Transcript Document 7379206

Experimental Aspects of Extra Dimensions
Andy Parker
Cambridge University
Outline
•
•
•
•
Experimentalists view of the theory
Gravity experiments
Other limits
Large extra dimensions at LHC
– Real and virtual effects
– Tevatron limits
– NLC
• Warped extra dimensions
• Black hole production
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An experimentalists view of the theory
• SM is wonderful!
– All experimental data is explained to high precision
– Theory checked at distance scales of 1/MW= 2.5 x 10-18 m
– Only one state is unaccounted for - the Higgs
– There is only one free parameter which is unknown - MH
– No contradiction between the best fit Higgs mass and search
limit.
• But theorists don’t agree!
– Higgs mass is unstable against quantum corrections
– Hierarchy problem - MW=80 GeV, MH<1 TeV, MPl=1019 GeV
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Higgs search limit at LEP
In SM framework, Higgs mass is
well constrained.
Only a matter of time ….
In SUSY models, very difficult to
raise lightest higgs mass
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Two views of the world….
Supersymmetry ….
Extra dimensions….
…different scales
….hidden perfection
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Epicycles
Typical Ptolemaic planetary model
Symmetry is assumed: all orbits are
based on circles
But the Earth is not at the centre of
the circle (the eccentric)
The planet moves on an epicycle
The epicycle moves around the
equant
From Michael J. Crowe,
Theories of the World from Antiquity
to the Copernican Revolution.
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Supersymmetry
Conventional method to fix Higgs mass:
Invoke SUSY
Double the number of states in model
Invoke SUSY breaking
Fermion/boson loops cancel (GIM)
Higgs mass stabilised!
105 new parameters (MSSM)
+48 more free parameters if RP not conserved
=> SUSY is a good pension plan for experimentalists!
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Extra Dimensions
Hypothesize that there are extra space dimensions
Volume of bulk space >> volume of 3-D space
Hypothesize that gravity operates throughout the bulk
SM fields confined to 3-D
Then unified field will have “diluted” gravity, as seen in 3-D
If we choose n-D gravity scale=weak scale then…
Only one scale -> no hierarchy problem!
Can experimentally access quantum gravity!
But extra dimension is different scale from “normal” ones
-> new scale to explain
Extra dimensions are more of a lottery bet than a pension plan!
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Scale of extra dimensions
For 4+n space-time dimensions
M M
2
Pl
2n
Pl(4 n)
R
n
For MPl(4+n) ~ MW
R 10
n=1, R=10

13 cm
30/ n17
1TeV 12 / n
cm (
)
mW
ruled out by planetary orbits
n=2, R~100 mm-1mm OK (see later)

-> Conclude extra dimensions must be compactified at <1mm
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Kaluza Klein modes
4-D brane
M
1/R
r
Compactified
dimension
Particles in compact extra
dimension:
•Wavelength set by periodic
boundary condition
•States will be evenly spaced in
mass
– “tower of Kaluza-Klein
modes”
•Spacing depends on scale of ED
– For large ED (order of mm)
spacing is very small - use
density of states
– For small ED, spacing can be
very large.
p  / ,
c  0.2GeVfm
  1mm,
p  0.2 /1012  2.1013 GeV
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Why are SM fields confined to 3-D space?
Interactions of SM fields measured
to very high precision at scales of
10-18 m
If gauge forces acted in bulk,
deviations would have been
measured
KK modes would exist for SM
particles
For large ED, mass splitting would
be small.
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H1 results on excited fermions
95% cl
Many channels examined: no evidence for f*.
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Gravity in 3-D space
Gauss’s theorem:
Field at r given by
 F /m dS  4 GM
M
F /m 4 r 2  4  GM
r
m
F  GMm /r 2



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Gravity in 4-D space
4-sphere
Compute volume of 4-sphere
V4 (r) 
r sinq
r

 V (r sin q ) r sin q dq
3
0
q



4
0 3
r 4 sin 4 q dq
 12  2 r 4

3-sphere
G  8R M
n
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d
2 3
S4  V4  2 r
dr
F /m S4  4 GM
2GMm
F
3
r
(2n )
D
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ED signature in Gravity experiments
x
r>R
Get 3-D result
r<R
Get 4-D result
y
R
F
Gaussian
surfaces
R
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r
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Measuring Gravity in the lab
Torsion balance
Henry Cavendish 1778 (apparatus by Michell)
Measured mean density of Earth (no definition of the
unit of force).
Sir Charles Boys inferred G=6.664x10-11Nm2/kg2 from
Cavendish’s data a century later.
Modern value
G = (6.6726 ± 0.0001)x10-11 Nm2/kg2.
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Measuring Gravity in the lab
Recent experiment of Long et al
hep-ph/0009062
Source mass oscillates at 1kHz
Signal is oscillation of test mass
Must isolate masses from acoustic
vibrations, EM coupling
•Run in vacuum
•Isolation stacks
•Conducting shield
•Low temperature
Capacitor
1 kHz
Detector
Shield
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Source mass
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Deviations from Newtonian gravity
Gravity experiments present results in terms of Yukawa interaction of form
G1 (r1 )2 (r2 )
V (r)    dr1  dr2
[1 a er12 /  ]
r12
 gives range of force
a gives strength relative to Newtonian gravity.
a depends on geometry of extra dimensions
Sensitive to forces of 4x10-14 N
Limited by thermal noise: next step, cool detector
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Limits on deviations from Newtonian gravity
Planetary orbits set very
strong limits on gravity at
large distances….
…but forces many orders of
magnitude stronger than
gravity are not excluded at
micron scales.
Parameterized as a Yukawa
interaction of strength a
relative to gravity and range

“moduli” = scalars in string
theories
hep-ph/0009062
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1mm
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Submillimetre gravity measurements: Eot-Wash
Torsion pendulum experiment
“Masses” are 10 holes in each ring
Lower attractor has two rings with
displaced holes, rotates slowly
Geometry designed to suppress
long range signals without affecting
shortrange ones
Membrane shields EM forces
All surfaces gold plated.
Separation down to 218mm
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Torsional pendulum data
Data from one turn of base plate,
with fitted expected curve
Angular precision 8nrad
Signal would have higher
harmonic content and different
dependence on distance.
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Deviations in data
Measured torques at 3 frequencies
a=3 =250mm
Deviations from Newtonian
prediction
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Limit from torsional pendulum
New limit sensitive
to scales <3.5 TeV
for n=2
n=2
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Casimir effect
r
Casimir (1948) predicted force between
2 plates from field fluctuations
Fc 
Plate area A
d
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c
240 r
4
A
This will become a background at
distances around 1mm
Gold probe
d

2
Scan gold probe across surface

2d
Fgrav varies as probe moves, but Fc is
constant.
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Pioneer 10
Pioneer 10 is leaving the solar
system after 30 years in flight.
Orbit shows deccelaration from
force of 10-10 g
Radiation pressure?
– Solar?
– Antenna?
– Heat?
– Gas leaks
Time dependence?
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Limits from g-2 experiments
g-2 is best measured number in physics:
Theory:
aSM = (g-2)/2
= 11659159.7(6.7)x10-10
Experiment (PDG):
= 11659160(6)x10-10
LED can give contributions from KK
excitations of W, Z, g,O(1010)
(Cirelli, Moriond)
Brookhaven experiment: hep-ph/0105077
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Astrophysical Constraints
Supernova remnants lose energy
into ED, but production of KK states
restricted to O(10MeV)
Remnant cools faster
Data from SN1987A implies
MD > 50 TeV for n=2
PRL 83(1999)268
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Neutrino oscillations
Neutrino oscillations could occur into sterile neutrinos
KK excitations of SM fermion singlets can mix with neutrinos to
form sterile states
Oscillation data (SNO, Super-Kamiokande…) are well fitted by
oscillations into standard neutrino states
-> little room for sterile states
-> bound on ED models
-> model dependent limits on parameters
Eg LBNL-49369 gives R<0.82 mm
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Signatures for Large Extra Dimensions at Colliders
ADD model (hep-ph/9803315)
Each excited graviton state has
normal gravitational couplings
-> negligible effect
LED: very large number of KK
states in tower
Sum over states is large.
x
G
y
R
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=> Missing energy signature with
massless gravitons escaping into
the extra dimensions
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LEP Searches for Extra Dimensions
Search for real graviton production
e e  Gg
 

Cross section
( s /M )
2
D
n
No evidence for excess rate
in
photon+Etmiss -> Set limits
Search for deviations in di-lepton

and di-boson production
e e  G*  f f ,VV
  F(  / M s4 )
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LEP Limits on direct graviton production
Limits on MD (TeV)
Number of extra dimensions
Energy
range GeV
2
3
4
5
6
7
ALEPH
189-209
1.28
0.97
0.78
0.66
0.57
-
DELPHI
181-209
1.38
-
0.84
-
0.58
-
L3
189
1.02
0.81
0.67
0.58
0.51
0.45
OPAL
189
1.09
0.86
0.71
0.61
0.53
0.47
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LEP limits on virtual graviton interactions
Search for deviations from SM in
dilepton and diboson production
MS ~ 1TeV? Set 95% CL
 depends on quantum gravity theory
e+e-
1
1
MS
L3
0.98
1.06
limits
OPAL
1.00
1.15
1
1
gg
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DELPH 0.70
I
0.77
L3
0.99
0.84
OPAL
0.89
0.83
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Signatures at the LHC
Good signatures are
• Jet +missing energy channels:
– gg -> gG
– qg -> qG
– qq -> Gg
• Photon channels
LBNL-45198
ATL-PHYS-2001-012
– qq -> Gg
– pp -> ggX
Virtual graviton exchange
• Lepton channels
– pp -> l
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lX
Virtual graviton exchange
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Real graviton production
Cross section:
d
m

2
2
dm dpT jet,g dy jet,g dyG
2
4
n2
G
Sn1 d m
f i (x1 ) f j (x 2 )

n 2
i, j
MD
dt
x1
x2
Note ED mass scale and n do not separate ->
difficult to extract n
Can use cutoff in MD from parton distributions
For n>6, cross section unobservable at LHC
Quantum gravity theory above MD unknown ->
Calculation only reliable at energies below MD
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Missing ET analysis
pp -> jet + ETMiss
Jet energies > 1 TeV
Dominant backgrounds:
Jet + Z -> nn
W-> tn
Jet W-> e n
Jet
}
Use lepton veto
Veto isolated leptons (<10 GeV within DR=0.2)
Instrumental background to ETMiss is small
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High PT jet cross section
ETJet > 1 TeV
|hJet| < 3
100fb-1 of data
expected
SM Background
~500 events
SM Background
No prediction for
n>4
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Lepton veto and trigger
Veto efficiency = 98%
per lepton
Reject
0.2% signal
23.3% JWt
74.3% JWe
61.1% JWm
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Jet multiplicity - signal scenarios
Jet multiplicity in
signal increased
by gg production
process and
higher mass
Mean ~2.5
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Jet multiplicity background
Background: lower jet
multiplicity
Lower mass
Less gg production
Mean ~2.0
But at high ET, mean ~4
is similar
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PT and h distributions
PT of jet is harder in signal
Discrimination in h is too
poor to be useful
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Rejection of W(tn) background
W(tn) background has
jet near missing ET
Cut at df=0.5
Reject :
6% signal
27% W(tn)
11% total background
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Final missing ET distributions
Signal and backgrounds
after cuts for 100fb-1
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Missing ET signal
Signal:
Excess of events at high
ET
Dominant background
Z->nn
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Calibration of Z-> nn background
Use Z-> ee
Two isolated electrons,
PT>15, Mee within 10 GeV of
MZ
Account for acceptance
differences e, m, n
BR’s differ by factor 3, so
calibration sample has
less statistics
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Background estimates
ETmiss >
Type
1 TeV
jZ(nn)
120.6
414.0
jW(tn)
34.5
122.7
jW(en)
2.7
8.8
jW(mu)
3.3
11.0
Total
161.1
556.5
jZ(nn)
36.1
124.7
jW(tn)
9.2
30.1
jW(en)
0.6
2.0
jW(mu)
0.9
2.9
Total
46.9
159.7
jZ(nn)
11.1
37.4
jW(tn)
2.8
9.6
jW(en)
0.1
0.6
jW(mu)
0.2
0.8
Total
14.3
48.4
1.2 TeV
1.4 TeV
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Low L 30fb-1
Helsinki
High L 100fb-1
45
Signal event numbers ET>1TeV
n
MD
2
4
187.6
49.5
18.7
5
77.6
20.4
6
38.7
7
3
4
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S
S/sqrtB
S/sqrB
S/sqr7B
645.4
92.8
35.1
7.7
272.8
39.1
14.8
10.2
3.9
128.8
18.5
7.0
19.7
5.2
2.0
66.5
9.5
3.6
8
11.6
3.1
1.2
39.4
5.7
2.2
4
142.5
37.8
14.3
479.8
68.9
26.1
5
46.2
12.3
4.6
159.8
23.0
8.7
6
18.8
5.0
1.9
64.0
9.2
3.5
7
8.5
2.3
0.9
29.4
4.2
1.6
4
97.1
25.6
9.7
324.4
46.6
17.6
5
25.2
6.6
2.5
86.7
12.5
4.7
6
8.6
2.3
0.9
28.4
4.2
1.6
Helsinki
S/sqr7B S
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Discovery potential
5 discovery limits, ET>1 TeV, 100fb-1
n
MDmin
MDMax (TeV)
R
2
~4
7.5
10 mm
3
~4.5
5.9
300 pm
4
~5
5.3
1 pm
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Single photon signal at LHC
pp  Gg
Potential confirmation of discovery
g
gnn
Main background
pp  Z 
Other backgrounds from W small, not simulated.
Require Etg>60 GeV and |h|<2.5 for trigger
Signal in region Etg>500 GeV


Calibrate background with gZ-> ee sample
pTe>20 GeV, invariant mass within 10 GeV of Z
Sample is 6x smaller than sample, use S/sqr(6B)
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Significance of single photon signal
Background
ETMiss
Type
High L 100fb-1
500 GeV
gZ(nn)
80.7
gW(tn)
2.2
Total
82.9
Signal
n
MD (TeV)
2
3
194.4
21.4
8.7
4
61.8
6.8
2.8
4
49.2
5.4
2.2
3
S
S/sqr(B)
S/sqr(6B)
Only useful if n and MD small
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Extracting n and MD
d 4
mGn2 Sn1 d m
f i (x1 ) f j (x 2 )


2
2
n 2
i, j
dm dpT jet,g dy jet,g dyG
2 MD
dt
x1
x2
Cannot separate n and MD at fixed energy
Run LHC at 10 TeV as well as 14 TeV
MD limited kinematically by pdfs
-> can separate n and MD with precise
cross section measurement
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Variation with ECM at LHC
Cross section ratio
(10 TeV/14TeV)
Need to measure to 5%
to distinguish n=2,3
Need O(10) more L at 10
TeV
Need luminosity to <5%
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Virtual graviton processes at LHC
s-channel graviton exchange contributes to
qq  gg
gg  gg
qq 
gg 
Potential information from angular distribution differences and
interference between SM background and graviton exchange

ATL-PHYS-2001-012
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Diphoton production at LHC
SM background peaks at high h
Signal events central
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Diphoton signals at LHC
gginvariant mass
distributions
(log scale)
Signal can be
optimised with cut on
Mgg>Mmin
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Cut value
Diphoton reach at LHC
5 reach for diphoton signal for
10 fb-1 and 100 fb-1
Can optimise reach at any n with
cut on Mmin
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Dilepton signals at LHC
Invariant mass of l+l- pair
(log scale)
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Forward-backward asymmetry in dileptons
Interference between G and SM modifies predicted FB asymmetry
100fb-1
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Dilepton reach at LHC
5 reach for diphoton
signal for
10 fb-1 and 100 fb-1
Can optimise reach at
any n with cut on Mmin
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Limits from the Tevatron
Searches performed by D0 and
CDF
D0 Run I data taken without B
field
-> use EM clusters only
Fake background from miss id
jets
No evidence for excess events
hep-ex/0108015
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D0 data
Compare data and MC in
Mass/cosq* plane
Data compatible with
expected backgrounds
from SM and miss ID jets
hep-ex/0103009
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D0 LED Signature
Dedicated MC generator
includes SM, ED and
interference terms.
Signal appears at large M, low
cosq*
MD>1.44 TeV for n=3
MD>0.97 TeV for n=7
Run II will extend reach to
3-4 TeV
Luminosity? 2? 10? 30 fb-1
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Single photons at the NLC
Finding signal is one
thing…
n=2,4,6
…interpreting it is
another …
Single photon+ETMiss
signal at NLC
SM background from
e e  G˜ G˜ g
 
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xg 
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2E g
e e  nng
s
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Single photon angular distribution at NLC
Assume:
500 GeV LC
Pol(e-)=80%
Pol(e+)=60%
Cross-section measured to
1% precision
(>270fb-1 required)
Distinguish n=2 from n=3
up to MD=4.6 TeV
Gravitino production is
indistinguishable from
n=6!
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Warped 5-d spacetime
Higgs vev
suppressed by
“Warp Factor”
exp(krc  )
Gravity
Planck scale brane
x y
z
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Our brane
5th space dimension r
rc  10 32 m
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x y
z
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Warped Extra dimensions
Consider Randall and Sundrum type models as test case
Gravity propagates in a 5-D non-factorizable geometry
Hierarchy between MPlanck and MWeak generated by “warp factor”
Need k r  10
: no fine tuning
c
Gravitons have KK excitations with scale
   MPl exp(krc )
This gives a spectrum of graviton excitations which can be detected
as resonances at colliders.
First excitation is at
where
0.01 
k
1
MP l
k
m1  kx1 exp(krc  )  3.83

M Pl
Analysis is model independent: this model used for illustration
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Implementation in Herwig
Model implemented in Herwig to calculate general spin-2 resonance
cross sections and decays.
Can handle fermion and boson final states, including the effect of
finite W and Z masses.
Interfaced to the ATLAS simulation (ATLFAST) to use realistic model
of LHC events and detector resolutions.
Coupling
1


Worst case when
k
giving smallest couplings.
 0.01
MPl
For m1=500 GeV, =13 TeV
Other choices give larger cross-sections and widths
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Angular distributions
Angular distributions expected of decay products in CM are:
qq -> G -> ff
1  3cos2   4cos4 
gg -> G -> ff
1  cos4 
qq -> G -> BB
1  cos4 
gg -> G -> BB
1  6cos2   cos4 
This gives potential to discriminate from Drell-Yan background with
1  cos2 
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Angular distributions of e+e- in graviton frame
Angular distributions are
very different depending
on the spin of the
resonance and the
production mechanism.
=>get information on the
spin and couplings of the
resonance
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ATLAS Detector Effects
Best channel G->e+e-
Good energy and angular resolution
Jets: good rate, poor energy/angle resolution, large background
Muons: worse mass resolution at high mass
Z/W: rate and reconstruction problems.
Main background Drell-Yan
Acceptance for leptons:
|h|<2.5
Tracking and identification efficiency included
Energy resolution
Mass resolution
DE 12% 24.5%


 0.7%
E
E
ET
m
m
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(500 GeV)  0.8%
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Graviton Resonance
 
G e e
Graviton resonance is very
prominent above small SM
background, for 100fb-1 of
integrated luminosity
Plot shows signal for a 1.5
TeV resonance, in the test
model.
The Drell-Yan background
can be measured and
subtracted from the
sidebands.
Detector acceptance and
efficiency included.
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70
1000
GeV
500
GeV
1.5
TeV
5/23/2016
Signal and
background
for increasing
graviton
mass
2.0
TeV
Helsinki
71
Events expected from Graviton resonance
Signal
100fb-1
NS
NB
NSMIN=Max
(5 ¦N B,1 0 )
( .B) MIN
fb
500
Mass
window
( GeV)
± 1 0 .46
2 0 75 0
816
143
1. 9 41
1 0 00
± 1 8 .21
814
65
40
0. 5 42
1 5 00
± 2 4 .37
84
11
1 6 .5
0. 2 35
1 7 00
± 2 6 .53
39
5. 8
1 2 .0
0. 1 78
1 8 00
± 2 7 .42
27
4. 3
1 0 .4
0. 1 56
1 9 00
± 2 8 .29
19
3. 2
1 0 .0
0. 1 52
2 0 00
± 2 8 .76
13
2. 3
1 0 .0
0. 1 57
2 1 00
± 3 0 .55
9. 4
1. 8
1 0 .0
0. 1 59
2 2 00
± 3 1 .46
6. 8
1. 4
1 0 .0
0. 1 62
MG
( GeV)
Limit
Background
Mass window is ±3x the mass resolution
5/23/2016
Helsinki
72
Production Cross Section
10 events produced for
100fb-1 at mG=2.2 TeV.
G  ee
Search
limit
With detector
acceptance and
efficiency, search limit is
at 2080 GeV, for a signal
of 10 events and S/√B>5
10 events
5/23/2016
Helsinki
73
Angular
distribution
changes with
graviton mass
Production more
from qq because of
PDFs as graviton
mass rises
5/23/2016
Helsinki
74
Angular distribution observed in ATLAS
G  ee
1.5 TeV resonance mass
Production dominantly
from gluon fusion
Statistics for 100fb-1 of
integrated luminosity (1
year at high luminosity)
Acceptance removes
events at high cos q*
5/23/2016
Helsinki
75
Determination of the spin of the resonance
One ATLAS run
With data, the spin can be determined from a fit to the angular
distribution, including background and a mix of qq and gg
production mechanisms.
Establish how much data is needed for such a fit to give a
significant determination of the spin:
1. Generate NDY background events (with statistical fluctuations)
2. Add NS signal events
3. Take likelihood ratio for a spin-1 prediction and a spin-2
prediction from the test model
4. Increase NS until the 90% confidence level is reached.
5. Repeat 1-4 many times, to get the average NSMIN needed for spin2 to be favoured over spin-1 at 90% confidence
6. Repeat 1-5 for 95 and 99% confidence levels
5/23/2016
Helsinki
76
Angular distribution observed in ATLAS
G  ee
Model independent
minimum cross
sections needed to
distinguish spin-2 from
spin-1 at 90,95 and 99%
confidence.
Assumes 100fb-1 of
integrated luminosity
Discovery
limit
5/23/2016
Helsinki
For test model case,
can establish spin-2
nature of resonance at
90% confidence up to
1720 GeV resonance
mass
77
Graviton discovery contours
Confidence limits in plane of
 vs graviton mass
Coupling = 1/ 
Test model has k/MPl=0.01,
giving small coupling.
For large k/MPl coupling is
large enough for width to be
measured.
(Analysis assumes
width<<resolution)
5/23/2016
Helsinki
78
Muon analysis
Muon mass resolution much
worse than electron at high
mass 
Discovery reach in muon
channel for MG<1700 GeV
Muons may be useful to
establish universality of
graviton coupling
5/23/2016
Helsinki
79
Measurement of the graviton coupling to m+mConfidence limits in plane of
 vs graviton mass
D.B/.B

Gm m

Coupling = 1/ 
Test model has k/MPl=0.01,
giving small coupling.
For large k/MPl coupling is
large enough for width to be
measured.
(Analysis assumes
width<<resolution)
5/23/2016
Helsinki
80
Photon analysis
Photon pair mass resolution as
good as electrons
But background uncertain. For
standard model (ptmin=150 GeV)
HERWIG=0.36 pb
Included:
Not included:
for example
Graviton mass (GeV)
5/23/2016
Helsinki
FNAL data indicates HERWIG is 5x
too small  use 1.8 pb
Do not trust cosqdistribution for
background.
81
Measurement of the graviton coupling to gg
G  gg
Confidence limits in plane of
 vs graviton mass
Coupling = 1/ 
Test model has k/MPl=0.01,
giving small coupling.
For large k/MPl coupling is
large enough for width to be
measured.
(Analysis assumes
width<<resolution)
5/23/2016
Helsinki
82
Graviton to jet-jet backgrounds
k/MPl = 0.08
(64x higher cross-section)
5/23/2016
Helsinki
83
Graviton to jet-jet signal at 1.9 TeV
Significant signal after
background subtraction
k/MPl = 0.08
(64x higher cross-section)
5/23/2016
Helsinki
84
Graviton to jet-jet search reach
Reach is limited because of high
background
5/23/2016
Helsinki
85
Graviton to WW
Look for G WW en jj
Select 1e, 0 m, 2 jets, PTmiss from ATLFAST
hjet <2
Require Mjj compatible with W mass
take highest pT pair in mass window
Solve for pzn using W mass constraint
Plot MWW look for resonance above SM background
SM background from WW, WZ and ttbar
5/23/2016
Helsinki
86
Graviton to WW: signal and background
WW
channel is
viable for
graviton
5/23/2016
Helsinki
87
Graviton to WW channel
Efficiency drops at very high jet ET
Reach of W+jets channel - low cuts
5/23/2016
Helsinki
88
Exploring the extra dimension
Check that the coupling of the resonance is universal: measure rate
in as many channels as possible: mm,gg,jj,bb,tt,WW,ZZ
Use information from angular distribution to separate gg and qq
couplings
Estimate model parameters k and rc from resonance mass and .B
For example, in test model with MG=1.5 TeV, get mass to ±1 GeV
and .B to 14% from ee channel alone (dominated by statistics).
Then measure
k  (2.43  0.17) 1016 GeV
rc  (8.2  0.6) 10 32m
5/23/2016
Helsinki
89
Black hole production
Low scale gravity in extra
dimensions allows black hole
production at colliders.
Decay by Hawking radiation
(without eating the planet)
8 TeV mass black hole decaying to
leptons and jets in ATLAS
8 partons produced with
pT>500 GeV
Work in progress: Richardson,
Harris
5/23/2016
Helsinki
90
Black hole production cross-sections at LHC
10000 evs/yr
Classical approximation to cross-section
(Controversial…)
Very large rates for n=2-6
5/23/2016
 BH ~  r
2
h
hep-ph/0111230

Helsinki
91
Black hole decay
Decay occurs by Hawking radiation
Hawking Temperature TH
TH  (n  1) /4  rh
1
Black Hole radius rh
 m h  n 1
rh ~
 
M D c M D 
Use observed final state energy spectrum to measure TH and hence
n?

5/23/2016
Helsinki
92
Particle spectra from black hole decays
Example:
n=6 extra dimensions
MD = 2 TeV
Mh = 7-7.5 TeV
All jets
Hawking Temperature TH= 400 GeV
Multiplicity N~ Mh/2 TH ~ 9
Isolated e’s
Electron spectrum deviates from
Black body
-effect of isolation cut?
-recoil effect?
Black body
Fit
5/23/2016
Fit gives 388 GeV
Helsinki
93
Extracting n from Black Holes
Preliminary!
Fit TH against
Black Hole mass
No experimental
resolution yet
(500 GeV bins…)
Effect of heating?
Input n=6
Fit gives
n=5.7+-0.2
5/23/2016
Helsinki
94
Black hole production at the Tevatron
pb
105
Rate expected to be large at Tevatron
Events/yr
102
n=4 extra dimensions
Cross-section drops rapidly at high
mass
100

10-2
Assume 10fb-1
Non-observation implies MD>1.4 TeV
10-5
1.0
0.7
1.3
1.6
hep-ph/0112186
MD
5/23/2016
Helsinki
95
Conclusions
Extra dimensional theories provide an exciting alternative to the
normal picture of physics beyond the standard model
A wide variety of new phenomena are predicted within reach of
experiments.
Time to bet on the lottery!
5/23/2016
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96