Black Holes and Flavor Violation

Gia Dvali

CERN TH LHCb meeting 29/05/09

Outline

1) Some general properties of macroscopic Black Holes

2) What about the microscopic ones?

3) Lesson from the black hole physics: Existence of species (flavors) affects short-distance gravity.

4) Flavor violating processes mediated by micro Black Holes.

5) Phenomenological implications

6) Conclusions

Hawking flux with T = 1/R

In Einstein’s GR Black holes are strongly gravitating objects with escape velocity at the horizon > speed of light. Therefore, classically, they are absolutely black. However, quantum mechanically Black Holes evaporate with the Hawking temperature T = 1/ R

R

Evaporation of Einsteinian Black Holes is thermal and is fully democratic in all the particle species (flavors). The rate of mass change is:

dM/dt = T4 R2 N = T2 N ,

where N is the number of particle flavors.

The condition of quasi-classicality: The rate of temperature-change is slower than the temperature-squared,

dT/dt < T2 . The Black Holes that violate this condition cannot be quasi-classical, because they half-evaporate faster than their size!

Einsteinian Black Holes carry no hair

Such Black Holes can only be distinguished by exactly conserved quantum numbers measurable at infinity. For example, such numbers are the mass of a Black Hole and its electric charge.

On the other hand, quark and lepton flavors in the Standard Model are not exactly-conserved quantum numbers of nature, and are impossible to measure outside the Black Hole horizon.

Flavor -violation by Black Holes can be visualized by the following thought experiment.

In Standard Model we can produce a large classical black hole by colliding particles of a given flavor , e.g., electron-positron. If the Hawking Temperature of this Black Hole is sufficiently high, it will evaporate in all threelepton generations (and in other possible species) fully democratically,

e+ + e-

e-

e+

μ-

τ+

Thus, macroscopic Black Holes violate flavor maximally.

Everything possible

What about the microscopic Black Holes that may be produced at LHC?

The Black Hole production at LHC is a prediction of class of theories in which gravity gets strong at TeV energies (‘98, ADD, AADD).

It was understood recently that the class of such theories is much larger.

Thus, before turning to the flavor violation let me put this picture in an unified perspective.

The well-understood large-distance black hole physics + effective field theory consistency gives a powerful tool for understanding short distance gravitational physics. Existence of species in the low energy theory implies modification of short distance gravity by lowering the gravitational cutoff below MP

and by emergence of extra gravitational dimensions.

This follows from the consistency of the gravitational physics, independently of our input assumptions about the nature of short distance geometry.

Consider a low energy theory with N particle species (flavors).

Under species we mean weakly interacting particles, with the decay width lessthan their mass, Γ < m

In the opposite case we deal with broad resonances, and our analysis has to be modified accordingly.

It follows from the consistency of Black Hole physics that in any theory with N species the scale of quantum gravity is inevitably lowered, relative to the Planck mass

M2

* = M2P /N !

The fundamental length scale at which classical gravity is getting strong is

L* = M-1* = √N / MP .

This can be proven by black hole thought experiments.

[G.D.; G.D. and Redi, ’07]

The fact that in a theory with N particle species, the quantum gravity scale is

M2* = M2

P /N

can be seen by number of arguments, perhaps the most elegant being, that black holes of size R < M-1

* , have the lifetime

tBH < R

and thus, cannot be regarded as semi-classical states of the Hawking temperature TH = 1/R !

Thus, black holes of this size are quantum objects.

Hawking flux with T = 1/R

The black holes of size R < L* = √N / MP cannot afford to be quasi-classical, because they half-evaporate faster than their size!

Or equivalently, the rate of temperature-change is faster than the temperature-squared dT/dt > T2

L*

Hawking flux of N species with T = 1/R

Einsteinian black holes would half-evaporate during the time

t = R3 M2P N

And for R2

< N / M2P , we have t < R,

or equivalently

dT/dt > T2

Thus, the fundamental length scale below whichno quasi-classical black holes can exist in any consistent theory with N species is

L* = √N / MP

and the corresponding mass scale marks the cutoff.

The well known explicit example, where the relation

M2* = M2

P /N

is fixed by the fundamental theory , is extra dimensions.

So consider a theory with n extra dimensions compactified on n-torus of radii R .

As a result of the dilution, there is a simple relation between the true quantum gravity scale and the Planck mass measured at large distances:

M2P = M2

* (M*R)n

Volume of extra space

Notice, that the above relation can be rewritten as,

M2P = M2

* N,

Where N is the number of Kaluza-Klein species . This very important, because the latter expression turns out to be more general than the former: What matters is the number of species!

Alternative proof of the bound comes from quantum information. [G.D., Gomez, `08]

Species exist as long as we can distinguish them by physical measurements. Equivalently, we can encode information in the species numbers. With N species, a simple message can be an N-sequence of 1-s and 0-s, each referring to an occupation number of a given species in the message.

A typical message = (0,1,0,0,0, ….. 1, 1,1)

The simplest message includes a single 1, and all other 0-s:

A simplest Message = ( 0,0, 0,1,0,…..0)

What is the minimal space-time scale L on which we can decode such a message?

The decoder contains samples of all N species in each pixel . So the space-time resolution is set by the size of the pixel. How small can this size be?

Without gravity, there is no limit to the smallness of L.

Message encoded in a green flavor

Pixel of size L, with all the sample flavors

L

A processor of information encoded in species contains N species localized within the pixel of scale L . In a theory without gravity, L can be arbitrarily small.

However, because of gravity, we must have L > √N / MP , or else the processor itself collapses into a black hole!

M-1P √N/MP R

mrg

m-1

Strength of Gravity as Function of Distance

Classical modification of graviton propagator in the interval

M2P /N > p2 > 1/R2 ,

implies that there is a tower of (Spin-2) states. This can be seen from the spectral representation,

G(p2) = ∫ ds ρ(s) /(p2 + s) .

Since G(p2) ≠ p-2, there must be new poles within the interval M2

P /N > p2 > 1/R2.

These poles can be regarded as Kaluza-Klein tower of the new dimensions.

The statement that species are separated in a true dimension, is also supported by the locality properties in the species flavor .

Consider a microscopic black hole of mass ~ M * , produced in a particle-anti- particle annihilation of i-th flavor of species at energies ~ M *. .

By unitarity decay rate of such a black hole back to i-th species is Γ ~ M *

And the decay rate into all other flavors j ≠ i must be suppressed by 1/N.

i

i

j

jBHi

Although at no point did we assumed any input geometric substructure, the species flavor leads us to the existence of the gravitational extra dimensions.

The model-independent non-Einsteinianity interval for the black hole mass is al least

MP /√N < MBH < MP √N

at the lower end of this interval black holes are maximally non-democratic in the species flavor, and conserve it.

Since, flavors are separated in new dimensions, what about flavor -violating processes mediated by the virtual microscopic black holes?

Flavors are displaced in extra dimension (space of species)

Rdb

d b Extra D

Probability to produce b-quarks in a decay of a small (quantum) black hole produced at the d-quark site is exponentially suppressed.

Processes mediated by such Black Holes will be flavor-conserving. However, a quasi-classical Black Hole of R > Rdb, will violate the flavor Maximally.

b

d

b

d

bd bdM2

1

The low energy decoupling of processes mediated by quasi-classical Black Holes of mass M, are very different from the ones mediated by quantum particles of the same mass:

An analogous process mediated by a virtual quasi-classical black hole of mass M = M* (M*R)n+1 would be exponentially suppressed at least by the factor

exp (- SB )

Where SB = (M*R)n+2 is the Beckenstein entropy of a (4+n) - dimensional Black Hole.

This decoupling is due to he fact that large Black holes are quasi-classical objects.

However, unlike other quasi-classical objects (e.g. solitons) at high energies the black hole mediated processes sharply catch up.

In particular, for center of mass energies

E > Mdb = M* (M*R db )n+1 ,

d-b transition processes become order one.

d

d

s b

The number of quanta emitted Nfinal = (E/M* )(n+2)/(n+1)

Generic features:

1) Exponentially sharp increase of flavor-violation in the final states at high energies.

2) Softening of the final state momenta:

pfinal / E = (M* /E)n+2

3) Total number of flavors produced democratically :

Nfinal = (E/M* )(n+2)/(n+1)

Conclusions:

Our current understanding of microscopic Black Hole physics suggests that the rate of flavor –violating processes mediated by microscopic Black Holes should be characterized by sharp increase at high energies.

If the strong TeV scale gravity solution to the Hierarchy Problem has anything to do with nature, such Black Holes may be accessible at LHC, and LHCb would be the right place for testing their flavor violating effects.

Micro Black Hole Non-Democracy Puzzle. GD, Pujolas ‘08.

We have seen that the microscopic black holes, by unitarity cannot evaporate democratically in all the particle species. Thus, different species must ``see’’ different horizons and be produced at different thermal rates.

Thus, the micro black holes can be labeled by species. Micro black holes carry the species hair.

But, how is this possible for quasi-classical micro black holes?

The resolution of the puzzle is in democratic transition, during which the microscopic black holes become democratic and loose the species hair !

Black hole

Extra dimension

After democratic transition all branes share the same black hole

Black hole stabilized by the stretched string

String shortens and brane gets connected to black hole

The resolution of black hole non-democracy puzzle, shows that microscopicblack holes have two characteristic time scales:

1) Quantum Hawking evaporation time;

2) Classical democratization time, set by N.

For the smallest black holes, the evaporation is the dominant effect, and such black holes therefore conserve the species flavor for all the practical purposes. For larger ones, the democracy sets in, and correspondingly they can mediate flavor-violating interactions.

The latter processes are however suppressed because creation of the democratic (heavy) black holes is very costly.

Implications for the Hierarchy Problem

It is well established, that for the energies E < MW the world of (known) elementary particles is described by the STANADARD MODEL

GAUGE FORCES SU(3)xSU(2)xU(1)

MATTER:

QUARKS : (u,d) (c,s) (t,b), LEPTONS: (e,νe) (μ, νμ) (τ, ντ)

HIGGS: H

The weak scale is set by the vacuum expectation value of the Higgs

field, which is related to the mass of the Higgs boson, mH .

This mass is UV-unstable!

H H

t

t

H H

H

+

UV-instability of the Higgs mass

δm2H ≈ Λ2 !

+

The natural cutoff is the gravity scale Λ = MP

Without gravity the problem could have been less severe, but with gravity there is no way out:

The particles running in the loop cannot have arbitrarily high energies without becoming big black holes.

THUS, THERE MUST BE SOME NEW PHYSICS NOT FAR ABOVE THE WEAK SCALE , THAT STABILIZES THE HIGGS MASS, AND LHC SHOULD PROBE IT.

WHAT IS THIS NEW PHYSICS?

Planck mass MP =1019GeV

Weak Scale MW = 102 GeV

Supersymmetry

E

Quantum Gravity (String) Scale

Standard Paradigm ‘74 - ‘98

’98 Quantum Gravity at TeV Idea:

Weak scale is stable, because the quantum gravity scale M* ≈ TeV ! (Arkani-Hamed, Dimopoulos, G.D.; Antoniadis et al)

But, if gravity becomes strong around the TeV scale, why is the large distance gravity so much weaker than all the other forces of nature?

For example, gravitational attraction between the two protons at 1 m distance is 1037 times weaker of their Coulomb repulsion!

Original Realization: Extra Dimensions

As a result of the dilution, there is a simple relation between the true quantum gravity scale and the Planck mass measured at large distances:

M2P = M2

* (M*R)n

Volume of extra space

Notice, that the above relation can be rewritten as,

M2P = M2

* N,

Where N is the number of Kaluza-Klein species . This very important, because the latter expression turns out to be more general than the former: What matters is the number of species!

The black hole arguments show, that the class of theories which solve the Hierarchy Problem by TeV quantum gravity scale, is much larger.

In particular, any theory with N = 1032 particle species, will do this.

The role of these 1032 species, can equally well be played by 1032 Kaluza-Klein gravitons from large extra dimensions, or by 1032 copies of the Standard Model!

Experimental signatures of low scale quantum gravity theories are pretty spectacular.

One model-independent prediction is the formation of mini black holes in particle collisions. The small black holes carry ``hair”, which becomes ``shorter’’ with their increasing size. In the same time the cross-sections soften out with the increase of the collision energy. This is very different from supersymmetry.

In some realizations, the black holes can be semi-classical, and live very long. For us, such black holes will look as very long lived charged states, with continuously decreasing mass, that at the final stage explode in very energetic Standard Model particles.

Another signature is production of string vibrations, and emission of particles in Extra Dimensions.

Conclusions

This is an exciting time for the particle physics community.

LHC will directly probe the mechanism which is responsible for generating the weak interaction scale and masses of the elementary particles.

And, there is a strong theoretical indication, that LHC will also probe physics that is behind the stability of the above scale.

If the ideas presented in this talk have anything to do with nature, LHC has an exceptional chance of experimentally discovering and studying the nature of quantum gravity.