Experimental Probes for Extra Dimensions
Greg Landsberg
WHEPP-8 WorkshopJanuary 5-16, 2004
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 2
Outline
More Fun in Extra DimensionsADD ModelTeV-1 ScenarioRS ModelUniversal Extra Dimensions“Contracted” Extra Dimensions
Current Constraints on Models with Extra Dimensions
Gravity at Short DistancesCosmology and AstrophysicsCollider Probes
Black Holes at the LHC and BeyondConclusions
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 3
Math Meets Physics?
Math physics: some dimensionalities are quite specialExample: Laplace equation in two dimensions has logarithmic solution; for any higher number of dimensions it obeys power law insteadSome 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 notDo we live in a special space, or only believe that we are special?
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 4
A $1B Question
Can we use extra dimensions to solve the hierarchy problem?
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 5
Life Beyond the Standard Model
The natural mH value is , where 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
This new theory takes over at a scale comparable to the mass of the Higgs boson, i.e. 1 TeVBut: 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) – ADDExplore modification of the RGE in (4+n)-dimensions to achieve low-energy unification of the gauge forces (Dienes, Dudas, Gherghetta)
v MGUT MPl
GravitationalForce
E [GeV]
EM/HyperchargeForce
Weak Force
Strong ForceInvers
e S
treng
th
RGE equations
1016102 1019
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 6
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?
Ruled out for flat extra dimensions, but has not been ruled out for sufficiently small compactified extra dimensions:
Flat Dimension
Com
pact
Dim
ensi
on
1
2123
212
11
nnn
PlPl r
mm
Mr
mm
MrV
Rr
rR
mm
MrV
nnnPl
for
1 2123
Gravity is fundamentally strong force, bit we do not feel that as it is diluted by the volume of the bulkG’N = 1/MD
2; 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
4 ,106
3 , 3
2 , 7.0
1 ,108
2
1
12
12
/2
nm
nnm
nmm
nm
M
M
MR
n
D
Pl
D
2]3[/1 nPlM
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 7
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
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 8
Extra Dimensions at Work
Burst of the ideas to follow: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 (Arkani-Hamed, Cohen, Georgi)
All these models result in rich low-energy phenomenologyMZ 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
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 9
Sub-millimeter gravity measurements could probe n=2 case in the ADD hypothesisThe 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 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 distance
Constraints from Gravity Experiments
PRL 86, 1418 (2001)E.Adelberger et al.
~ ~
[J. Long, J. Price, hep-ph/0303057]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 10
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 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 estimateStill, n=2 is largely disfavored
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 11
Collider Signatures for Large Extra Dimensions
Kaluza-Klein gravitons couple to the momentum tensor, and therefore contribute to most of the SM processesFor 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-timeSince 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 2Depending 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
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 Emission Fermion or VB pairs at hadron or e+e- colliders
V
V
GKKGKK
f
ff
f
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 12
LEP2 Constraints
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
1.1/1.0 (<202)
OPAL 1.151.00
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 [MS(Hewett)]
ee G ee ZG
Experiment
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
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 13
HERA Search for Virtual Graviton Effects
ep ept-channel exchange, similar to Bhabha scattering diagrams; based on the GRW formalism (both H1 and ZEUS in fact set limits on T, but call it MS)
Usual SM, Z/* interference, and direct GKK termsAnalysis method: fit to the d/dQ2 distribution Current H1 limits: T > 0.82/0.78 TeV (MS > 0.73/0.70 TeV)
Current ZEUS limits: T > 0.81/0.82 TeV (MS > 0.72/0.73 TeV) Expected sensitivity up to 1 TeV with the ultimate HERA data set
H1 81.5 pb-1
T > 0.58 TeV,
T > 0.61 TeV,
T > 0.77 TeV,
T > 0.73 TeV,
H1 Preliminary
ZEUS Preliminary
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 14
Hadron Colliders: Virtual Graviton Effects
Expect 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 > 1.0-1.4 TeV (n=2-7)Combined with the Run I DØ result:
MPl > 1.1-1.6 TeV – tightest to dateSensitivity in Run II and at the LHC:
Run II, 130 pb-1
V
V
GKKGKK
f
ff
f
M,cosfM
nbM,cosf
M
nadMcosd
d
dMcosd
d
*
P
*
P
*SM
*
2814
22
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 15
Colliders: Direct Graviton Emission
ee + GKK at LEP + MET final stateMP > 1.4-0.5 TeV (ADLO), for n=2…7
qq/gg q/g + GKK at the Tevatronjets + MET final stateZ()+jets is irreducible backgroundChallenging 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…7CDF just announced similar limitsExpected 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
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 16
Novel Signature for Direct Graviton Emission
Single vector boson production at hadron colliders has been looked at briefly [Balazs, He, Repko, Yuan, Dicus, PRL 83, 2112 (1999)], but:
Only leptonic decays have been consideredSensitivity to MD in Run IIa is 0.9-1.1 TeV, i.e. slightly worse than in the monojet channelCross section is large: ~1 pb for both channels in Run II
We propose a novel channel: W/Z(jj) + GKK, with a clear advantage of an enhanced branching fraction (xB ~ 0.6 pb)This channel (≥2j + MET) is sensitive to both q/g+GKK and W/Z(jj) + GKK channels (!)Furthermore, the dominant Z()+jets background can be reduced significantly for the latter signal by requiring Mjj ~ 85 GeVSome phenomenological work remains to be done to calculate the cross section accurately; it’s certainly worth doing as the sensitivity should be superior to that in any other channel!
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 17
Stringy Models
Recent attempts to embed the idea of large extra dimensions in string models:
Shiu/Shrock/Tye [Phys. Lett. B 458, 274 (1999)]
Type I string theory on a Zn orbifold
Consider resulting twisted moduli fields which sit on the fixed points of the orbifolds and their effects on gg gg scatteringThese fields acquire mass ~1 TeV due to SUSY breaking, and their coupling with the bulk fields is suppressed by the volume factorSince they couple to gravitons, these fields can produce bulk KK modes of the latterCurrent sensitivity to the string scale, MS, from CDF/DØ dijet data is ~1 TeV
Cullen/Perelstein/Peskin, [Phys. Rev. D 62, 055012 (2000)]
Embed QED into Type IIB string theory with n=6Calculate corrections to ee and Bhabhascattering due to string Regge excitationsL3 has set limit MS > 0.57 TeV @ 95% CLAlso calculate ee,gg G cross sectionAnother observable effect is a resonance in qq g at MS
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 18
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
SM gauge bosons can propagate in these extra dimensionsExpect ZKK, WKK, gKK resonancesEffects of the virtual exchange of the Kaluza-Klein modes of vector bosons at lower energies
Gravity is not included in this model
[ABQ, PL B460, 176 (1999)]
IBQ ZKK
TeV-1 Extra Dimensions
Antoniadis/Benaklis/Quiros [PL B460, 176 (1999)] – direct excitations; require LHC energies
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 19
Current Limits on TeV-1 ED
From Cheung/GL [PRD 65, 076003 (2002)]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 20
Tevatron and LHC Sensitivity
We expect the dijet and DY production to be the most sensitive probes of TeV-1 extra dimensionsThe 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)]Similar (or slightly better) sensitivity is expected in the dijet channel; detailed cuts and NLO effects need to be studiedRun IIb could yield sensitivity similar to the current limits from indirect searches at LEPThese tests are complementary in nature to those via loop diagrams at LEP
From Cheung/GL [PRD 65, 076003 (2002)]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 21
Randall-Sundrum Scenario
Randall-Sundrum (RS) scenario [PRL 83, 3370 (1999); PRL 83, 4690 (1999)]
Gravity can be localized near a brane due to the non-factorizable geometry of a 5-dimensional space+ brane (RS) – no low energy effects+– branes (RS) – TeV Kaluza-Klein modes of graviton++ branes (Lykken-Randall) – low energy collider phenomenology, similar to ADD with n=6–+– branes (Gregory-Rubakov-Sibiryakov) – infinite volume extra dimensions, possible cosmological effects+–+ branes (Kogan et al.) – very light KK state, some low energy collider phenomenology
G
Planck branex5
SM brane
Davoudiasl, Hewett, Rizzo PRD 63, 075004 (2001)
Drell-Yan at the LHC
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 22
Current ConstraintsNeither gravity experiments, nor cosmology provide interesting limits on most of the RS modelsExisting limits come from collider experiments, dominated by precision electroweak measurements at LEPAs the main effect involves direct excitation of the GKK levels, energy is the keyGiven the existing constraints and the theoretically preferred parameters, there is not much the Tevatron can do to test RS models Extra degree of freedom due to the compact dimension results in a light scalar field – the radion Tevatron sensitivity is very limited; LHC is the place to probe RS models
; 1 2352 ckr
Pl ek
MM
ckr
PleM
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 23
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 = M0
2 + 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)
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 24
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
Odd fields do not have 0 modes, so we identify them w/ “wrong” chiralities, so that they vanish in the SM
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
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 25
UED Spectroscopy
First level KK-states spectroscopy
[CMS, PRD 66, 056006 (2002)]
Decay:B(g1→Q1Q) ~ 50%B(g1→q1q) ~ 50%B(q1→q) ~ 100%
B(t1→W1b, H1
+b) ~
B(Q1→QZ1:W1:1) ~ 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→1L) ~ 100%B(1→1) ~ 100%
B(H1
→1, H
±*1) ~ 100%Production: q1q1 + X → MET + jets (~had/4); but:
low MET
Q1Q1+ X→ V1V’1 + jets → 2-4 l + MET
(~had/4)
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 26
Production Cross Section
Q1Q1, q1q1
[Rizzo, PRD 64, 095010 (2001)]
Run II, s = 2 TeV
Reasonably high rate up to M ~ 500 GeV
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 27
Sensitivity in the Four-Lepton Mode
Only the gold-plated 4-leptons + MET mode has been considered in the original paperSensitivity in Run IIb can exceed current limitsMuch more promising channels:
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 MCOne could use SUSY production with adjusted masses and branching fractions as a quick fix
L is per experiment;(single experiment)
[Cheng, Matchev, Schmaltz, PRD 66, 056006 (2002)]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 28
Almost No Extra Dimensions
Novel idea: build a multidimensional theory that is reduced to a four-dimensional theory at low energies [Arkani-Hamed, Cohen, Georgi, Phys. Lett. B513, 232 (1991)]An alternative EWSB mechanism, the so-called Little Higgs (a pseudo-goldstone 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 rangeUnfortunately, the Tevatron reach is very poor; LHC would be the machine to probe this modelHowever: keep an eye on it – this is currently the topic du jour in phenomenology of extra dimensions; new signatures are possible!
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 29
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 resonancesTeV-1 dimensions: VKK, virtual effectsRS: graviton excitations, SM particle excitation, radion, direct graviton emissionUniversal 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, ZZ/Z couplings
Monoleptons TeV-1, some RS W’
Dijet + MET ADD, Universal SUGRA, Leptoquarks
Leptons + MET
Universal SUGRA
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 30
Black Holes at the LHC
NYT, 9/11/01
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 31
Theoretical FrameworkBased on the work done with Dimopoulos two 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 workYoshino/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
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 32
Black 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)
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)]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 33
Black 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 componentThe decay into a particle on the brane and in the bulk is thus the sameSince 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
[Dimopoulos, GL, PRL 87, 161602 (2001)]
Stefan’s law: ~ 10-26 s
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 34
LHC: Black Hole Factory
Drell-Yan +X
[Dimopoulos, GL, PRL 87, 161602 (2001)]
Spectrum of BH produced at the LHC with subsequent decay into final states tagged with an electron or a photon
n=2
n=7
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 35
Space-Probes 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
[Dimopoulos, GL, PRL 87, 161602 (2001)]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 36
Higgs Discovery in BH Decays
Example: 130 GeV Higgs particle, which is tough to find either at the Tevatron or at the LHCHiggs with the mass of 130 GeV decays predominantly into a bb-pairTag 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 resultsTime 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 well-understood detectors!
An exciting prospect for discovery of other new particles w/ mass ~100 GeV!
MP = 1 TeV, 1 LHC-hour (!)
= 15 nb
[GL, PRL 88, 181801 (2002)]
W/Z h t
ATLASresolutions
boost
Wt
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 37
Black Hole Event Displays
First studies already initiated by ATLAS and CMSATLAS –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]
WHEPP-8 Greg Landsberg, Experimental Probes for Extra Dimensions 38
ConclusionsStay 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!
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 patent, this portal "allows energy from another dimension to accelerate plant growth." from the AIP’s “What’s New”, 3/17/00
If you think that gravity is weak force, you might be spending too
much time in the lab!
Top Related