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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

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Supersymmetry: triumph of symmetry

concept!

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• 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?