mfxf

x

dx

s

M

dM

dL

BHabdM

dL

dM

XBHppd

BH

BH

21

2

2

2

,

ˆˆ

tot = 0.5 nb (MP = 2 TeV, n=7)

LHCn=4

tot = 120 fb (MP = 6 TeV, n=3)

[Dimopoulos, GL, PRL 87, 161602 (2001)]

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Black Hole DecayBlack Hole DecayBH radiates mainly in our 3D world: Emparan/Horowitz/Myers [PRL 85, 499 (2000)] ~ 2/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 l±, and ~2%, 10%, and 5% respectively Averaging over the BB spectrum gives average multiplicity of decay products:

H

BH

T2

MN

Note that the formula for N is strictly valid only for N » 1 dueto the kinematic cutoff E < MBH/2; If taken into account, it increasesmultiplicity at low N

[Dimopoulos, GL, PRL 87, 161602 (2001)]

Stefan’s law: ~ 10-26 s

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Black Hole FactoryBlack Hole Factory

Drell-Yan +X

Dimopoulos, GL [PRL 87, 161602 (2001)]

Spectrum of BH produced at the LHC with subsequent decay into final states tagged with an electron or a photon

n=2n=7

Black-Hole Factory

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Shape of Gravity at the LHCShape of Gravity at the LHC

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

constMln1n

1Tln BHH

Dimopoulos, GL [PRL 87, 161602 (2001)]

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Randall-Sundrum Black HolesRandall-Sundrum Black HolesNot nearly as studied as ADD BH Originally suggested by

Anchordoqui, Goldberg, Shapere [PRD 66, 024033 (2002)]

A few authors extended work to various cases: Rizzo [JHEP 0501, 28 (2005); hep-ph/0510420; hep-ph/0603242] Stojkovic [PRL 94, 011603 (2005)]

The event horizon has a pancake-like shape (squashed in the 5th dimension by ekRc)

Nevertheless comparison with the ADD BH is trivial GL [J. Phys. G32, R337 (2006)] For BH production, in the

RS model plays the same role as the fundamental Planck scale MD in the ADD model

Then if one sets = MD and k = 1/8 0.04, the RS case turns into the ADD one!

TH = 1/(2RS) (the ADD formula in 5D)

1~

k~M

3

1R BH

S

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Wien’s LawWien’s Law

Impressive precisionin proving n=1!

k = 1/8MD

~

100 fb-1 @ the LHC

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Black Hole EventsBlack Hole EventsFirst 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]

3333STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

ConclusionsConclusionsBlack hole production at future colliders is likely to be the first signature for quantum gravity at a TeVLarge production cross section, low backgrounds, and little missing energy would make BH production and decay a perfect laboratory to study strings and quantum gravityPrecision tests of Hawking radiation may allow to determine the shape of extra dimensions and distinguish between various scenariosProperties of black holes in the Randall-Sundrum model are similar to those in models with large extra dimensionsA possibility of studying black holes at future colliders is an exciting prospect of ultimate ‘grand unification’ – that of astro-particle physics and cosmology!

Backup SlidesBackup Slides

3535STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

Fine Tuning Explained…Fine Tuning Explained…

Fine tuning explained: Numerology: 987654321/123456789 =

8.000000073 ?

Numerology it is not!

Seeing is believing:

In hexadecimal system,

FEDCBA987654321/123456789ABCDEF =

14.000000000000000183

2123456789

987654321

N

LMN

NMLN ...

...lim

3636STSci, 4/23/07STSci, 4/23/07 Greg Landsberg - Out-of-this-World Physics: Black Holes at Future CollidersGreg Landsberg - Out-of-this-World Physics: Black Holes at Future Colliders

Black Holes in the Cosmic RaysBlack Holes in the Cosmic RaysDiscussed by Feng/Shapere [PRL 88 (2002) 021303]; Anchordoqui/ Goldberg [PRD 65, 047502 (2002)]; Emparan/ Massip/Rattazzi [PRD 65, 064023 (2002)]; …Proton primaries have very high SM interaction rate; consider BH production by quasi-horizontal UHE neutrinos

Detect them, e.g. in the Pierre Auger fluorescence experiment or AGASAA few to a hundred BHs can be detected before the LHC turns onMight be possible to establish the uniqueness of the signature by comparing several neutrino-induced processes

MBH = 1 TeV, n=1-7

Auger, 5 years of running

[Feng & Shapere, PRL 88 (2002) 021303]

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Other Recent DevelopmentsOther Recent DevelopmentsPhenomenology of mini-BH became a popular subject (~380 citations of the original papers)There have been a lot of studies of various second-order effects in BH formation and decay Many of the estimates suffer from the

intrinsic lack of knowledge of the quantum gravity effects, which will affect these fine features tremendously

Grey-body factor calculation has been attempted by many authors[e.g., Kanti, March-Russell, PRD 66, 024023 (2002); PRD 67, 104019 (2003)] Kerr black holes have been considered extensively [e.g., Ida, Oda, Park, PRD 67, 064025 (2003), erratum PRD 69, 049901 (2004)]

Accounting for recoil effects [e.g. Frolov, Stojkovic, PRD 66, 084002 (2002), PRL 89, 151302 (2002)]Number of people discussed the effect of Gauss-Bonnet terms, which arise naturally in perturbative expansion of string theory [e.g., Torii, Maeda, hep-ph/0504127 and hep-ph/0504141]Randall-Sundrum BH studies [Anchordoqui, Goldberg, Shapere, PRD 66, 024033 (2002)]Exploring AdS/QFT duality to relate formation of black holes in AdS to QCD colorless scattering and Froissart unitarity bound saturation [Giddings, PRD 67, 126001 (2003); Kang, Nastase, hep-th/0409099, hep-th/0410173]RHIC fireball/BH duality [Nastase, hep-th/0501068]

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String Balls at the LHCString Balls at the LHCDimopoulos/Emparan, [PL B526, 393 (2002)] – an attempt to account for stringy behavior for MBH ~ MS

GR is applicable only for MBH > Mmin ~ MS/gS

2, where gS is the string coupling; MP is typically less than Mmin

They show that for MS < M < Mmin, a string ball, which is a long jagged string, is formedProperties of a string-ball are similar to that of a BH: it evaporates at a Hagedorn temperature:

in a similar mix of particles, with perhaps a larger bulk component

Cross section of the string ball production is numerically similar to that of BH, due to the absence of a small coupling parameter:

It might be possible to distinguish between the two cases by looking at the missing energy in the events, as well as at the production cross section dependence on the total mass of the objectVery interesting idea; more studies of that kind to come!

22S

H

MT

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Geometrical Cross Section Geometrical Cross Section Suppression?Suppression?

Geometrical cross section approximation was argued in early follow-up work by Voloshin [PL B518, 137 (2001), PL B524, 376 (2002)]

More detailed studies showed that the criticism does not hold: Dimopoulos/Emparan – string theory calculations [PLB 526, 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)]

Further improved by Yoshino/Rychkov [hep-th/0503171] 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)]

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New Physics in BH DecaysNew Physics in BH DecaysExample: Higgs with the mass of 130 GeV decays predominantly into a bb-pairExample: 130 GeV Higgs boson – tag BH events with leptons or photons, and look at the dijet invariant mass; does not even require b-tagging!Use typical LHC detector response to obtain realistic results

MP = 1 TeV, 1 LHC-hour (!)

W/Z h t

= 15 nb

GL, PRL 88, 181801 (2002)

boost

Wt

Higgs observation in the black hole decays is possible at the LHC as early as in the first day of running even with the incomplete and poorly calibrated detectors!For MP = 1, 2, 3, and 4 TeV one needs 1 day, 1 week, 1 month, or 1 year of running to find a 5 signalHiggs is just an example – this applies to most of the new particles with the mass ~100 GeV