Post on 26-Dec-2015
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mysteries of extra dimensions
Joseph LykkenFermi National Accelerator Laboratory
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a revolution in the making
the physics of extra dimensions is a revolution in the making
like the quantum mechanics revolution of the 1920’s, it is the result of many new ideas (from many people) coming together to give a radically new picture of physics and of the universe
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the universe: traditional view
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the universe: a bigger view
extra dimensions of space
the rest is terra incognita
everything we know about is on this slice
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why do physicists think that there are extra dimensions of space?
what is the physics that hides extra dimensions?
how can experiments discover and explore extra dimensions?
questions for this talk
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why do physicists think that there are extra dimensions of space?
supermassive black hole inthe center of galaxy M87
Reason #1: string theory
particle physicists developed string theory tounderstand quantum gravity - to explain extremephysics such as goes on inside black holes
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string theory
in string theory, all the elementary particlesare merely different vibrations of asingle substance called strings.
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string theory
physicists have shown that quantum theoryonly allows one unique theory of quantumstrings… but there is a catch:
quantum strings need 9 spatial dimensions to wiggle in!
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why do physicists think that there are extra dimensions of space?
Reason #2: mysteries of particle physics
all ordinary matter is composed of justthree kinds of elementary particles.
but in particle accelerators we producemany more!
why do these extra particles exist,and why these particles but not others?
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in string theory the answer liesin the shape of the extra dimensions
determines how many ways the strings can vibrate,and thus whether there are 3, 12, or 137 kinds ofelementary particles.
particle physics data already in our hands may be anencrypted map of the geography of extra dimensions.
slice of a 6 dimensional Calabi-Yau space
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why do physicists think that there are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions thatwe see are changing – expanding
we don’t understand what is thedark energy driving the expansiontoday
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why do physicists think that there are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions thatwe see are changing – expanding
we don’t understand what drovecosmic inflation in the earlyuniverse
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why do physicists think that there are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions thatwe see are changing – expanding
we don’t understand whatthis was
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why do physicists think that there are extra dimensions of space?
Reason #3: the Big Bang
the three spatial dimensions thatwe see are changing – expanding
extra dimensions may be theextra ingredient that explainsthe history of the universe
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if extra spatial dimensions exist, they must be(for some reason) difficult to probe
physicists have uncovered several possible explanations:
hidden dimensions
e.g. the extra spatial dimensionsare compact and small
Nordstrom, Kaluza, and Klein, circa 1920Nordstrom, Kaluza, and Klein, circa 1920
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compact extra dimensionscompact extra dimensionswhat do we look for experimentally?…
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Kaluza-Klein modesKaluza-Klein modes
if spatial dimension is compactthen momentum in thatdimension is quantized: R
np R
np
from our point of view we see new massive particles!
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220
2
R
nmm 2
220
2
R
nmm
pR
1R
1R
2R
2R
3R
3R
4R
4
0
KK momentumtower of states
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how do we look for Kaluza-Klein particles?
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2121stst century particle physics century particle physics
Fermilab’s Tevatron is the highest energy accelerator in the world today.
protons collide with antiprotons at 2 TeV
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Kaluza-Klein dark matterKaluza-Klein dark matter
H-S Cheng, J. Feng, and K. MatchevG. Servant and T. Tait
if we live in the “bulk” of compact extra dimensions,then Kaluza-Klein parity (i.e. KK momentum)is conserved.
could be a KK neutrino, bino, or photon
so the lightest massive KK particle (LKP) is stable
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how heavy is the LKP?
current data requires MLKP ~> 300 GeV
LKP as CDM wants MLKP ~ 600 – 1200 GeV
might be too heavy for the Tevatron, but theLHC collider experiments will certainly see this
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furthermore, we could have signals fromdirect searches in the next generation ofWIMP detectors
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recently, we have uncovered some more radical explanations for hidden dimensions:
hidden dimensions
e.g. it may be that not all particles(in a certain energy range)move, probe, or seethe same number of spatial dimensions
a dramatic realization of this is called
the braneworld
braneworldsbraneworlds
Standard Model particles are trapped on a brane and Standard Model particles are trapped on a brane and can’t move in the extra dimensionscan’t move in the extra dimensions
only gravitons and exoticsonly gravitons and exoticsmove in the “bulk” of themove in the “bulk” of theextra dimensional universeextra dimensional universe
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in the most extreme version of braneworld,only gravity tells us about the extra dimensions
this hides the extra dimensions quiteefficiently, since gravity effects are hard to measure…
only the graviton (the force particle of gravity)can move off the brane into extra dimensions
various kinds of braneworld scenariosare quite natural in string theory
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gravitonsgravitonsmay be our only probe of extra dimensions
but gravity is so weak that we have never even seen a graviton.
The gravitational attraction between two electrons is about 1042 times smaller than the electromagnetic repulsion.
F=GF=GNN
melectronmelectron
r2
rmelectron melectron
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gravity gets stronger at extremely high energiesMPlanck = 1019 GeV (or very short distances)
forc
e st
ren
gth
energy
4d gravity
(4+n
)d g
ravi
ty
it gets stronger at not-so-high energies(not-so-short distances) if there are extra dimensions….
extra dimensions change gravity
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2*
2 ~ nnPlanck MRM
ADD braneworld modelsADD braneworld modelsArkani-Hamed, Dimopoulos, Dvali
assume that only gravity sees assume that only gravity sees nn largelarge extra extra compact dimensions with common size compact dimensions with common size R:R:
in ADD models in ADD models MM** ~ ~ 1 TeV, in order to1 TeV, in order to
eliminate the hierarchy problem of theeliminate the hierarchy problem of theStandard Model. This energy scale isStandard Model. This energy scale isperhaps in reach of the Fermilab Tevatronperhaps in reach of the Fermilab Tevatron
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fm 10~ 7,6
nm1~ 3
mm1~ 2
Km10~ 1 9
Rn
Rn
Rn
Rn
fm 10~ 7,6
nm1~ 3
mm1~ 2
Km10~ 1 9
Rn
Rn
Rn
Rn
Solar system
Pinhead
Gold atom
these are large extra dimensionsthese are large extra dimensions
we can test these models in a varietyof experiments
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force lawsforce laws
single photon exchange
single graviton exchange
both give both give 1/r1/r potentials potentials
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force lawsforce laws
if extra dimensions appear at some length scale R,exchange of massive graviton KK modes givesadditional Yukawa potentials
ee-r/-r/rrlook for these deviations in short-range gravity expts
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Eot-WashEot-WashGroupGroup
::
no deviations seen at ~200 microns
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still possible to see something at ~ 10 micronsstill possible to see something at ~ 10 microns
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astrophysics and cosmology constrainADD (or other) models with too manylow mass KK gravitons
lower bounds on lower bounds on MM* * , , in TeVin TeV
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quantum gravity at collidersquantum gravity at colliders
if ADD is correct collider expts should seeeffects of both real and virtual massive KK gravitons
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quantum gravity at collidersquantum gravity at colliders
because we are on a brane, 2 SM particlescan collide to produce a single massivegraviton
the graviton “escapes”the graviton “escapes”into the extra dimensions into the extra dimensions
gluon (becomesjet of hadrons)
graviton
quark
antiquark
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tree diagrams for qqbar graviton + gluon
implementedimplementedin PYTHIAin PYTHIA
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these gravitons are heavy!these gravitons are heavy!
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CDF simulation courtesy M. Spiropulu
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now let’s look at real datafrom the Tevatron:
Caveat:while the monojet signature isspectacular, it can be mimickedby several Standard Model processes
43CDF preliminary
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CDF preliminary
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Angular distributions
ATLAS can distinguish spin 2 vs 1 up to 1.72 TeV
graviton has spin 2graviton has spin 2
M=1.5 TeV 100fb-1
B.C. Allanach, K. Odagiri, M.A. Parker, B.R. Weber (JHEP 09 (2000) 019 – ATL-PHYS-2000-029)
gravitons at the LHC
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virtual KK graviton exchanges will interferevirtual KK graviton exchanges will interferewith SM diagrams in a variety of processeswith SM diagrams in a variety of processes
theory treatment is slightly bogus becausetheory treatment is slightly bogus becausesum of KK modes is sensitive to details ofsum of KK modes is sensitive to details ofthe real UV theorythe real UV theory
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Randall–Sundrumwarped space
zero mode graviton likes tozero mode graviton likes tobe near mother, but Kaluza-Kleinbe near mother, but Kaluza-Kleingraviton modes do notgraviton modes do not
mother branemother brane
GG
weak braneweak brane5th dimension5th dimension5th dimension5th dimension
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in warped space, it isnatural for gravity to be weak
• if we live anywhere but the “mother brane”, gravity will seem weak
• gravity is weak because of small probability for graviton to be near the weak brane
• on the weak brane the mass hierarchy of the Standard Model becomes natural
• this scenario is testable at high energy colliders
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compactified space: R <~ 10-16 cm ADD braneworlds: R <~ 200 microns warped braneworld : R <= infinity!
the warped braneworlds hide theextra dimensions even more efficientlythan ADD braneworlds:
current experimental upper boundson the size of extra dimensions:
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collider signals can also be dramatically different
H. Davoudiasl, J. Hewett, T. Rizzo
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science fiction, science factscience fiction, science fact
although extra dimensions isalthough extra dimensions isa pretty weird concept,a pretty weird concept,physics has already producedphysics has already producedmany even weirder phenomenamany even weirder phenomena
the real leap of imaginationthe real leap of imaginationis designing experiments tois designing experiments toexplore the extra dimensions - if they exist.explore the extra dimensions - if they exist.
54Large Hadron Collider (CERN, 2007)
new accelerators for new physics
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new accelerators for new physics
Linear Collider
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long ago philosopher Immanuel Kant gavea ~500 page proof that space and time area priori
however to make sense of quantum gravity, not to mention the Big Bang singularity, this cannot be true
in the real theory of everything, spacetime should be emergent.
emergent spacetime
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emergent spacetime
a great theoretical challenge for the futureis to figure out where spacetime comes fromin the first place
spacetime must somehow arise “dynamically”,but what does dynamics mean without spacetime?
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what is a dimension, anyway?
a good starting point is to realize that, operationally,an extra dimension of space just means new degreesof freedom of a certain type (Kaluza-Klein modes).
but we already have discovered examples instring theory (e.g. AdS/CFT) where new degreesof freedom can be interpreted either as an extradimension or as new dynamics without anextra dimension!
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deconstructing dimensions
recently we have even discovered how to dothis in simple models that do not carry allthe heavy baggage of full-blown string theory
these “deconstruction models” are a first stepto a more dynamical understanding ofspacetime dimensions
N. Arkani-Hamed, A. Cohen, H. GeorgiH-C Cheng, C. Hill, S. Pokorski, J. Wang
particle theorists are learning to think differently…
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