Black Hole Production N. Okada T. Matsuo (Taiwan Normal) T. Matsuo - - PowerPoint PPT Presentation

Black Hole Production Black Hole Production at at Collider Collider

Kin-ya Oda Kin-ya Oda (Osaka)

based on work with

• D. Ida
• D. Ida (Gakushuin)
• S. C. Park
• S. C. Park (Seoul National)

PRD 67 [th/0212108]; 71 (2005); 73 (2006) and also

• N. Okada
• N. Okada (KEK)

PRD 66 [ph/0111298]

M.

• M. Drees

Drees and C.

• C. Alig

Alig (Bonn)

JHEP 0612 (2006)

• T. Matsuo
• T. Matsuo (Taiwan Normal)

in preparation

Outline

• 1. Planck scale, as low as TeV
• 2. BH production, inevitably
• 3. BH decay through Hawking radiation
• 4. Precise determination of BH event
• Hints for quantum gravity
• 5. Summary & Outlook

Planck scale

– Natural unit: hbar = c = 1

• Highest energy:

– Gravity neglected for E << MP

• Lowest energy:

– Quantum corrections neglected for E >> MP

M P = hc G ~10µg ~1019GeV ~10-35m

Particle physics’ paradigm for decades:

• 1. At some high UV scale M,

– write down ALL interactions – allowed by your symmetry, – including non-renormalizable ones.

• 2. At low IR scale << M,

– If there are

• quantum mechanics,
• Lorentz symmetry,
• cluster decomposition principle,

– the theory NECESSARILY looks like – a renormalizable QFT.

Effective field theory

S ~ d 4x

• 1

2 ˙

• 2 ()2 M 22 4 4 6

6 M 2 8 8 M 4 +L

Hierarchy problem

• A “problem” within the EFT paradigm:
• Gravity is not renormalizable.

– The Einstein-Hilbert action is not. – Graviton loop cut-off by MP

• So we know QFT breaks down at ~ MP .
• Higgs mass: mh ~ 100 GeV ~ 10-17MP !
• Very much smaller than cut-off scale.
• Worse,

– mh unprotected from quantum corrections. – Must fine-tune between tree and radiative.

New paradigm: TeV gravity

mh << MP

• Hierarchy problem: How keep mh small?

– Most popular solution: SUSY – But, current experimental bound requires O(10-2) fine-tuning (little hierarchy).

• Why not putting MP small instead?

– “Problem” disappears! – MP ~ TeV scale gravity!

• But how?

Lowered Planck scale

• Setup: n extra dimensions

– compactified with length L, say, y ~ y+L .

F(r) = G4 m1m2 r2

• GD

m1m2 r2+n (r << L) GD m1m2 Lnr2 (r >> L)

• Newton’s law is modified in D=4+n dims.

L For r >> L, G4 ~ GD Ln , i.e., M 4

2 ~ M D 2n

Ln .

M D ~ M 4

2

Ln

• 1/(2+n)
• MD can be small for large L !!

SEH = 1 16GD d Dx

• g(D)R(D) ~

Ln 16G4 d 4x g(4)

• R(4)

Planck scale can be as low as TeV!

• How large should L be to have MD~TeV?

– For n=1, L ~ solar system size.

• Observationally excluded.

– For n=2, L ~ sub mm.

• Gravitational experiment does NOT excl’d!!

– For n>2, L ~ μm is sufficient.

• No bound at all!
• But we know Coulomb’s law is,

– or more properly QED (or SM) is, – perfect up to lengths > am ~ TeV-1.

• How can one keep SM unchanged?

Arkani-Hamed Arkani-Hamed, , Dimopoulos Dimopoulos, , Dvali Dvali ’ ’98 98

Large extra dimension scenario

• Confine SM on 3-brane (3+1 subspace).

– We are living on 3-brane.

That is,

– SM confined on 3-brane. – Graviton propagate in D=4+n dimensional bulk.

L

• Naturally implemented by D-branes

in string theory

Arkani-Hamed Arkani-Hamed, , Dimopoulos Dimopoulos, , Dvali Dvali ’ ’98 98

Alternative: Warped comp’n from D=5

Randall-Sundrum Randall-Sundrum ’ ’99 99

ds2 = eky(dt 2 + dr x

2)+ dy2

• Extra dimension is

compactified with warping on AdS5.

• Energy scale scales

exponentially with y.

• At IR brane,

UV cut-off is TeV.

Outline

• 1. Planck scale, as low as TeV
• 2. BH production, inevitably
• 3. BH decay through Hawking radiation
• 4. Precise determination of BH event
• Hints for quantum gravity
• 5. Summary & Outlook

Black hole

• Event horizon at rS = (GDM)1/(1+n).
• Hawking radiation:

– Quantum treatment of SM fields on classical gravitational background.

ds2 = 1 GDM r1+n

• dt 2 +

1 1 GDM r1+n

• dr2 + r2d2
• Schwarzshild metric in D=4+n:

Geometrical cross section

RS 1 M P MBH M P

• 1

n+1

(M P ~ TeV)

b

parton parton

R RS

S: Schwarzschild radius of the BH.

: Schwarzschild radius of the BH.

’ ’t t Hooft Hooft ’ ’87 87

‘ ‘BH forms whenever BH forms whenever b b< <R RS

S ’

’ Cross section rises with energy! Cross section rises with energy!

prod = RS

2 ˆ

s

2 n+1

(for RS << L)

MBH = ˆ s

• Growing cross section.
• BH production dominates over all other

interactions above TeV.

• “The end of short distance physics”

TeV gravity inevitably leads to BH production

Closed trapped surface forms Closed trapped surface forms when when b b < < b bmax

max.

. t z b b

• Classical BH production,

PROVEN with finite impact parameter.

Eerdley, Giddings 02 Yoshino et al. 02, 05

Correspondence principle

gs2M

S, T (σ)

• corr. point

α’ -1/2

Truly QG effects Truly QG effects, observed as , observed as a a deviation deviation from asymptotic behavior (in BH picture). from asymptotic behavior (in BH picture). Crucial to predict BH behavior Crucial to predict BH behavior

as precisely as possible!! as precisely as possible!!

BH picture String picture There is no complete description

Horowitz, Polchinski ’96, ’97

Also: Also: Correspondence in Correspondence in

• hard scattering

hard scattering suppression suppression

K.O., ., Okada Okada K.O., ., Okada Okada ’ ’02 02

• rotating SB/BH

rotating SB/BH production production

K.O., ., Matsuo Matsuo K.O., ., Matsuo Matsuo ’ ’08 08

Classical
gravity Classical
gravity Quantum
gravity Quantum
gravity Perturbative Perturbative Non- Non- perturbative perturbative Low Low
 
enegy/mass enegy/mass string string
picture 
picture High High
energy/mass 
energy/mass black
hole black
hole
picture 
picture Intermediate
scale Intermediate
scale Final
theory Final
theory (easy) (easy)

Outline

• 1. Planck scale, as low as TeV
• 2. BH production, inevitably
• 3. BH decay through Hawking radiation
• 4. Precise determination of BH event
• Hints for quantum gravity
• 5. Summary & Outlook

BH life in detector

Temperature gets higher and higher.

1.

• 1. Balding Phase

Balding Phase (negligible?)

• Dynamical production phase
• BH loses its “hair”.

2.

• 2. Spin Down Phase

Spin Down Phase

• BH loses its mass and angular

momentum. .

3.

• 3. Schwarzschild Phase

Schwarzschild Phase

• Angular momentum is small.
• BH loses its mass.

4.

• 4. Planck Phase

Planck Phase

• Truly QG, highly unpredictable
• A few quanta would be emitted.

?

What follows from BH production

• Decay

– Radiates mainly on brane – decay proportional to #(dof) h : q : l : v = 4 : 72 : 18 : 24

• Typically at LHC

– Produced every second – M ~ 1-10 TeV – T > 0.1 TeV – Tens of multiple emissions – Life time ~ 10-27sec Hawking radiation 3-brane

Fig in higher dim Giddings, Thomas; Giddings, Thomas; Dimopoulos Dimopoulos, , Landsberg Landsberg; ; … …

Typical BH event at LHC

Simulation with MBH ~ 8 TeV in ATLAS … and in CMS

A clean signal per second! A clean signal per second!

from Kobayashi DPF/JPS 06

in Schwarzschild approximation in Schwarzschild approximation

Outline

• 1. Planck scale, as low as TeV
• 2. BH production, inevitably
• 3. BH decay through Hawking radiation
• 4. Precise determination of BH event
• Hints for quantum gravity
• 5. Summary & Outlook

What we found

• BH is produced with large

angular momentum.

• Obtained brane fi

field equations essential for Hawking radiation

• Spin down phase

contributes a lot.

– Gauge bosons are emitted along the angular momentum axis perpendicular to beam

• axis. “polar emissision”
• (Black ring might form)

Ida, KO, Park (Fig now in 3 dim)

beam axis beam axis

Equatorial plane Equatorial plane

BH is produced with large angular momentum

b

parton parton

M /2 M /2 angular angular momentum momentum momentum momentum

J = bM /2

Ida, KO, Park

= bmax

2

= (1.1~ 1.9)r

S 2

Yoshino et.al.

Fits numerical results qualitatively:

• Increased from rS-disc
• becomes larger for higher D

Cross section increases with Cross section increases with angular momentum!! angular momentum!!

(Jmax = bmaxM /2)

d dJ = 8J / M 2 (J < J max) (J > J max)

• d = 2bdb

db

d dσ σ/ /dJ dJ ~ ~ J J/ /s s for for J J < < s s(2+

(2+n n)/2(1+ )/2(1+n n) ) (in Planck unit)

(in Planck unit)

Hawking radiation

• Difference between two vacua at

– Near horizon (NH): r ~ rh – Far field (FF): r → ∞

• Vacumm state for NH

– = many particle state for observer at FF

• Graybody factor

– gives spectrum of emitted particles

• The larger, the cooler: T ~ 1/rS ~ M-1/(1+n)
• Precise determination of Greybody

factor is important.

Higher dim. Kerr metric

(just to show how it looks)

ds2 = g(4)(r,)+ r2 cos2 dn

2

g(4)(r,) = a2 sin2

• ( r2 a2)asin2
• *

[(r2 + a2)2 a2 sin2 ]sin2

• vanishes on the brane

= r2 + a2 cos = r2 1 µ rn+1 + a2 r2

• Mayers, Perry

Newman Penrose formalism (just to show)

= r2 + a2 cos = r2 1 µ rn+1 + a2 r2

• Null tetrads:

Null tetrads:

Spinor Spinor: : Vector:

g(4)µµ = 0

Scalar: Scalar:

Field equations on brane

angular part: radial part: K = (r2 + a2) ma ,0,0 ~ ei t + im Rs,l,m

• (r)Ss,l,m
• ( )

,l,m

• Decomposition:

Decomposition:

= r2 + a2 cos = r2 1 µ rn+1 + a2 r2

• Ida, KO, Park

Separation of variables Separation of variables

Greybody factor determines Hawking radiation and BH evolution

Greybody Greybody factors factors for Brane fields determine determine the evolution

• f BH mass and angular momentum (up to Planck phase).

BH radiates mainly into the brane brane (SM) fields (SM) fields via Hawking Hawking radiation radiation.

dNs,l,m dt d d = 1 2 s,l,m () e(mBH )/T m1 Ss,l,m (,)

2

d dt M J

• = 1

2 gs

s,l,m

• d

s,l,m e(mBH )/T m1

• m

greybody factor

purely ingoing in

• ut

absorption rate absorption rate = penetration rate of = penetration rate of grav

• grav. pot. well

. pot. well in a in a “ “time-reversed time-reversed” ” sense sense

Greybody factor for vector

Ida, KO, Park

Power spectrum for various dim

Spinor peaks for high rotation are only for Randall-Sundrum (D=5) BH

Ida, KO, Park

Angular spectrum

cos

r

h

a* =1.5

r

h

dE dt d d cos

• ang. mom.

beam axis

• Ida, KO, Park 02

Ida, KO, Park 02 Casals Casals, Doran, , Doran, Kanti Kanti 06 06

(fig (fig w/ w/ one

• ne helicity

helicity) ) (fig (fig w/ w/ both both helicities helicities) )

(through
e.g.
correspondence (through
e.g.
correspondence for for
 
BH/string) BH/string)