The hierarchy problem - Indico

The hierarchy problem
(On the origin of the Higgs potential)
Electroweak symmetry breaking (EWSB) in the SM
is triggered by the Higgs VEV:
1 2 2 1 4
V (h) = − µ h + λh
2
4
λ
2
2
2
4
2
38
µ = λv = 2 4MW ∼ 10 GeV << MP ∼ 10 GeV
g
2
2
Why so different?
Even worse, at the quantum level, scalar masses
are extremely sensitive to heavy states
h
h
1
2
M
∼
2
16π
mass of the particle
in the loop
Not the same situation for fermions or gauge bosons
➠ gauge symmetries can protect them
No symmetry in the SM protects the Higgs mass
Not a singlet if
ΨR transform:
ΨR → eiθ ΨR
vs
2
µ |H|
{
mΨ̄L ΨR
{
In general:
2
Always a singlet
under phase
transformations
(chiral symmetry)
Expected: µ ∼ heavier scale² ~ MGUT², MP², Mstring²
2
➥ This is the hierarchy problem
Let me emphasize that is not a problem
of consistency but of naturalness
Example:
Fine-tune system
c ∂t
the magnetic field is frozen, whereas it is expelled. This implies that superconductivity will be d
Analogy
with Superconductivity
magnetic field H such that
c
Hc2 (T )
fs (T ) +
= fn (T ) ,
8π
EWSB
Breaking of U(1)EM
where f (T ) are the densities of free energy in the the
phase at zero magnetic
−superconducting
−
Higgs Modelof free energyGL
= of�ethe critical
e �magnetic field with temperature w
in theModel
normal phase. The�h�
behavior
s,n
to be parabolic (see Fig. 2)
Give the GL Model a
good description
of superconductors?
B
�
Hc (T ) ≈ Hc (0) 1 −
�
T
Tc
�2 �
.
N phase
B
H
c (T)
______
c1
H c (0)
�h� = 0
0.8
0.6
0.4
0.2
SC phase
�h� =
� 0
0.2
FIG. 2 The critical field vs. temperature.
0.4
T
___
0.6
0.8
1c
T
1.2 Tc
T
∂t
1c∂B
∇∧E=−
,
c
∂t
the magnetic field is frozen, whereas it is expelled. This implies that superconductivity will be d
Analogy
with
Superconductivity
magnetic
field
H
such
that whereas it is expelled. This implies that superconductivity will be dest
the magnetic field is frozen,
c
magnetic field Hc such that
Hc2 (T )
fs (T ) + 2
= fn (T ) ,
EM
Hc8π
(T )
fs (T ) +
= fn (T ) ,
8π
where fs,n (T ) are the densities of free energy in the the
phase at zero magnetic
−superconducting
−
of where
free energy
thethe
normal
phase.
Theenergy
behavior
of the superconducting
critical magneticphase
field with
temperature
fs,n (Tin
) are
densities
of free
in the
at zero
magnetic fiew
energy in
theFig.
normal
to ofbefree
parabolic
(see
2) phase. The behavior of the critical magnetic field with temperature was
to be parabolic (see Fig. 2)
�
� �2 �
�
T�2 �
�
Hc (T ) ≈ Hc (0) 1 − T
.
T
c
Hc (T ) ≈ Hc (0) 1 −
.
Tc
EWSB
Breaking of U(1)
Higgs Model
GL Model �h� = �e e �
B
Give the GL Model a
good description
of superconductors?
N phase
B
H
c (T)
______
H
1
c (T) c
______
H c (0) 1
H c (0)
0.8
0.8
NO, it only works close
0.6
0.6
to the critical line
0.4
0.4
only there �h� is small and it
makes sense to Taylor-expand
the potential:
�h� = 0
SC phase
�h� =
� 0
0.2
0.2
0.2
0.2
0.4
0.4
V (h) = m |h| + λ|h| + · · ·
2
2
FIG.
Thecritical
criticalfield
fieldvs.
vs. temperature.
temperature.
FIG.
2 2The
4
T
T___
___
0.6
0.6
0.8
0.8
Tc
11
1.2
1.2Tc Tc
T
Possibilities that theorists envisage
to tackle the Hierarchy Problem:
1) Supersymmetry:
Protecting the Higgs mass by a symmetry
2) Composite Higgs: The Higgs is not elementary:
As in superconductivity: h ~ ee
or QCD: pions ~ qq
3) Large extra dimensions:
Gravity strong at the EW-scale: Λ ~ Mstring ~ TeV
➥ In all cases New Physics at ~TeV
Strong motivation for the LHC !
Supersymmetry
Following notation and formulae of
“A Supersymmetry Primer”, Stephen P. Martin
(hep-ph/9709356)
We want a symmetry to protect the Higgs mass:
Idea:
Scalar
symmetry trans.
It exists, it is a Supersymmetry:
Simplest case:
Φ → Φ + δΦ
Ψ → Ψ + δΨ
since fermion masses
protected by chiral
symmetry
Ψ = Majorana fermion
Φ = Complex scalar
1
2
∂Ψ
L = |∂µ Φ| + i Ψ̄/
2
Invariant under:
Fermion
δΦ → ξ¯ (1 − γ5 )Ψ
δΨ → i(1 − γ5 )γ µ ξ ∂µ Φ
The scalar must be massless!!
Parameter of the trans.
being a Majorana fermion
from a very heavy fermion are canceled by the two-loop effects of some v
unately, the cancellation of all
such contributions to scalar masses is not onl
†
lly
complex
objects,
so
Q
(the
hermitian
conjugate
of
Q)
is
also
a
Supersymmetry
Algebra
y unavoidable,
once we merely assume that there exists a symmetry relating fer
†
Q are fermionic operators, they carry spin angular momentum 1/
aand
supersymmetry.
(Maximal
extension
of
Poincare
in
a
QFT)
metry
must
be
a
spacetime
symmetry.
The
possible
formsstate,
for such
sym
mmetry transformation turns a bosonic state into a fermionic
and vice
m generates
field theory
are
highly restricted
by
the
Haag-Lopuszanski-Sohnius
at
such
transformations
must
be
an
anticommuting
spinor,
with
Minimal SUSY (N=1): One extra generator Q
ula theorem [4]. For realistic theories that, like the Standard Model, h
|Fermion!, pieces Q|Fermion!
= |Boson!. under the gau
s whoseQ|Boson!
left- and=right-handed
transform differently
ty of parity-violating
interactions,
thishermitian
theorem implies
that
theisgenerat
ntrinsically
complex objects,
so Q† (the
conjugate
of Q)
also a
Schematic
form:
gebra
ofand
anticommutation
and
commutation
relations
with momentum
the schema1
cause
Q
Q† are fermionic
operators,
they
carry
spin
angular
[Q, Mµν ] = Q
ersymmetry must be a spacetime
symmetry.
The possible forms for such sym
†
µ
} = Prestricted
,
quantum field theory{Q,
areQhighly
by the Haag-Lopuszanski-Sohnius
n-Mandula theorem [4].
{Q,For
Q}realistic
= {Q† , theories
Q† } = 0,that, like the Standard Model,
µright-handed
µ pieces
†
fermions whose left- and
differently under the ga
[P , Q] = [P , Q ] = transform
0,
possibility of parity-violating interactions, this theorem implies that the genera
fy
an algebra of
anticommutation
and commutation
relations
the schema
-momentum
generator
of spacetime
translations.
Here with
we have
ruthl
† ; after developing some notation we will, in section 3
dicesQon
Q
and
Q
†
commutes with P² {Q,
andQany
generator
of the gauge symmetries:
}=
P µ,
eqs. (1.6)-(1.8) with indices restored.† In† the meantime, we simply not
{Q, Q} = {Q , Q } = 0,
the right-hand
side ofand
eq.Boson
(1.6)
ishave
unsurprising,
sinceand
it transforms
The Fermion
masses
charges unde
µ
µ equal
†
[P , Q] †= [P , Q ] = 0,
as a spin-1 object while Q and Q on the left-hand side each transform a
Minimal Supersymmetric SM (MSSM)
Imposing supersymmetry to the SM ➡ MSSM
The spectrum is doubled:
SM fermion ➡ New scalar (s-”...”)
SM boson ➡ New majorana fermion
(“ ...“-ino)
... but not yet realistic:
The model has a quantum anomaly (due to the Higgsino)
and the down-quarks and leptons are massless
Extra Higgs needed
➡ Two Higgs doublets:
Hu : (1, 2, 1)
➞ give mass to the up quarks
Hd : (1, 2, −1)
➞ give mass to the down quarks
and leptons
+ two Higgsino doublets:
� u : (1, 2, 1)
H
� d : (1, 2, −1)
H
Names
squarks, quarks
(×3 families)
MSSM
spin 0 Spectrum
spin 1/2 SU (3)C , SU (2)L , U (1)Y
Q
u
Squarks
d
sleptons, leptons
L
Sleptons
!L d!L )
(u
(uL dL )
( 3, 2 , 16 )
†
uR
†
dR
( 3, 1, − 23 )
(ν! e!L )
(ν eL )
!∗R
u
d!∗R
e!∗R
(×3 families)
e
Higgs, higgsinos
Hu
(Hu+ Hu0 )
NamesHd
−
0 H1/2
(Hspin
d
d )
gluino, gluon
g!
bino, B boson
!0
B
1
( 3, 1, 3 )
1
( 1, 2 , − 2 )
†
eR
!+ H
! 0)
(H
u
u
!0
spin
(H
d
g
( 1, 1, 1)
( 1, 2 , + 12 )
Higgsinos
SU (2)
1! − ) SU (3)C ,
H
d
U1(1)
Y
( 1, 2L,, −
)
2
( 8, 1 , 0)
hiral supermultiplets in the Minimal Supersymmetric Standard Model. Th
" ± are
" 0left-handed
Gauginos
scalars, and
the spin-1/2
W
W
winos,
W bosonsfields
W ± W 0 two-component
( 1, 3 , 0)Weyl fermio
B0
( 1, 1 , 0)
ifferent reason: because of the structure of supersymmetric theories, only a
1) Superpart.
interact
intopairs
multiplet
can Gauge
haveR-parity
the
Yukawa
necessary
to give
masses
charge
Table
1.2:
supermultiplets
in the Minimal
Supersymmetric
Standard
Mo
particles:
= 1 couplings
2) have
Lightest
stable ne
harm, superpartners:
top), and only R-parity
a Y = −1/2
the superpart.
Yukawa couplings
= -1 Higgs can
!0
H
u
!0
H
u
3(
!0
H
u
i
i
i (a)
i
∗ y jkn and (b)
plings:
(a) (scalar)3 interaction
vertex M
(c)in
(d)
(e)
(b)
ij and (d) conjugate fermion mass term
nigure
mass
term
M
3 interaction
∗ y jkn and (b)
†
†
†
† (a) !
3.2:
Supersymmetric
dimensionful
couplings:
(scalar)
vertex
M
∗
!
!∗ ji
in
!
t
t
t
t
t
t
t
t
t
t
t
t
j
j
j
L
L
L
L
j
j
L
L
R
R
i
i
j . conjugate interaction
R
R i R
R i
in y ∗ , (c) fermion
ij and (d) conjugate
he
M
mass
term
M
fermion
mass
term
(a)
(b)
(c)
j ∗(a)
(d)
(e)
k k j (b) jkn k ∗ kj (c)
Mij , and (e) scalar
M .
(a) squared-mass term
(a) Mik(b)
(b)
(c)
an
(e) ! i0
Hu
wo
Hu
i
i
(c)
(c) (a)Yukawa
(d)and its “supersymmetrizations”
(c) (a)
(d) (c), (e)
(e) all of
(a)
The (b)
top-quark
Yukawa
coupling
and itscoupling
“supersymmetrizations”
(b),
all of gauginos
Figure 5.1:
The(b)
top-quark
(b), (c),
re
t
i
c
.se
strength yt .
3 interaction
∗ y jkn and (b)
3 interaction
∗ y jkn vertex
e 3.2: Supersymmetric
dimensionful
couplings:
(a) (scalar)
Min
metric
dimensionful couplings:
(a) (scalar)
vertex
Min
and (b)
in y ∗ , (c) fermion
ij and (d) conjugate fermion mass term
∗ , (c) fermion
ij mass
onjugate
M
term
M
tion
M in yinteraction
mass
term
M
and
(d)
conjugate
fermion mass term
jkn
jkn
of the gauge
(3)of
color
and SU
isospin]
eq. family
(5.1) are
space.[SUAll
gauge
[SU(2)
(3)
colorkj
and SUand
(2)Lfamily
weak indices
isospin]inand
indices in eq. (5.1) are
C the
LCweak
∗
∗
kj
and
(e)
scalar
squared-mass
term
M
M
.
uared-mass
term
M
.
αβ , where
αβ , where
iktraditionally
The “µ suppressed.
term”,
as it M
is ik
traditionally
called,
can
be written
out(d)
ascan
µ(H
slepton,
squark
The
“µ
term”,
as
it
is
called,
be
as
µ(H
)
(H
)
!
u )written
α (Hd )β !out
slepton,
squark
u
α
d
β
(a)
(b)
(c)
(e)
(c) αβ(f)
(d)
(e)
(g)
(h) (f)
(i) (g)
(h)
fe
(d) k0
(d
dle
Huk0
j
giF
(c)
st
Getting them from “supersymmetrization”:
j
j
j
p
nil
Type of interactions
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a oc s c3 tid oc
o ro).s
o
o
.y
r
itr a hc eru ceri
r
s
h
o
n
o
fi
u
e
a
r
t
o
.q
n
h
oi
m
F
Figure 3.2: Supersymmetric dimensionful couplings:
(scalar) inter
∗ y jkn and (a)
: Supersymmetric dimensionful couplings: (a) (scalar)3 interaction
vertex
M
(b)
∗ , (c) fermion
in
the conjugate interaction
M in yjkn
mass term M ij and (d)
in
∗
ij
ate interaction M yjkn, (c) fermion
mass term M and (d) conjugate fermion
mass term
∗
∗
kj
∗M
ijkj, .and (e) scalar squared-mass term Mik M .
e) scalar squared-mass
term
M
M
ikj
j
j
i
i i
i
dn
i
ug
i
no
2.3
)i(
opagator; note the directions of the arrows in Figure 3.2c,d. There is no such arrow-reversal
r
wo
j
to tie together
SU (2)
weak
isospinSU
indices
α, β =isospin
1, 2 inindices
a gauge-invariant
way.
Likewise,
! is used
toL tie
together
(2)L weak
α, β = 1, 2 in
a gauge-invariant
way. Likewise,
j
αβ , where
ia
yu QHu can
written
outu Supersymmetric
as
(H
iFigure
=(H
1,u2,)β33.3:
is ,aSupersymmetric
familyi index,
uyu QH
canuiabe(ywritten
out
as
(yu )i j Qjαa
!αβ
where
= 1, 2, 3 is gauge
a familyinteraction
index,
the be
term
u )i Qjαa
u )βu! interaction
Figure
3.3:
gauge
vertices.
ve
representation
SUrepresentation
(3)C .
2, 3 is a color
which
lowered
(raised)
3 (3) (raised)
of SU (3)C .
and aindex
= 1, 2,
3 is ais color
index
whichinisthe
lowered
in the 3of(3)
erm in eq. (5.1)
the supersymmetric
version
of the Higgsversion
boson mass
the Standard
The µis term
in eq. (5.1) is the
supersymmetric
of theinHiggs
boson mass in the Standard
∗
ure
3.1cModel.
is exactly
the
needed
to cancel
the
quadratic
quantum
unique,
because
Hu∗ Hspecial
or Hd∗type
Hterms
forbidden
ind∗the
which
must
beinneeded
tion
of
Figure
exactly
of the
special
type
to cancel
ubecause
Itterms
is of
unique,
H
H
Hisd superpotential,
are
forbidden
indivergences
the superpotential,
which
must bethe qua
d are
u Hu or3.1c
sthe
to chiral
scalar
masses,
as
in(g)
the
Introduction
andineq.
(1.11)].
superfields
(ordiscussed
equivalently
in the
scalar
treated
asFigure
complex
variables,
ascomplex
analytic
in
chiral
superfields
(or
equivalently
inmasses,
the scalar
treated
as
variables,[compare
as
(f)the
(h)[compare
(i) 1.1,
corrections
tofields)
scalar
asfields)
discussed
the
Introduction
gauginos
ction
3.2.(a)
We
can
also
see 3.2.
fromWe
the
form
of
eq.
(5.1)
bothof
Heq.
Hinteractions
are(d)
needed
order
3.2 shows
the
only
interactions
corresponding
toshows
renormalizable
supersymmetric
vertices
u and
dand
shown
in
section
can
also
see
from
the
form
(5.1)
why
both Hin
and
Hd are
needed
order
u corresponding
(c)
(e) to in
3.2why
the
only
renormalizab
(h) Figure 3.3:(b)
(i)Figure
Supersymmetric
gauge
interaction
vertices.
(b)
(c)
(d)
(e)
2the
3 the
awa
masses,
all ofthus
quarks
and
leptons.
Since
to giveand
Yukawa
couplings,
and
masses,
to
all
of
the
quarks
andsuperpotential
leptons.
Since
superpotential
ing couplings,
dimensions
ofthus
[mass]
and to[mass]
.
First,
there
are
(scalar)
couplings
in Figure
3.2a,b,
2 . the
with
coupling
dimensions
of
[mass]
and
[mass]
First,
there are (scala
∗
∗
ij
ijk
alytic,
the
uQH
Yukawa
terms
cannot
be
replaced
by
something
like
uQH
.
Similarly,
Higgs
must
beu analytic,
thesuperpotential
uQHu Yukawa mass
terms parameters
cannot be replaced
byYukawa
something
like uQHyd . ,Similarly,
etric gauge
interaction
vertices.
d
entirely
determined
by
the
M
and
couplings
∗
∗
Higgs
which
are
entirely
determined
superpotential
massanalogous
parameters M
on ofeLH
Figure
3.1c
iscannot
exactly
of the
special
type
needed
tolike
cancel
thesomething
quadratic
divergences
quantum
∗ inand
∗ . The
and
be
replaced
by
something
dQH
and eLHby
. the
The
analogous
d terms
dQH
and
eLH
terms
cannot
be
replaced
by
like
dQH
eLH
the
u
u
d
d
u
u scalars
d by thetosecond
and third
termsasin
eq. Introduction
(3.50).byThe
propagators
of
the
and
orrections
scalar
masses,
asa discussed
inindicated
the
[compare
Figure
1.1,
and fermions
eq. but
(1.11)].
the
second
and
third
terms
in
eq.
(3.50).
The
propagat
plings would
be
allowed
in
general
non-supersymmetric
two
Higgs
doublet
model,
are
gauginos
Yukawa
couplings
would
be
allowed
in
a
general
non-supersymmetric
two
Higgs
doublet
model,
but
are
ij
Higgsino
are
constructed
inquadratic
the
usualSo
way
using
the
fermion
mass
M
andinvoking
scalar vertices
squared
mass
Figure
3.2
shows
the
only
interactions
corresponding
toH
renormalizable
and
supersymmetric
eory
to
cancel
the
divergences
in
quantum
y needed
the
structure
of
supersymmetry.
we
need
both
and
H
,
even
without
the
in
the
theory
are
constructed
in
the
usual
way
using
fermion
u
d
forbidden by the structure
of supersymmetry.
So we need 3both Hu and Hd , even without the
invoking
the mass
ij
2
ith
coupling
dimensions
of [mass]
andand
[mass]
.kj
First,
there
couplings in Figure
3.2a,b, in the
The
fermion
mass
terms
M
each
leadare
to(scalar)
a chirality-changing
∗M
ij insertion
ased
on
anomaly
cancellation
mentioned
inij
the
Introduction.
he
Introduction
[compare
Figure
1.1,
and
eq.
(1.11)].
M
M
.
The
fermion
mass
terms
M
and
M , each lead to a chira
argument
based
on
anomaly
cancellation
mentioned
in
the
Introduction.
ik
hich are entirely determined by the superpotential
mass parameters M ij and Yukawa couplings y ijkij
Up to scalar trilinear and quartics:
(b)
(c)
(d)
(e)
i
j
i
(f)
(c)
j
(g)
k
(d)
(h)
(i)
Figure
3.3:MSupersymmetric
gauge
vertices.
a) Gaugino
mass
scalarinteraction
squared
a ; (b) non-analytic
and (d) scalar cubic coupling aijk .
is exactly of the special type needed to cancel the quadratic divergences in quantum
f a masses,
simple factor
of the gauge
group,
then there[compare
are
ar
as discussed
in the
Introduction
Figure 1.1, and eq. (1.11)].
mass
between the corresponding
ψa
ws
theterms
only interactions
correspondingfermions
to renormalizable
and supersymmetric vertices
mensions of [mass] and [mass]2 . First, there are (scalar)3 couplings in Figure 3.2a,b,
determined
by the superpotential mass parameters M ij and Yukawa couplings y ijk ,
a
λ ψa + c.c.
(4.3)
e second and third terms in eq. (3.50). The propagators of the fermions and scalars
constructed
the does
usualnot
way
using
the represenfermion mass M ij and scalar squared mass
field
content, in
which
have
adjoint
ij and M
rmion
terms
Mto
leadoftothe
a chirality-changing insertion in the
(4.1) ismass
usually
taken
be the general
ij eachform
me
exceptions,
[54]-[65].
or; interesting
note the directions
ofsee
therefs.
arrows
in Figure 3.2c,d. There is no such arrow-reversal
etry, because
they with
involve
onlysupersymmetry;
scalars and gauginos
gator
in a theory
exact
as depicted in Figure 3.2e, if one treats
soft terms
Lsoft
capableinof the
giving
masses to all
-mass
terminas
an are
insertion
propagator,
the arrow direction is preserved.
gauge
fermions ininchiral
supermultipletstheory. Figures 3.3a,b,c occur only
ws
thebosons
gaugeand
interactions
a supersymmetric
ses Mis
always allowed
by gauge for
symmetry.
a are
roup
non-Abelian,
for example
SU (3)CThe
color and SU (2)L weak isospin in the
transform
in are
complex
conjugate representations
of which derive from the first term
.3a
and 3.3b
the interactions
of gauge bosons,
lar this is true of course when i = j, so every scalar
he MSSM these are exactly the same as the well-known QCD gluon and electroweak
Hu [GeV]
Higgs potential, for a typical case with tan β ≈ − cot α ≈ 10.
Aarked
contour
of the
potential,
for a typical
with tan β ≈
by map
+, and
theHiggs
contours
are equally
spacedcase
equipotentials.
0
0
0
mon,
of the
potential
is
marked
by
+,
and
the
contours
are
equally
spaced
with Hu /Hd ≈
10, correspond
to the mass works?
eigenstate h , while
How
supersymmetry
0 /H 0 ≈ 10, correspond to the mass eige
ong
the
shallow
direction,
with
H
0
u
responds to the mass eigenstate H d.
0
l steeper direction corresponds to the mass eigenstate H .
m2h0 ) =
t
0
h
+
t̃
t̃
h0
+
h0+ h0
+
t̃
t̃
+ h0
{
SSM
lightesttoHiggs
mass lightest
from top-quark
andfrom
top-squark
one-loop
ontributions
the
MSSM
Higgs
mass
top-quark
and top-s
Fermion loop
Boson loop
due to soft
supersymmetry
breaking,
leads tobreaking,
a large positive
complete
cancellation,
due to soft
supersymmetry
leads to a
m
in the
limit
vy2h0 top
squarks.
μ²of=heavy
+ A top squarks.
μ² = - A
onally
to bethat
negative;
−π/2 <mα <
0 (provided
m
gative;chosen
it follows
−π/2it<follows
α < 0that
(provided
>
m
).
The
0
Z
A
smass
for couplings
of Higgs
the mass
eigenstate
scalarsModel
to the quarks
Standard
Mo
eigenstate
scalars
to theHiggs
Standard
and
he
electroweak
vector
bosons,
as
well
as
to
the
various
sparticles,
have
b
μ
²
total
=
0
bosons, as well as to the various sparticles, have been worked out
f. [182, 183].
Its not the first time that symmetries
force doubling the known spectrum:
Relativistic quantum field theories:
Particle ➞ Antiparticles
Made the electron-mass corrections not linearly divergent:
e−
γ
e+
e−
e−
γ
e−
−iδme + . . . = (−ie)2
�
�
d k −i γ i(� p− � k + me )γµ
(2π)4 k 2
(p − k)2 − m2e
4
µ
∆me ∝ me
•
•
�
The second diagram is the correct interpretation of the contributions
from Ep − Ek < 0
Note this represents an interaction with virtual e+e- pairs in the vacuum.
e possible to have gauged discrete symmetries that do not owe their exact conse
g continuous gauged symmetry, but rather to some other structure such as can
It is also
possible
that R-parity is broken, is
or isexact:
replaced by some alternative d
But
if supersymmetry
will briefly consider these as variations on the MSSM in section 10.1.
MF = MB ➡ e.g. Me = Mẽ
persymmetry breaking in the MSSM
It must be broken to give masses to the superpartners
description of the MSSM, we need to specify the soft supersymmetry breaking
Supersymmetry
breaking
“softterms
terms”:
learned
how to write down
the mostmust
generalafford
set of such
in any supersym
(terms
not spoil
good UV properties of the Susy)
g this recipe
tothat
the do
MSSM,
we the
have:
LMSSM
soft
$
1!
#W
# + M1 B
"B
" + c.c.
= − M3 g"g" + M2 W
2!
"
"
" d−"
" d + c.c.
"
e ae LH
− u au QHu − d ad QH
$
†
†
"
"
2 "
†
2
2
2
2 "†
"
"
"
"
"
−Q mQ Q − L mL L − u mu u − d md d − e me e
− m2Hu Hu∗ Hu − m2Hd Hd∗ Hd − (bHu Hd + c.c.) .
"†
+µH̃u H̃d
36
for 3 families, more than100
terms are possible!!
Hu [GeV]
gs potential, for a typical case with tan β ≈ − cot α ≈ 10.
of the
potential,
for a typical
with tan β ≈ − co
dtour
by map
+, and
theHiggs
contours
are equally
spacedcase
equipotentials.
0
0
0
he
potential
is
marked
by
+,
and
the
contours
are
equally
spaced equi
with Hu /Hd ≈ 10,How
correspond
to the mass eigenstate
h , while
supersymmetry
works?
0 /H 0 ≈ 10, correspond to the mass eigenstat
he
shallow
direction,
with
H
0
u
d.
onds to the mass eigenstate
H
(including soft-masses) 0
per direction corresponds to the mass eigenstate H .
=
t
0
h
+
t̃
t̃
h0
+
h0+ h0
+
t̃
t̃
+ h0
{
lightesttoHiggs
mass lightest
from top-quark
andfrom
top-squark
one-loop
butions
the
MSSM
Higgs
mass
top-quark
and top-squar
Fermion loop
Boson loop
elete
to soft
supersymmetry
breaking,
leads tobreaking,
a large positive
cancellation,
due to soft
supersymmetry
leads to a larg
n the
limit
op
squarks.
μ²of=heavy
+ A top squarks. μ² = - A + mstop² B
ye;chosen
to bethat
negative;
−π/2 <mα <
0 (provided
m A0 >
it follows
−π/2it<follows
α < 0that
(provided
>
m
).
The
0
Z
A
couplings
of Higgs
the mass
eigenstate
scalars
to the quarks
Standard
Model q
Superpartners
expected
eigenstate
scalars
to theHiggs
Standard
Model
and
μ²as
totalwell
~ masstopto² the various sparticles, have been w
ctroweak
vector
bosons,
around
~ 100out
GeV
ns, as well as to the various sparticles, have
been vworked
2, 183].
Constraints on superpartner masses
from flavor physics:
Breaking of lepton
symmetry:
γ
!R
µ
µ−
γ
"−
W
e!R
!
γe−
ν!µ −ν!e
µ−
B
"
W
!R
µ
e!R
(a)
(b)
−
−
−
!−11
ν!µ toν!ethe proc
µFigure
µ
B
e
5.6: Some of the diagrams that contribute
ẽ
µ̃
flavor-violating soft supersymmetry breaking parameters (indica
(b) of m2 , m
contribute to(a)
constraints on the off-diagonal elements
e
Exp: BR(µ → eγ) < 10
➡ m �m
up to 1% - 0.1%
Large contributions
_
to K-K mixing:
Figure 5.6: Some
that contribute
s̃∗R ofd˜∗Rthe diagrams
s̃∗R d˜∗R to the d¯pro
d¯
s̄
s̄
flavor-violating soft supersymmetry breaking parameters (indic
2, m
contribute to
constraints
on
the
off-diagonal
elements
of
m
!
!
g
g
e
g!
g!
s̃R
s̃∗Rd˜R d˜∗R
s̄ d
g!
(a)
d¯s
g!
ds̃˜L∗
s̄d
R
g!
(b)
sd¯
R
g!
Figure 5.7: Some of the diagrams that contribute to K 0 ↔ K
˜R s̃R
˜L s̃L
d
d
s
s b
d
d
violating soft supersymmetry breaking parameters (indicated
constraints on the off-diagonal elements of (a) md2 , (b) the comb
(a)
➡
s̃d˜L∗
(b)
Figure 5.7: Some of the diagrams that contribute to K 0 ↔ K
! is nearly a mass eigenstate. This result is to be compa
ms̃ �violating
m
thed˜binosoft
B
supersymmetry breaking
parameters (indicated
−11
limit Br(µon→the
eγ)off-diagonal
fromof[106].
So,
if the
right
2 , (b)
exp < 1.2 × 10
constraints
elements
(a)
m
the
com
2
d
up to 0.1% - 0.001%
m were “random”, with all entries of comparable size, then th
Soft terms must be generated in a clever way
Most interesting possibilities:
1) Gauge mediation
2) Gravity/Moduli/Extra-dim mediation
The famous scenario “minimal sugra”
not a model, just an Ansatz:
At Q=MGUT
At Q=MZ
{
All gaugino masses equal = M1/2
All scalar masses equal = M0
All trilinear equal = A0
➥ Why?
600
Mass [GeV]
500
Hd
(µ
2
2 1/2
+m0)
Hu
400
M3
300
M2
m1/2
M1
200
squarks
100
0
2
m0
sleptons
4
6
8
10
12
14
Log10(Q/1 GeV)
16
18
I don’t know,
but experimentalists
like it a lot!
1) Gauge mediation
New sector
Susy breaking sector
gauge bosons
MSSM
Gauge interactions are “flavor blind”:
Universal masses for squarks/sleptons with equal charges
~
dL
8
tan" = 3
Very predictive (in the minimal case).~t
~
6
Just calculate loops:
g
~
uR
µ<0
~
m / M1
1
!FS "
the MSSM gaugino masses
metry breaking models come
ng virtual messenger parti-
! W
" , g̃
B,
gaugino masses
VEVs, one finds quadratic mass terms in the potential for the messenger
= |y2 !S"|2 (|!|2 + |!|2 ) + |y3 !S"|2 (|q|2 + |q|2 )
$
2
order Mmess ∼ yI "S# for I = 2, 3. The running mass parameters can then be RG-evolved down to the
electroweak scale to predict the physical masses to be measured by future experiments.
The scalars of the MSSM do not get any radiative corrections to their masses at one-loop order.
The leading contribution to their masses comes from the two-loop graphs shown in Figure 6.4, with
L
the messenger fermions (heavy solid lines) and messenger scalars (heavy dashed lines) and ordinary
gauge bosons and gauginos running around the loops. By computing these graphs, one finds that each
Rgiven by:
MSSM scalar φi gets a squared mass
Depends on 3 parameters:
1) μ-term: Higgsino mass
2) Susy-breaking scale: F
3) Scale where the soft-terms
are induced: M
+ quartic terms.
(6.49)
presents supersymmetric mass terms that go along with eq. (6.44), while
ft supersymmetry-breaking masses. The complex scalar messengers !, !
matrix equal to:
%
s |y2
|y2 !S"|2
−y2 !FS "
!S"|2
−y2∗ !FS∗ "
|y2 !S"|2
&
t the effect of supersymmetry breaking is to split each messenger super-
m2fermions = |y3 !S"|2 ,
m2scalars = |y2 !S"|2 ± |y2 !FS "| ,
m2scalars = |y3 !S"|2 ± |y3 !FS "| .
(6.51)
(6.52)
apparent in this messenger spectrum for !FS " =
$ 0 is communicated to
radiative corrections. The MSSM gauginos obtain masses from the 1-loop
Figure 6.3. The scalar and fermion lines in the loop are messenger fields.
tices in Figure 6.3 are of gauge coupling strength even though they do not
e Figure 3.3g. In this way, gauge-mediation provides that q, q messenger
no and the bino, and !, ! messenger loops give masses to the wino and
-loop diagrams, one finds [159] that the resulting MSSM gaugino masses
Ma =
αa
Λ,
4π
(a = 1, 2, 3),
(6.53)
~
u
(6.54)
m2φi
!"
~
~g
g
2
= 2Λ
α3
4π
#2
~
t1
C3 (i) +
"
α2
4π
#2
~" #
t1α1 2
C2 (i) +
4π
$
C1 (i) ,
N=
=5
1
N
µ<
<0
0
µ
(6.55)
with the quadratic Casimir invariants Ca (i) as in eqs. (5.27)-(5.30). The squared masses in eq. (6.55)
are positive (fortunately!).
The terms au , ad , ae arise first at two-loop order, and are suppressed by an extra factor of αa /4π
compared to the gaugino masses. So, to a R
very good approximation one has, at the L
messenger scale,
~
u
4
~ ~
t2 d
(6.56)
~
t
~
a significantly stronger condition than eq. (5.19).
eL2Again, eqs. (6.55) and (6.56) should be applied at
au = ad = ae = 0,
an RG scale equal to the average mass of the messenger fields running in the loops. However, evolving
the RG equations down to the electroweak scale generates non-zero au , ad , and ae proportional to the
corresponding Yukawa matrices and the non-zero gaugino masses, as indicated in section 5.5. These
will only be large for the third-family squarks and sleptons, in the approximation of eq. (5.2). The
L
parameter b may also be taken to vanish near the messenger scale, but this is quite model-dependent,
and in any case b will be non-zero when it is RG-evolved to the electroweak scale. In practice, b can be
R
fixed in terms of the other parameters by the requirement of correct
electroweak symmetry breaking,
as discussed below in section 7.1.
Because the gaugino masses arise at one-loop order and the scalarRsquared-mass contributions
appear at two-loop order, both eq. (6.53) and (6.55) correspond to the estimate eq. (6.27) for msoft , with
Mmess ∼ yI "S#. Equations (6.53)
to
6 and (6.55) hold in the limit9of small "FS #/yI "S#2 , corresponding
12
mass splittings within each messenger supermultiplet that are small compared to the overall messenger
mass scale. The sub-leading corrections in an expansion in "FS #/yI "S#2 turn out [160] to be quite small
Giudice,Rattazzi 97
iscussed in section 5.4, where we have introduced a mass parameter
Λ ≡ !F "/!S" .
8
6
!=
= 15
74 TeV
TeV
!
tan" =
=3
3
tan"
~
d
(6.50)
± |y2 !FS "|. In just the same way, the scalars q, q get squared
m2fermions = |y2 !S"|2 ,
~
scalar masses
e
Figure 6.4: MSSM scalar squared masses in gauge-mediated supersymmetry breaking models arise in
leading order from these two-loop Feynman graphs. The heavy dashed lines are messenger scalars, the
solid lines are messenger fermions, the wavy lines are ordinary R
Standard Model gauge bosons, and the
solid lines with wavy lines superimposed are the MSSM gauginos.
~
m / M1
#
4
~
eL
!S"
− y2 !FS "!! + y3 !FS "qq + c.c.
~
t2
~
e
~
e
2
~
e
0
8
10
10
10
1015
M (GeV) ! = 15 TeV N = 5
e communication occurs via a direct interaction, this ratio is just given by a coupling
ant, like the parameter λ in the case described by eq. (2.5). It can be argued that this
a very
light
= Mass
suppressed
:
ingPredicts
should be smaller
than
1, bygravitino
requiring perturbativity
up to
the GUT scale by
[16].M
If Pthe
➥ partner of the graviton
munication occurs radiatively, then k is given by some loop factor, and therefore it is much
er than 1. We thus rewrite the gravitino mass as
! √
"2
F
F
1
m3/2 = √
2.4 eV ,
=
k 100 TeV
k 3MP
(3.2)
e the model-dependent coefficient k is such that k <
and possibly k $ coefficient
1.
k =1,model-dependent
n gauge-mediated models, the gravitino is the lightest supersymmetric particle (LSP) for
➥ Lightest Superparticle
elevant value of F . Indeed, as argued in sect. 2.4, a safe solution to the flavour problem
res that gravity-mediated contributions to the sparticle spectrum should be much smaller
gauge-mediated contributions. Since m3/2 is exactly the measure of gravity-mediated
s, it is indeed the solution of the flavour problem in gauge mediation, see eq. (2.44), which
es that the gravitino is the LSP.
R parity is conserved, all supersymmetric particles follow decay chains that lead to grav-
s. In order to compute the decay rate we need to know the interaction Lagrangian at lowest
√
in the gravitino field. Since, for F $ M , the dominant gravitino interactions come
Quantum corrections in AdS5
2) Gravity/Moduli/Extra-dim mediation:
...to be discussed later
gauge or
gravity
No-Susy
Susy-breaking
MSSM Matter
Sector
AdS5
H
R
Spectrum at high-energies
(Q~1/R)
dependent
G =model
AdS propagators
"
#
p
! d4 p
V(H) = (2π)4
An example:
ln
1 + m2B (H) GB
p
1 + m2F (H) GF
p
Scalar masses = 0 (at tree-level)
Gaugino masses = M1/2 ≠0
Lightest superpartner:
FINITE
(From
non-local
effects)
Neutralino (mixture of gaugino and Higgsino)
Higgs sector
the MSSM, the description of electroweak symmetry breaking is slightly complicated by
at there are two complex Higgs doublets Hu = (Hu+ , Hu0 ) and Hd = (Hd0 , Hd− ) rather than
the ordinary Standard Model. The classical scalar potential for the Higgs scalar fields in th
given by
Only 3 parameters:
V = (|µ|2 + m2Hu )(|Hu0 |2 + |Hu+ |2 ) + (|µ|2 + m2Hd )(|Hd0 |2 + |Hd− |2 )
+ [b (Hu+ Hd− − Hu0 Hd0 ) + c.c.]
1 2
1 2 + 0∗
"2
0 2
+ 2
0 2
− 2 2
+ (g + g )(|Hu | + |Hu | − |Hd | − |Hd | ) + g |Hu Hd + Hu0 Hd−∗ |2 .
8
2
he terms proportional to |µ|2 come from F -terms [see eq. (5.5)]. The terms proportional t
are the D-term contributions, obtained from the general formula eq. (3.75) after some rear
nally, the terms proportional to m2Hu , m2Hd and b are just a rewriting of the last three
(5.12). The full scalar potential of the theory also includes many terms involving the squ
quartic
coupling
pton fields that we can ignore here, since they do not get VEVs because they have large
related to gauge-couplings
uared masses.
We now have to demand that the minimum of this potential should break electroweak sy
wn to electromagnetism SU (2)L × U (1)Y → U (1)EM , in accord with experiment. We can
edom to make gauge transformations to simplify this analysis. First, the freedom to make
2 x allows
4 = 8usscalars
3 Goldstones
W,
Z) isospin com
uge transformations
to rotate=
away
a possible VEV(eaten
for one ofby
the
weak
+ = 0 at the minimu
one of the scalar fields, so without loss+3
of generality
we can take
neutral Higgs
= h,HH,
u A
tential. Then one can check that a minimum of the potential satisfying ∂V /∂Hu+ = 0 m
+
Charged
Higgs
=
H⁺,
H⁻
−
ve Hd = 0. This is good, because it means that at the minimum of the potential electroma
Spectrum:
2 unknown parameters (since
parameters:
�H �
u
1) tan β = �H �
d
m21 , m22 , m23
2) mA
At tree-level:2 �m2 − m2 tan2 β�
{
m2Z =
1
v 2 = �Hu �2 + �Hd �2 ):
2
tan2 β − 1
m2H2+ =2 m2A 2+ m2W
sin 2β =
−→
1 complex
vF ,
tan β
2
2m3
m2A
2
mA =m1 + m2
mH + = m2A + mW
�
�
�
1
2
2
2
2
2
2 2
mh,H =
mA + mZ ± (mA − mZ ) + 4 sin 2β m2A m2Z
2
mh ≤ mZ
Was a great prediction for Higgs hunters at LEP!
splayed in Fig. 1.7 as a function of MA for the two values tan β = 3 and 30. The full set
iative corrections has been included and the “no–mixing” scenario with Xt = 0 (left)
√
maximal mixing” scenario with Xt = 6MS (right) have been assumed. The SUSY
t the other SUSY parameters
t̃
has been set to MS = 2 TeV and
except for At to 1 TeV;
t̃
M input parameters are fixed to mt = 178 GeV, mb = 4.88 GeV and αs (MZ ) = 0.1172.
rogram HDECAY [129] which incorporates the routine FeynHiggsFast1.2 [130] for the
ation of the radiative corrections in the MSSM Higgs sector, has been used.
... but quantum effects (mostly loops of top/stop)
t̃
7.3:
Integrating out the top quark and top squarks yields large positive contributio
modifyFigure
the
bound:
quartic Higgs coupling in the low-energy effective theory, especially from these one-loop diag
An alternative way to understand the size of the radiative correction to the h0 mass is to
an effective theory in which the heavy top squarks and top quark have been integrated out. T
Higgs couplings in the low-energy effective theory get large positive contributions from the the
diagrams of fig. 7.3. This increases the steepness of the Higgs potential, and can be used to o
same result for the enhanced h0 mass.
An interesting case, often referred to as the “decoupling limit”, occurs when mA0 ! m
2
2
2
m
0 can saturate the upper bounds just mentioned, with m 0 ≈ m cos (2β)+ loop correct
h
Z
h
Upper bound 0 0
±
particles A , H , and H will be much heavier and nearly degenerate, forming an isospin do
~130decouples
GeV from sufficiently low-energy experiments. The angle α is very nearly β − π/2, and h
same couplings to quarks and leptons and electroweak gauge bosons as would the physical Hi
of the ordinary Standard Model without supersymmetry. Indeed, model-building experie
shown that it is not uncommon for h0 to behave in a way nearly indistinguishable from a
Model-like Higgs boson, even if mA0 is not too huge. However, it should be kept in mind
couplings of h0 might turn out to deviate significantly from those of a Standard Model Higg
Top-squark mixing (to be discussed in section 7.4) can result in a further large positive con
to m2h0 . At one-loop order, and working in the decoupling limit for simplicity, eq. (7.24) gene
!
"
3 as2 a function
e 1.7: The masses of the
MSSM
Higgs
bosons
of M
2
2
2
2
2
#
for2 two 2values
2
2
Djouadi 05
2
2
2
where λij = (1 − Mi2 /s − Mi2 /s)2 − 4Mi2 Mj2 /s2 is the two–body phase space function; the
additional factor for the last process accounts for the fact that two spin–zero particles are
produced and the cross section should be proportional to λ3ij as discussed in §I.4.2.2.
LEP searches:
e+
e+
Z
A
Z∗
Z∗
•
•
e−
e−
h
h
Figure 1.14: Diagrams for MSSM neutral Higgs production at LEP2 energies.
with decays to taus and bottoms
tan!
tan!
2
2
Since gAhZ
= cos2 (β − α) while ghZZ
= sin2 (β − α), the processes e+ e− → hZ and
e+ e− → hA are complementary11 . In the decoupling limit, MA ' MZ , σ(e+ e− → hA)
2
2
vanishes since ghAZ
∼ 0 while σ(e+ e− → hZ) approaches the SM limit since ghZZ
∼ 1. In
11
As will be discussed in the next section, this remark can be extended to the heavier m
CP–even
-maxHiggs
+ −
h°
boson and the complementarity is doubled in this case: there is one between the processes e e → HZ and
mh°-max
e+ e− → HA as for the h boson, but there is also a complementarity between the production of the h and
H bosons. The radiative corrections to these processes will also be discussed in §4.1.
10
10
69
Excluded
by LEP
1
Excluded
by LEP
1
Theoretically
Inaccessible
0
20
40
60
80 100 120 140
mh° (GeV/c2)
0
200
400
mA° (GeV/c2)
After LEP, a heavy stop is essential to keep the MSSM alive
Higgs bound:
2
mh
=
<
2
mZ
+
4
3mt
2
2
2π v
ln(mstop /mt ) + · · ·
Needed to be large to be above
the experimental bound
Higgs searches rules out a big chunk
of the parameter space of the MSSM!
In
minimal
Sugra:
2
2
M0 /µ
Only the thin
“withe spike” is left!
2
2
M1/2 /µ
Giudice, Rattazzi
MSSM Higgs hunting at the LHC
Bad news: h too light to decay to WW/ZZ
A, H⁺ have very small couplings to WW/ZZ
H small regions with sizable
couplings to WW/ZZ
Good news: Regions where the decays of H, A, H⁺ to
leptons are enhanced (Large Tanβ region)
Due to:
mτ = Yτ �Hd �
can be larger than in the SM, if �Hd � is smaller than v
roduction with
Near future:
ree "" channels
ne leptonic decay:
!e!#
s scaled from
TeV
5# discovery
95% exclusion
overed, down
at low mA
Expected sensitivity to the MSSM Higgs boson
in the !! channel
More interestingly: MSSM could be ruled out
if a Higgs ➞ WW/ZZ with mass ~160 GeV
is discovered in the first LHC run
ck 2010 – June 3, 2010
21
50
tan !
In the long run....
3. MSSM Higgses: detection at th
40
30
20
0
0 0
h HA
10
9
8
7
6
5
4
0
3
0
h H
2
1
50
100
150
200
Superpartners at Hadron Colliders
Superpartners at Hadron Colliders
Neutral gaugino + Higgsino mix:
0
χ
Mass-eigenstate =
neutralino
Charged gaugino + Higgsino mix:
+
χ
Mass-eigenstate =
chargino
Main consideration:
Due to R-parity superpartners are produced in pairs, and
decay, in cascade, down to the lightest one (neutral) that,
being Typical
stable,
goes
away
from
the
detector
SUSY Event at LHC
Physics at the ILC
SUSY, LHC+ILC
A classic:
Jörgen Samson (DESY)
Physics at the ILC
22. January 2007
28 / 38
Strategy: Detect leptons or jets + Missing ET
Physics at the ILC
SUSY, LHC+ILC
Typical SUSY Event at LHC
Jörgen Samson (DESY)
Physics at the ILC
22. January 2007
28 / 38
Final states with same-charge dilepton
due to the Majorana nature of the gluino
Tevatron
From P. Wittich at
“Physics at the LHC 2010” conference
susy in jets + met:generic squark/gluino production
• Large production cross section,
bkgnds from multi-jet, Z→νν, top
• Optimize searches as a function of
(Missing ET, njet)
• No excess seen so far
• Limits for 2 (2.1)/fb of data for CDF
(D0)
• interpret results in mSUGRA-like
SUSY scenario
!"#
20
Trileptons: Chargino-Neutralino Search, 3.2/fb
~
• Very clean signature:
• Missing ET due to undetected ν, χ01
• 3 isolated leptons, lower momentum
~
3 identified leptons (e,μ)
• 2 identified leptons + track (l)
• “Tight” and “loose” e,μ categories
•
• Rejection using kinematic selections
on: ml+l-, njets, Missing ET, Δφ
between leptons...
Good agreement between data
and SM prediction → set limit
Peter Wittich
Channel
SM expected
Trilepton
1.5 ± 0.2
Lepton+trk 9.4± 1.2
Data
1
6
!"#
16
Chargino-neutralino results
PRL 101, 251801 (2008)
• interpret null result in mSugra SUSY scenario as
excluded region in
mSUGRA m0-m! space
a convenient/conventional benchmark
m0 = 60 GeV, tan β=3, A0=0, μ>0
CDF @ 2 fb-1
~
~
~
~
Excludes mχ±1 < 164 (154 Exp.) GeV/c2
Limits depend on relative χ02-l masses
!
mχ2 > ml ~increases BR to e/μ
!
mχ2 ! ml reduces acceptance
D0 limit in 2.3/fb: Phys. Lett. B 680, 34 (2009)
Peter Wittich
!"#
17
2 b jets + ETMiss - ~q and LQ ZH → ν ν̄bb̄
• Final state familiar from Higgs searches
• missing ET and b quarks
0
0
˜
pp̄
→
b̃
b̄
→
b
χ̃
b̄
χ̃
1
1
1
1
• Also good signal for leptoquarks and SUSY
LQ3 → ντ b
• event selection:
• b tagging (D0: neural-net algo)
jet1
jet2
6
• two b-tagged jets, ETmiss, Sign., ΣET
p
+
p
T
T
miss
X
=
• optimize pT, ET , HT, Xjj for SUSY/LQ3
jj
ystematic uncertainty
SM
CDF RunII DATA (L=2.65 fb )
HT
signals
Total Syst. Uncertainty
SM + MSSM
een 19% and 18% as
-1
low !M analysis
MSSM signal, various
102
102
M = 123 GeV/c
cted cross sections at
M = 90 GeV/c
10
10
no2, are considered:
low δM(LSP, b squark)
pre-tag
tagged 1
puted using the Hes1
o a 12% uncertainty
100
200 high !300
400
600
M analysis 200
ons of the renormalM = 193 GeV/c
10
10
factor of two change
M = 70 GeV/c
out 26%. Uncertainhi δM(LSP, b squark)
final-state gluon radi1
1
enerated samples in6
100
200
300
200
400
600
ignal yields. The 3%
E/ T [GeV]
HT + E/ T [GeV]
ergy scale translates
al
systematic
uncertainty
SM
CDF RunII DATA (L=2.65 fb-1)
!"#
e MSSM
predictions.
Syst.
SM + MSSM
/T distributions (black
etween
and 18% FIG.
as 1: Measured E/T Total
and
HTUncertainty
+E
dots)
21
de:
a 4% 19%
uncertainty
Peter Wittich
2
events per bin
~
b1
0
#
"
2
1
2
~
b1
0
#
"
1
2
Supersymmetric top in the e+μ+bb+MET, 3.1/fb
• 3rd generation again - special role in SUSY
• Look for decay mode in e μ final state with ETMiss >18 GeV
• Low SM backgrounds (Z→ττ,ttbar)
B(t̃1
• Reject with δΦ(lepton, ETMiss) cuts
• no explicit b tag required
pp̄
→ ν̃b�)
→
=
¯
t̃1 t̃1
100%
R parity conserving
• Consider small and large δm(stop, sneutrino)
• drives kinematics of accepted events
14
120
220<ST
e! +ee Obs (1.1 fb-1)
-1
WZ
e! Obs (3.1
Dfb
’ )Run
e! Exp (3.1 fb-1)
)+
12
8
Z A oo
TOP
ZAee
QCD
Dzero data
80
M[110,80]
60
4
M[150,50]
LEP II
excluded
240
0
LEP I excluded
50
60
200
250
300 200
350
80100 100150
120
140
160
180
HT [GeV]
Stop mass (GeV)
Blue: this result
Peter Wittich
WW
W
Z A !!
M(
b
100
10
-1
II Preliminary, 3.1 fb
6
D0 Conference Note 5937-CONF
ZZ
e! +ee Exp (1.1 fb-1)
M(
i¾)
140
M( ~
t1 )
=
• Null result: set limits in sneutrino/stop mass plane
D’ Preliminary Result
eventsSneutrino mass (GeV)
• Bin events in two kinematic variables
• HT: scaler sum of jet pT
• ST: scalar sum of lepton pT, ETMiss
23
LHC
From P. Jenni at
“Physics at the LHC 2010” conference
!"#$%&%'%()$*+,$-.&&%&/$0%))
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#/4$+&""/(EFG(>'H ?/(EIJK
)%
Q|Boson! = |Fermion!,
Q|Fermion! = |Boson!.
Other
nsically
complex MSSM
objects, so goodies:
Q† (the hermitian conjugate of Q) is also
se Q and Q† are fermionic operators, they carry spin angular momentum
ymmetry must be a spacetime symmetry. The possible forms for such s
● Gauge
unification
antum field
theorycoupling
are highly
restricted by the Haag-Lopuszanski-Sohn
Mandula theorem [4]. For realistic theories that, like the Standard Mode
● The lightest supersymmetric particle (LSP)
mions whose left- and right-handed pieces transform differently under the
can
be
Dark
matter
ibility of parity-violating interactions, this theorem implies that the gen
n algebra
anticommutation
and must
commutation
relations
with the sche
● of
Local
supersymmetry
incorporate
gravity:
†
µ
{Q, Q } = P ,
{Q, Q} = {Q† , Q† } = 0,
● Fits well EWPT
µ from LEP/Tevatron
µ
†
[P , Q] = [P , Q ] = 0,
four-momentum generator of spacetime translations. Here we have ru
† ; has
allowed
us to write
than 20,000
papers
r indices on Q and ➥
QIt
after
developing
somemore
notation
we will,
in secti
n of eqs. (1.6)-(1.8) with indices restored. In the meantime, we simply
on the right-hand side of eq. (1.6) is unsurprising, since it transforms u