Transcript Out-of-this-World Physics: Probing Quantum Gravity in the Lab

Experimental Probes for
Extra Dimensions
Greg Landsberg
NEPPSR ‘04
Craigville, MA
August 27, 2004
Out-Sketch
Theory/Phenomenology Tabletop Experiments
Accelerator Searches
Ultimate probes:
 ADD Model
 TeV-1 Scenario
 RS Model
 Universal ED
 Use-Them-n-Lose-Them
Some highlights:
 Gravity at short distances ED (e.g., little Higgs models)
 Cosmology constraints  Black Holes in the Lab?
Brief overview:
 Intro to Models
 Phenomenology
 Much more in Nima’s talk
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Big Why?
(Or Math Meets Physics)
Math physics: some dimensionalities are quite special
Example: Laplace equation in two dimensions has logarithmic
solution; for any higher number of dimensions it obeys power
law instead
Some of these peculiarities exhibit themselves in condensed
matter physics, e.g. diffusion equation solutions allow 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 not
Do we live in a special space, or only believe that we are
special?
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Brief History of Space:
XIX Century
In the XIXth century people were
convinced that the universe is threedimensional
Bernhard Riemann was the first
person to question this seemingly
natural conclusion
In 1854, as a completion of his
Habilitation degree at Göttingen, he
gives a lecture: “Über die Hypothesen
welche der Geometrie zu Grunde
liegen” (“On the hypotheses that lie
at the foundations of geometry” ),
where he gave a definition of what is
known today as Riemannian space
and the curvature tensor
It was not until Einstein’s general
theory of relativity that Riemann’s
ideas were fully appreciated and
understood
August 2004
Edwin Abbot’s “Flatland” (1884)
The story is told by Mr. A. Square
(four-sided polygon), a middle-class
inhabitant of a two-dimensional
world, the flatland
He is taken on a journey to a threedimensional world, and upon return
tries to explain higher dimensions to
his cohabitants, just to be imprisoned
as an imbecile…
Greg Landsberg, Experimental Probes for Extra Dimensions
4
Brief History of Space:
XXth Century
1915: Albert Einstein formulates general
theory of relativity, based on Riemannian
space
The space is curved due to gravity; in fact
curvature of the space IS gravity
One of the most striking prediction of this
theory was existence of black holes
1919-1926: Theodore Kaluza and Oscar
Klein showed that adding an extra
compact dimension to general relativity
allows to unify it with electromagnetism
Since 1970-ies: string theory implements
the idea of compact dimensions to
generalize Einstein’s relativity theory into
quantum theory of gravity
These extra dimensions are curled-up
extremely tight, with radii ~10-32 m
The preferred number of extra spatial
dimensions is 6 or 7
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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N.B. Large Hierarchies Tend
to Collapse...
Collapse of the Soviet Union
The eighties…
August 2004
The nineties…
Greg Landsberg, Experimental Probes for Extra Dimensions
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A Falsifiable Prediction
A 2001-2002 Rise…
A 2004 Collapse?
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Although 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)
Numerology: 987654321/123456789 =
8.000000073
Politics: Florida recount, 2,913,321/2,913,144 =
1.000061
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Hierarchy of the Standard
Model
Beauty … and the Beast
RGE evolution
Inverse Strength
Gravitational
Force
EM/Hypercharge
Force
Weak Force
Strong Force
vev
102
MGUT
MPl
1016 1019 E [GeV]
Extra dimensions might get rid of the beast while preserving the beauty!
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Life Beyond the Standard
Model
Inverse Strength
RGE equations
Gravitational
Force
EM/Hypercharge
Force
Weak Force
Strong Force
v
102
MGUT
MPl
19
16
E [GeV] 10 10
The natural mH value is L, where L
is the scale of new physics; if SM is
the ultimate theory up to GUT
scale, an extremely precise
((v/mGUT)2) fine-tuning is required
We must conclude that the SM is an
effective theory, i.e. a low-energy
approximation of a more complete
model that explains things only
postulated in the SM
August 2004
This new theory takes over at a scale L
comparable to the mass of the Higgs
boson, i.e. L  1 TeV
But: the large hierarchy of scales picture
is based solely on the log extrapolation
of gauge couplings by some 14 decades
in energy
How valid is that?
1998: abstract mathematics meets
phenomenology. Extra spatial
dimensions have been first used to:
“Hide” the hierarchy problem by making
gravity as strong as other gauge forces
in (4+n)-dimensions (Arkani-Hamed,
Dimopoulos, Dvali) – ADD
Explore modification of the RGE in
(4+n)-dimensions to achieve low-energy
unification of the gauge forces (Dienes,
Dudas, Gherghetta)
Greg Landsberg, Experimental Probes for Extra Dimensions
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The ADD Model
SM fields are localized on the (3+1)brane; gravity is the only gauge force
that “feels” the bulk space
What about Newton’s law?
1 mm
1
V r   2 1 2 
M Pl r
M Pl3 n


n 2
m1m2
r n1
Ruled out for flat extra dimensions, but
has not been ruled out for sufficiently
small compactified extra dimensions:
V r  
August 2004
1
M   
3 n n 2
Pl
m1m2
for r  R
Rnr
Gravity is fundamentally strong
force, bit we do not feel that as it is
diluted by the volume of the bulk
2
G’N = 1 / M Pl[ 3n ]   1/MD2; MD  1 TeV
M Dn 2  M Pl2 R n
More precisely, from Gauss’s law:
8  1012 m, n  1
2/n



1
M Pl
0.7 mm, n  2

  
R
2  MD  MD 
3 nm, n  3
6  1012 m, n  4
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
Greg Landsberg, Experimental Probes for Extra Dimensions
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Shakespeare on Compact
Dimensions
“…Why bastard? wherefore base?
When my dimensions are as well compact,
My mind as generous, and my shape as true,
As honest madam's issue?”
(Edmund, bastard son to Gloucester)
Shakespeare, King Lear, Act 1, Scene 2
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Examples of
Compactified Spatial
Dimensions
M.C.Escher, Mobius Strip II (1963)
M.C.Escher, Relativity (1953)
[All M.C. Escher works and texts copyright © Cordon Art B.V., P.O. Box 101, 3740 AC The Netherlands. Used by permission.]
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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An Importance of Being
Compact
Compactified dimensions offer a way to
increase tremendously gravitational
interaction due to a large number of the
available “winding” modes
This tower of excitations is known as
Kaluza-Klein modes, and such gravitons
propagating in the compactified extra
dimensions are called Kaluza-Klein
gravitons, GKK
From the point of view of a 3+1dimensional space time, the KaluzaKlein graviton modes are massive, with
the mass per excitation more  1/R
Since the mass per excitation mode is
so small (e.g. 400 eV for n = 3, or 0.2
MeV for n = 4), a very large number of
modes can be excited at high energies
August 2004
GKK
R
Compactifie
d
dimension
x   x  2kR, k  0, 1, 2,
M(GKK) = Px2 = 2k/R
Each Kaluza-Klein graviton mode
couples with the gravitational
strength
For a large number of modes,
accessible at high energies,
gravitational coupling is therefore
enhanced drastically
Low energy precision measurements
are not sensitive to the ADD effects
Greg Landsberg, Experimental Probes for Extra Dimensions
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Extra Dimensions at Work
Burst of the ideas to follow:
Inverse Strength
Gravitational
Force
Real
GUT Scale
EM/Hypercharge
Force
Virtual
Image
Weak Force
MPl=1/GN
Strong Force
L ~ 1 TeV
MZ
August 2004
MS
M’Pl
M’GUT
MGUT
logE
1999: possible rigorous
solution of the hierarchy
problem by utilizing metric of
curved anti-deSitter space
(Randall, Sundrum)
2000: “democratic” (universal)
extra dimensions, equally
accessible by all the SM fields
(Appelquist, Chen, Dobrescu)
2001: “contracted” extra
dimensions – use them and
then lose them (ArkaniHamed, Cohen, Georgi)
All these models result in rich
low-energy phenomenology
Greg Landsberg, Experimental Probes for Extra Dimensions
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Randall-Sundrum
Scenario
Randall-Sundrum (RS) scenario [PRL 83, 3370
(1999); PRL 83, 4690 (1999)]
G
+ brane – no low energy effects
+– branes – TeV Kaluza-Klein modes of
graviton
Low energy effects are given by L; for
krc ~ 10, L ~ 1 TeV and the hierarchy
problem is solved naturally
AdS5
ds  e
2
r



 dx dx  r d
2
2
L  M Pl ekr
k – AdS curvature
SM brane
(  )
August 2004
2 kr 
x5
Reduced Planck mass:
Planck brane
( = 0)
M Pl  M Pl
8
Greg Landsberg, Experimental Probes for Extra Dimensions
16
Difference Between the
Models
ADD Model:
“Eliminates” the
hierarchy problem by
stating that physics
ends at a TeV scale
Only gravity lives in the
“bulk” space
Size of ED’s (n=2-7)
between ~100 m and
~1 fm
Doesn’t explain how to
make ED large
TeV-1 Scenario:
Lowers GUT scale by
changing the running
of the couplings
Only gauge bosons
(g/g/W/Z) propagate in
a single ED; gravity is
not in the picture
Size of the ED ~1 TeV-1
or ~10-19 m
RS Model:
A rigorous solution to the
hierarchy problem via
localization of gravity
Gravitons (and possibly
other particles)
propagate in a single ED,
w/ special metric
Size of this ED as small
as ~1/MPl or ~10-35 m
G
x5
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Kaluza-Klein Spectrum
ADD Model:
TeV-1 Scenario:
Winding modes with
nearly equal energy
spacing ~1/r, i.e. ~TeV
Can excite individual
modes at colliders or
look for indirect effects
Winding modes with
energy spacing ~1/r,
i.e. 1 meV – 100 MeV
Can’t resolve these
modes – they appear as
continuous spectrum
M i  M 02  i 2 r 2
E
E
~1 TeV
~MGUT
RS Model:
“Particle in a box” with a
special metric
Energy eigenvalues are
given by zeroes of Bessel
function J1
Light modes might be
accessible at colliders
M 0  0; M i  M 1 xi x1  M 1 , 1.83M 1 ,
2.66 M 1 , 3.48M 1 , 4.30 M 1 , ...
E
~MPl
…
…
Mi
M0
August 2004
Mi
M1
Greg Landsberg, Experimental Probes for Extra Dimensions
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Constraints from Gravity
Experiments
[J. Long, J. Price, hep-ph/0303057]
E.Adelberger et al.
PRL 86, 1418 (2001)
Sub-millimeter gravity
measurements could probe
only n=2 case only within the
ADD model
The 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 < 0.15 mm (MD > 4 TeV)
~
~
Sensitivity vanishes quickly with
the distance – can’t push limits
further down significantly
Started restricting ADD with 2
extra dimensions; can’t probe
any higher number
Ultimately push the sensitivity
by a factor of two in terms of
the distance
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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Astrophysical and
Cosmological Constraints
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  gg decays [Hall and Smith, PRD
60, 085008 (1999)]:
MD > 100 TeV (n=2)
MD > 5 TeV (n=3)
August 2004
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 g-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
Greg Landsberg, Experimental Probes for Extra Dimensions
20
Collider Signatures for
Large Extra Dimensions
Kaluza-Klein gravitons couple to the
momentum tensor, and therefore
contribute to most of the SM processes
For Feynman rules for GKK see:
Han, Lykken, Zhang, PR D59, 105006
(1999)
Giudice, Rattazzi, Wells, Nucl. Phys. 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
Since the spin 2 graviton in generally has
a bulk momentum component, its spin
from the point of view of our brane can
appear as 0, 1, or 2
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 production
Direct Graviton Emission
Monojets at hadron colliders
q
g
g
g
q
GKK
g
GKK
Single VB at hadron or e+e- colliders
V
GKK
V
GKK
GKK
V
V
Virtual Graviton Emission
Fermion or VB pairs at hadron or e+e- colliders
f
f
GKK
f
August 2004
GKK
V
GKK
f
Greg Landsberg, Experimental Probes for Extra Dimensions
V
21
Looking for ED at
Colliders
[M.Spiropulu]
[© 2000 Ferminews]
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
22
Virtual Graviton Effects
In the case of pair production via virtual
graviton, gravity effects interfere with the
SM (e.g., l+l- at hadron colliders):
Therefore, production cross section has
three terms: SM, interference, and direct
gravity effects:
d 2
d 2SM


*
*
d cos dM d cos dM
2


a n 
a
n
*
*



f
cos

,
M

f
cos

,M
1
2
4
8
MS
MS
August 2004
The sum in KK states is divergent in the
effective theory, so in order to calculate
the cross sections, an explicit cut-off is
required
An expected value of the cut-off MS 
MD, as this is the scale at which the
effective theory breaks down, and the
string theory needs to be used to
calculate production
There are three major conventions on
how to write the effective Lagrangian:
Hewett [PRL 82, 4765 (1999)]
Giudice, Rattazzi, Wells [NP B544, 3
(1999);
revised version, hep-ph/9811291]
Han, Lykken, Zhang [PRD 59, 105006
(1999);
revised version, hep-ph/9811350]
Fortunately all three conventions turned
out to be equivalent and only the
definitions of MS are different
Greg Landsberg, Experimental Probes for Extra Dimensions
23
CDF Search for Virtual
Graviton Effects
ee
Mee = 371 GeV
CDF
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
24
DØ Search for Virtual
Graviton Effects
Sensitivity is dominated by the diphoton
channel (2  1 + 1)
Combine diphotons and dielectrons into
“di-EM objects” to maximize efficiency
High-mass, low |cos*| tail is a
characteristic signature of LED Cheung,
GL [PRD 62, 076003 (2000)]
200 pb-1
Data agree well with the SM predictions;
proceed with setting limits on large ED:
alone or in combination with published
Run I result [PRL 86, 1156 (2001)]:
Hewett
l = +1
l = 1
1.22
1.10
1.28
1.16
(TeV, @95% CL)
n=2
n=3
n=4
n=5
n=6
n=7
1.36
1.56
1.61
1.36
1.23
1.14
1.08
1.43
1.67
1.70
1.43
1.29
1.20
1.14
170
m
1.5
nm
5.7
pm
0.2
pm
21
fm
4.2
fm
rmax
MS = 1 TeV
n=6
HLZ
GRW
These are the most stringent constraints
on large ED for n > 2 to date, among all
the experiments
For n=2, sensitivity is approaching that of
the tabletop gravity measurements (MD =
1.7 TeV, r < 160 m)
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
25
Interesting 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
August 2004
Mgg = 436 GeV, cos* = 0.03
Greg Landsberg, Experimental Probes for Extra Dimensions
26
Colliders: Direct Graviton
Emission
ee  g + GKK at LEP
g + 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
CDF recently announced similar limits
Expected reach for Run II/LHC:
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
August 2004
Theory:
[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999)
and corrected version, hep-ph/9811291]
[Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]
[PRL 90, 251802 (2003)]
q
g
q
GKK
Greg Landsberg, Experimental Probes for Extra Dimensions
27
Search for Monojets
Challenge: large instrumental background from MET mismeasurement and cosmics
Irreducible physics background from Z() + jet(s): forced to use high jet PT, MET cuts
Pioneered in Run I by DØ [PRL 90, 251802 (2003)]: MD > 0.63 – 0.89 TeV (n=6-2)
Recently superseded by CDF [PRL 92, 121802 (2004)]: MD > 0.71 – 1.00 TeV (n=6-2)
CDF also pioneered similar search in g+MET, albeit less sensitive [PRL 89, 281801 (2002)]
New Run II analysis from DØ based on 85 pb-1 of data collected with special trigger
Major systematics from jet energy scale – to be reduced soon
Sensitivity already exceeds that for DØ in Run I, but still below the CDF’s Run I result
Impressive sensitivity already achieved with less data due to superior detector and higher energy
85 pb-1
84 events observed
100 ± 9 +50–30 expected
Tevatron/LEP complementarity
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
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TeV-1 Extra Dimensions
Intermediate-size extra dimensions
with TeV-1 radius
Introduced 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 TeV
No dedicated experimental searches
at colliders to date
August 2004
Antoniadis, Benaklis, Quiros [PL B460, 176 (1999)]
ZKK
Greg Landsberg, Experimental Probes for Extra Dimensions
29
First Dedicated Search for
TeV-1 Extra Dimensions
200 pb-1, e+eEvent
Callas
While the Tevatron sensitivity is inferior
to indirect limits, it explores 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, gKK  e+e-)
Interference effect
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 on
their size:
1/r = 0.8 TeV
August 2004
1/r > 1.13 TeV @ 95% CL
r < 1.75 x 10-19 m
Greg Landsberg, Experimental Probes for Extra Dimensions
30
Search for Randall-Sundrum
Gravitons
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 k / M Pl
To avoid fine-tuning and nonperturbative regime, coupling can’t
be too large or too small
0.01 ≤ k / M Pl≤ 0.10 is the
expected range
Gravitons are narrow
Expected Run II
sensitivity in DY
k / M Pl
Drell-Yan at the LHC
M1
August 2004
Davoudiasl, Hewett, Rizzo [PRD 63, 075004 (2001)]
Greg Landsberg, Experimental Probes for Extra Dimensions
31
CDF Search for RS Gravitons
CDF pioneered this search in 2003
Based on e+e-, +- (200 pb-1) and gg (345 pb-1, central photons only) modes
N.B.: B(G  gg) ≈ 2B(G  e+e-); diphotons also have higher acceptance
Counting experiment in a resolution-driven sliding window in mass (gg) or fit (l+l-)
Data agree with expected SM background
Interpret this as a search for narrow RS gravitons to set limits on the model
parameters
Hot!
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
32
CDF Limits on RS Model
Sensitivity is driven by the diphoton channel
Gravitons with masses up to 690 GeV have been excluded for the coupling of 0.10
Further improvement can be achieved by combining three channels (to be done!)
Assume K-factor of 1.3
for the signal
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
33
The Highest Mass Diphoton
Event
Mgg = 405 GeV
CDF
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
34
DØ Search for RS Gravitons
DØ has just completed a similar analysis and produced first results
Analysis based on 200 pb-1 of e+e- and gg data – the same data set as used for searches for
large ED
“Naturally” combine two channels by NOT distinguishing between electrons and photons!
Search window size has been optimized to yield maximum signal significance
Analysis technique is similar to CDF’s; acceptance is significantly higher due to forward
photons
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
35
DØ Limits in the ee+gg
Channel
The tightest limits on RS gravitons
to date
Assume fixed K-factor of 1.3 for the
signal
Masses up to 780 GeV are
excluded for k/MPl = 0.1
CDF gg
Hotter
!
DØ Run II Preliminary, 200 pb-1
DØ Run II Preliminary, 200 pb-1
Already better limits than the
sensitivity for Run II, as predicted
by theorists!
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
36
Universal Extra Dimensions
The most “democratic” ED model: all the SM fields are free to propagate in extra
dimension(s) with the size Rc = 1/Mc ~ 1 TeV-1 [Appelquist, Cheng, Dobrescu, PRD 64,
035002 (2001)]
Instead of chiral doublets and singlets, model contains vector-like quarks and leptons
Gravitational force is not included in this model
The number of universal extra dimensions is not fixed:
it’s feasible that there is just one (MUED)
the case of two extra dimensions is theoretically attractive, as it breaks down to the chiral Standard
Model and has additional nice features, such as guaranteed proton stability, etc.
Every particle acquires KK modes with the masses Mn2 = M02 + Mc2, n = 0, 1, 2, …
Kaluza-Klein number (n) is conserved at the tree level, i.e. n1  n2  n3  … = 0;
consequently, the lightest KK mode cold be stable (and is an excellent dark matter candidate
[Cheng, Feng, Matchev, PRL 89, 211301 (2002)])
Hence, KK-excitations are produced in pairs, similar to SUSY particles
Consequently, current limits (dominated by precision electroweak measurements,
particularly T-parameter) are sufficiently low (Mc ~ 300 GeV for one ED and of the same
order, albeit more model-dependent for >1 ED)
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
37
UED Phenomenology
Naively, one would expect large
clusters of nearly degenerate
states with the mass around
1/RC, 2/RC, …
Cheng, Feng, Matchev, Schmaltz:
not true, as radiative corrections
tend to be large (up to 30%);
thus the KK excitation mass
spectrum resembles that of
SUSY!
Minimal UED model with a single
extra dimension, compactified on
an S1/Z2 orbifold
Q, L (q, l) are SU(2) doublets
(singlets) and contain both
chiralities
[Cheng, Matchev, Schmaltz, PRD 66, 056006 (2002)]
MC = 1/RC = 500 GeV
Odd fields do not have 0 modes,
so we identify them w/ “wrong”
chiralities, so that they vanish in
the SM
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
38
UED Spectroscopy
First level KK-states spectroscopy
[CMS, PRD 66, 056006 (2002)]
August 2004
Decay:
B(g1→Q1Q) ~ 50%
B(g1→q1q) ~ 50%
B(q1→qg1) ~ 100%
+
B(t1→W1b, H1 b) ~
B(Q1→QZ1:W1:g1) ~ 33%:65%:2%
B(W1→L1:1L) = 1/6:1/6 (per flavor)
B(Z1→1:LL1) ~ 1/6:1/6 (per flavor)
B(L1→g1L) ~ 100%
B(1→g1) ~ 100%

±
B(H1 →gg1, H *g1) ~ 100%
Production:
q1q1 + X → MET + jets (~had/4); but:
low MET
Q1Q1+ X→ V1V’1 + jets → 2-4 l + MET
(~had/4)
Greg Landsberg, Experimental Probes for Extra Dimensions
39
Production Cross Section
Reasonably high rate up to M ~ 500 GeV
Q1Q1, q1q1
Run II, s = 2 TeV
[Rizzo, PRD 64, 095010 (2001)]
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
40
Sensitivity in the FourLepton Mode
Only the gold-plated 4leptons + MET mode has
been considered in the
original paper
Sensitivity in Run IIb can
exceed current limits
Much more promising
channels:
[Cheng, Matchev, Schmaltz, PRD 66, 056006 (2002)]
dileptons + jets + MET + X
(x9 cross section)
trileptons + jets + MET + X
(x5 cross section)
Detailed simulations is
required: would love to see
this in a MC
One could use SUSY
production with adjusted
masses and branching
fractions as a quick fix
August 2004
L is per experiment;
(single experiment)
Greg Landsberg, Experimental Probes for Extra Dimensions
41
Almost No Extra Dimensions
Novel idea: build a multidimensional theory that is reduced to a fourdimensional theory at low energies Arkani-Hamed, Cohen, Georgi [PL
B513, 232 (1991)]
An alternative EWSB mechanism, the so-called Little Higgs (a pseudogoldstone boson, responsible for the EWSB) Arkani-Hamed, Cohen, Katz,
Nelson [JHEP 0207, 034 (2002)]
Limited low-energy phenomenology: one or more additional vector
bosons; a charge +2/3 vector-like quark (decaying into V/h+t), necessary
to cancel quadratic divergencies), possible additional scalars (sometimes
even stable!), all in a TeV range
Unfortunately, the Tevatron reach is not very impressive; LHC would be
the machine to probe this model
However: started looking for this types models as a part of more generic
search for Z’
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
42
CDF Limit On ZH
Littlest Higgs model: an additional gauge boson ZH with the SU(2) coupling parameter cot
Han, Logan, McElrath, Wang [PRD 67, 095004 (2003)]
Search done in the e+e-, +- (200 pb-1) mode; best sensitivity is in dielectrons
Straight extension of the RS graviton/Z’ analyses
Limits are far from theoretically motivated masses, but a good start!
Masses up to 800 GeV
are excluded for cot = 1
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
43
Most Promising Tevatron
Signatures
ED are one of the most exciting novel ideas, and yet barely tested experimentally:
ADD: virtual graviton effects, direct graviton emission, string resonances
TeV-1 dimensions: VKK, virtual effects
RS: graviton excitations, SM particle excitation, radion, direct graviton emission
Universal extra dimensions: rich SUSY-like phenomenology
Channel
Extra Dimensions Probe
Other New Physics
Dilepton
ADD, TeV-1, RS
Z’, compositeness
Diphotons
ADD, some RS
Compositeness, higgs, monopoles
Dijet
ADD, TeV-1, Strings
Compositeness, technicolor
Monojets
ADD, some RS
Light gravitino, other SUSY
Monophotons
ADD, some RS
GMSB, light gravitino, ZZg/Zgg couplings
Monoleptons
TeV-1, some RS
W’
Dijet + MET
ADD, Universal
SUGRA, Leptoquarks
Leptons + MET
Universal
SUGRA
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
44
Mother of all Signatures:
Black Holes at the LHC
Only applicable to the ADD model
August 2004
NYT, 9/11/01
Greg Landsberg, Experimental Probes for Extra Dimensions
45
Black Holes in GR
Black Holes are direct prediction of Einstein’s general relativity
theory, established in 1915 (although they were never quite
accepted by Einstein!)
In 1916 Karl Schwarzschild applied GR to a static nonspinning massive object and derived famous metric with a
singularity at a Schwarzschild radius r = RS  2MGN/c2 :
} time
space
Albert Einstein
If the radius of the object is less than RS, a black hole with
the event horizon at RS is formed
The term “black-hole” was introduced only around 1967 by
John Wheeler
August 2004
Karl
Schwarzschild
Greg Landsberg, Experimental Probes for Extra Dimensions
46
Black Hole Evolution
Naїvely, black holes would only grow once they are formed
In 1975 Steven Hawking showed that this is not true [Commun.
Math. Phys. 43, 199 (1975)], 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 perfect black-body spectrum with the
Hawking temperature :
c
TH 
4kRS
Stephen Hawking
In natural units ( = c = k = 1), one has the following
fundamental relationship: RSTH = (4)1
If TH is high enough, massive particles can also be
produced in evaporation
Information paradox: if we throw an encyclopedia in a
black hole, and watch it evaporating, where would the
information disappear?
This paradox is possibly solved in the only quantum
theory of gravity we know of: string theory
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
47
Black Hole Evaporation
As the BH evaporates, its mass
becomes smaller, RS decreases,
and Hawking temperature
increases
Consequently, as the BH evolves,
the radiation spectrum becomes
harder and harder, until the BH
evaporates completely in a giant
flash of light
Ergo, the BH spends most of its
time at the lowest temperature,
when the radiation is soft
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
48
Theoretical Framework
Based on the work done with Savas Dimopoulos
three 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 phenomenology
Big 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:
 ~ RS2 ~ 1 TeV 2 ~ 1038 m2 ~ 100 pb
parton
RS
August 2004
M2 = s^
parton
Fundamental limitation: our lack of
knowledge of quantum gravity effects close
to the Planck scale
Consequently, 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
BH
Use 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
Greg Landsberg, Experimental Probes for Extra Dimensions
49
Black Hole Production
Schwarzschild radius is given by Argyres et
al. [hep-th/9808138] after Myers/Perry
[Ann. Phys. 172 (1986) 304]; it leads to:

 n  3
8



1  M BH  2  
2
2

( sˆ  M BH )  RS  2 
MP  MP
n2 


[Dimopoulos, GL, PRL 87, 161602 (2001)]
2
n 1
Hadron colliders: use parton luminosity w/
MRSD-’ PDF (valid up to the VLHC energies)
d pp  BH  X 
dL

ˆ ab  BH  sˆ  M 2
BH
dM BH
dM BH
dL
2M BH

dM BH
s
2
 M BH
dxa
f a xa  f b 
xa
 sxa
1
 
a ,b M 2
BH
tot = 0.5 nb
(MP = 2 TeV, n=7)
LHC
n=4
tot = 120 fb
(MP = 6 TeV, n=3)



s
Note: at c.o.m. energies ~1 TeV the
dominant contribution is from qq’ interactions
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
50
Black Hole Decay
[Dimopoulos, GL, PRL 87, 161602 (2001)]
Hawking temperature: RSTH = (n+1)/4 (in
natural units  = c = k = 1)
Note that the formula for N is
BH radiates mainly on the brane
strictly valid only for N » 1 due
[Emparan/Horowitz/Myers, hep-th/0003118]
to the kinematic cutoff E < M /2;
l ~ 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
BH
If taken into account, it increases
multiplicity at low N
Democratic couplings to ~120 SM d.o.f. yield
±
probability of Hawking evaporation into g, l ,
and  ~2%, 10%, and 5% respectively
Averaging over the BB spectrum gives
average multiplicity of decay products:
August 2004
M BH
N 
2TH
Stefan’s law: t ~ 10-26 s
Greg Landsberg, Experimental Probes for Extra Dimensions
51
LHC: Black Hole Factory
[Dimopoulos, GL, PRL 87, 161602 (2001)]
n=2
n=7
Drell-Yan
g+X
Spectrum of BH produced at the LHC with subsequent decay into final states
tagged with an electron or a photon
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
52
Shape of Gravity at the LHC
[Dimopoulos, GL, PRL 87, 161602 (2001)]
log TH  
1
log M BH  const
n 1
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
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
53
Higgs Discovery in BH
Decays
Example: 130 GeV Higgs particle, which
is tough to find either at the Tevatron or
at the LHC
Higgs with the mass of 130 GeV decays
predominantly into a bb-pair
Tag BH events with leptons or photons,
and look at the dijet invariant mass; does
not even require b-tagging!
Use a typical LHC detector response to
obtain realistic results
Time required for 5 sigma discovery:
MP = 1 TeV – 1 hour
MP = 2 TeV – 1 day
MP = 3 TeV – 1 week
MP = 4 TeV – 1 month
MP = 5 TeV – 1 year
Standard method – 1 year w/ two wellunderstood detectors!
August 2004
 = 15 nb
MP = 1 TeV, 1 LHC-hour (!)
ATLAS
resolutions
W/Z
t
h
boost
t
W
[GL, PRL 88, 181801 (2002)]
An exciting prospect for discovery of other
new particles w/ mass ~100 GeV!
Greg Landsberg, Experimental Probes for Extra Dimensions
54
Black Hole Event Displays
First 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
Simulated black hole event in the
ATLAS detector [from ATLAS-Japan Group] CMS detector [A. de Roeck & S. Wynhoff]
August 2004
Greg Landsberg, Experimental Probes for Extra Dimensions
55
Conclusions
http://www.extradimensions.com
On 2/15/00 patent 6,025,810 was issued to David
Strom for a "hyper-light-speed antenna." The
concept is deceptively simple: "The present
invention takes a transmission of energy, and
instead of sending it through normal time and
space, it pokes a small hole into another
dimension, thus sending the energy through a
place which allows transmission of energy to
exceed the speed of light." According to the
If you
think"allows
that gravity
is another
weak
patent,
this portal
energy from
force, to
you
mightplant
be growth."
spending too
dimension
accelerate
much
time in
the3/17/00
lab!
from the AIP’s
“What’s
New”,
August 2004
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 TeV
Many other exciting consequences
from effects on precision
measurements to detailed studies
of quantum gravity
If 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!
Greg Landsberg, Experimental Probes for Extra Dimensions
56