Black Holes at colliders: progress since 2002
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Transcript of Black Holes at colliders: progress since 2002
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Seong Chan Park (SNU)
SUSY08,COEX, SEOUL June 21, 2008
Seong Chan Park (SNU)
SUSY08,COEX, SEOUL June 21, 2008
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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
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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
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Observed Black Holes in the sky
SUSY08, Seong Chan Park
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 .
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‘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.
SUSY08, Seong Chan Park
distance
energy
~1/x p
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Big Question
Does this curve keep going and touch 0??
Will this program go on forever?
SUSY08, Seong Chan Park
distance
energy
~1/x p
Answer: No!
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‘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!
SUSY08, Seong Chan Park
‘t Hooft (1987)
distance
energy
~ ( ) 2Sx r E GE
pM
1/ pM
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The big Picture:Heisenberg-‘t Hooft
SUSY08, Seong Chan Park
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
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D>4
SUSY08, Seong Chan Park
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)
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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.
SUSY08, Seong Chan Park
22
1( )
TeVCMr E
Banks-Fischler (1999), Dimopoulos- Lansberg (PRL87,2001), Giddings-Thomas(PRD65, 2002)
G. Landsberg SUSY02
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Around 2002
• Several different communities started
talking about ‘Mini-Black holes’• Particle physics, String theory, GR community even SF-community
etc..
People got excited
SUSY08, Seong Chan Park
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Seoul in 2002
SUSY08, Seong Chan Park
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Some people concerns if bh eats us :a survey by BBC
SUSY08, Seong Chan Park
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Official comment by the CERN
SUSY08, Seong Chan Park
http://public.web.cern.ch/Public/en/LHC/Safety-en.html
CERN homepage:
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BHs from cosmic rays• Anchordoqui-Feng-Goldberg-Shapere (PRD 2002)
SUSY08, Seong Chan Park
( )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.
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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)
SUSY08, Seong Chan Park
** Penrose (b=0, D=4) long ago
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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!!
SUSY08, Seong Chan Park
This is the hoop r = GM
I am a BH (M)
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It’s like putting an elephant into a freezer..
SUSY08, Seong Chan Park
Mass=MR= RBH(M)
It is hard to do this. But once you can do it, you will have a BH.
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Classical BH formation provedusing two Aichelberg-Sexl
shocks
SUSY08, Seong Chan Park
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
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Latest result: bmax/rs
SUSY08, Seong Chan Park
Yoshino-Rychkov PRD71, 2005
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Another approach:(based on Hoop conjecture, taking angular momentum into
account)
SUSY08, Seong Chan Park
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
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Angular momentum
SUSY08, Seong Chan Park
)2/( maxmax MbJ
)(0
)(/8
max
max2
JJ
JJMJ
dJ
d
bdbd 2
db
Most of BHs are produced with “large” angular momentum!
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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.
SUSY08, Seong Chan Park
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Closer look: Hawking radiation
• Here is the master equationHere is the master equation
SUSY08, Seong Chan Park
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
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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!
SUSY08, Seong Chan Park
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SUSY08, Seong Chan Park
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)
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SUSY08, Seong Chan Park
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
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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.
SUSY08, Seong Chan Park
Ida,Oda,SCP PRD67, 2003
Believe me. This guy is tough!
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Schematic view of the greybody factor calculation
SUSY08, Seong Chan Park
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
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Ida, Oda, Park PRD 06’
D=5,S=1/2
SUSY08, Seong Chan Park
Greybody
Number
Angular mom
Energy
Non-rotating rotating Highly Rotating
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Ida, Oda, Park PRD 06’
D=10,s=1/2
SUSY08, Seong Chan Park
Greybody
Number
Angular mom
Energy
Non-rotating rotating Highly Rotating
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Ida, Oda, Park PRD 06’
SUSY08, Seong Chan Park
D=5, s=1
Greybody
Angular mom
Energy
Non-rotating rotating Highly Rotating
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Ida, Oda, Park PRD 06’
SUSY08, Seong Chan Park
Greybody
Angular mom
Energy
D=10, s=1
Non-rotating rotating Highly Rotating
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Evolution of BHEvolution of BH
SUSY08, Seong Chan Park
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.
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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 )
SUSY08, Seong Chan Park
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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.
SUSY08, Seong Chan Park
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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)
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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
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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
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Two most importantcharacteristics of BH signal
• Large Entropy high Multiplicity.• Thermal radiation Flavor Blind.
SUSY08, Seong Chan Park
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)
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Multi-’hard’-jet
SUSY08, Seong Chan Park
J. -H. Kim, SCP, S. Schumann (in preparation)
BlackMax1.0
,
min *
0.4
| | 4.5
200GeV
m 5
T j
R
E
m
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Multi-`harder’-jet
SUSY08, Seong Chan Park
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) )
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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.
SUSY08, Seong Chan Park
Message from Steffen Schumann
Wonderful Collaboration!
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Finally, some comments onRandall-Sundrum
SUSY08, Seong Chan Park
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
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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!
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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
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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.
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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
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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.
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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!
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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
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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
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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
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• 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.
SUSY08, Seong Chan Park
BHs at ATLAS
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Backups
SUSY08, Seong Chan Park
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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.
SUSY08, Seong Chan Park
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The legal defense fund site
SUSY08, Seong Chan Park
Seeking for donations to shut-down the LHC
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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
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Thinking experiment:with E=10^6 Mp
SUSY08, Seong Chan Park
(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.
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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.
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Excellent agreement
SUSY08, Seong Chan Park
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)