out-of-this-world physics: from particles to black holes

Out-of-this-World Physics: Out-of-this-World Physics: From Particles to Black HolesFrom Particles to Black Holes

Greg LandsbergGreg Landsberg

L.G.Landsberg L.G.Landsberg

SymposiumSymposiumDecember 19, 2005

22December 19, 2005December 19, 2005 Greg Landsberg - Out-of-this-World Physics: From Particles to Black HolesGreg Landsberg - Out-of-this-World Physics: From Particles to Black Holes

OutlineOutline

A Word on Hierarchies

Standard Model: Beauty and the Beast

How to Make Gravity Strong?

Looking for Extra Dimensions…

Production of Black Holes at Colliders


N.B. Large Hierarchies Tend to N.B. Large Hierarchies Tend to Collapse...Collapse...


Hierarchy of the Standard ModelHierarchy of the Standard Model

Extra dimensions might get rid of the beast while preserving the beauty!

Beauty …

vev MGUT MPl

GravitationalForce

E [GeV]

EM/HyperchargeForce

Weak Force

Strong ForceInvers

e S

trength

RGE evolution

1016102 1019

and the Beast


But Keep in Mind…But Keep in Mind…Fine tuning (required to keep a large hierarchy stable) exists in Nature: Solar eclipse: angular size of the sun is the same as the

angular size of the moon within 2.5% (pure coincidence!) Politics: Florida recount, 2,913,321/2,913,144 =

1.000061 Numerology: 987654321/123456789 =

8.000000073

(HW Assignment: is it really numerology?)

But: beware the anthropic principle Properties of the universe are special because we exist in it Don’t give up science for philosophy: so far we have been

able to explain how the universe works entirely by science


Math Meets PhysicsMath Meets PhysicsMath physics: some dimensionalities are quite specialExample: Laplace equation in two dimensions has a logarithmic solution; for any higher number of dimensions it obeys the power lawSome of these peculiarities exhibit themselves in condensed matter physics, e.g. diffusion equation solution allows for long-range correlations in 2D-systems (cf. flocking)Modern view in topology: one dimension is trivial; two and three spatial dimensions are special (properties are defined by the topology); any higher number is notDo we live in a special space, or only believe that we are special?


The ADD ModelThe ADD ModelSM fields are localized on the (3+1)-brane; gravity is the only force that “feels” the bulk space

What about Newton’s law?

Ruled out for infinite extra dimensions, but does not apply for sufficiently small compact ones

1

2123

212

11

nnn

PlPl r

mm

Mr

mm

MrV

Gravity is fundamentally strong force, bit we do not feel that as it is diluted by the volume of the bulk

G’N = 1/MD2; MD 1 TeV

More precisely, from Gauss’s law:

Amazing as it is, but no one has tested Newton’s law to distances less than 1mm (as of 1998)

Thus, the fundamental Planck scale could be as low as 1 TeV for n > 1

nPl

nD RMM 22

4106

33

270

1108

2

1

12

12

2

nm

nnm

nmm

nm

M

M

MR

n

D

Pl

D

,

,

, .

,/

231 ][/ nPlM

Rr

rR

mm

MrV

nnnPl

for 21

23

1


Longitudinal EDLongitudinal EDSimultaneously, another idea has appeared: Explore modification of the

RGE in (4+n)-dimensions to achieve low-energy unification of the gauge forces [Dienes, Dudas, Gherghetta, PL B436, 55 (1998)]

To achieve that, allow gauge bosons (g, , W, and Z) to propagate in an extra dimension, which is “longitudinal” to the SM brane and compactified on a “natural” EW scale: R ~ 1 TeV-1

MZ MGUT

MPl=1/GN

MS M’GUT

GravitationalForce

logE

EM/HyperchargeForce

Weak Force

Strong Force

Real GUT Scale

VirtualImage

Invers

e S

tren

gth

M’Pl ~ 1 TeV


Randall-Sundrum ScenarioRandall-Sundrum ScenarioRandall-Sundrum (RS) scenario [PRL 83, 3370 (1999); PRL 83, 4690 (1999)] + brane – no low energy effects +– branes – TeV Kaluza-Klein modes

of graviton Low energy effects on SM brane are

given by ; for krc ~ 10, ~ 1 TeV and the hierarchy problem is solved naturally

G

Planck branex5

SM brane

2222

drdxdxeds kr

8PlPl MM

r

Planck brane ( = 0)

SM brane()

AdS5

k: AdS curvature

kr

PleM

Reduced Planck mass:

AdS


Differences Between the ModelsDifferences Between the ModelsADD Model:

Pro: “Eliminates” the hierarchy problem by stating that physics ends at a TeV scaleOnly gravity lives in the “bulk” spaceSize of ED’s (n=2-7) between ~100 m and ~1 fmBlack holes at the LHC and in the interactions of UHE cosmic raysCon: Doesn’t explain why ED are so large

TeV-1 Scenario:Pro: Lowers GUT scale by changing running of the couplingsOnly gauge bosons (g//W/Z) “live” in ED’sSize of ED’s ~1 TeV-1 or ~10-19 mCon: Gravity is not in the picture

RS Model:Pro: A rigorous solution to the hierarchy problem via localization of gravityGravitons (and possibly other particles) propagate in a single ED, w/ special metricCon: Size of ED as small as ~1/MPl or ~10-35 m

G

Planck

brane

x5

SM brane


Kaluza-Klein SpectrumKaluza-Klein SpectrumADD Model:

Winding modes with energy spacing ~1/r, i.e. 1 meV – 100 MeVCan’t resolve these modes – they appear

as continuous spectrum

TeV-1 Scenario:Winding modes with nearly equal energy spacing ~1/r, i.e. ~TeVCan excite individual modes at colliders or look for indirect effects

RS Model:“Particle in a box” with a special metricEnergy eigenvalues are given by zeroes of Bessel function J1

Light modes might be accessible at colliders

~1 TeVE

~MGUT

E

…

M0

Mi

2220 riMM i

~MPl

E

…

M1

Mi

... ,30.4 ,48.3 ,66.2

,83.1 ,;0

111

11110

MMM

MMxxMMM ii Gravitational coupling

per mode; many modes

ge

GN for zero-mode;

~1/ for others

M0


Using the ED ParadigmUsing the ED Paradigm

EWSB from extra dimensions: Hall, Kolda [PL B459, 213 (1999)] (lifted

Higgs mass constraints) Antoniadis, Benakli, Quiros [NP B583, 35

(2000)] (EWSB from strings in ED) Cheng, Dobrescu, Hill [NP B589, 249

(2000)] (strong dynamics from ED) Mirabelli, Schmaltz [PR D61, 113011

(2000)] (Yukawa couplings from split left- and right-handed fermions in ED)

Barbieri, Hall, Namura [hep-ph/0011311] (radiative EWSB via t-quark in the bulk)

Flavor/CP physics from ED: Arkani-Hamed, Hall, Smith, Weiner [PRD

61, 116003 (2000)] (flavor/CP breaking fields on distant branes in ED)

Huang, Li, Wei, Yan [hep-ph/0101002] (CP-violating phases from moduli fields in ED)

Neutrino masses and oscillations from ED: Arkani-Hamed, Dimopoulos, Dvali,

March-Russell [hep-ph/9811448] (light Dirac neutrinos from right-handed neutrinos in the bulk or light Majorana neutrinos from lepton number breaking on distant branes)

Dienes, Dudas, Gherghetta [NP B557, 25 (1999)] (light neutrinos from right-handed neutrinos in ED or ED see-saw mechanism)

Dienes, Sarcevic [PL B500, 133 (2001)] (neutrino oscillations w/o mixing via couplings to bulk fields)

Many other topics from Higgs to dark matter


ED and Flavor PhysicsED and Flavor PhysicsED models offer a powerful paradigm for explaining flavor sector and CP-violationNew amplitudes and phases could be transmitted to our world via gravity (or other bulk fields), thus naturally introducing small parameters needed for description of CP-violation, flavor physics, etc.Some realizations of this class of models give realistic CKM matrix (e.g., Arkani-Hamed, Hall, Smith, Weiner [PRD 61, 116003 (2000)])The idea of “shining” mentioned in the original ADD papers could explain why these effects were stronger in early universe

SM

bulk

gauge

fields

via gravity

bulk

big bang

“CP-

bran

e”“shining”

SM


Flavor Physics from GeometryFlavor Physics from GeometryArkani-Hamed/Schmaltz [Phys. Rev. D61, 033005 (2000)] – split fermions embedded in a “fat” braneWave-functions of different families of quarks and leptons are spatially offset, thus the overlap areas are reduced exponentiallyA fruitful paradigm to build models of flavor and mixing with automatically suppressed FCNC and stable protonPossible to construct realistic CKM matrices via geometry of extra braneSimilar attempts in Randall-Sundrum class of modelsIn some of these models LFV decays of kaons are predicted and could be sought

Quark doubletsof 3 generations

Quark singletsof 3 generations

Branco/de Gouvea/Rebelo [Phys. Lett. B506, 115 (2001)]

Huber [NP 666, 269 (2003)]


Sub-millimeter gravity measurements could probe only n=2 case only within the ADD modelThe best sensitivity so far have been achieved in the U of Washington torsion balance experiment – a high-tech “remake” of the 1798 Cavendish experiment R < 0.16 mm (MD > 1.7 TeV)

Sensitivity vanishes quickly with the distance – can’t push limits further down significantlyStarted restricting ADD with 2 extra dimensions; can’t probe any higher numberUltimately push the sensitivity by a factor of two in terms of the distanceNo sensitivity to the TeV-1 and RS models

Tabletop Gravity ExperimentsTabletop Gravity Experiments

PRL 86, 1418 (2001)E.Adelberger et al.

~

~

[J. Long, J. Price, hep-ph/0303057]


Astrophysical and Cosmological Astrophysical and Cosmological ConstraintsConstraints

Supernova cooling due to graviton emission – an alternative cooling mechanism that would decrease the dominant cooling via neutrino emission Tightest limits on any additional cooling

sources come from the measurement of the SN1987A neutrino flux by the Kamiokande and IMB

Application to the ADD scenario [Cullen and Perelstein, PRL 83, 268 (1999); Hanhart, Phillips, Reddy, and Savage, Nucl. Phys. B595, 335 (2001)]:

MD > 25-30 TeV (n=2) MD > 2-4 TeV (n=3)

Distortion of the cosmic diffuse gamma radiation (CDG) spectrum due to the GKK decays [Hall and Smith, PRD 60, 085008 (1999)]: MD > 100 TeV (n=2) MD > 5 TeV (n=3)

Overclosure of the universe, matter dominance in the early universe [Fairbairn, Phys. Lett. B508, 335 (2001); Fairbairn, Griffiths, JHEP 0202, 024 (2002)] MD > 86 TeV (n=2) MD > 7.4 TeV (n=3)

Neutron star -emission from radiative decays of the gravitons trapped during the supernova collapse [Hannestad and Raffelt, PRL 88, 071301 (2002)]: MD > 1700 TeV (n=2) MD > 60 TeV (n=3)

Caveat: there are many known (and unknown!) uncertainties, so the cosmological bounds are reliable only as an order of magnitude estimate

Still, n=2 is largely disfavored


Collider Signatures for Large EDCollider Signatures for Large EDKaluza-Klein gravitons couple to the energy-momentum tensor, and therefore contribute to most of the SM processes

For Feynman rules for GKK see: [Han, Lykken, Zhang, PRD 59, 105006

(1999)] [Giudice, Rattazzi, Wells, NP B544, 3

(1999)]

Since graviton can propagate in the bulk, energy and momentum are not conserved in the GKK emission from the point of view of our 3+1 space-time

Depending on whether the GKK leaves our world or remains virtual, the collider signatures include single photons/Z/jets with missing ET or fermion/vector boson pair productionGraviton emission: direct sensitivity to the fundamental Planck scale MD

Virtual effects: sensitive to the ultraviolet cutoff MS, expected to be ~MD (and likely < MD)The two processes are complementary

Real Graviton EmissionMonojets at hadron colliders

GKK

gq

q GKK

gg

g

Single VB at hadron or e+e- colliders

GKK

GKK

GKK

GKK

V

VV V

Virtual Graviton Effects Fermion or VB pairs at hadron or e+e- colliders

V

V

GKKGKK

f

ff

f


L’EPilogue (Large ED)L’EPilogue (Large ED)

Experiment ee qq f f WW ZZ Combined

ALEPH 1.04 0.81

0.65 0.67

0.60 0.62

0.53/0.57 0.46/0.46 (bb)

1.05 0.84

0.81 0.82

0.75/1.00 (<189)

DELPHI 0.59 0.73

0.56 0.65

0.60 0.76

0.83 0.91

0.60/0.76 (ff) (<202)

L3 0.98 1.06

0.56 0.69

0.58 0.54

0.49 0.49

0.84 1.00

0.99 0.84

0.68 0.79

1.0/1.1 (<202)

OPAL 1.15

1.00

0.62

0.66

0.62 0.66

0.89 0.83

0.63 0.74

1.17/1.03 (<209)

Color coding

184 GeV

189 GeV

>200 GeV

=-1 =+1 GL

Virtual Graviton Exchange

ee G ee ZGExperiment n=2 n=3 n=4 n=5 n=6 n=2 n=3 n=4 n=5 n=6

ALEPH 1.28 0.97 0.78 0.66 0.57 0.35 0.22 0.17 0.14 0.12

DELPHI 1.38 1.02 0.84 0.68 0.58

L3 1.02 0.81 0.67 0.58 0.51 0.60 0.38 0.29 0.24 0.21

OPAL 1.09 0.86 0.71 0.61 0.53

LEP Combined: 1.2/1.1 TeV

All limits are in TeV


Colliders: Graviton EmissionColliders: Graviton Emissionee + GKK at LEP + MET final state MP > 1.4-0.5 TeV (ADLO), for n=2…7

qq/gg q/g + GKK at the Tevatron jets + MET final state Z()+jets is irreducible background Challenging signature due to large

instrumental backgrounds from jet mismeasurement, cosmics, etc.

DØ pioneered this search and set limits [PRL, 90 251802 (2003)] MP > 1.0-0.6 TeV for n=2…7

Later, CDF achieved slightly better limits Expected reach for Run II/LHC:

Theory:[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291][Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]

n MD reach, Run I

MD reach, Run II

MD reach, LHC 100 fb-1

2 1100 GeV 1400 GeV 8.5 TeV

3 950 GeV 1150 GeV 6.8 TeV

4 850 GeV 1000 GeV 5.8 TeV

5 700 GeV 900 GeV 5.0 TeV

[PRL 90, 251802 (2003)]

GKK

gq

q

85 pb-1


Tevatron: Virtual Graviton EffectsTevatron: Virtual Graviton EffectsExpect an interference with the SM fermion or boson pair production

High-mass, low |cos| tail is a characteristic signature of LED [Cheung, GL, PRD 62 076003 (2000)]Best limits on the effective Planck scale come from new DØ Run II data: MPl > 1.1-1.6 TeV (n=2-7)

Combined with the Run I DØ result: MPl > 1.1-1.7 TeV – tightest to date

Sensitivity in Run II and at the LHC:

V

V

GKKGKK

f

ff

f

M,cosfM

nbM,cosf

M

nadMcosd

d

dMcosd

d

*

P

*

P

*SM

*

2814

22

Run II, 200 pb-1


Interesting Candidate EventsInteresting Candidate Events

While the DØ data are consistent with the SM, the two highest-mass candidates have anomalously low value of cos* typical of ED signal:

Event Callas: Mee = 475 GeV, cos* = 0.01 Event Farrar: M = 436 GeV, cos* = 0.03


Intermediate-size extra dimensions with TeV-1 radiusIntroduced by Antoniadis [PL B246, 377 (1990)] in the string theory context; used by Dienes, Dudas, Gherghetta [PL B436, 55 (1998)] to allow for low-energy unification Expect ZKK, WKK, gKK resonances at

the LHC energies At lower energies, can study effects

of virtual exchange of the Kaluza-Klein modes of vector bosons

Current indirect constraints come from precision EW measurements: 1/r ~ 6 TeVNo dedicated experimental searches at colliders to date

Antoniadis, Benaklis, Quiros [PL B460, 176 (1999)]

ZKK

TeVTeV-1-1 Extra Dimensions Extra Dimensions


First Dedicated Search for TeVFirst Dedicated Search for TeV-1-1 Extra DimensionsExtra Dimensions

While the Tevatron sensitivity is inferior to indirect limits, it explores the effects of virtual KK modes at higher energies, i.e. complementary to those in the EW data

DØ has performed the first dedicated search of this kind in the dielectron channel based on 200 pb-1 of Run II data (ZKK, KK e+e-)

The 2D-technique similar to the search for ADD effects in the virtual exchange yields the best sensitivity in the DY production [Cheung, GL, PRD 65, 076003 (2002)]

Data agree with the SM predictions, which resulted in the following limit: 1/R > 1.12 TeV @ 95% CL R < 1.75 x 10-19 m

200 pb-1, e+e-

EventCallas

Interference effect

1/R = 0.8 TeV


Randall-Sundrum Model Randall-Sundrum Model ObservablesObservables

Need only two parameters to define the model: k and rc

Equivalent set of parameters: The mass of the first KK mode, M1 Dimensionless coupling

PlMk /

Drell-Yan at the LHC

M1

PlMk /

Davoudiasl, Hewett, Rizzo [PRD 63, 075004 (2001)]

To avoid fine-tuning and non-perturbative regime, coupling can’t be too large or too small0.01 ≤ ≤ 0.10 is the expected rangeGravitons are narrow

PlMk /

Expected Run II sensitivity in DY


First Search for RS GravitonsFirst Search for RS GravitonsAlready better limits than sensitivity for Run II, as predicted by phenomenologists!

Assume fixed K-factor of 1.3 for the signal

The tightest limits on RS gravitons to date

[PRL 95, 091801 (2005)]


Black Holes on DemandBlack Holes on Demand

NYT, 9/11/01


Theoretical FrameworkTheoretical FrameworkBased on the work done with Dimopoulos a few years ago [PRL 87, 161602 (2001)] and a related study by Giddings/Thomas [PRD 65, 056010 (2002)]Extends previous theoretical studies by Argyres/Dimopoulos/March-Russell [PL B441, 96 (1998)], Banks/Fischler [JHEP, 9906, 014 (1999)], Emparan/Horowitz/Myers [PRL 85, 499 (2000)] to collider phenomenologyBig surprise: BH production is not an exotic remote possibility, but the dominant effect!Main idea: when the c.o.m. energy reaches the fundamental Planck scale, a BH is formed; cross section is given by the black disk approximation:

Geometrical cross section approximation was argued in early follow-up work by Voloshin [PL B518, 137 (2001) and PL B524, 376 (2002)]More detailed studies showed that the criticism does not hold:

Dimopoulos/Emparan – string theory calculations [PL B526, 393 (2002)]

Eardley/Giddings – full GR calculations for high-energy collisions with an impact parameter [PRD 66, 044011 (2002)]; extends earlier d’Eath and Payne work

Yoshino/Nambu - further generalization of the above work [PRD 66, 065004 (2002); PRD 67, 024009 (2003)]

Hsu – path integral approach w/ quantum corrections [PL B555, 29 (2003)]

Jevicki/Thaler – Gibbons-Hawking action used in Voloshin’s paper is incorrect, as the black hole is not formed yet! Correct Hamiltonian was derived: H = p(r2 – M) ~ p(r2 – H), which leads to a logarithmic, and not a power-law divergence in the action integral. Hence, there is no exponential suppression [PRD 66, 024041 (2002)]

RS

parton

parton

M2 = s

~ RS ~ 1 TeV ~ 10 m ~ 100 pb


Assumptions and ApproximationAssumptions and ApproximationFundamental limitation: our lack of knowledge of quantum gravity effects close to the Planck scaleConsequently, no attempts for partial improvement of the results, e.g.: Grey body factors BH spin, charge, color hair Relativistic effects and time-dependence

The underlying assumptions rely on two simple qualitative properties: The absence of small couplings; The “democratic” nature of BH decays

We expect these features to survive for light BHUse semi-classical approach strictly valid only for MBH » MP; only consider MBH > MP

Clearly, these are important limitations, but there is no way around them without the knowledge of QG


Black Hole ProductionBlack Hole ProductionSchwarzschild radius is given by Argyres et al., hep-th/9808138 [after Myers/Perry, Ann. Phys. 172 (1986) 304]; it leads to:

Hadron colliders: use parton luminosity w/ MRSD-’ PDF (valid up to the VLHC energies)

Note: at c.o.m. energies ~1 TeV the dominant contribution is from qq’ interactions

1

2

222

22

38

1

n

P

BH

PSBH n

n

M

M

MRMs )ˆ(

a

BHbaa

bas

M a

aBH

BH

MsBHBH

sx

Mfxf

x

dx

s

M

dM

dL

BHabdM

dL

dM

XBHppd

BH

BH

21

2

2

2

,

ˆˆ

tot = 0.5 nb (MP = 2 TeV, n=7)

LHCn=4

tot = 120 fb (MP = 6 TeV, n=3)

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


Black Hole DecayBlack Hole DecayHawking temperature: RSTH = (n+1)/4(in natural units = c = k = 1)BH radiates mainly on the brane [Emparan/Horowitz/Myers, hep-th/0003118] ~ 2/TH > RS; hence, the BH is a point

radiator, producing s-waves, which depends only on the radial component

The decay into a particle on the brane and in the bulk is thus the same

Since there are much more particles on the brane, than in the bulk, decay into gravitons is largely suppressed

Democratic couplings to ~120 SM d.o.f. yield probability of Hawking evaporation into l±, and ~2%, 10%, and 5% respectively Averaging over the BB spectrum gives average multiplicity of decay products:

H

BH

T

MN

2

Note that the formula for N is strictly valid only for N » 1 dueto the kinematic cutoff E < MBH/2; If taken into account, it increasesmultiplicity at low N


Stefan’s law: ~ 10-26 s


Black Hole FactoryBlack Hole Factory

Drell-Yan +X


Spectrum of BH produced at the LHC with subsequent decay into final states tagged with an electron or a photon

n=2n=7

Black-Hole Factory


Shape of Gravity at the LHCShape of Gravity at the LHC

Relationship between logTH and logMBH allows to find the number of ED, 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



Black Hole EventsBlack Hole EventsFirst studies already initiated by ATLAS and CMS ATLAS –CHARYBDIS HERWIG-based generator with more

elaborated decay model [Harris/Richardson/Webber] CMS – TRUENOIR [GL]

Simulated black hole event in the ATLAS detector [from ATLAS-Japan Group]

Simulated black hole event in the CMS detector [A. de Roeck & S. Wynhoff]


ConclusionsConclusions

Stay tuned – next generation of collider experiments has a good chance to solve the mystery of large extra dimensions!If large extra dimensions are realized in nature, black hole production at future colliders is likely to be the first signature for quantum gravity at a TeVMany other exciting consequences from effects on precision measurements to detailed studies of quantum gravityIf any of these new ideas is correct, we might see a true “Grand Unification” – that of particle physics, astrophysics and cosmology – in just a few years from now!

If you still think that gravity is weak force, you may be spending

too much time in the lab!

out-of-this-world physics: from particles to black holes

Documents

world physics

physicsmath physics

black holeshierarchy

black holesmath

black holesthe

black holesbut

black holesn

black holes greg landsbergl