extra dimensions in particle physics
DESCRIPTION
EXTRA DIMENSIONS IN PARTICLE PHYSICS. Ferruccio Feruglio. EPS conference – Aachen, July 2003. SET-UP. brane. in the 1 st part of this talk. bulk. length. length. volume. only gravity is admitted to the bulk (few exceptions). KK modes - PowerPoint PPT PresentationTRANSCRIPT
EXTRA DIMENSIONS INPARTICLE PHYSICS
EPS conference – Aachen, July 2003
Ferruccio Feruglio
SET-UPbrane 1)TeV1( L
0L in the 1st part of this talk
bulkSpace) Extra(4 ESM
length R21SES
TES volume
21 / ZSES length R
)2( RV
only gravity is admitted to the bulk(few exceptions)
warped geometry branes can carry some energy density and, by the laws of GR, they may warp the space-time geometry.
KK modesgraviton momentum along ED is quantizedin units of 1/R. To the 4D observer, gravitonscome in infinite copies with 4D masses n/R(=a tower)
particles
MNGfull space-time metric in D = 4+ contains
4D graviton )(xg )()( xg n
radionone combination of specifies the volume of the extra spacee.g. = 1
MNG
)()0(55 xrG MRxr )(
much as scale Fermi2
vH
KK modesand itsR
nmKK
other particles, specifying the shape of the ES or the fluctuationsof the brane, can be present (not covered by this review…)
General motivationunification of gravity with other fundamental interactionsKaluza-Klein (1919-1926), still valid today. String theories, candidates for a unified descriptionof all interactions, are formulated in D = 10 (or D = 11)
specific motivations
1. Hierarchy problem
2. ``little’’ hierarchy problem
3. flavour problem
4. problems of conventional GUTs
5. cosmological constant
PMscale e.w.
scale e.w.Hm
tdue mmmm ,...,,uscbub VVV
yrKp 33102)(
43eV)10(
HIERARCHY PROBLEMthere is only one fundamental scale in D=4+ dimensions TeV1DM
Rr 12
11
rMV
Dgrav all KK gravitons contribute
Rr only the 4D graviton zero mode contributes
rVMV
PM
Dgrav
11
2
2
VM
M
MD
D
P
2
4D gravity is weak because the graviton wave functions is diluted in a big volume.
Now we should explain why1 DMR
(L=0 here)
...)(
),(
V
xgyxG
.
VM P
11
Arkani-Hamed, Dimopoulos, DvaliAntoniadis
R
1
2
3
… … …
7
1-R
mm1.0Km108
mm10 6
mm10 12
eV10 18
eV10 3
eV100
MeV100
TeV1DM
excluded: R ~ Sun-Earth distance
of special interest: sizeable deviations from Newton law
clearly allowed
KK graviton states can be produced- at colliders- in processes of astrophysical and/or cosmological relevance
Sub-mm tests of gravity
re
r
mGrV
rN 1)(
we expect 2
degeneracy of the1st KK level
R 2wavelength of the 1st KK mode
2 CLm %95150
Further improvements are an experimental challenge!
EOT-WASHex/0202008
important: deviations in this range are expected also in other scenarios(more on this later on…)
FLAVOUR I: and LEDLED provide a nice argument for the smallness of masses:standard Yukawa couplings to a singlet fermion who lives in the bulk s
)()(2
v )0( xxM
Mysa
P
DYuk
L ...
)(),(
)0(
V
xyx s
s
originates from
can we test this idea?
then, few might take part in oscillations
but
large mixing angles between and are excluded (SN1987A)
oscillations into disfavoured by both atmospheric and solar data
effects subdominant, if present
)(ns
)(nsa
s)(n
s
if some states are sufficiently light
eV01.0mass)( 2, solatmm
)(ns
(not unconceivable:R ~ 0.02 mm)
Dienes, Dudas, Gherghetta, Arkani-Hamed,Dimopoulos, Dvali, March-Russell, Barbieri, Creminelli, Strumia
Collider bounds on LED:
1KK graviton production in association with a or a jet
)(missing or TEj
2
DM
Esingle KK production
PM
1 rescued by the very
large phase space
combined 95% CL limits on from LEP and Tevatron'DM
2 3 4 5 6
(TeV) 1.45 1.09 0.87 0.72 0.65
2 virtual graviton exchange
sensitive to UV physics: divergent amplitudes already at the tree-level for parametrized in terms of effective operators(or computed in string theory)
2)(ng
RMM
MD
D
P )'(8'
2
reviews: Cheung; Hewett, Spiropulu; Sanders this conf.
Giudice, Strumia
22
TTTT
cc
2
5
fYY ffcc
d=8 (tree-level)
d=6 (one-loop)
energy-momentum tensorT
Y is C-even and singlet under all gauge and global symmetries (flavour universal);
No more d8 operators from fermion-gauge boson sectors alone
2
2
DM
c
42
22
DY
Mc
cut-off scale
present 95% CL limits
TeV3.18
4/1
c
TeV21164
2/1
Yc
dilepton (LEP)diphoton (Tevatron)
contact interaction (LEP)dijet, Drell-Yan (Tevatron)
pepe
pepe
(Hera)
(Hera)
If, naively, then Y gives the strongest bound onDM DMotherwise DD MM TeV1 remember GIM where
Fc Gm /1
Chang, Lebedev, Loinaz, Takeuchi
Giudice, Strumia
Limits on from astrophysics (in TeV)
RMM
MD
D
P )''(''
2)(
=2 =3
31 2.75
454 27
1680 60
)('' DM
SN cooling form KK-g productionSN1987A
Diffuse -rays from decay ofKK-g trapped in NS halo
NS heat excess from KK-gdecay
they are the strongest limits on fundamental scale
bounds rapidly soften for higher
They rely on the (essentially) gapless spectrum of KK gravitons
Hannestad, Raffelt
cosmology reminder
The universe has a standard evolution up to temperatures of order
6)(GeV102)(MeV10 T
above the cooling proceeds mainly by bulk graviton production(instead of standard adiabatic expansion) =2 barely consistent with BBN
T
such a low makes inflation and baryogenesis problematic T
both astrophysical and cosmological problems are eliminated if the spectrum of KK gravitons has a sufficient gap
for instanceevades all the astrophysical bounds of present hottest astrophysical object
MeV100KKm TMeV100
How can we make ? MeV100KKm
1. KK spectrum also depends on the shape of ES, not just from R
2. New relation between and due to warped geometry
in RS set-up the branes carry some energy density and this warps the surrounding ST
2)(22 dydxdxeds Ryk
V
kR
DD
P
k
eM
M
M
)1( 22
in a loose sense, since Vcannot be precisely defined
PM DM
if a large can be obtained with a natural
TeV1kMD PM 110 kR
KK modes are now at and astrophysical and cosmologicalbounds do not apply
TeV/1 R
Randall, Sundrum
Dienes
collider phenomenology
TeV KKm
)1(1 )( nTgM
n
D
(unevenly spaced)
resonance enhancements at hadron colliders in Drell-Yan processesa portion of the parameter space already probed by Tevatron
radion
TeV )11.0( rm
TrMD
1
KK gravitons
large anomalous couplingto gluons. At hadron colliders- production mainly through gluon fusion- decay into dijet or into ZZ if kin. allowed(similar to Higgs. Indeedradion-Higgs mixing possible)no significant bound frompresent data
Up to now
SM fields confined on a brane having vanishing width
strong and e.w. interactionssuccessfully tested only up to
a part of (or all=UED) the SM fields might live in a sized ED
0L
TeV)(OE
1-TeV)(1-TeV)(L
motivations for 1-TeV)(L
early: SUSY breaking via compactificationL
mSUSY2
more recently: solutions to the `little’ hierarchy problem scale e.w.Hm
EW precision tests search for new physics
indirect evidence for a gapbetween the Higgs mass and theEW symmetry breaking scale
Antoniadis
`LITTLE’ HIERARCHY PROBLEM22
22
2
3newtFH mmGm
from the solution to the `big’ hierarchy problem: finite corrections controlledby the mass of some new particle
from EWPT CL95%GeV204Hm
GeV100newm or even lighterexpected (think, for instance to the chargino in constraint MSSM)
modest gap (factor ~ 10) can be filled
1. by a moderate fine-tuning of the parameters in the underlying theory
2. by looking to specific theories where this gap is natural
1-TeV)(L
new light weakly interacting particles: not seen in either direct searches or in EWPT
in ED with new states are expected at the TeV scale
can be protected by either- SUSY or
- gauge symmetry
2Hm
1. SUSYbroken by boundary conditions on an interval of size L
EWSB triggered by the top Yukawa couplings
is finite and calculable in terms of2 parameters (L,M)
including two-loop corrections
t
),( st
Hm
GeV)125110( HmTeV)42(1 L
42 ML
characteristic spectrum mild experimental bounds: momentum conservation along EDpreserved by gauge interactionsas in UED
- no single KK mode production- no 4f operators from tree-level KK exchange
Pomarol, Quiros; Barbieri, Hall, Nomura; Ghilencea, Groot Nibbelink, Nilles;Scrucca, Serone, Silvestrini, Zwirner,…
Appelquist, Cheng, Dobrescu
Barbieri, Marandella,Papucci
2. gauge symmetry: Higgs-gauge unificationYang-Mills theory in D>4gauge group G
MA
D gauge vector bosons
3,2,1,0De ,...,5 4D vector bosons
4D scalars
Example: G = SU(3) (8 independent generators)
A eAaA
aAaeAˆ a
eA
aeA
aeAˆ
aA ˆ
aA ˆ
8,3,2,1a7,6,5,4ˆ a
7,6,5,4ˆ a8,3,2,1aunseen unseen
WZ ,, Higgs
we can eliminate the `unseen’ by compactification on an orbifold
all fields required to have a well-defined parity
the `unseen’ states have no zero modes because they are odd
2Z
2Z
21 / ZS
Manton 1979
4D viewpoint: SU(2)xU(1) gauge symmetry + 1 Higgs doublet
general problems solutions
Higgs embedding Y(H)=1/2usually leads to wrong
- large corrections from branes at y=0,L- choose the right group e.g.
W2sin
25.0sin22 WG
Higgs self-coupling for EWSB D=5: from D-terms if SUSYD6 includes Higgsself-interactions
MNMNFF
absence of quadratic divergences from gauge sector (crucial)
key feature: residual gauge symmetry
aaa AA ˆ5
ˆ5
ˆ5
realistic Yukawa couplingsinteractions of H are universalif minimally coupled
Wilson lines
D=5 forbiddenD=6 absent in specific models
Csaki, Grojean, MurayamaBurdman, Nomura
Von Gersdorff, Irges, Quiros
)(][)0( 0
ˆ5 )(
LfePfy Lj
yAdyi
RifijYuk
La
L
invariant under both local and residual gaugetransformations
YL USU )1()2( aaa AA ˆ
5ˆ
5ˆ
5 [however may reintroduce quadratic divergences for at 1 or 2 loops]
fijy Hm
features:
- naturally light Higgs boson- KK gauge vector bosons of an extended group G- not necessarily KK replica for fermions
remarkable progress towards a realistic model in the last year!
we put fermions here and here
Csaki, Grojean, MurayamaScrucca, Serone, Silvestrini
FLAVOUR II
In ED we have a new tool to understand fermion mass hierarchy:geometry
tdue mmmm ,...,,uscbub VVV
examples
generations are `copies’ inED. FS broken by a non-trivialHiggs VEV
c ty y
several generations may arise as independent zero modes ofa single higher-dimensional fermion.
related to the properties of compactification mechanism unexplained in D=4!
gN
D.B. Kaplan, Arkani-Hamed, Schmaltz, Mirabelli
Dvali, Shifman
Troitsky, Libanov, Nougaev, FrereBiggio, Feruglio, Masina, Perez-Victoria
can we test these ideas?
most stringent bounds from FCNC
KK modes of gauge bosonshave non-constant wavefunctions
sAsgdAdg ssdd)1()1()1()1(
)1()1(ddss gg
after rotation from flavour basis to mass eigenstate basis
...2sin
2
2)1(
stdstdM
g aa
c
dd
2sin)100(/1 TeVOL
Km
Del Aguila, Santiago; Delgado, Pomarol, Quiros; Lillie, Hewett,…
Sub-mm gravity (again)
all previous statements assume that some dynamics stabilizes the radionat the right scale:
1-TeV)1()(
2
DM
xrL
in explicit models of weak scale compactification(not a theorem)
TeV1/1 LM c
eV10 32
P
cr M
Mm
radion couplingto matter mgravity-like
PM
m
observable deviations from Newton’s law at 100 m even for
1-TeV)1(Lradion becomes cosmologically `active’ if
inflation of scalecM
Chacko, Perazzi
Kolb, Servant, Tait
generic problems of ED models with cut-off scale TeV1
potentially large corrections to EW observables, conflict with EWPT
how can we understand approximate B and L conservation?
yrep
yrKp330
33
104.4)(
109.1)(
WMAPeV1
eV105.2 232
ii
atm
m
m
B & L violating operators d>4are allowed by knownlow-energy symmetries
...2
v))((2
2
LHLHL uu
QQQL
B 0 suggest GUTM
gauge coupling unification 002.0118.0)(exp3 Zm 118.0)(3 Zm
SUSY 1-loop LO
01.03 2-loop, thresholds
- the running is log- high sensitive to light particle content- unification conditions at
323
5 YGUTM
approximate B & L conservationgauge coupling unification
natural within `UV desert’
possible, but not a generic feature of IR desert
scale e.w.D1/MR
problematic if TeV1L
especially if complemented by a Grand Unified picture where
- particle classification clarified
- unification condition automatic323
5 Y GUTMat
GRAND UNIFICATION AND EDUrgent problems of conventional 4D GUTs
The Problem: DT splitting
D
du
Tdu
duH
HH
,
,,
GUTM
scale e.w.- fine-tuned in minimal models- baroque Higgs structure in non-minimal ones- usually spoiled by radiative corrections after SUSY breaking or by non-renormalizable operators
p-decay
yrGeVm
Kp T2
17
2
232
10
)(
tan1
tan210)(
Hisano, Murayama, Yanagida;Goto, Nihei
CLyrKp %90109.1)( 33
minimal SUSY SU(5) predictions
Altarelli, Feruglio, Masina
both solved if G=SU(5) is broken by compactification
AaA
aA ˆ
aA ˆ
aA
bosons gauge SMa
SM/)5(ˆ SUa
the zero modes of can be removed by appropriate parity assignment
)1()2()3()5( USUSUSU
aA ˆ
if then, for a 4D observer:
scale e.w.'/1 GUTMR
SU(5) does not exist in 4D!
in SUSY version additionalstates and one more parity
DduH ,
TduH , and parities fixed
from gauge sector
AUTOMATIC DT SPLITTINGKawamura
p-decayAltarelli, FeruglioHebecker, March-Russel
d=5 operators arise from a mass term
such a term is forbidden by a U(1) symmetry characteristicof the bulk action and extendibleto the whole theoryno d=5 (and d=4) p-decay
duHH
3)(
3)(
3)2(
33 )()( hlZ
LOZ mm
130.0...log)(
7
3 23
c
LO
M
GeV
GeVM c
17
15
10
10
Hall, Nomura Contino, Pilo, Rattazzi, Trincherini
Hall, Nomura
gauge coupling unification preserved
test:p-decay dominated by d=6 operators
FFTTM
gcO
c2
2
yrp
3410
KKKeep ,,,,, 0000
uncertainties: mixing angles and cno uncertainties from SUSY breakingRc /1
TcT brane coupling
Hebecker, March-Russel Hall, Nomura
cosmological constant and EDTwo problems
1. why is nearly zero?
2. cosmic coincidence why now? (nothing to say about this here)
1. 4D + generalcovariace
massless gravitonuniversally coupled to all sources
43 eV)10( 4scale) e.w.(
4)( PM
matter
2
1
PN
MG
then vacuum energy curves our space-time
22
PN
MGH
this is what we measure
in D>4 this is not necessarily true: can curve the ED space leaving our space flat
this might occur if depends on the wavelength of the sourceNG
wavelength coupling )(NG
cmH 2810 10 2
1
PM
10H
standard cosmology
2
1
PM
vacuum energy is the sourcewith the largest wavelengtha large does not curveour 4D space time
21
02 )(
PN
MHGH
...)( 2442* RMgxdRgydxdMS Pind
2/1 PN MG )/(1)( 2*
MGN
Dvali, Gabadadze, PorratiDvali, Gabadadze, Shifman
)2(2
2
*2
2
PPP MM
M
MH
here ED are infinite , otherwise a massless 4D graviton exists10HR
gravity modified belowdeparture from Newton potential at the sub- mm scale expected
mM 1001*
eV10 3*
Mabove gravity becomes strong and should be soften e.g. by string theory (production of Regge states)
one testable prediction
- effective field theory necessitates careful treatment - closely related picture derivable from string theory
- related approaches
PMM *
SundrumArkani-Hamed, Dimopoulos, Dvali, Gabadadze
Antoniadis, Minasian, Vanhove
Rubakov, Luty, Porrati, Rattazzi
The fine-tuning is not eliminated but the hierarchy becomes stable
Laurels beckoned us, so we started outWith Nightingale towards a mountain height.While I grappled with the sheer cliffs below,She seized her prize in easy, graceful flight.
What I may perhaps never ever reach, Took but a brief moment for the bird; O Heaven don't be so unjust, I plead, Grant me wings too. Let my prayer be heard. Roland von Eotvos