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)
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
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 ~ 180220 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
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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 exp1  

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  g2
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=0.1270.010
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)
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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?
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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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
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A different point of view
Vacuum structure of string
theory
~ 10500 vacua
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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?” )
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“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?
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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)
M S n dMS
dP  n 
 Qc  M S
for M S  Qc
M Z2
92t 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)
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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
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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 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
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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
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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
 YWW  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
*
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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
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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
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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 ccfinal states
At ILC (g / g -1) = 0.01 - 0.05
• BR(cc H)
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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
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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 Mc=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?
31