black holes at colliders: progress since 2002

Seong Chan Park (SNU)

SUSY08,COEX, SEOUL June 21, 2008

Seong Chan Park (SNU)

SUSY08,COEX, SEOUL June 21, 2008

What’s BH? (1 min summary)

• Best known as classical solutions to the Einstein equation.

• Classically stable (nothing can come out)• Quantum mechanically unstable (Hawking

radiation~Thermal radiation, anything can come out of it)

• T=surface gravity~1/r (smaller hotter)• S=surface area~ r^(D-2)• BH is unique (4D), not unique (D>4)• Black Ring (S^2XS), Black String (S^2XR)

etc.SUSY08, Seong Chan Park

Black hole is interestingBlack hole is interesting

• Everybody knows it is interesting. • Perfect place to do ‘quantum gravity’• Has provided a nice testing ground for theory calculations (e.g. microscopic entropy counting of stringy-BH etc.)• Has deep implication to ‘energy-distance’ relation. • Even it is real!!

SUSY08, Seong Chan Park

Observed Black Holes in the sky


Name of Binary System

Companion Star

Spectral Type

Orbital Period(days)

Black Hole Mass

(Solar Units)

Cygnus X-1 B supergiant 5.6 6-15

LMC X-3B main

sequence1.7 4-11

A0620-00 (V616 Mon)

K main sequence

7.8 4-9

GS2023+338 (V404 Cyg)

K main sequence

6.5 > 6

GS2000+25 (QZ Vul)

K main sequence

0.35 5-14

GS1124-683 (Nova Mus 1991)

K main sequence

0.43 4-6

GRO J1655-40 (Nova Sco 1994)

F main sequence

2.4 4-5

H1705-250 (Nova Oph 1977)

K main sequence

0.52 > 4 Circinus galaxy

Cygnus X-1The list goes more than 100 now.

That’s great. But notice that they allIndirectly observed .

‘energy-distance’ relation

“To probe smaller distance, you need higher energy” W. Heisenberg This is exactly the reason why we want to build big colliders.


distance

energy

~1/x p

Big Question

Does this curve keep going and touch 0??

Will this program go on forever?


distance

energy

~1/x p

Answer: No!

‘t Hooft picture of Trans-Planckian domain

• Gravity becomes strong/dominate in Ultrahigh-Energy Scattering. New window of bh production opens.

• The smallest distance scale we can probe is now determined by the size of event horizon (~GE) which becomes larger with higher E!


‘t Hooft (1987)

distance

energy

~ ( ) 2Sx r E GE

pM

1/ pM

The big Picture:Heisenberg-‘t Hooft


distance

energy

~1/x p ~x GE

PM

1/pl pll M

UV-IR duality

Trans-Planckian Domain E>>Mp-gravity dominance-new windows of bh production open-Classical gravity!!

Classical Gravity

Quantum Gravity

0~ ( / )nQG Pl l

Planck domain E~Mp-Quantum Gravity-String theory-no concrete prediction , yet

Sub-Planckian domain E<<Mp-gauge interaction-(broken)SUSY-GUT

D>4


distance

energy

~1/x p 1/( 3)~ ( ) D

Dx G E

DM

1/D Dl M

Compactl

If MD~TeV, as is the case in ADD(1998) and RS(1999), the Heisenberg-’t Hooft picture is actually relevant at the LHC

**TeV dimension was first suggested by I. Antoniadis(1990)

LHC: a BH factory

• Large Cross-Section. Because there is no small dimensionless constant, analogous to alpha, suppress the production of BHs.

• 10^5 fb (M>5TeV, 10D), 10fb (M>10TeV, 10D) • Hard, Prompt, Charged Leptons and Photons Because thermal decays are flavor-blind. This signature has practically vanishing

SM background.

• Little Missing Energy.

• Large Cross-Section. Because there is no small dimensionless constant, analogous to alpha, suppress the production of BHs.

• 10^5 fb (M>5TeV, 10D), 10fb (M>10TeV, 10D) • Hard, Prompt, Charged Leptons and Photons Because thermal decays are flavor-blind. This signature has practically vanishing

SM background.

• Little Missing Energy.


22

1( )

TeVCMr E

Banks-Fischler (1999), Dimopoulos- Lansberg (PRL87,2001), Giddings-Thomas(PRD65, 2002)

G. Landsberg SUSY02

Around 2002

• Several different communities started

talking about ‘Mini-Black holes’• Particle physics, String theory, GR community even SF-community

etc..

People got excited


Seoul in 2002


Some people concerns if bh eats us :a survey by BBC


Official comment by the CERN


http://public.web.cern.ch/Public/en/LHC/Safety-en.html

CERN homepage:

BHs from cosmic rays• Anchordoqui-Feng-Goldberg-Shapere (PRD 2002)


( )N BH

If the LHC can produce microscopic black holes, cosmic rays of much higher energies would already have produced many more. Since the Earth is still here, there is no reason to believe that collisions inside the LHC are harmful.

Pierre-AugerIce CubeEtc..are searchingfor these events.

Two major Progresses since 2002

Production• BH production by collision

proved.

• (b=0,D>4) Eardley-Giddings

(2002)• (b>0, D>4) Yoshino-Nambu

(2003)

Decay• Greybody factors of black hole in D>4 for

brane fields with spin s=0,1/2,1

(i.e. for all the SM particles)

obtained

• Ida-Oda-SCP (2003,2004,2005,2006)• Duffy-Harris-Kanti-

Winstanley(2005), Casals-Kanti-Winstanley (2006), Casals-Dolan-Kanti-Winstanley(2007)


** Penrose (b=0, D=4) long ago

Production: Hoop Conjecture(Kip Thorne 1972)

• “An imploding object forms a Black Hole when, and only when, a circular hoop with a specific critical circumference could be placed around the object and rotated. The critical circumference is given by 2 times Pi times the Schwarzschild Radius corresponding to the object’s mass.”

big energy in a small space, BH always appears!!


This is the hoop r = GM

I am a BH (M)

It’s like putting an elephant into a freezer..


Mass=MR= RBH(M)

It is hard to do this. But once you can do it, you will have a BH.

Classical BH formation provedusing two Aichelberg-Sexl

shocks


Boundary Value Problem:Setup: two particles (BHs) with

• boost→∞,• mass→0,• energy: fixed.

•Close Trapped Surface forms when b<b(max)(CTS=a closed spacelike surface on which the outgoing orthogonal null geodesics converge)•The Area Theorem : Classically the horizon area of the ultimate bh must begreater than the original CTS. i.e. BH really forms

Eardley-Giddings 2002 Yoshino-Nambu PRD66, 2003Yoshino-Nambu PRD67, 2003

Yoshino-Rychkov PRD71, 2005

t

z

=t-z

=t+z

Latest result: bmax/rs


Yoshino-Rychkov PRD71, 2005

Another approach:(based on Hoop conjecture, taking angular momentum into

account)


b

22 1

2 2 2max

24 1 ~1/

2

n

S

nb r TeV

, / 2M J Mb

M/2

M/2

2 1/ 1

1/ 14

( , ) ( )(1 )

( ) ( ) , (1)

nH S

nS n n n

r M J r M a

r M C G M C O

Hoop Conjecture:

SCP-Song 2001Ida-Oda-SCP 2003

Error ~3% (D=5)-17%(D=11)This picture is essentially correct

Angular momentum


)2/( maxmax MbJ

)(0

)(/8

max

max2

JJ

JJMJ

dJ

d

bdbd 2

db

Most of BHs are produced with “large” angular momentum!

Signal: How will we know if we’ve seen one?

• Black hole decays by emitting Hawking radiation.

• We will see the radiated particles.• Smaller black holes are hotter and

radiate more efficiently. (T~ TeV, every SM particles can come out of the bh!)

• Live short!! Life Time~10^-25 sec or shorter.

• So please don’t worry about the possible destroy of the earth by mini black holes.


Closer look: Hawking radiation

• Here is the master equationHere is the master equation


me

dgJ

M

dt

dTmmls

mlss

12

1/,,

,,

:The probability is not equal to every particlebut crucially depends on spin and angular mode .

Anisotropic and nontrivial Hawking radiation is expected.We have to know this “greybody factorgreybody factor” to understand HawkingRadiation.

, .s l m

S. Hawking (1975)

T= surface gravity ~1/rh :Smaller bh is hotter

GreybodyGreybody factorfactor

Modification factor to take the curved Modification factor to take the curved geometry NH into account. geometry NH into account. = Absorption Probability of wave mode (s, l, m)= Absorption Probability of wave mode (s, l, m)

me

dgJ

M

dt

dTmmls

mlss

12

1/,,

,,

T

Looks not black to me.It looks Grey!Grey!



Brief History of greybody factors

for rotating BHs

Brief History of greybody factors

for rotating BHs

•Derivation of Teukolsky equation Derivation of Teukolsky equation (Kerr)(Kerr)=Wave equation for general (s,l,m) wave for 4D Kerr BH S. Teukolsky 1972,1973)•Generalized to (D=4+n, Meyers-Perry) for brane fields Ida-Oda-SCP, PRD67(2003)

Solution to Teukolsky eq./ Greybody Factors (D=4, Kerr)Solution to Teukolsky eq./ Greybody Factors (D=4, Kerr): Analytic and Numerical methods were developed byTeukolsky-Press, Starobinsky, Unruh, Page in 1973-1976Analytic sol.(5D),low energy limit,s=0,1/2,1: Ida-Oda-SCP, PRD67(2003)

Numerical (D>4),full energy,s=0 Ida-Oda-SCP PRD71(2005) Result Presented at JGRG meeting by SCP (Dec.2004, arXiv:0501210) Duffy-Harris-Kanti-Winstanley (arXiv:0507274, JHEP0509, 2005)


For s=0,D>4 Ida, Oda, SCP (s=1/2,1, arXiv:0602188, PRD73, 2006) Casals,Kanti,Winstanley (for s=1 only) (arXiv: 0511163 JHEP 0602, 2006) Casals, Dolan, kanti,Winstanley (s=1/2) JHEP 0703, (2007)

For s=0,D>4 Ida, Oda, SCP (s=1/2,1, arXiv:0602188, PRD73, 2006) Casals,Kanti,Winstanley (for s=1 only) (arXiv: 0511163 JHEP 0602, 2006) Casals, Dolan, kanti,Winstanley (s=1/2) JHEP 0703, (2007)

Finally!! Hawking radiation and its evolutionFinally!! Hawking radiation and its evolution: Hawking 1975, Page 1976 (4D) Ida, Oda, SCP ,PRD73, 2006(D>4) including all the SM fields.

Finally!! Hawking radiation and its evolutionFinally!! Hawking radiation and its evolution: Hawking 1975, Page 1976 (4D) Ida, Oda, SCP ,PRD73, 2006(D>4) including all the SM fields.

Still s>1 modes (i.e. s=3/2, 2) missingGraviton part can be important when D>>4Because of large number of helicity states

Still s>1 modes (i.e. s=3/2, 2) missingGraviton part can be important when D>>4Because of large number of helicity states

Generalized Teukolsky eq.

• Meyers-Perry sol. (rating D>4 BH)• Define Null tetrad• Use ‘Newman-Penrose’ formalism, derive

the equation• Turned out to be separable (Petrov Type-D) +angular part spin-weighted spheroidal harmonics +radial 2nd order ODE with singular

BCs.


Ida,Oda,SCP PRD67, 2003

Believe me. This guy is tough!

Schematic view of the greybody factor calculation


Near the HorizonPurely ingoing Sol (NH)

Far from the HorizonSol (FF)

GeneralizedTeukolsky Eq.

“Matching”

Analytic or Numericintegration

Sol (whole space)

Greybody factor(Absorption Probability) =[In]/[Out]

Ida, Oda, SCP I, II, III

Ida, Oda, Park PRD 06’

D=5,S=1/2


Greybody

Number

Angular mom

Energy

Non-rotating rotating Highly Rotating


D=10,s=1/2


Greybody

Number

Angular mom

Energy




D=5, s=1

Greybody

Angular mom

Energy




Greybody

Angular mom

Energy

D=10, s=1


Evolution of BHEvolution of BH


sf

v

SM

J

M

5D

The full result (SM) is almost exactly described by ‘Vector’.

•Vector emission is the most efficient way to extract angular momentum.•Large Gluon emission•10D similar

Obtained by integrating Hawking’s Formula with the calculated GreybodyFactors.

Black Hole’s Life Black Hole’s Life made simplemade simple

?

Time

Balding Phase

Spin Down PhaseSpin Down Phase

Schwarzschild PhaseSchwarzschild Phase

Planck PhasePlanck Phase

(Production of BHs.Study “Dynamics” required.)

(Losing energy and angular momentum:60-80% Energy lost For D>4, to mostly gluons, anisotropic)

(Losing Mass: 20-40% energy, spherical, to every fields)

(Remnant ???, Stringy study required )


New MC event generators are available.

• BlackMax [arXiv:0711.3012 ], Dai,Stojkovic,Issever,Rizvi,Tseng

• Greybody factors for rotating BH implemented. • “Most realistic MC” simulation for bh events at

the LHC. (N.B.)Yesterday (James Frost’s talk P6 (on behalf

of ATLAS))I’ve learned that BlackMax has some bugs which

should be removed.• CHARIBDIS ver.2. is under development with

Greybody factors for rotating BH.


It seems we are more or lessready now but..

• There are still rooms to be improved (mostly theoretical)– Balding phase should be understood by

dynamical simulation (most probably numerical) (cf) success of Bh-Bh merging process (this is important!!)

– For D>>4, spin-2 graviton emission can be sizable. non-rotating case done for D>4

– BH final state: Full QG (string theory )calculation is required.

– Many other issues :Chromosphere (Alig-Drees-Oda , Anchordoqui et.at.), recoil(Stojkovic et.al), split-brane (Stojkovic), etc

– Unification of ‘convention’ required.SUSY08, Seong Chan Park

Cardoso,Cavaglia,Gualtieri JHEP0602(2006)

Conventions

• Planck scale (I would take PDG convention)

• In the PDG convention

4

4

4 2

1

8 2

8

n

n

nn n

D

RS d x

G

NG

M

(2 ) ( ),1( ),8 ( ), 2(2 ) ( )..n n

nN PDG RS DL GT

1

1

1

1

2

1( ) ( )

(2 )( ) 0.46( 1) 2.4( 6)

( 2)

n

SD D

n n

n

Mr M k n

M M

k n n nn

Physical quantities (PDG convention)

1/ 2

55

1/ 7

1010

( 1) 0.34

( 6) 0.23

MT n M

M

MT n M

M

3/ 2

5

8/ 7

10

( 1) 1.9

( 6) 3.8

MS n

M

MS n

M

25 5

2/ 7

210 10

ˆ32 1( 1)

39

ˆ 1( 6) 33

sn

M M

sn

M M

Two most importantcharacteristics of BH signal

• Large Entropy high Multiplicity.• Thermal radiation Flavor Blind.


Typically, BH signals contains-Many jets-Statistically, N(e)=N(mu)=N(tau)

Typically, BH signals contains-Many jets-Statistically, N(e)=N(mu)=N(tau)

Multi-’hard’-jet


J. -H. Kim, SCP, S. Schumann (in preparation)

BlackMax1.0

,

min *

0.4

| | 4.5

200GeV

m 5

T j

R

E

m

Multi-`harder’-jet


BlackMax1.0

J. -H. Kim, SCP, S. Schumann (in preparation)

,

min *

0.4

| | 4.5

500GeV

5

T j

R

E

m m

Again, there is Chromospherissue here. Dense jets look not really likeJets but fuzzy Chromospher.(Alig,Drees,Oda JHEP0612 (2006) Anchordoqui , Goldberg PRD67 (2003) )

SM background –(Njet ≤ 6)• For the background calculation I used Sherpa.• In my setup I combined matrix element calculations for 2,3

and 4jet production with parton showers attached.• The underlying method is referred to as CKKW (Catani-

Krauss-Kuhn-Webber) and it avoids any double counting of jet configuration emerging from the matrix element or the parton shower.

• However, in this approach the 5th jet is produced from the parton shower, what means it may be underestimated and a full matrix element calculation could yield a higher rate here, but this is a very complicated computation and cutting edge with present day tools.

• Anyhow, at some point we may want to include higher matrix elements yielding an improved background estimate for Njet>5. However, I do not expect the overall pattern to change and the difference between the QCD background and your multijet rates is significant.


Message from Steffen Schumann

Wonderful Collaboration!

Finally, some comments onRandall-Sundrum


UV IR

Y=0 Y=d

/0( ) y lM y M e

2 2 / 2 2y lds e dx dy

/ 1510 ; 35d lIR

UV

Me d l

M

‘Scale’ runs with the position:

UV/IR hierarchy is explained by ‘Warping’:

AdS5

Relevant energy scale for IR-localized scattering is M(d)~TeV

BH production on UV brane

AdS5

Y=0 Y=d

UV IR

0 2

ˆ32 1

39

s

M M

We will not see this event since it isMpl suppressed!

BH production at an arbitrary `y’

AdS5

Y=0 Y=d

UV IR

2 / 2 /0 2

ˆ32 1( )

39y l y ls

y e eM M

BH production on IR brane

AdS5

Y=0 Y=d

UV IR

2 /2

ˆ32 1

39d l

IR

se

M M

2

ˆ32 1

39

s

M M

*Note: (E/M) is scale invariant.*Cross section~1/TeV^2.

RS1-orginal

• All the SM particles lie on the IR brane.

• They `feel’ strong gravity at the IR scale.

• BH production rate ~1/TeV2

• The LHC as a BH factory

AdS5

Y=0 Y=d

UV IR

2 /2

ˆ32 1

39d l

IR

se

M M

2

ˆ32 1

39

s

M M

Profile: RS1-bulk SM

AdS5

Y=0 Y=d

UV IR

Higgs

Top,bottom

Up, Down

Gluon, W, Z, photon

KK graviton,KK gluon,Other KK states

Zero-modegraviton

2 3PM M l

(See K. Agashe’s PL talk)

•Higgs, top, bottom as well as the longitudinal components of (W, Z) `feel’ the TeV gravity.•The IR-tip of gluon, photon and the transverse components of (W, Z) `feel’ the TeV gravity.•Others (such as 1st, 2nd generation fermions) `feel’ the Planck –weak- gravity.

Closer look: bb+bbbar

1 2 1 1 2 2 1 2 1 2ˆ( ) ( , ) ( , ) ( ) ( )b bbb bbs dx dx f x x x s f x x x s x x s b b

2

ˆ32 1ˆ ˆ( )

39

ss

M M

x1

x2

1 2BHM x x s

Suppressed by PDF!

Closer look: gg

• Only `tip’ of the gluon contribute to the bh formation.

• `Bulk’ contribution is exponentially suppressed.(negligible)

1 2 1 1 2 2 1 2 1 2

2

2

ˆ( ) ( , ) ( , ) ( )

ˆ32 1 1ˆ ˆ( )

39 2 /

gg g gs dx dx f x x x s f x x x s x x s

ss

M M d l

~1/70

Closer look: WL, ZL

• By the equivalence theorem, the longitudinal components of the weak gauge bosons are effectively the unphysical Higgs.

• Localized on the IR brane and feel the TeV gravity.• Suppressed by

WL

u

d

WL

ud

WL

2

/ 4 ,

( / 4 )

W

W

Production Cross section

Thermal black hole production is highly suppressed. (See, Meade-Randall arXiv:0708.3017)But still sizable to be detected.

SCP 2008Prelim.

L L L L L Lgg W W Z Z gW gZbb bb gb gb

• BH plays important role in Heisenberg-’t Hooft picture.• BHs can be produced by scattering. (proved

for D>4 cases in 2002-2005)• Greybody factors for brane-fields are

obtained for generic spin(<2), rotating, higher dimensional black holes in 2003-2007

• MC gens are available (BlackMax, CHARIBDIS ver.2. CATFISH..)

• The LHC will test all these beautiful ideas and will show us results for Md~TeV case soon.

• BH plays important role in Heisenberg-’t Hooft picture.• BHs can be produced by scattering. (proved

for D>4 cases in 2002-2005)• Greybody factors for brane-fields are

obtained for generic spin(<2), rotating, higher dimensional black holes in 2003-2007

• MC gens are available (BlackMax, CHARIBDIS ver.2. CATFISH..)

• The LHC will test all these beautiful ideas and will show us results for Md~TeV case soon.


BHs at ATLAS

Backups


Future/open issues

• Dynamics of BH formation by ‘merging’ two particles will be important. We will be able to understand ‘balding phase’

• Hawking radiation to the Bulk graviton is still missing. It can be important if there are several large extra dimensions because of large number of angular momentum vectors. [2+n/2]

• Blackhole-String transition (entropy, scattering), Information paradox etc.


The legal defense fund site


Seeking for donations to shut-down the LHC

Conventions

• Planck scale (I would take PDG convention)

• I would follow the PDG convention

4

4

4 2

1

8 2

8

n

n

nn n

D

RS d x

G

NG

M

(2 ) ( ),1( ),8 ( ), 2(2 ) ( )..n n

nN PDG RS DL GT

1

1

1

1

2

1( ) ( )

(2 )( ) 0.46( 1) 2.4( 6)

( 2)

n

SD D

n n

n

Mr M k n

M M

k n n nn

Thinking experiment:with E=10^6 Mp


(E/2,0,0,E/2)

(E/2,0,0,-E/2)

Once the impact parameter is less than GE = 10^6/Mp, BH forms!!

We cannot see behind the event horizonwhich is now million times larger thanthe Planck length.

RS1-bulk SM• To address the hierarchy problem, we would put the

Higgs boson on the IR brane (or in the vicinity of the IR brane)

• For flavor problem, longevity of proton, better low energy data fit, etc., we would put 1st,2nd generations on the UV brane (or in the vicinity of UV brane).

• 3rd generation (bR, tL, tR) may be on the IR brane. As a bonus, Large Yukawa for the top is also understandable due to the large overlap with the Higgs.

• (Massless, zero-mode) Gauge bosons are `flat’ in the bulk.

• (Probably) The most realistic set-up in RS1 models.

Excellent agreement


n 1 2 3 4 5 6 7

RYN 1.145 1.333 1.441 1.515 1.570 1.613 1.648

RIOP 1.110 1.170 1.218 1.262 1.300 1.334 1.364

Sr

bnR max)(

Yoshino-Rychkov 2005

Ida, Oda, SCP 2003

Error ~3% (D=5)-17%(D=11)

black holes at colliders: progress since 2002

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