Supersimmetria, naturalezza e selezione ambientale
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Transcript Supersimmetria, naturalezza e selezione ambientale
Supersimmetria,
naturalezza e
selezione ambientale
G.F. Giudice
N. Arkani-Hamed, G.F.G., R. Rattazzi, in preparation
N. 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)
1
Central problem of particle physics:V H H H
2
H
2
H2 very sensitive to high-energy corrections
3GF
2
2
2
2
2
2
2m
m
m
4m
0.2
W
Z
H
t
2
8 2
m H 10% 1/ 2
max T eV
No large tuning < TeV
115GeV
2H
Can mH ~ 180220 GeV reduce the tuning? NO!
Abuse of effective theories: finite (or log-div)
corrections at remain
˜
Ex.: in SUSY quadratic divergences cancel, but H m
2
2
2
4
Naturalness < 1 TeV
M Z2
Necessary t uning 2
M Z2
28
10
2
M GUT
a dn a ™emiT kciu Q
ros ser pm oc ed ) de sse rpmoc nU ( FF IT
.e rut cip siht ee s ot de dee n e ra
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
search for new physics
n
Cancellation of
Existence of
electron self-energy
+-0 mass difference
KL-KS mass difference
gauge anomaly
positron
charm
top
cosmological constant
CAVEAT
EMPTOR
10-3 eV??
3
Supersymmetry: triumph
of symmetry concept!
• Gauge-coupling unification
• Dark Matter
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• Radiative EW breaking
4
Hierarchy: a problem of criticality
broken phase
unbroken phase
H2
SM
Exact supersymmetry on critical point
Small breaking of supersymmetry MS MPl exp1
5
˜ t2
3GF mt2 m
log
2
˜t
m
2
In supersymmetry:
2
H
less than 10% tuning
Higgs mass
˜t ~
m
300 GeV
2
˜ t2
3GF mt4
m
2
2
m H M Z cos 2
log 2
2
mt
2
m H 114 GeV
˜ t 1 TeV
m
~
The theory is tuned at few % or worse
(not much wrt (MW/MGUT)2~10-28, but it bites into LHC territory)
6
EW breaking computable as a function of soft terms
In natural supersymmetry: MS<<Qc<<MPl and MZ~MS
Little hierarchy only if Qc~MS
7
g 2 g2
2
2
V
H1 H 2
8
2
m H1 m H 2 m32 H1H 2 h.c.
2
1
2
2
2
2
• A measure of the fine tuning
• A characterization of the tuning
8
9
DARK MATTER
Natural 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): m
e
~ > 100
110 GeV (LEP: m
e
GeV)
H-ino, W-ino: annihilation
through gauge bosons (too
fast)
10
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?
11
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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TIFF (Uncompressed) decompressor
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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 revolution
String theory low-energy susy SM
12
A different point of view
Vacuum structure of string
theory
~ 10500 vacua
QuickTime™ and a
TIFF (Uncompressed) decompressor
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(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
13
Not a unique “final” theory with
parameters = O(1) allowed by symmetry
but a statistical distribution
In which vacuum do we live?
Determined by
“environmental selection”
• 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?
I will show two examples relevant to supersymmetry and LHC
14
“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?” )
15
“Mysterium Cosmographicum” gives a geometrical explanation
Sphere
Planetary orbits lie within the only 5
Saturn
Platonic solids that can be both
Cube
Jupiter
circumscribed and inscribed within a
Tetrahedron
Mars
sphere. It well matched planetary distances
Dodecahedron
known at that time.
Earth
Icosahedron
Venus
Octahedron
Mercury
Sphere
We are confident about the anthropic
explanation because we observe a vast
universe with a multitude of stars
The ultimate Copernican
revolution?
16
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)
M S n dMS
dP n
Qc M S
for M S Qc
M Z2
92t 1
2
2
MS
4
n
• Susy prefers to be broken at high scale
• Prior sets an upper bound on MS
Loop factor
< ln MS/Qc>
Susy near-critical
Little hierarchy: Supersymmetry visible at LHC,
but not at LEP (post-diction)
17
18
If and MS scan independently:
MS
1
2
5 10
2
tan
16
• solution to problem
• prediction for and tan
19
A more radical approach:
Split Supersymmetry
SM + gauginos + higgsinos
Squarks + sleptons
at TeV
~
at m
ABANDON NATURALNESS BUT REQUIRE:
• Gauge-coupling unification
• Dark matter
With respect to
ordinary susy:
• no FCNC, no excessive CP
• dim-5 proton decay suppressed
• heavier Higgs boson
20
Gauge-coupling unification as successful (or better)
than in ordinary SUSY
21
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 gaugecoupling 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 c 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
22
Why Supersymmetry?
~
X 1 2m
4
*
*
2
~2 m
~2
~
d
X
X
Q
Q
m
d
X
W
W
M
m
~
Q
g
4
*
~2
d
X
X
H
H
B
m
1
2
2
3
~
d
X
Q
A
m
4
*
~
d
X
H
H
m
1
2
R - invariantsoft terms
(chooseR[ H 1 H 2 ] 0 so that
2
d
H 1 H 2 forbidden)
R - violatingsoft terms
(R[ X ] 0, R - symmetry
broken by FX )
• R-symmetry “splits” the spectrum (Mg~ and mix through renorm.)
• R-invariant dim = 2
R-violating dim = 3
23
Split Supersymmetry determined by susy-breaking pattern
~2
D - breaking Y 1 4 m
4
*
4
~2 m
~2
~2
d
YQ
Q
m
d
YH
H
B
m
Q
1 2
Non renorm.operators
~2
1
m
4
3
d
YQ
A
M*
M*
~2
1
m
4
d
YWW M g~
M*
M*
~2
1
m
4
2
H 1 H 2
d
YD
M*
M*
• Analogy: in SM, L not imposed but accidental. mn small,
although L-breaking is O(1) in underlying theory
• In supergravity, not generated at O(MPl) but only O(MS2/MPl)
~ but only O(m
~2/M )
• Here, M ~ and not generated at O(m)
g
*
24
Unavoidable R-breaking from CC cancellation
z z*
M2
Pl
K
2 3W 2
2 M Pl2 W
V e
F 2
W 0 breaks R - symmetry m3 / 2 e
2
M
M
Pl
Pl
3
m3 / 2
Loopeffects M g~
16 2 M Pl2
Potentially larger effect from anomaly med. M g~
Eq. motion for conformal compensator F m3 / 2
g
K 2
g
F
3M Pl2
In theories where susy breaking is tied to gravity and
supersymmetry is restored in the flat limit, F 0
m33/ 2
g2
M g~
m3 / 2
2
2
2
16 M Pl
16
m3/2 and ~
m are in general independent parameters of SpS
25
How to test Split
Supersymmetry:
• Higgs mass
• Gluino lifetime
• Gaugino couplings
• Electric dipole moments
• Dark Matter
HIGGS MASS
26
ELECTRIC DIPOLE MOMENTS
~ ~
arg (g*u g d* M )
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
27
GAUGINO COUPLINGS
In SUSY, gauge (g) and gaugino ( ~
g) couplings are equal
~
~
g
• Fit of M, , u , gd from c cross
~
section and distributions
At LHC ( g / g -1) = 0.2 - 0.5
~
• H ccfinal states
At ILC (g / g -1) = 0.01 - 0.05
• BR(cc H)
28
GLUINO LIFETIME
Age of the universe
Gamma rays
Nucleosynthesis
Decays outside detector
Gluino hadronizes
• 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
29
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 Mc=mH
• Gravitino induced
Present limit:
10-41 --10-42 cm2
Future sensib.:
10-44 --10-45 cm2
30
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?
31