Production and detection of Black Holes at the LHC

Sven Vahsen

Overview

• “Introduction”– General Relativity– Cosmic black holes– The Hierarchy Problem– Extra dimensions

• BH production at the LHC• BH decay and detection with ATLAS.

For more information (=material taken from):

• Black holes at the LHC– Overview / introduction: Greg Landsberg (Brown Univ.): EPS (European Physical Socienty) 2003 meeting.

See both Talk and procedings.

• Extra-dimension studies by ATLAS collaboration– Nothing in Detector and physics Performance TDR because the topic is wacky or because it is new?– Exotics working group webpage:

• http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/EXOTICS/• many studies underway within ATLAS

• ATLAS studies on Black Holes written up by several groups:– Harris, C M; Palmer, M J; Parker, M A; Richardson, P; Sabetfakhri, A; Webber, B R

Exploring Higher Dimensional Black Holes at the Large Hadron Collider ATL-PHYS-2004-033

– Tanaka, J; Yamamura, T; Asai, S; Kanzaki, J : Study of Black Holes with the ATLAS detector at the LHC -- ATL-PHYS-2003-037

– J. GrainSearch for Gauss-Bonnet Black Holes, Dec. 2003 meeting

– LBL?

General Relativity

Newtonian Gravity

• Overall distribution of mass at a certain time determines gravitational field throughout space.

• An object with mass experiences force proportional to gravitatiol field and mass. (Mass is graviational charge).

– F = G mM / r2

• Inertia is the same as mass all massive objects experience same acceleration in gravitational field.

– g = F/m = GM / r2

• One may wonder why any object’s gravitational mass and inetertia are the same.

• Action at a distance is instantaneous. Example: The Sun somehow instantaneously “tells” the earth how to move. (Newton apparently thought this was absurd.)

• What about massless particles - photons and neutrinos?

General Relativity

• Overall distribution of mass/energy (not only rest mass) in universe determines curvature of spacetime.

• At each point in time and space, the local curvature of spacetime tells matter how to move.

• The curvature of spacetime propagates with the speed of light gravity waves

• Since spacetime’s curvature tells matter how to move, all matter, regardless of restmass, experiences the same acceleration by gravity.

• This “Universality of graviational coupling” experimentally verified to 1 part in 1012

• Gravitational lensing is one consequence of gravity’s effect on photons. There’s a talk on this at LBL today.

“Spacetime tells matter how to move, matter tells spacetime how to curve”

John Wheeler

This includes light (photons)

Black Holes (BH’s)• Once you accept that gravity accelerates/deflects light, as well as massive particles…it’s not far fetched to imagine

a gravitational field strong enough to retain photons

• If enough mass/energy MBH contained within a volume of radius RS 2MGN/c2, gravity is so strong that nothing inside RS can get out. RS is the Swarzschild radius, and the surface at R=RS is the “eventhorizon” of the black hole.

• GR established in 1915 by Einstein• Black Holes predicted by Karl Schwarzschild in 1916• Name “Black Hole” by John A. Wheeler in 1967

• Given a certain amount of mass, one needs to somehow compress it within the Schwarzschild radius– Example: RS of the earth is 8.8mm

• 1) Stellar evolution – A Star’s fuel, hydrogen, subject to fusion (pressure outward) and gravitational pull inward.– Once hydrogen is burned up, gravity dominates– The further fate of the star depens on the mass

• A star less than 1.4 times the mass of the sun will become a white dwarf. • A star between 1.4 and 3 times the mass of the sun will become a neutron star. • It's only those stars greater than 3 times the mass of the sun that become black holes upon collapse.

• 2) Additionally, a black hole can be formed by compression through external forces. This type of black hole is called a primordial black hole.

• 3) Collisions of highly energetic particles: Cosmic rays and particle accelerators– Since all energy (not only restmass) is gravitational in GR, all we need is large sqrt(s).\

- need √s > ~ M_plank = 1019 GeV No chance at any future colider!- need impact parameter < Rs

How is a black hole formed?

Black Hole EvolutionBlack Hole Evolution• Naїvely, black holes would only grow once

they are formed

• In 1975 Steven Hawking showed that this is not true, as the black hole can evaporate by emitting pairs of virtual photons at the event horizon, with one of the pair escaping the BH gravity

• These photons have a black-body spectrum (Plank) with the Hawking temperature:

• The smallest black holes are the hottest!

• Usual Stefan-Boltzmann blackbody formula givess the Luminosity: L~TH

4

• The smallest are also the brightest!

SH kR

cT

4

• If the Hawkings Temperature is

high enough, then particle/ antiparticle pairs (other than two photons) are created as well, and the black hole luminosity increases.

• Total luminosity directly proportionally to the degrees of freedom available.

Do Black Holes Exist?• While there is little doubt that BHs exist,

we don’t have an unambiguous evidence for their existence so far

• Many astronomers believe that quasars are powered by a BH (from slightly above the Chandrasekhar limit of 1.5 M to millions of M), and that there are supermassive (~106 M) black holes in the centers of many galaxies, including our own

• The most crucial evidence, Hawking radiation, has not been observed (TH ~ 100 nK, ~ 100 km, P ~ 10-27 W: ~1014 years for a single to reach us!)

• The best indirect evidence we have is spectrum and periodicity in binary systems

• Astronomers are also looking for “flares” of large objects falling into supermassive BHs

• LIGO & VIRGO hope to observe gravitational waves from black hole collisions

Some Black Hole Candidates

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

Chandra X-ray Spectrum

Cygnus X-1

Dates?

The hierarchy problem“Why is gravity so much weaker than the other forces of nature”?

– The electroweak scale: MZ,W ≈ 100 GeV. – The Plank scale: MPlank ≈ 1019GeV (≈ 2^10-8 kg)

– PDG review: “MPlank is defined to be the energy scale where the gravitational interactions of elementary particles become comparable to gauge interactions”

– In plain terms: Can “derive” MPlank as follows: Comparing electrostatic and gravitation forces between two test particles of charge=e, at what mass does the gravitational force equal the electrostatic?

– PDG review: “It is possible that supersymmetry may ultimately explain the origin of this hierarchy.”

– Why? Supersymmetry can make the hierarchy stable, while in the Standard Module alone this is not possible.

– Today, we’ll look at an alternative, proposed solution to the hierarchy problem, i.e. to why gravity is so weak.

Proposal solution: Gravity may not be weak!

Gravity may be strong, but appear

weak, because it is leaking into extra dimensions!

• Extra dimensions in physics date back to 1920’s, when Kaluza tried to unify relativity and EM by adding a 5th dimension to Einstein’s spacetime.

• In order to “hide” the extra dimension, Klein proposed that the extra dimension may be undetectable because it’s “compactified.”, e.g. rolled up, with a very small radius

• In 1970’s and 1980’s, renewed interest in (multiple) extra dimensions: supersymmetry and string theory

• In recent years (1998 to now), we have seen the appearance of new models with extra dimensions, which address the hierarchy problem by exploiting the geometry of space time

• These models may have verifiable consequences at the TeV (=LHC) scale• Common features of these models:

– We live in a 3+1 dimensional subspace: “3-brane” (as in “membrane”). – The brane is embedded in a D(=3+d+1) - dimensional space time: “the bulk”– The d dimensions transverse to the brane hava a common size R– All fields/particles which propagate in the bulk are replicated in Kaluza-Klein Towers,

corresponding to states with non-zero momentum in the bulk

• Size / geometry of bulk, and which particles are allowed to propagate in the bulk and on the brane is model dependent.

• Example: Universal Extra Dimensions (UED). See Joes talk.

Extra dimensions

• In 1998, N. Arkani-Hamed, S. Dimopoulus, G. Dvali suggested: What if gravity is the only force aware of the extra dimension?

• Using Gauss’ law, and geometrical arguments, we can check that the behavior of gravity now depends on which length-scale on is probing! (let’s try derivation on the blackboard?)

• at distances smaller than R (compactification scale), gravity will low follow a F ~ G/r2+n force law

• At distances larger than R, gravity will go as F~G/Rn x 1/r2

Classical gravity, with diluted coupling G’ ≈ G/Rn recovered at large distances

• Can switch this around and vary R,n to tune G, the undiluted coupling as desired: G~G’ Rn. More dimensions & larger radius stronger gravitation coupling lower planck scale (MPl

2 = 1/G)

“Gravity may appear weak, because it’s leaking into extra dimensions.”

Flat Dimension

Com

pact

Dim

ensi

on

Now let’s (re)move the hierarchy problem: We’d like MPl≈ MW,Z

• Setting MPlank = 1 TeV, one obtains:

• Experimentally, it turns out that (~1/r^2) has only been verified down to distances 1 mm (as of 1998) or 0.15 mm (2002)

• Therefore, large spatial extra dimensions, compactified at a sub-millimeter scale are, in principle, allowed!

• If this is the case, gravity can be ~1038 times stronger than what we think!

4 106

3 3

2 7.0

1 108

2

1

12

12

2

n,m

n,nm

n,mm

n,m

M

M

MR

n/

S

Pl

S

If gravity is actually strong, it becomes much easier to create black holes.•requirements:

–√s ~ MPl ~1 TeV (now within LHC reach)–Impact parameter b < RS

•Black disc approximation, strictly valid for √s >> MPl

•Folding this with parton distribution functions at LHC givess the total cross section for production of BH’s with MBH> MPl:

• 15pb < pb, for 1 TeV< MPl <5 TeV• Varies ~10% for n between 2 and 7, and with choice of fi(xi)

•production rate at LHC for MPl =1 TEV ≈ 15 pb = 1.5x10-35 cm-2

at expected luminosities of 10-33 to 10-34, we’ll see several BH’s per minutesIf LHC is not far above plank scale, (unkown) quantum corrections to GR properties expected to be large BH studies should focus on robust effect, and may as well disregard spin, BH quantum number, grey factors etc

Remember the black holes?

RS

parton

parton

M2 = s

~ RS ~ 1 TeV ~ 10 m ~ 100 pb

What would a mini-black hole produced at the LHC look like?

• Decay process– Mini black holes produced at LHC would be light & tiny, compared to cosmic black

holes. (~TeV versus >3 Solar masses)– As a result, they would be extremely hot (T~100 GeV) and evaporate almost

instantaneously, mainly via Hawking radiation. [Decay involvates other stages (balding, spin down), but we won’t get into that.]

– Democratic production: Hawking radiation produces particle/antiparticle pairs for all degrees of freedom accessible around ~ 100 GeV, at roughly equal rates.

• Decay Signature– Average of ~ 6 particles for each decay, emitted spherically– ~120 Particle degrees of freedom ~ 1% chance for each.

– Summing over spin and color gives:– 75 % quarks and gluons– 10 % charged leptons– 5 % neutrinos– 5 % photons or W/Z bosons– Also get new particles around 100GeV, including light highs (1% ?)

– Small fraction of invisible neutrinos and gravitons BH’s easy to reconstruct– 10% high PT leptons trigger

A simulated black hole event in the ATLAS detector

Surprise: courtesy Laurent Vacavant!

LHC as a Black Hole Factory

Drell-Yan +X

Spectrum of BH produced at the LHC w/ subsequent decay into final states tagged with an electron or a photon [Dimopoulos, G. Landsberg, PRL 87, 161602 (2001)]

n=2n=7

100 fb-1

For Planck scale up to ~ 5TeV, clean and large samples of BH’s at the LHC

(Before cuts?)

Given abundant production black holes… what to do with them?

• Obvious: Counting experiment to detect BH production over background

• Reconstruct black hole mass and temperature verify process of Hawking Radiation

• Use MBH vs TH to measure MPL& n, independent of shape of extra dimensions

• Discover the Higgs with M≈130 GeV.

• Note: At √s >> MPL BH production becomes the dominant process: “The End of short distance physics”

BH discovery potential, including detector simulation

[Robindra Pabhu, Univ. of Oslo, Atlas Exotics WG meeting Nov ’04]

Discovery luminosity defined by: S/√B>5.0 and S>10.0

• Strong dependence on MPL, weak dependence on n• We could see something very early!

(confusing labels!)

Shape of Gravity at the LHC

• Relationship between logTH and logMBH allows to find the number of ED; n

• 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

constMn

T BHH

loglog1

1

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

Conclusion• Large Extra dimensions (ED) provide an alternative to SUSY in addressing

the hierarchy problem

• If Large ED’s realized in nature, gravity could be stronger than we think

• In that case, the actual plank scale may be within reach of the LHC

• Black hole production could be abundant, and we could see something early on

• Black hole production could become the dominant process at the LHC, or future colliders - “The end of short distance physics”

• BH production would provide an unexpected window into geometry of spacetime, as well as a new production process for other undiscovered particles