1 supersimmetria, naturalezza e selezione ambientale g.f. giudice n. arkani-hamed, g.f.g., r....
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Supersimmetria, naturalezza e selezione
ambientale
Supersimmetria, naturalezza e selezione
ambientale
G.F. GiudiceN. Arkani-Hamed, G.F.G., R. Rattazzi, in preparationN. Arkani-Hamed, A. Delgado, G.F.G., NPB 741, 108 (2006)A. Delgado, G.F.G., PLB 627, 155 (2005)N. Arkani-Hamed, S. Dimopoulos, G.F.G., A. Romanino,
NPB 709, 3 (2005)N. Arkani-Hamed, S. Dimopoulos, JHEP 0506, 073 (2005)G.F.G., A. Romanino, NPB 699, 65 (2004)
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€
V H( ) = −μ H2 H
2+ λ H
4Central problem of particle physics:
H2 very sensitive to high-energy corrections
€
Λmax = TeVmH
115 GeV
⎛
⎝ ⎜
⎞
⎠ ⎟10%
δ
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 2
No large tuning Λ < TeV
€
δH2 =
3GF
8 2π 22mW
2 + mZ2 + mH
2 − 4mt2
( ) Λ2 = − 0.2 Λ( )2
Can mH ~ 180220 GeV reduce the tuning? NO!
Abuse of effective theories: finite (or log-div) corrections at Λ remain
Ex.: in SUSY quadratic divergences cancel, but
€
δH2 ≈ ˜ m 2
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Cancellation of Existence of
positron
charmtop
10-3 eV??CAVEAT EMPTOR
electron self-energy+-0 mass differenceKL-KS
mass differencegauge anomaly
cosmological constant
Naturalness Λ < 1 TeV
search for new physics
€
Necessary tuning MZ
2
Λ2→
MZ2
MGUT2
≈10−28
Qu
ickTim
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and
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nco
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eco
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Supersymmetry: triumph of symmetry
concept!
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are needed to see this picture.
• Gauge-coupling unification
• Dark Matter
• Radiative EW breaking
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Hierarchy: a problem of criticality
H2
broken phase unbroken phase
SM
Exact supersymmetry on critical point
Small breaking of supersymmetry
€
MS = MPl exp −1 α( )
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In supersymmetry:
€
δH2 =
3GF mt2 ˜ m t
2
2π 2log
Λ˜ m t
€
mH2 = MZ
2 cos2 2β +3GF mt
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2π 2log
˜ m t2
mt2
less than 10% tuning
€
⇒ ˜ m t < 300 GeV
€
mH >114 GeV ⇒ ˜ m t >1 TeV
Higgs mass
The theory is tuned at few % or worse
(not much wrt (MW/MGUT)2~10-28, but it bites into LHC territory)
~
~
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EW breaking computable as a function of soft terms
In natural supersymmetry: MS<<Qc<<MPl and MZ~MS
Little hierarchy only if Qc~MS
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€
V =g2 + ′ g 2
8H1
2− H2
2
( )2
+ m12 H1
2+ m2
2 H2
2− m3
2 H1H2 + h.c.( )
• A measure of the fine tuning
• A characterization of the tuning
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DARK MATTERNatural thermal relic with DMh2=0.1270.010
Quantitative difference after LEP & WMAP
For MS>MZ : neutralino is almost pure state
B-ino: annihilation through sleptons (too slow): me < 110 GeV (LEP: me > 100 GeV)
H-ino, W-ino: annihilation through gauge bosons (too fast)
~~
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DM is possible in “special” regions:
• coannihilation
• Higgs resonance
• “Well-tempered”
or non-thermal
Both MZ and DM can be reproduced by low-energy supersymmetry, but at the price of some tuning.
Unlucky circumstances or wrong track?
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What determines the physical laws?What determines the physical laws?The reductionist’s dream:
Unique consistent theory defined by symmetry properties
(no deformation allowed, no free parameters)
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Could God have made the Universe in a different way? Does the necessity of logical
simplicity leave any freedom at all?
• Monotheistic view God• M-theoristic view 2nd string revolutionString theory low-energy susy SM
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A different point of view
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Vacuum structure of string theory
~ 10500 vacua
(N d.o.f in M config. make MN)
Expansion faster than bubble propagation
Big bang universe expanding like an inflating balloon
Unfolding picture of a fractal universe multiverse
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In which vacuum do we live?
Λ
• Large and positive blows structures apart
• Large and negative crunches the Universe too soon Weinberg
Is the weak scale determined by “selection”? Are fermion masses
determined by “selection”? Will these ideas impact our approach to the final theory?
Not a unique “final” theory with parameters = O(1) allowed by symmetry
but a statistical distribution
Determined by “environmental
selection”
I will show two examples relevant to supersymmetry and LHC
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“A physicist talking about the anthropic principle runs the same risk as a cleric talking about pornography: no matter how much you say you are against it, some people will think you are a little too interested” S. Weinberg
In 1595 Kepler asked the question “Why are there 6 planets?” It seems a proper scientific question ( “Why are there 3 quark families?” )
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Sphere
Cube
Tetrahedron
Dodecahedron
Icosahedron
Octahedron
Sphere
Saturn
Jupiter
Mars
Earth
Venus
Mercury
“Mysterium Cosmographicum” gives a geometrical explanation
Planetary orbits lie within the only 5 Platonic solids that can be both circumscribed and inscribed within a sphere. It well matched planetary distances known at that time.
We are confident about the anthropic explanation because we observe a vast universe with a multitude of stars
The ultimate Copernican revolution?
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Assume mi=ci MS, and MS scans
Qc = MPl f(ci,a) does not depend on MS
MS>Qc <H> = 0, MS<Qc <H> 0
Impose prior that EW is broken (analogy with Weinberg)
€
dP = nMS
Qc
⎛
⎝ ⎜
⎞
⎠ ⎟
ndMS
MS
for MS < Qc
MZ2
MS2
=9λ t
2
4π 2×
1
n
Little hierarchy: Supersymmetry visible at LHC, but not at LEP (post-diction)
• Susy prefers to be broken at high scale
• Prior sets an upper bound on MS
Susy near-critical
Loop factor
< ln MS/Qc>
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If and MS scan independently:
€
MS
≈1
tanβ≈
λ2
16π 2≈ 5 −10
• solution to problem
• prediction for and tan
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A more radical approach: Split Supersymmetry
SM + gauginos + higgsinos at TeV
Squarks + sleptons at m~
ABANDON NATURALNESS BUT REQUIRE:
• Gauge-coupling unification
• Dark matter
• no FCNC, no excessive CP• dim-5 proton decay suppressed• heavier Higgs boson
With respect to ordinary susy:
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Gauge-coupling unification as successful (or better) than in ordinary SUSY
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Not unique solution, however…
• Minimality: search for unification with single threshold, only fermions in real reps, and 1015 GeV < MGUT < 1019 GeV SpS has the minimal field content consistent with gauge-coupling unification and DM
• Splitting of GUT irreps: in SpS no need for new split reps either than SM gauge and Higgs• Light particles: R-symmetry protects fermion masses• Existence and stability of DM: R-parity makes stable• Instability of coloured particles: coloured particles are necessary, but they decay either by mixing with quarks (FCNC!) or by interactions with scale < 1013 GeV
SpS not unique, but it has all the necessary features built in
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Why Supersymmetry?
)by broken forbidden)
symmetry-R 0,](R[ that so 0]R[ (choose
soft terms violating-R soft termsinvariant -R
~
~~
~~~
~1
212
21
21*4
32221
*4
~222**4
2
X
gQ
FHHd
XHH
mHHXd
mAQXdmBHHXXd
mMWWXdmmQQXXd
mX
∫
∫∫∫∫∫
==
=→
=→=→
=→=→
+=
θ
θ
θθ
θθ
θ
• R-symmetry “splits” the spectrum (Mg and mix through renorm.)
• R-invariant dim = 2 R-violating dim = 3
~
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Split Supersymmetry determined by susy-breaking pattern
( )*
2
2124
**
234
*
*
2
~4
*
221
422*4
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~1
~1
~1 operators renorm.Non
~~~
~1 breaking-D
M
mHHYDd
MM
mAYQd
M
M
mMWYWd
M
mBHYHdmmQYQd
mY
g
Q
=→=→
=→
=→=→
+=
∫∫
∫
∫∫
μθθ
θ
θθ
θ
αα
μ
• Analogy: in SM, L not imposed but accidental. m small, although L-breaking is O(1) in underlying theory
• In supergravity, not generated at O(MPl) but only O(MS2/MPl)
• Here, Mg and not generated at O(m) but only O(m2/M*)~ ~
~
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Unavoidable R-breaking from CC cancellation
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2/32
22 22
*
symmetry-R breaks 0 3
Pl
M
K
Pl
M
zz
M
WemW
M
WFeV PlPl =⇒≠
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−=
⎟⎟⎠
⎞⎜⎜⎝
⎛
22
32/3
~16
effects LoopPl
g M
mM
≈⇒
Potentially larger effect from anomaly med.( )
φ
Fg
gM g =⇒ ~
Eq. motion for conformal compensator22/3 3
2
PlM
KmF θ
φ +=
In theories where susy breaking is tied to gravity and supersymmetry is restored in the flat limit, F 0
2/32
2
~22
32/3
1616m
gM
M
mg
Pl ≤≤
m3/2 and m are in general independent parameters of SpS~
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• Higgs mass• Gluino lifetime• Gaugino couplings• Electric dipole moments• Dark Matter
How to test Split Supersymmetry:
HIGGS MASS
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ELECTRIC DIPOLE MOMENTS
g~
arg ( u d M ) g~* *
Exp:
de<2 10-27 ecm
dn<6 10-26 ecm
Yale: de ~10-29 10-31
Sussex: de ~10-30
Los Alamos: de dn
~10-31 10-35
BNL: d ~ 10-24
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GAUGINO COUPLINGS
g~In SUSY, gauge (g) and gaugino ( ) couplings are equal
• Fit of M, , u , d from cross section and distributions
• H final states
• BR( H)
g~ g~
At LHC ( / g -1) = 0.2 - 0.5
At ILC ( / g -1) = 0.01 - 0.05
g~
g~
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• Charged R-hadrons. Time delay & anomalous ionization energy loss. At LHC, M<2.5 TeV. Mass resolution better than 1%
• Neutral R-hadrons. Tagged jet M<1.1 TeV. Once tagged, identify gluino small energy deposition
• Flippers. Difficulty in tagging
• Gluinonium. M<1 TeV, direct mass reconstruction
• Stopped gluinos. Possibility of measuring long lifetimes
GLUINO LIFETIME
Gluino hadronizes
Age of the universe
Decays outside detector
Nucleosynthesis
Gamma rays
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DARK MATTER
• Higgsino =1.0--1.2 TeV• W-ino M2=2.0--2.5 TeV
• B-ino/Higgsino M1~
• B-ino/W-ino M1~M2
• Higgs resonance M=mH
• Gravitino induced
Present limit: 10-41 --10-42 cm2
Future sensib.: 10-44 --10-45 cm2
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CONCLUSIONS
• Supersymmetry is still the best candidate to overthrow the SM, but it suffers from tunings at the level of %
• Absence of new discoveries at LEP, failure to explain the cosmological constant, and developments in string landscape suggest a possible change of approach to the final theory
• Can we test “anthropic” solutions?