p. kanti - footprints of higher-dimensional decaying black holes

Footprints of Higher-DimensionalDecaying Black Holes

Panagiota Kanti

(University of Ioannina, Greece)

SEENET-MTP Workshop BW2011“Particle Physics from TeV to Planck Scale”

Donji Milanovac, Serbia, 28 August - 1 September 2011

P.Kanti – p.1

Outline :

Introduction: Creation of Black Holes in models with Extra

Dimensions

Decay of Spherically-Symmetric Black Holes

Decay of Rotating Black Holes

– Emission of Brane Particles: a problem and a solution

– Emission of Bulk Particles

– The role of the mass of the emitted particles

Current Limits from LHC

Conclusions

P.Kanti – p.2

Introduction: Creation of Black Holes

Large Extra Dimensions (1998) : (Arkani-Hamed, Dimopoulos & Dvali;

Antoniadis, Arkani-Hamed, Dimopoulos & Dvali)

A 4D Brane with all the SM fields

and scale for gravity GeV

A D Extra Space (Bulk) with

gravitons and scale for gravity

Then, we obtain:

Gravitonsand Scalars

(M*)

SM fields(MP)

y

P.Kanti – p.3


The Most Optimistic scenario: a few TeV Collider

experiments with can probe the strong gravity regime!

Can we then produce a Black Hole? (Banks & Fischler)

During a scattering process with impact parameter :

r (s)i

j

3-brane

h

if , elastic and inelastic processes are expected,

dominated by the exchange of gravitons

if , a BH will be formed according to the...

Thorne’s Hoop Conjecture (1972): “A BH is formed when a mass M gets compacted into

a region whose circumference in every direction is ”P.Kanti – p.4


The produced BH: A higher-dimensional object

The Schwarzschild-Tangherlini BH: A spherically-symmetric,

neutral -dimensional BH with line-element

where is the line-element of a -dim. unit sphere.

Horizon Radius: From the Gauss law in , we find :

P.Kanti – p.5


Basic Criterion: The Compton wavelength of the colliding

particle of energy must lie within the Schwarzschild radius

This can give us , necessary for the BH creation

(Meade & Randall)

8.0 9.5 10.4 10.9 11.1 11.2

Note : The center-of-mass energy of LHC will be 14 TeV.P.Kanti – p.6


Stages of the life of the produced black hole: A highlyasymmetric, rotating object that goes through the following:(Giddings & Thomas)

Balding phase: shedding of all quantum numbers andmultipole moments apart from () – some visiblebut mainly invisible energy emission

Spin-down phase: Loss of angular momentum – emissionof Hawking radiation through mainly visible channels

Schwarzschild phase: Loss of mass – emission of Hawkingradiation through mainly visible channels

Planck phase: when – a few energetic quanta,or a stable “quantum” remnant?

P.Kanti – p.7


Hawking Radiation: What is it? A classical phenomenon

(similar to black body radiation) with a quantum origin

creation of a virtual pair of particles just outside the horizon

the antiparticle falls into the BH whose mass decreases

the particle escapes to infinity where it gets observed

Radiation Spectrum: The fluxes at infinity are given by (Unruh)

where is the greybody factor that follows by solving a

scattering problem in the given backgroundP.Kanti – p.8

Decay of Spherically-Symmetric BH’s

“Master” Equation for Fields on the Brane with spin : By

writing

we find: [Teukolsky ( ); Kanti & March-Russell; Frolov & Stojkovic ( )]

The solution for determines the greybody factor

The spin-weighted spherical harmonics satisfy a

well-known eigenvalue equation with

Due to the spherical symmetry, it offers no new informationP.Kanti – p.9

Decay of Spherically-Symmetric BH’s

The amount of energy emitted per unit time strongly dependson the number of transverse-to-the-brane spacelike dimensions

(Harris & Kanti)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 1 2 3 4 5

d2E

(1/2

) /dtdω

[r-1 H

]

ω rH

0 1 2 3 4 5 6 7

Scalars 1.0 8.94 36.0 99.8 222 429 749 1220Fermions 1.0 14.2 59.5 162 352 664 1140 1830G. Bosons 1.0 27.1 144 441 1020 2000 3530 5740

P.Kanti – p.10


The line-element of a simply-rotating, neutral, higher-dimensional black hole is given by the Myers-Perry solution

where

and

and the parameters and are associated to the black hole massand angular momentum as

P.Kanti – p.11


In this case, the radial “master” e.o.m. for fields on the brane

becomes(Casals, Kanti & Winstanley)

Æ

where . Solving the above, we find again

the greybody factor .The differential emission rates at infinity are now given by:

P.Kanti – p.12

Decay of Rotating Black HolesThe temperature and rotation velocity of this BH are

0

0.002

0.004

0.006

0.008

0.010

0 0.5 1 1.5 2 2.5 3

a*=0

a*=0.5 a*=1.0

a*=1.25

a*=1.5

Pow

erFl

ux

0

0.05

0.1

0.15

0.2

0.25

0 2 4 6 8 10 12 14 16 18

Pow

er F

lux

ω rh

a* = 1.0

n = 1n = 2n = 3n = 4n = 5n = 6n = 7

For all species of brane fields (scalars, gauge bosons andfermions), as or increases, all emission rates are enhanced

(Frolov & Stojkovic; Kanti & Harris; Duffy, Harris, Kanti & Winstanley; Casals, Kanti &

Winstanley; Casals, Dolan, Kanti & Winstanley; Ida, Oda & Park) P.Kanti – p.13


The problem: Two parameters determine the Hawking

radiation spectra – how can we find the value of each?

We need an observable that depends strongly on only one of them

The solution: The angular distribution of the emitted radiation

... as it follows from the equation of the spin-weighted spheroidal

harmonics (Teukolsky; Kanti; Ida, Oda & Park)

P.Kanti – p.14


Angular Distribution of the emitted power : For the different

species of fields, and , we find:

-1-0.5

0 0.5

1

0 0.5

1 1.5

2 2.5

3 3.5

0

0.004

0.008

0.012(n=2, a*=1)

cos(θ)ω rh

Power Flux (s=0)

0 0.5 1 1.5 2 2.5 3 3.5 4 -1

-0.5 0

0.5 1

0

0.004

0.008

0.012(n=2, a*=1)

ω rh cos(θ)

Power Flux (s=1/2)

-1-0.5

0 0.5

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0

0.04

0.08

0.12 (n=2, a*=1)

cos(θ)ω rh

Power Flux (s=1) Centrifugal potential : emissionon the equatorial plane

Spin-rotation coupling : emissionparallel to the axis of rotation

(Casals, Dolan, Kanti & Winstanley;Dai & Stojkovic)

P.Kanti – p.15

Decay of Rotating Black Holes[Casals, Dolan, Kanti & Winstanley ( ); Flachi, Sasaki & Tanaka ( )]

The gauge boson emission can determine the axis of rotation

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

ω rh = 0.5

a* = 0.0a* = 0.5a* = 1.0a* = 1.5

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

ω rh = 1.0

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

ω rh = 2.0

The fermionic emission can determine the angular momentum

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

ω rh = 0.5

n = 2

a* = 0.0a* = 0.5a* = 1.0a* = 1.5

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

ω rh = 1.0

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

ω rh = 2.0

P.Kanti – p.16


During the Schwarzschild phase, the brane channel is the

dominant one (Harris & Kanti; Cavaglia, Cardoso & Gualtieri)

Emission of Bulk Scalar Particles : For the spin-down phase,

the brane dominance persists – it actually increases with

(Casals, Dolan, Kanti & Winstanley)

0.001

0.01

0.1

1

10

1 2 3 4 5 6

Tot

al P

ower

number of bulk dimensions, n

a* = 0.0a* = 0.5a* = 1.0

0

5

10

15

20

25

30

35

1 2 3 4 5 6

% o

f tot

al s

cala

r po

wer

em

itted

in b

ulk

number of bulk dimensions, n

a* = 0.0a* = 0.5a* = 1.0

P.Kanti – p.17


Emission of Gravitons in the Bulk : The equations for

gravitational perturbations in a higher-dimensional rotating BH

background are not all known yet

For tensor-type perturbations and for a simply-rotating BH, they

were derived in 2008 (Kodama)

2 4 6 8 10Ω rh

0.1

0.2

0.3

0.4

0.5d2Edt dΩ n7

n6n5

a1

(Kanti, Kodama, Konoplya, Pappas & Zhidenko;Doukas, Cho, Cornell & Naylor)

Scalars Tensor-type gravitons

3 0.1646 0.0013 0.8%

4 0.3808 0.0222 5.8%

5 0.7709 0.1853 24%

P.Kanti – p.18


The Role of the Mass : We studied the emission of massive

scalar fields in both brane and bulk channels (Kanti & Pappas)

2 4 6 8 10 12 14

Ω rh

0.05

0.1

0.15

0.2

0.25

0.3

d2E

dtdΩ

r h1 n7

n4n2

a1

aThe mass decreases the radiation emission rates in both channels

– but it increases the bulk/brane energy ratio by up to 34% for

low values of P.Kanti – p.19

Current Limits

Many experiments, looking for beyond the SM physics, have

included searches for miniature BH’s in their research programs

CMS collaboration (LHC): Data from March-October 2010

( collisions,

, integrated luminosity of ! ")

(arXiv:1012.3375 [hep-ex])

No excess was observed above the predicted QCD background

At 95% CL, no BH’s exist with minimum mass of 3.5-4.5 TeV in

models with and !! !TeV

ATLAS collaboration (LHC): collisions,

,

integrated luminosity of " (arXiv:1103.3864 [hep-ex])

No BH’s exist in models with and !! !TeVP.Kanti – p.20

Conclusions

In the context of theories with Extra Dimensions (large or

slightly warped), strong gravity effects such as the creation of

Black Holes may become manifest at high-energy collisions

The Large Hadron Collider (LHC), with its final c.o.m energy

of 14 TeV, lies on the edge of both the classical regime and of

the BH creation threshold – we have no signs of them yet though

The Hawking radiation spectra are now well studied and may

be used to determine quantities such as the number of extra

dimensions of the spacetime or the angular-momentum of the

black hole

P.Kanti – p.21

Introduction: Creation of Black HolesCurrent limits on the fundamental energy scale

Type of Experiment/Analysis

Collider limits on the production

of real or virtual KK gravitons1.6 TeV ( ) 0.95 TeV ( )

Torsion-balance Experiments 3.2 TeV ( ) ( m)

Overclosure of the Universe 8 TeV ( )

Supernovae cooling rate 30 TeV ( ) 2.5 TeV ( )

Non-thermal production of KK modes 35 TeV ( ) 3 TeV ( )

Diffuse gamma-ray background 110 TeV ( ) 5 TeV ( )

Thermal production of KK modes 167 TeV ( ) 1.5 TeV ( )

Neutron star core halo 500 TeV ( ) 30 TeV ( )

Neutron star surface temperature 700 TeV ( ) 0.2 TeV ( )

BH absence in neutrino cosmic rays 1-1.4 TeV ( )P.Kanti – p.22


Warped Extra Dimensions (1999) : (Randall & Sundrum)

An observable brane with all the SM fields

and a hidden brane

A 5D Bulk with a negative cosmological

constant #

" !

y = 0 y = L

ΛB < 0

MP MEW

with " # the AdS curvature.

" "# : BH’s should resemble the 5-dimensional

Tangherlini solution

" "# : BH solutions may not exist at all (Tanaka)P.Kanti – p.23


Production Cross-section : For the individual parton-parton

production cross-section, we may write:

#

$

Realistic Collision: The colliding particles are composite

(Giddings & Thomas; Dimopoulos & Landsberg)

# $$

%

%

%

& &%

#

where is the parton-momentum fraction, % , and &

are the parton distribution functions (PDF’s)

P.Kanti – p.24


How far up can we go? Not much ...

The PDF’s & decrease rapidly with

the center-of-mass energy

(Campbell, Huston & Stirling)

If we assume that TeV and

, we finally get

TeV TeV

& fb & fb

' 1/sec ' 3/day

(Giddings & Thomas; Dimopoulos & Landsberg)

P.Kanti – p.25


Horizon Radius: How small are these black holes? Assuming

again that TeV and !TeV, we find

1 2 3 4 5 6 7

( fm) 4.06 2.63 2.22 2.07 2.00 1.99 1.99

For the creation of BH’s, we need to access subnuclear distances

BH Temperature : Defined as , it takes

values that are easily accessed at present and future experiments

1 2 3 4 5 6 7

( (GeV) 77 179 282 379 470 553 629

Typical lifetime: % ! !! sec, for

P.Kanti – p.26

Current Limits

Observables : If extra spacelike dimensions and higher-dimen-

sional BH’s exist, then we should observe the following in high-

energy collisions:

large production cross-sections, increasing with

emission of particles with a thermal profile and large

multiplicity(Harris, Palmer, Parker, Richardson & Webber)

Type Quarks Gluons Charged leptons Neutrinos Photons ) * Higgs

(%) 63.9 11.7 9.4 5.1 1.5 2.6 4.7 1.1

particles from the spin-down phase with an angular

distribution

significant proportion of missing energyP.Kanti – p.27

Introduction : Extra Dimensions

Warped Extra Dimensions (1999) : (Randall & Sundrum)

An observable brane with all the SM fields

and a hidden brane

A 5D Bulk with a negative cosmological

constant #

"

y = 0 y = L

ΛB < 0

MP MEW

with " # the AdS curvature. Then: (Giddings)

" !$ %&'()&* +, '& #$+

" !$ %&'()&*-% +, '&#$+ *

P.Kanti – p.28

p. kanti - footprints of higher-dimensional decaying black holes

Education

creation of black holes

black body radiation

produced black hole

bh creation meade randall

produced bh

quantum origin creation

neutral dimensional

schwarzschildtangherlini