TOPATLHC
topconstraintsfromLEP singletopandVbar+Xproduc,on
ShahramRahatlou
FisicadellePar,celleElementari,AnnoAccademico2015-16
http://www.roma1.infn.it/people/rahatlou/particelle/
TOP@LEP
ZRESONANCE
Cross-section (pb)
Figure 1.1: The lowest-order s-channel Feynman diagrams for e+ e− → ff. For e+ e− final states,
the photon and the Z boson can also be exchanged via the t-channel. The contribution of Higgs
boson exchange diagrams is negligible.
10 5
Z
10 4
Cross section near the Z pole
is commonly referred to as the Z lineshape
+ !
e e #hadrons
10 3
!
+
e
10
2
CESR
DORIS
+
PETRA
KEKB
PEP-II
10
e
SLC
LEP I
0
20
40
60
80
100
140
160
180
!
f
e
f
Figure 1.1: The lowest-order s-channel Feynman diagrams for e+ e− → ff. For e+ e− final states,
the photon and the Z boson can also be exchanged via the t-channel. The contribution of Higgs
boson exchange diagrams is negligible.
LEP II
120
f
Z
"
!
TRISTAN
e
-
WW
PEP
!
+
f
200
220
Cross-section (pb)
Centre-of-mass energy (GeV)
10 5
Z
1.2: and
The hadronic
as a function ofproviding
centre-of-mass energy.
The solid
line is
•Figure
LEP
SLCcross-section
are Z factories
copious
sample
of Z bosons
in 1990s
the prediction of the SM, and the points are the experimental measurements. Also indicated
+ !
e
e #hadrons
are the energy ranges of various e e accelerators. The cross-sections have been corrected for
•the Dedicated
detectors covering almost full solid angle to study Z decays
eﬀects of photon radiation.
• Bhabha scattering cross section known very precisely allows very precise
measurement of luminosity
needed for normalization
+ 15
WW
+ −
10 4
10 3
10 2
CESR
DORIS
PEP
PETRA
KEKB
PEP-II
Shahram Rahatlou, Roma Sapienza & INFN
10
TRISTAN
SLC
LEP I
LEP II
29
Z
W
addition,
the
relationship
between
the
neutral
an
andby
independent
of,
any
small
(<
MeV)
neutrino
masses.
These tree-level quantities are modified
radiative
corrections
to
the
propagators
and
vertices
Figure 1.9: Higher-order corrections to the gauge boson
of
the W
Ztheory;
boson in
masses:
The ρ0 such
parameter
[25]
is
determined
by
the
Higgs
structure
of and
thecorrections
therenormalized
Minimal
as those shown in Figures 1.9 and 1.10.
When
these
are
in the
loops.
Standard
Model containing
onlywhich
Higgswe
doublets,
ρ0 =the
1. form of Equation2 1.5 is maintained, and taken
“on-shell”
scheme [26],
adopt here,
mW
Thetofermions
areon-shell
arranged
in weak-isospin
doublets
for, ρto
left-handed
particles
weak. and
= orders,
0 all
define the
electroweak
mixing
angle,
θ
in
terms
of
the
vector boson
2
tree
2
W
m
cos
θ
1.4
Standard
Model
Relations
Z interaction
W
isospin pole
singlets
for right-handed particles, as shown in Table 1.3. The
of the Z
masses:
TheseThe
tree-level
quantities
are modified
radiative
corr
boson with fermions depends on charge,
component
of weak-isospin,
T3 , by
and
g
g
L Q, and the third
ρ
by
the
H
Rparameter [25] is determined
0
2
In
the
SM
at
tree
level,
the
relationship
between
the
we
those shown in Figures 1.9 and 1.10. When the
is given by the left- andm
right-handed
couplings: such as
W
Standard
Model containing only Higgs doublets,
ρ0 =
.
(1.10)
given
by
2
2
“on-shell”
scheme
[26],
which
we
adopt
here,
the
form of
√ mZf cos θW 2 tree
tree
The
fermions
are
arranged
in
weak-isospin
gL
=
ρ0 (T3 − Qf sin θW )
(1.6)
to
define
the
on-shell
electroweak
mixing
angle, θW , to a
πα
1
√
f
isospin
singlets
for
right-handed
particles,
as sh
2
2
N
C
3
em
5
√
In
the
ρ0 2=θtree
1 is, assumed.
G
=
,
F
J
=
j
sin
✓
j
=
ū
[
(1
)T
Q
sin
✓
]u
SM
current:
gRtree
= following,
− ρ0 Qf sin
(1.7)
pole masses:
2 tree
W µ
f
W f
2 f µ
µ
µ
W
3
2m
sin
θ
boson
with
fermions
depends
on
charge,
Q,
and
2
W
W at the Z-pole is absorbed into
1 [25] to the5 couplings
The bulk of the electroweak
N C corrections
2
Jµ axial-vector
= ūf µ (g
gA )u
current:
V is given
fm
by
the
left- and
right-handed
couplings:
or, phenomenological
equivalently
terms
of vector
and
couplings:
complex in
form
factors,
Rf for
the overall
scale
and
K
for
the
electroweak
mixing
angle,d
Won-shell
f
where2 GF ρis0 the
Fermi
constant
determined
in
muon
=
.
2
m
cos2 is
θ√
√
resulting
in
complex
eﬀective
couplings:
Wthe Wf boson mass,
tree
tree
tree
f
2 tree constant,
treeZm
2 treeand sin2 θ tre
structure
W
W
gV
≡ gL + gR = ρ0 (T3 − 2Qf sin θW )
gL
=
ρ0 (T3 − Qf sin (1.8)
θW )
!
√
√is assumed.
the
relationship
the neutral
tree ρ0 = between
tree (1.9)and charged
In
the
following,
1
f ρ Tf .
2addition,
gAtree ≡GVfgLtree=− gRtree
=
gR
= − ρ0 Qf sin2 θW
,
0 3f Kf sin θW )
Rf (T3 − 2Q
(1.11)
of the WThe
andbulk
Z boson
of themasses:
electroweak corrections [25] to the c
!
Rf T3f .
GAf =
(1.12)
complex
factors,
Rf terms
for theofoverall
Kf for
or, form
equivalently
in
vectorscale
and and
axial-vect
2
26
m
• In SM with simple Higgs doublet resulting
W
ratio between
charged and neutral
.
ρ0 = in
complex
couplings:
√by W andfZ mass
2 tree2 tree eﬀective
determined
treecurrents
tree
m
cos
θ
In
terms
of
the
real
parts
of
the
complex
form
factors,
Z gV ! W
≡ gL + gR = ρ0 (T3 − 2Qf sin
– ρ =1 in minimal SM
f
tree R (T ftree
treesin2 θ√)
G
=
−
2Q
K
Vf
f
f
f
W
ρ
T
. (1.13)
g
≡
g
−
g
=
3
0 3Higgs
Thef ρ0 parameter
[25] is Ldetermined
by the
struc
A !
R
ρf ≡ ℜ(Rf ) = 1 + ∆ρse + ∆ρ
f only Higgs doublets, ρ = 1.
Standard
Model
containing
0(1.14)
R
G
=
T
Af
f
κf ≡ ℜ(Kf ) = 1 + ∆κse + ∆κ
,
3.
f
26
• SM is renormalizable, such relationThe
holds
at all orders
(on-shell
scheme) doublets
fermions
are arranged
in weak-isospin
terms
the right-handed
realfor
parts
of the
complex
form
factors,
eﬀective
mixingappropriate
angle
andInthe
realofeﬀective
couplings
are
definedas
as:shown
isospin
singlets
for
particles,
in T
– the
One
needselectroweak
to incorporate
corrections
each
order
boson withρfermions
depends
on∆ρ
charge,
Q, and the third
2 f
2
≡
ℜ(R
)
=
1
+
+
∆ρ
f
f
se
f
sin θeﬀ ≡ κf sin θW
flavor (1.15)
is
given
by
the
leftand
right-handed
couplings:
√
f
κf ≡ ℜ(Kf ) = 1 + ∆κse + ∆κf , specific
ρf (T3f − 2Qf sin2 θeﬀ
)
(1.16)
gVf ≡
√
√
tree
f
2 tree
f 2009
g
=
ρ
(T
−
Q
sin
θW )
Giugno
Carlo
Dionisi
FNSN
II
12
0
f
ρf T3 ,
(1.17)
gAf ≡
L
3
the eﬀective electroweak
mixing
angle and the real
eﬀec
self-energy
A.A.2008-2009
√
tree
2 tree
gR
= − ρ0 Qf sin θW ,
Shahram Rahatlou, Roma Sapienza & INFN
30
2
27 2 f
NEUTRALCURRENTINSM
SELF-ENERGYCORRECTIONS
proportional to
W
f
mf2
",Z/W
!
",Z/W
",Z/W
f /f’
vacuum polarization
",Z/W
W/",Z
H
H
Z/W
proportional to log(m_H)
Z/W
Z/W
Z/W
W
f
Z/W
",Z/W
!
",Z/W
",Z/W
Figure 1.9: Higher-order corrections to the gauge boson propagators
due to boson and fermion W/",Z
f /f’
loops.
• precise measurement of 1-loop corrections to boson propagators
H
H
• Sensitive to new physics contribution
–
–
–
",Z/W
X
These tree-level quantities are modified by radiative corrections to the propagators and vertices
A new
particle
provide
additional
such X
as those
shown could
in Figures
1.9 and 1.10.
When thesediagram
corrections are renormalized in the
Z/W
Z/W
Z/W
Z/W
“on-shell”
scheme
[26],
which
we
adopt
here,
the
form
of
Equation
1.5
is
maintained,
and
taken
interference with SM diagrams could result in
Z/Wvery different observed rate
to define the on-shell electroweak mixing angle, θW , to all orders, in terms of the vector boson
Constraints
pole masses: on top and Higgs mass before either was discovered
ρ0 =
m2W
.
m2Z cos2 θW
Figure 1.9: Higher-order corrections to the gauge boson propagators due to boson and fermion
loops.
(1.10)
These tree-level quantities are modified by radiative corrections to the propagators and vertices
In the following, ρ0 = 1 is assumed.
such as those shown in Figures 1.9 and 1.10. When these corrections are renormalized in the
Shahram Rahatlou, Roma
Sapienza
The
bulk &ofINFN
the electroweak corrections [25]
to the couplings at the Z-pole is absorbed into
31
“on-shell” scheme [26], which we adopt here, the form of Equation 1.5 is maintained, and taken
FLAVOR-DEPENDENTVERTEXCORRECTIONS
!
+
e
!
+
b
e
b
!
W
t
W
"/Z
t
"/Z
t
!
e
W
!
b
e
b
Figure 1.10: Vertex corrections to the process e+ e− → bb.
• Same
diagrams exist for all fermions (quarks + leptons)
so that:
!
"
GVf
gVf
f
1 − 4|Qf | sin2 θeﬀ
. specific fermion (flavor dependence)
(1.18)
=
ℜ much= dependent
• Magnitude
very
on
g
G
–
–
–
–
Af
Af
Very
small
corrections
for
leptons
The
quantities
∆ρse and ∆κ
se are universal corrections arising from the propagator selfenergies,
while ∆ρf V
and
∆κf are
flavour-specific
vertexelements
corrections. For simplicity we ignore
CKM
elements
only
for diagonal
ij large
the small imaginary components of these corrections in most of the following discussion. The
contributions
from
quarks suppressed due to their mass
leading order terms
in ∆ρlight
se and ∆κse for mH ≫ mW are [27]:
$
%significant
&
#b diagrams
2
|Vtb| ~ 1 makes
the
the
most
contribution
2
2
2
sin θW
mH
5
3GF mW mt
∆κse
√
−
ln 2 −
mW 6
8 2π 2 m2W cos2 θW
#
$
3GF m2W m2t cos2 θW 10
m2H
√
=
−
ln 2 −
2
2
2
mW sin θW
9
mW
8 2π
∆ρse =
+···
%
#
m2t
2
m2Z
m2H
&
5
+···
6
For mH ≪ mW , the Higgs terms are modified, for example:
2
Shahram Rahatlou, Roma Sapienza &3G
INFN
F mW
(1.19)
7π mH mZ
&
(1.20)
32
Rf (T3f − 2Qf Kf sin2 θW ) For mH ≪ mW , the Higgs terms are
!
Figure 1.10: Vertex corrections to the process e+ e
#
2
Rf T3f .
=
3G m
2m
m2
GVf =
SUMMARYOFCORRECTIONS
GAf
∆ρse =
In terms of the real
so parts
that: of the complex form factors,
t
√F W
+
2
2
mW 3 m
8 2π
Higgs loops are
Vf f where only internal
2 f
≡ ℜ(Rf ) = g1Vf+ =
∆ρseℜ +G∆ρ
flavor = 1 − 4|Qf | sin θeﬀ .
gAf
GAf
Higgs
correction for low mH seen in
specific
!
"
ρf
κf ≡ ℜ(Kf ) = 1 + ∆κse + ∆κf ,
• Self-energy
contributions
from the
derivative
of
The quantities ∆ρse and
∆κse are universal
corrections
arising
− defined
the eﬀective electroweak
angle
and
the
real
eﬀective
couplings
are
self-energy
energies,mixing
while ∆ρ
∆κ
flavour-specific
vertex
Existence
of the process
e+ ecorrections
→ Z∗ H
f and
f are
the small
imaginary components
of these1.21
corrections
in most
of the
in
Equation
[29].
The
radiative
2 f
2
sin θeﬀ
sin order
θWW: terms in ∆ρse and ∆κse for mH ≫ mW are [27]:
corrections
for≡mleading
m
Hκf>>
√
mass and a weaker logarithmic depe
f
2 f #
$
%
&
ρ
(T
−
2Q
sin
θeﬀ
g
≡
f
f
Vf
2
2
2 )
2
3
dependence on √
sin
θW for all
mHfermions,
5
3GF mW ismvery
small
except
t
f se =
√
−
ln
−
+
·
·
·
∆ρ
ρf T3 ,
gAf ≡
2
2
2
2
m
cos θW
m
6
8 2π
– quadratic
top mass
– only logarithmic dependence on Higgs mass
#Figure
W
1.10 are significant,
$
%due to
& th
3GF m2W and 27
10the diagonal
cos2 θsize
m2H
5 CKM m
W of
the
√
∆κse =
−
ln
−
+···
2
2
2
9 bbmproduction
6
sin θW for
8 2π contribution
W
[28]
mH ≪ mW , the Higgshere
termsnegligible.):
are modified, for example:
• Vertex corrections: dominantFor
contribution &
#
2
2
2
2
3GF mW mt
2 mZ
mHG m
7π2mH mZ
from b quark
F
√
∆ρse =
+∆κ 2 ln
− t +2· · ·+, · · ·
2
2 √
2
=
mW 3 mbW mZ
3 2 mW
8 2π
4 2π
• Exact calculation of such corrections where only internal Higgs loops∆ρ
are considered.
Note the change
b = −2∆κb + · · · .
W
m2t
m2W
provided strong limits on topHiggs
masscorrection for low mH seen in Equation 1.21 compared to Equ
contributions from the derivative
of the Z self-energy
with respect
t
By
interpreting
the
Z-pole
measu
• Remember: top was yet to beExistence
discovered!
of the process e+ e− → Z∗ H (Higgsstrahlung) would tend to
can be determined indirectly, and co
in Equation 1.21 [29]. The radiative corrections have a quadratic de
ments, even when taken alone, have
mass and a weaker logarithmic dependence on the Higgs boson mas
Shahram Rahatlou, Roma Sapienza & INFN
is very small for all fermions, except for the b-quark, where the eﬀect
Figure 1.10 are significant, due to the large mass splitting between t
and the size of the diagonal CKM matrix element |Vtb | ≃ 1 , resulting
33
R⇥
=
3s
= Nc 3 + 2
9
9
=
TREE-LEVEL(BORN)DIAGRAMS
⌅(e+ e
⇤
µ+ µ
)
4⇤
3s
2
Q2e Q2µ
9
for five quark flavors where the top quark is too heavy to be produced at the given e+ e collider en
!
!
+
+
R as a function of theecollider energy is a beautiful
measurement
of the number and charges
of the qu
f
e
f
ssive intermediate states
Z
"
!
!
move on to describing
e incoming quarks inside fprotons we eshould briefly consider the
f second Feynm
ntributing to the Drell-Yan production rate in Eq.(2.11), the on-shell or off-shell Z boson
+ −
+ −
Figure 1.1:
The
lowest-order
s-channel
Feynman
diagrams
for
e
e
→
ff.
For
e
e final states,
2
2
2
2
|M
MZcan
| also
= |M
| + |M
| +
2 Re M
,
ZM
the|M|
photon=and
the Z+boson
be exchanged
viaZthe
t-channel.
The
contribution
of Higgs
boson exchange diagrams is negligible.
Cross-section (pb)
ference
occurs
in phase spaceto
regions
wheresection
for both at
intermediate
states the invariant masses of the
• Two
contributions
the cross
leading order
same. For
photon
the intermediate
on-shell pole isstates
not a problem. It has zero mass, which means that we hit t
– Zthe
and
gamma
matrix element
squared between
only in thethem
limitvery
of zero
incomingand
energy.
Strictly
speaking we never hit it,
5
– interference
important
visible
experimentally
10
– Cross section depends on coupling constants of each fermion to Z boson
• Experimental observables
10 4
Z
+ !
e e #hadrons
10 3
Shahram Rahatlou, Roma Sapienza & INFN
34
con
F
=
d /d(cos )dcos ,
B
=
ρ0 =
.
d /d(cos )dcos
2
2θ
m
cos
W
Z
cast into a Born-type
onance can be
structure us
The diﬀerential cross-sections for fermion
pair production
(see Figu
In
the
following,
ρ
=
1
is
assumed.
0
constants
given
in
the
previous
section.
Eﬀects
fro
dove è lF angolo di scattering del fermione positivo
onance can be cast into a Born-typeThe
structure
using
the
complexbulk of the electroweak corrections
into account by the running
electromagnetic
couplin
complex form
factors,
Rf for
the overall
sca
constants given in the previous section.
Eﬀects
from
photon
vacuu
small imaginary
piece.
Neglecting
initial
an
resulting
in complex
eﬀective
couplings:
into accountquires
by the arunning
electromagnetic
coupling
constant
(Equa
,
!
f
• Several experimental
gluon
radiation
and
fermion
masses,
the
electroweak
f
2
quires a small- imaginary piece. Neglecting
initial
and
final
state
G
=
R
(T
−
2Q
K
sin
θWph
)
Vf
f
f
f
3
,
e
!
canand
thus
be written
theelectroweak
sum of three
contributio
observables closely related to
gluon radiation
fermion
masses,asthe
f kernel cross-sect
Rf T3 .
GAf =
+
from
their
interference
[32],
+
e
SM predictions
can thus be fwritten as the sum of three contributions, from s-chann
1
0
EWCROSSSECTIONNEARZPOLE
• cross section vs. energy
In terms of the real parts of the complex f
from their interference [32],
2s 1 dσew
π Ncf dcos θ
– confirm interference of 2
diagrams
– Absence of additional
intermediate vector bosons
Giugno 2009
• Z mass position
– fixed if mW and θW known
• Z total and partial width
– # of generations
• Charge asymmetry (parity
violation) to test V-A structure
with:
2s 1 dσew + −
f ≡
(e e ρ→
ff)ℜ(R
=f ) = 1 + ∆ρse + ∆ρf
f
− c dcos θ
κf ≡ ℜ(K
Nc=1forf=leptons
f ) = 1 + ∆κse + ∆κf ,
(eπ+ eN
→ ff) =
Nc=3forf=quarks
2
thecos
eﬀective
mixing angle and
|α(s)Qf |2 (1 +
θ) electroweak
|α(s)Qf |2 (1 +! cos2 θ)
!
"#
$f
2
sin
θ
≡
κ
sin
θW
f
eﬀ
σ
√
f
ρf (T3f − 2Qf sin2 θeﬀ
)
g
≡
σ γ Dionisi FNSN
Carlo
II
24
%
& Vf
√
2 '(
A.A. 2008-2009
f
%
& α∗ (s)Q χ(s) gGAf G
ρ
T
,
≡
−8ℜ
(1
+
cos
θ) + 2G
f
f
Ve
Vf
3
∗
2
"#
$
2
γ
−8ℜ α (s)Q!f χ(s) GVe GVf (1 + cos θ) + 2G
"#Ae GAf cos θ
!
"#
$
γ–Z interference
γ–Z interference
2
2
2
2
2
2
2
2 Ve | 2+ |GAe | 2)(|GVf | +
2 |GAf | )
+16|χ(s)|
[(|G
+16|χ(s)| [(|GVe | + |GAe | )(|GVf | + |GAf | )(1 + cos θ)
∗ ∗ } ℜ {G G ∗ } co
G
Ve
+8ℜ {GVe GAe ∗ }+8ℜ
ℜ {G{G
G
} cos θ] Vf Af
Vf Af Ae
!
with:
!
"#
σZ
"#
σZ
$
GF m2Z
sF m2Z
G
s
√χ(s) = 2 √
χ(s) =
,
,
2
+ isΓ2Zs/m
8π 2 s − mZ 8π
Z
− mZ + isΓZ /mZ
Shahram Rahatlou, Sh.
Roma
Sapienza & INFN
Rahatlou
where θ is the
scattering
angle
of the out-going
with respect
where
θf is the
scattering
angle offermion
the out-going
ferm
The colour factor Nc is one for leptons
(f=νe , νµ , ντ , e, µ, τ ) and
th
f
35
The colour factor N is one for leptons (f=νe , νµ , ντ
written inRterms
QED of the partial decay widths of t
!
where
(1.42)
The
invisible
width
from
Z
decays
to
neutrinos,
Γinv2 = Nν Γνν , where N
!
Γhad =
Γqq . Γ
and
sΓ
peak
=
Γqqis. determined
Z
Z
1 , decay
had
neutrino
species,
from
the
measurements
of the
w
peak
0
σff = σff
q̸=t
=
σ
σ
2 production
2 ff
2 Γ2 /m2term
ff can
The
total
cross-section
arising
from
the
cos
θ-symmetric
Z
q̸
=
t
(s
−
m
)
+
s
12π
Γ
Γ
R
states
and
the
total
width,
Z
Z
Z
QED
ee ff
he final state QED correction included
of Γee .
0 in the definition
=
.
σ
written
in terms
of the
partial
decay
widths
of
the
initial
finalNstates,
Γee
and Γffo,
nvisible
width
from
Z
decays
to
neutrinos,
Γ
where
is
the
number
2= N
2Γνν ,and
ff
•
Integrating
over
θ
total
cross
section
inv
ν
ν
m
Γ
s-section is parametrised
in
terms
of
the
hadronic
given
by
and
where
Z Γ to width
Zneutrinos,
The invisible
width
from
Z
decays
Γ
inv = Nν Γνν , whe
Γ
=
Γ
+
Γ
+
Γ
+
+
Γ
.
Z
ee
µµ
τ
τ
had
inv
ino species, is determined from
2 the measurements of the decay widths to all visible
tates,
sΓZ The
neutrino
species,
is determined
from
the
12πofQED
Γthe
peak
Z
1 measurements
ee Γff deca
0
term
1/R
removes
the
final
state
corr
peak
0
QED
σff total
,
= σffwidth, Because
s and the
=
.
σ
the
measured
cross-sections
depend
on
products
of
the
pa
=
σ
σ
2 2
2 Γ2 /m2
2
2
ff
ff
(s
−
m
)
+
s
ff
m
Γ
states and Zthe totalZThe
width,
Zparametrise
Z
RQED
overallconstitute
hadronic
is
the total width, theZ widths
across-section
highly
correlated
parameter
(1.43)
•
Total
width
Γwhere
=
Γ
+
Γ
+
Γ
+
Γ
+
Γ
.
Z
ee
µµ
ττ
had the inv
sum
over
all quark final
states,
term 1/RQED removes th
correlations
among
the
fit parameters,
anThe
experimentally-motivated
and
ZTOTALCROSSSECTION
ΓZ = Γee + Γµµ + Γτ τ + Γhad + Γinv .
Thecross-sections
overall hadronic
cros
used
to
describe
the
total
hadronic
and
leptonic
around
!
1
ecauseto
dependNonisproducts
ofΓthe
partial
widths and a
peakmeasured cross-sections
0
12π
Γ
ecays
neutrinos,
Γ
=
N
Γ
,
where
the
number
of
light
ee
=
σthe
σ
the
Γhad cross-sections
=
Γqq . depend
ff sum over all quark final s
inv
ν νν
ν0
ff
ff
=
. on
σ
Because
the
measured
products
oftother
R
otal
width,
the
widths
a
highly
correlated
parameter
set.
In
order
QED •constitute
2
2
ff
the
mass
of
the
Z,
m
;
Z q̸=t to
mZall visible
ΓZ
ed from the measurements of the decay widths
final !
the
total
width, the an
widths
constitute a highlyΓhad
correlated
parame
lations
among
the
fit
parameters,
experimentally-motivated
set
of
six
paramet
=
Γ
.
qq
and
• the
Z total
width,
;width
The
invisible
fromremoves
Zaround
decays
tofinal
neutrinos,
Γinv
=
t
The
term
1/R
thethe
state
QED
Zcross-sections
QED
correlations
among
the
fit
parameters,
an
experimentally-motivat
to describe
the
total
hadronic
and
leptonic
Z q̸peak.
These
• Measurement
of partial
widths
needed
toΓ
prove
universality
of
fermion
coupling
12π Γee Γff
0
neutrino
species,
is
determined
from
the
measureme
The
overall
hadronic
cross-section
is from
parame
to
describe
the
total
hadronic
and
leptonic
cross-sections
arou
+ Γ•hadSimultaneous
(1.44)
.
σ+ff Γ=
The
invisible
width
Zd
inv .used
could
determine
partial
widths + peak position + total
•
the
“hadronic
pole
cross-section”,
2 fit to2 data
mZZ, m
ΓZZ ;
the mass of the
the sum
quarkneutrino
final states,
states and
the over
totalall
width,
species, is determin
width at once, BUT
ss-sections
depend
on correlated
products
oftostate
the
widths
and
alsoand
on
• highly
the
mass
offinal
the
Z,
mpartial
states
the
total
width, of
ZΓ;ee Γ
12π
!
had
–
partial
widths
due
constraint
on
total
sum
The
term
1/R
removes
the
QED
correction
included
in
the
definition
0
QED
the Z total width, ΓZ ;
;
σ
≡
Γ
=
Γ
+
Γµµ
+Γqq
Γτto
Γhad + Γinv .
Γ
=
.
had
Z
ee
τ +
2
2
had
constitute
a
highly
correlated
parameter
set.
In
order
reduce
mparametrised
ΓZ to reduce
overall hadronic
cross-section
isparameters
int terms
ofΓthe
hadronic
width
Z
• The
Convenient
to• define
different
set
of
correlation
=
Γ
+
Γ
+ Γτ τ
q̸
=
Z
ee
µµ
the
Z
total
width,
Γ
;
Z
arameters,
an
experimentally-motivated
of
six since
parameters
is could
the
pole
cross-section”,
the “hadronic
sum
over
all
quark
finaltypically
states,have
– ratio
of similar
quantities
reducedset
correlation
common
factors
cancel on
Because
the
measured
cross-sections
depend
• the three ratios
Because
measured
cro
out leptonic
Thewidth,
invisible
width
fromconstitute
Zare
decaystheto
neutrinos,
dronic and
cross-sections
around
the Zthe
peak.
These
!• the “hadronic
the pole
total
widths
a
highly
cor
cross-section”, the total width, the widths
Γ0had = 12πΓΓ
.
neutrino
species,
isfit
determined
fromantheexperim
measur
qqee Γhad
0
0
0
correlations
among
the
parameters,
; Re ≡ Γhad /Γee , Rµ ≡ Γhad /Γµµcorrelations
σhad ≡ q̸=t2
and Rτ ≡among
Γhad /Γthe
τ τ . fit p
2
states
and the
total
width,
mZ ΓZ
Γ
Γ
12π
used
to
describe
the
total
hadronic
and leptonic
cro
ee had
0
used
to
describe
the
total
ha
;
σ
≡
The invisible width from IfZ had
decaysuniversality
to neutrinos,
Γinv = Nνthe
Γννlast
, where
Nratios
number
ν is the
2
2 is assumed,
lepton
three
reduce
to a
m
Γ
Γ
=
Γ
+
Γ
+
Γ
+
Γ
+
Γ
.
Z
ee
µµ
τ
τ
had
inv
Z
Z
the
three
ratios
Shahram
Rahatlou,
Roma Sapienza
INFN
• the measurements
mass of the Z,ofmthe
• the mass
of the
Z, 36m
neutrino
species,
is &determined
from
widths
to all
visi
Z;
Z ; decay
SMINPUTTOZ-POLEMEASUREMENTS
The ∆α term arises from the running of the electromagnetic coupling due to ferm
the photon propagator, and is usually divided into three categories: from lepton
quark loops and light quark (u/d/s/c/b) loops:
(5)
• Precision measurements
LEP
rely
on
parameters
not
known a-priori
∆α(s) = at∆α
(s)
+
∆α
(s)
+
∆α
eµτ
top
had (s).
– coupling constants for weak, electromagnetic, and strong interaction
terms ∆αeµτ (s) and ∆αtop (s) can be precisely calculated, whereas the term
– fermionThe
masses
– vector boson
masses
best determined
by analysing low-energy e+ e− data using a dispersion relation (see
and Z massinto
‣ Correlation
Thesebetween
eﬀectsphoton,
are W
absorbed
– Higgs mass
α as:
α(0)
.
α(s) =
1 − ∆α(s)
• Some parameters are well known, others can be constrained from
precision
2
At LEP/SLC energies, α is increased from the zero q limit of 1/137.036 to 1/128
measurements
The weak part of the corrections contains ∆ρ (see Equation 1.24) plus a rema
– Light fermion masses well known. Small and well calculated corrections at Z pole
2 QED
– Photon mass fixed to be zerocos
from
θW
+···
− 2 at ∆ρ
w = precisely
– Z mass: can be∆r
measured
Z pole
From measurement of muon lifetime
sin θW
Calculation at 2-loop level GF
2 g2
∆rwf = −∆ρ + · · · .
=
= 1.16637(1) · 10 5 GeV 2
2
~c
8 mW
• W mass: correlated to Z mass and Fermi Constant GF
It should be noted that since GF and mZ are better determined than mW , Eq
– GF known with very high precision far beyond reach for mW measurements
and 1.25 are often used to eliminate direct dependence on mW [27]:
‣ Assume GF to be fixed and treat mW as function of mZ to be constrained with data
m2W
m2Z
=
2
⎛
#
$
$
⎝1 + %1 − 4 √
⎞
πα
1
⎠ . Running of α
2GF m2Z 1 − ∆r
This substitution introduces further significant mt and mH dependencies throu
lept
Shahram Rahatlou, Roma
Sapienza & INFN
example,
in Equation 1.15 sin2 θeﬀ
receives radiative corrections both from ∆κ
37 se
SMPARAMETERSTOBEEXTRACTEDFROMMEASUREMENTS
2
↵(m
• QED coupling constant
Z)
– more precisely the hadronic corrections to it ↵(m2Z ) ! ↵had (m2Z )
2
↵
(m
S
• QCD coupling constant
Z)
– most precise measurement if EW sector well understood
• Z mass mZ
• And more importantly two parameters not directly accessible at LEP
– Higgs mass mH
– Top mass mt
Source
(5)
∆αhad (m2Z )
ΓZ
0
σhad
[MeV]
[nb]
Rℓ0
Rb0
ρℓ
lept
sin2 θeﬀ
mW
[MeV]
0.00035
0.3 0.001 0.002 0.00001
—
0.00012
6
0.003
1.6 0.015 0.020
—
—
0.00001
2
mZ
2.1 MeV
0.2 0.002
—
—
0.00002
3
mt
4.3 GeV
1.0 0.003 0.002 0.00016 0.0004
0.00014
26
0.2
1.3 0.001 0.004 0.00002 0.0003
0.00022
28
0.1 0.001 0.001 0.00002
—
0.00005
4
2.3 0.037 0.025 0.00065 0.0010
0.00016
34
αS (m2Z )
log10 (mH /GeV)
Theory
Experiment
Shahram Rahatlou, Roma Sapienza & INFN
δ
—
Table 8.1: Uncertainties on the theoretical calculations of selected Z-pole observables and mW .
Top: parametric uncertainties caused by the five SM input parameters. For each observable,
38
complex form factors, Rf for the overall scale and K
1.4
Standard
Model
Relations
o define the on-shell electroweak mixing angle, θW , toresulting
all orders,
terms ofeﬀective
the vector
boson
in in
complex
couplings:
CHOOSINGBESTPSEUDO-OBSERVABLES
!
+
+
pole masses:
! e
e
b
n the SM at tree level, the relationship between the weak and electromagnetic
couplings
is
f
2
G
=
R
(T
−
2Q
K
sin
θ
)
2
Vf
f
f f
W
3
mW
!
iven ρby =
!
W
.
(1.10)
0
t
f
2
2
θW
Rf T3 . to SM parameters
GAf =
Z cos πα
• Eachmexperimental
measurement has different
sensitivity
W
t
GF = √ 2
,
(1.4)
2
tree
n the following,
ρ0to
= 1constrain.
is assumed.
we want
Choose
those with
2m
In terms of the real parts of the"/Z
complex form
W sin θW
"/Z
t
W
The bulk
of the electroweak
corrections
[25] to the couplings at the Z-pole is absorbed into
–
highest
sensitivity
to
m
t and mH (through radiative corrections)
where
GFform
is the
Fermi
constant
determined in muon decay,
is the
ρon-shell
1+
∆ρse +
∆ρf fineomplex
factors,
Rf for
the
electroweak
mixing
angle,
f ≡ αℜ(R
f )! =electromagnetic
! overall scale and Kf for 2the
tree
–
small
dependency
on
QCD
corrections
e
b
e
tructure
constant,
m
is
the
W
boson
mass,
and
sin
θ
theℜ(K
electroweak
mixing angle. In
W
Wκf is≡
esulting in complex eﬀective couplings:
f ) = 1 + ∆κse + ∆κf ,
ddition,
the relationship
between
the neutral
and charged
weak couplings
ismost
fixed
by the ratio
!
• Parameters
most
sensitive
to
radiative
corrections
will
be
+ − powerful
corrections
to the process
e e angle
→ bb. and the
f
the eﬀective
electroweak
mixing
= ZR
2Qf Kf sin2 θW )Figure 1.10: Vertex
(1.11)
f the GW
boson
masses:
Vf and
f (T3 −
!
!
b
facto
b
real
f
mf 2W
R
GAf =
T3f .
(1.12)
sin2 θeﬀ
≡ κf sin2 θW
.
(1.5)
ρ0 =
√
2
tree
2
f
2
f
so
that:
mZ cos θW
ρf (T3 − 2Qf sin θeﬀ )
gVf ≡
! form
" factors,
n terms of the real parts of gthe complex
√
GVf
f
Vf
2 f
ρ
T
g
≡
=
1
−
4|Q
|
sin
θ
.
(1
=
ℜ
f 3 , in the Minimal
f
eﬀ Af
The ρ0 parameter [25] is determined
by
the
Higgs
structure
of
the
theory;
gAf se + ∆ρf GAf
ρf ≡ ℜ(Rf ) = 1 + ∆ρ
(1.13)
flavor tandard Model containing only Higgs doublets,
ρ0 = 1.
27
The
quantities
∆ρsespecific
and ∆κse are universal corrections arising from
the propagator
κ
≡
ℜ(K
)
=
1
+
∆κ
+
∆κ
,
(1.14)
f
f
se
f
The fermions are energies,
arrangedwhile
in weak-isospin
doublets for left-handed particles and weak∆ρf and ∆κf are flavour-specific vertex corrections. For simplicity we ign
sospin
singlets
for right-handed
particles,
shown
in Table
1.3.arein
The
interaction
of the
Z
themixing
small imaginary
of these
corrections
most
ofas:
the following
discussion.
he eﬀective
electroweak
angle
andcomponents
theas
real
eﬀective
couplings
defined
self-energy
oson with fermions depends
on charge,
the third component of weak-isospin, T3 , and
leading order
terms inQ,
∆ρand
se and ∆κse for mH ≫ mW are [27]:
2 f
$
%
&
#
sinby
θeﬀ
sin2 θright-handed
(1.15)
s given
the ≡left-κf and
couplings:
W
2
2
2
2
sin θW
mH
5
3G
mt
√
F mW
f ∆ρ
2
f
−
ln 2 −
+···
(1
= θeﬀ√) 2
(1.16)
sef sin
√ ρf (T
2
2
tree gVf ≡
f 3 − 2Q
2 tree
mW cos θW
mW 6
8 2π
gL
=
ρ√
(1.6)
0 (T3 −
f Qf sin θW )
#
$
%
&
(1.17)
g
≡ √ ρf T3 , 2 tree
2
2
2
2
tree Af
3G
m
10
m
cos
θ
m
5
F
W
t
H
gR
= − ρ0 Qf sin∆κθse
,
(1.7)
√ W
−
ln
−
+
·
·
·
(1
W =
2
2
2
2
mW sin θW
9
mW 6
8 2π 27
r, equivalently in terms
couplings:
For of
mHvector
≪ mWand
, the axial-vector
Higgs terms are
modified, for example:
&
√ 3Gf m2 # m2 2 tree
2
2
tree
tree
tree
2 m)Z
mH 7π mH mZ
F− W
gV Rahatlou,
≡ gRoma
+ gR& INFN
=
ρ
(T
2Q
sin
θ
(1.8) 39 (1
t
0
f
L Sapienza
3
W
Shahram
√
∆ρ =
+
ln
−
+···
se
SENSITIVITYTOMtANDMH
()(5)
had
()(5)
had
MZ
MZ
%Z
%Z
$0had
R0l
A0,l
fb
$0had
!
+
e
b
b
W
"/Z
!
Al(P')
t
"/Z
t
e
A0,l
fb
W
t
R0b
R0c
A0,b
fb
0,c
Afb
!
b
R0b
W
e
R0c
b
Figure 1.10: Vertex corrections to the process e+ e− → bb.
A0,b
fb
0,c
so that:
gVf
gAf
Ab
= ℜ
!
GVf
GAf
"
Afb
f
= 1 − 4|Qf | sin2 θeﬀ
.
(1.18)
The quantities ∆ρse and ∆κse are universal corrections arising from the propagator selfenergies, while ∆ρf and ∆κf are flavour-specific vertex corrections. For simplicity we ignore
the small imaginary components of these corrections in most of the following discussion. The
leading order terms in ∆ρse and ∆κse for mH ≫ mW are [27]:
Ac
Al(SLD)
lept
sin2+eff
(Qfb)
∆ρse
mW*
∆κse
#
$
%
sin2 θW
m2H
5
3GF m2W m2t
√
−
ln
−
=
2
2
m2W 6
8 2π 2 mW cos θW
#
$
3GF m2W m2t cos2 θW 10
m2
√
=
−
ln 2H −
2
2
2
mW sin θW
9
mW
8 2π
&
+···
%
∆ρse
Mt
#
&
5
+···
6
For mH ≪ mW , the Higgs terms are modified, for example:
%W*
&
3GF m2W m2t
2 m2Z
m2H 7π mH mZ
√
=
+
ln
−
+···
2
2
3 m2W
8 2π 2 mW 3 mW m2Z
! !
sin +!!(e
+MS e )
sin2+W(&N)
g2L(&N)
g2R(&N)
GF m2t
√
+··· ,
4 2π 2
= −2∆κb + · · · .
0
0.2
|1O
theo
/1Mt| &(Mt)/$meas
mW*
(1.21)
%W*
Mt
QW(Cs)
2
! !
sin +!!(e
+MS e )
sin2+W(&N)
g2L(&N)
g2R(&N)
*preliminary
(1.22)
can be determined indirectly, and compared to the direct measurements. The Z-pole measurements, even when taken alone, have suﬃcient power to separate the Higgs and top corrections
Shahram Rahatlou, Roma Sapienza & INFN
Al(SLD)
(1.20)
∆ρ
(1.23)
0.4
0.6
0.8
1
By interpreting the Z-pole measurements in terms of these corrections, the top quark mass
b
Ac
lept
sin2+eff
(Qfb)
*preliminary
∆κb =
Ab
(1.19)
where only internal Higgs loops are considered. Note the change of sign in the slope of the
Higgs correction for low mH seen in Equation 1.21 compared to Equation 1.19, which is due to
contributions from the derivative of the Z self-energy with respect to momentum transfer [28].
Existence of the process e+ e− → Z∗ H (Higgsstrahlung) would tend to reduce the mH dependence
in Equation 1.21 [29]. The radiative corrections have a quadratic dependence on the top quark
mass and a weaker logarithmic dependence on the Higgs boson mass. The flavour dependence
is very small for all fermions, except for the b-quark, where the eﬀects of the diagrams shown in
Figure 1.10 are significant, due to the large mass splitting between the bottom and top quarks
and the size of the diagonal CKM matrix element |Vtb | ≃ 1 , resulting in a significant additional
contribution for bb production [28] (The eﬀects of the oﬀ-diagonal CKM matrix elements are
here negligible.):
QW(Cs)
2
e
!
Al(P')
R0l
!
+
28
0
0.2
0.4
0.6
0.8
1
|1Otheo/1logMH| &(logMH)/$meas
40
ΓINVDEPENDENCYONMtANDMH
250
Measurement
mt [GeV]
()(5)
had= 0.02758 ± 0.00035
)s= 0.118 ± 0.003
175
mH= 114...1000 GeV
100
0.495
0.5
3
%inv [GeV]
10
0.505
Measurement
mH [GeV]
()(5)
had= 0.02758 ± 0.00035
10
)s= 0.118 ± 0.003
mt= 178.0 ± 4.3 GeV
2
0.495
0.5
0.505
%inv [GeV]
Shahram Rahatlou, Roma Sapienza & INFN
41
EFFECTIVEMIXINGANGLE
0,l
Afb
0.23099 ± 0.00053
Al(P')
0.23159 ± 0.00041
Al(SLD)
0.23098 ± 0.00026
0,b
Afb
0,c
Afb
had
Qfb
0.23221 ± 0.00029
0.23220 ± 0.00081
0.2324 ± 0.0012
Average
mH [GeV]
10
10
2
, /d.o.f.: 11.8 / 5
3
2
0.23
Shahram Rahatlou, Roma Sapienza & INFN
0.23153 ± 0.00016
(5)
()had= 0.02758 ± 0.00035
mt= 178.0 ± 4.3 GeV
0.232
2 lept
sin +eff
0.234
2
lept
42
and mW . Each of these measurements imposes a constraint on the size of electroweak
0
ds
in
Figure
8.3)
hin
the
SM
framework,
the
measurement
of
R
eferring
anwhich
even
value
of
m
,
b therefore
corrections,
is lower
graphically
shown
in tFigure
8.3 as provides
a band inparticularly
the (mH , munambiguous
t ) plane.
0
mation
onstable
mhigher
been
measured
smaller
band shifted
upwards in Figure 8.3)
ve
toward
t . If R
b hadin
nt
non-linearities
occur
these
constraints
the its
allowed
mH range.
arkably
against
variations
inover(i.e.,
standard
deviation, the indirect
constraints as
onshown
mt andinmFigure
boththe
move
towardRhigher
H would1.10,
constraints.
gm
to
the
top-dependent
vertex
corrections
quantity
W
b
determination,
the
favoured
value
2 lept
es,
along
the almost parallel and overlapping
bands
of theit210
Γisℓℓ ,largely
sin θeﬀ insensitive
and mW constraints.
ve
to mminimum
decay
widths
to the
broad
t , while as a ratio of hadronic
2 lept
hat,
of
allvery
the sensitive
bands,
only
sin
θeﬀthat
m
to
H
The
Γ•ℓℓinput
band
shown
in Figure
8.3 implies
the Higgs
preferred
mt68
exhibits
minimum
%
CL ainbroad
rwer
SM
parameters,
including
the
mass
of
the
boson,
as
shown
Figure
7.8.
value of mt ,
0
0
nd
m
≈
50
GeV.
In
combination
with
the
R
bandprovides
preferring
an even lower
value of mt ,
arrow
in
Figure
8.3.
H
b
he
SM
framework,
the
measurement
of
R
therefore
particularly
unambiguous
b
nst
variations
in determination of m which is remarkably stable against variations in
0
results
in
an
indirect
tall
on
on
m
.
If
R
had
been
measured
smaller
(i.e., its band shifted
upwards in Figure 8.3)
are
ignored
here,
as
well
as
in
t
b
190
lept
favoured
value
θedard
In contrast
with
the enhanced
stability
of
the
mwould
the
favoured
value
t determination,
eﬀ . deviation,
the
indirect
constraints
on
m
and
m
both
move
toward
higher
%
t
H
lept
50
GeV.
For
50
GeV,
the
rise
2 m
ll
2 lept
2 lept
H <
lept
•
only
parameter
ds,
only
sin
θ
2
is
very
sensitive
to
sin
θ
.
It
should
also
be
noted
that,
of
all
the
bands,
only
sin
H
eﬀ
ong the almost parallel
andeﬀoverlapping bands of the Γℓℓ , sin θeﬀ and mW constraints. θeﬀ
(5) suppressed,
nd
would
be
somewhat
2
()
sensitive
to
nsitive
to
the
value
of
∆α
indicated
by the arrow
in Figure
8.3. minimum
.
Γℓℓ band shown in Figure 8.3
implies
the preferred
m170
a broad
had (m
Z ), as that
t exhibits
mW here, as well as in all
he
Z
decays
to
leptons
would
have
0
The
eﬀects
of
ZH
production,
or
real
Higgsstrahlung,
are
ignored
m
≈
50
GeV.
In
combination
with
the
R
band
preferring
an
even
lower value of mt ,
asH well as in all
b
prel.
ed
on
a
detailed
analysis
[29]
it
is
ts
quoted
in
this
paper.
They
are
negligible
for
m
>
50
GeV.
For
mH <variations
50 GeV, the
H
an indirect
determination of mt which is remarkably
stable
against
in rise
50 inGeV,
the rise
Rb
with
decreasing
m
by
the Γℓℓ of
constraint
band
would
be
somewhat
suppressed,
t In
H predicted
contrast
with
the
enhanced
stability
the
m
determination,
the
favoured
value
gsstrahlung
would
not
appreciably
t
what suppressed, 2 lept
150
2 lepthave
to
the
fact
that
most,
but
not
all,
ZH
events
where
the
Z
decays
to
leptons
would
•
Source
of
sensitivity
of
Higgs
2bands,
lept
very
sensitive
to
sin
θ
.
It
should
also
be
noted
that,
of
all
the
only
sin
θeﬀ
eﬀ
6.
sin
+
tons
would
have (5) to2 Γ rather than Γ . Based on a detailed
eff
classed
as
contributing
analysis [29] it is
had
ℓℓ
vethe
to the
value
of
∆α
(m
),
as
indicated
by
the
arrow
in
Figure
8.3.
mass
to
had
Z
Higgs
boson
the frame-of α , Higgsstrahlung would not appreciably
nalysis
[29]apart
it isfromwithin
luded
that,
the
determination
S are ignored here, as well as in all
eﬀects of ZH production, or real Higgsstrahlung,
130
ng
the
experimental
result
with
the
not
appreciably
the
results
of
the
SM
analyses
presented
in
Section
8.6.
3
uoted in this paper. They are negligible for mH > 50 GeV. For mH < 50 GeV, the 2rise
10 boson within10
10
he
minimalmSM
as
a
function
of
the
The
dependence
of
all
pseudo-observables
on
the
mass
of
the
Higgs
the
frameh decreasing
predicted
by
the
Γ
constraint
band
would
be
somewhat
suppressed,
H
ℓℓ
mresult
[GeV]
Parameter
Value
Correlations
of
the
SM
is
visualised
in
Figures
8.4
to
8.7,
comparing
the
experimental
with the
H
ithin
the
framen
Figure
8.3,
are
clearly
visible.
he fact that most, but not all, ZH(5)events
where
the
Z
decays
to
leptons
would
have
∆αhadthe
(m2Z ) framework
αS (m2Z )
mof
mt minimal
log10 (mH /GeV)
Z the
essed
of
the
observable
calculated
within
SM
as a function
of the
asmeasurements,
contributing
to
Γ
rather
than
Γ
.
Based
on
a
detailed
analysis
[29]
it
is
letry
result
with
the
it
has
already
had
ℓℓ
(5)
∆α
(m2Z ) Non-linear
0.02759±0.00035
1.00
had
s-boson
mass.
eﬀects, as already
observed
inConstraints
Figurewould
are
clearly
visible.
Figure 8.3:
on8.3,
m and
m
from
measurements
of R , Γ , sin θ
and m . Each
d
that,
apart
from
the
determination
of
α
,
Higgsstrahlung
not
appreciably
S
aon
function
of
the
2
thequantity
arising−0.04
from
2 lept
αSSM
(mZ ) prediction
0.1190±0.0027
1.00 band gives the ±1σ constraint from the indicated measurement. The parametric uncertainty
or
the
sin
θ
determined
in
various
asymmetry
measurements, it has already
eﬀ
due to the uncertainty in the hadronic vacuum polarisation, ∆α (m ) = 0.02758 ± 0.00035, is
results
of
the
SM
analyses
presented
in
Section
8.6.
mZ [GeV]
91.1874±0.0021
−0.01
−0.03 not
1.00
early
visible.
uncertainty
of
the
average.
As
a
included
in the
width
of these
bands as it is small
except for
the sin θ
band, where the
shown
in
Figure
7.6
that
the
parametric
uncertainty
on
the
SM
prediction
arising
from
13
dependence
of
all
pseudo-observables
on
the
mass
of
the
Higgs
boson
within
the
frame±1σ uncertainty
mt [GeV]
173±10
−0.03
0.19 −0.07
1.00 is indicated by the arrow labeled ∆α. The direct measurement of m used
2 has
s,)sation
it
already
here is preliminary.
is
one
of
the
limiting
factors
) is
non-negligible
compared
to
the comparing
experimental
uncertainty1.00
of result
the average.
0.43
Zlog
ad
he(mSM
is
visualised
in
Figures
8.4
to
8.7,
the
with theAs a
(m
/GeV)
2.05±
−0.29
0.25
−0.02
0.89experimental
H
10
0.34
ion
arising
from 111±
equence,
the uncertainty
on
the hadronic
vacuum
polarisation
isSM
one
ofa the
limiting
factors
ation
underlines
the190
importance
of0.25of−0.02
m
0.89
he observable
within
the −0.29
framework
the minimal
as1.00
function
of the
H [GeV] calculated
60
eson
As
e average.
extraction
of
theaSapienza
mass
Thisinsituation
underlines
thevisible.
importance of
Shahram Rahatlou,
Roma
& of
INFNthe
43
mass.
Non-linear
eﬀects,
as Higgs
alreadyboson.
observed
Figure 8.3,
are clearly
mt [GeV]
Z-POLERESULTS
t
H
0
b
(5)
had
2
ℓℓ
2
Z
2
lept
eﬀ
W
lept
eﬀ
W
GVf =
Rf!(T3f − 2Qf Kf sin2 θW )
IMPLICATIONOFPRECISIONMEASUREMENTS
GAf
!
f f (T f − 2Qf Kf sin2 θW )
G=
Vf =Rf TR
3
3.
!
f
R
G
=
T
Af
f
In terms of the real parts 3of. the complex form factors,
Inρterms
f ≡
κf ≡
ρf
of
the) real
complex form factors,
ℜ(R
= 1parts
+ ∆ρofse the
+ ∆ρ
f
f
flavor specific
ℜ(K
+ ∆κ
+ ∆κ
,
f ) =f ) 1 =
f
≡ ℜ(R
1 +se∆ρ
+
∆ρ
se
f
κf electroweak
≡ ℜ(Kf ) mixing
= 1 + ∆κ
∆κthe
se +
f , real eﬀective couplings are defined
the eﬀective
angle
and
self-energy
2 f
thesineﬀective
θeﬀ ≡electroweak
κf sin2 θW mixing angle and the real eﬀective couplings are d
√
f 2
2 f
2 ≡
f
ρ
(T
−
2Q
sin
θeﬀ )
g
f
f
Vf
sin θeﬀ ≡ κf 3sin θW
√ √f
f
2 f
ρ T ,
gAf g≡
Vf ≡ f 3ρf (T3 − 2Qf sin θeﬀ )
√
ρf T3f ,
gAf ≡
27
Having determined the five SM input parameters as given in Table 8.2, the parameters
27
discussed in Section 1.4 are then predicted to be:
sin2 θW = 0.22331 ± 0.00062
lept
sin2 θeﬀ
= 0.23149 ± 0.00016
b
sin2 θeﬀ
= 0.23293±0.00031
0.00025
ρℓ = 1.00509±0.00067
0.00081
ρb = 0.99426±0.00079
0.00164
κℓ = 1.0366 ± 0.0025
κb = 1.0431 ± 0.0036
(8.5)
−∆rw = 0.0242 ± 0.0021
∆r = 0.0363 ± 0.0019
The quantities presented here are obtained from the same data set. Hence they are correlated
with the five SM input parameters and cannot be used independently. Predictions of many
more observables within the SM framework are reported in Appendix G.
(5)
Besides the hadronic vacuum polarisation ∆αhad (m2Z ), only results from the Z-pole meaShahram Rahatlou, Roma
Sapienza & INFN
44
surements,
whose precision will not be improved in the near future, are used up to this point.
CONSTRAINTSONTOPMASS@LEP
Mt [GeV]
200
150
Tevatron
SM constraint
68% CL
100
Direct search lower limit (95% CL)
50
1990
1995
2000
2005
Year
Shahram Rahatlou, Roma Sapienza & INFN
45
CONSTRAINTSONTOPANDWMASS
LEP1/SLD/mW/%W
125
+ 12.3
9.5
181.1 !
150
175
200
mt [GeV]
Figure 8.8: Results on the mass of the top quark. The direct measurements of mt a
the Tevatron (top) are compared with the indirect determinations (bottom).
W-Boson Mass [GeV]
Top-Quark Mass [GeV]
CDF
176.1 ± 6.6
TEVATRON
80.452 ± 0.059
D2
179.0 ± 5.1
LEP2
80.412 ± 0.042
Average
178.0 ± 4.3
Average
80.425 ± 0.034
,2/DoF: 0.3 / 1
,2/DoF: 2.6 / 4
LEP1/SLD
172.6
+ 12.3
9.5
LEP1/SLD/mW/%W
125
+ 13.2
! 10.2
181.1 !
150
175
200
NuTeV
80.136 ± 0.084
LEP1/SLD
80.363 ± 0.032
LEP1/SLD/mt
80.373 ± 0.023
80
80.2
80.4
80.6
mW [GeV]
mt [GeV]
Figure
8.9:
Results on the mass of the W boson, mW . The direct measurements of mW
8: Results on the mass of the top quark. The direct measurements
of m
t at Run-I of
(preliminary) and at Run-I of the Tevatron (top) are compared with the indirect deter
ron (top) are compared with the indirect determinations (bottom).
(bottom). The NuTeV result interpreted in terms of mW is shown separately.
W-Boson Mass [GeV]
212
TEVATRON
Shahram Rahatlou, Roma Sapienza & INFN
80.452 ± 0.059
46
160
10
10
IMPORTANCE
OFDIRECT10
W
ANDTOPMEASUREMENTS
m [GeV]
2
3
H
80.5
2
2
High Q except mt
68% CL
High Q except mW/%W
68% CL
!
mW (LEP2 prel., pp)
mt [GeV]
mW [GeV]
200
80.4
180
mt (Tevatron)
80.3
Excluded
10
10
2
10
160
3
Excluded
10
10
2
10
3
mH [GeV]
mH [GeV]
74
215129±49
Shahram Rahatlou, Roma Sapienza & INFN
−0.46
0.18 80.4
0.06 0.67
W
mH [GeV]
[GeV]
Parameter
Value
Correlations
2
2
Contour curves of 68% probability in (top) the (mt∆α
, m(5)
and (bottom)
the mt log (mH /GeV)
H ) plane
had (mZ ) αS (mZ ) 80.5mZ
2 10
High
Q
except mW/%W
plane, based on all 18(5)measurements
except
the
direct
measurement
of
m
and
the
t
2
∆αhad
0.02767±0.00034
1.00 of these excluded
Z)
urements of mW and
ΓW(m
, respectively.
The direct measurements
68% CL
2
α
(m
)
0.1188±0.0027
−0.02
1.00
are shown as the horizontal
bands of width ±1 standard deviation. The vertical
S
Z
the 95% confidencemlevel
exclusion91.1874±0.0021
limit on mH of 114.4 GeV
derived−0.02
from the direct
−0.01
1.00
Z [GeV]
!
EP-II [39]. The direct
measurements178.5±3.9
of mW and ΓW used −0.05
here are preliminary.
mt [GeV]
0.11 −0.03 1.00
mW (LEP2 prel., pp)
log10 (mH /GeV)
2.11±0.20
−0.46
0.18
0.06 0.67
1.00
1.00
47
CONSTRAINTSONHIGGSMASS
80.5
LEP1, SLD data
!
LEP2 (prel.), pp data
mW [GeV]
68% CL
80.4
80.3
()
mH [GeV]
114
300
150
1000
175
200
mt [GeV]
Shahram Rahatlou, Roma Sapienza & INFN
48
INCLUSIONOFLHC
mW [GeV]
80.5
March 2012
LHC excluded
LEP2 and Tevatron
LEP1 and SLD
68% CL
80.4
80.3 mH [GeV]
114
300 600 1000
155
175
195
mt [GeV]
Shahram Rahatlou, Roma Sapienza & INFN
49
SINGLETOP
The single-top processes
SINGLETOP
Electroweak
top production
t-channel
W-associated (tW)
s-channel
single-top
Tevatron: pp @1.96
TeV( N. KidonakisPhys. Rev. D 82,
2.08±0.12 pb
0.22±0.08 pb
1.046±0.058 pb
LHC pp @7 TeV( N. Kidonakis
64.6±2.1 pb
15.6±1.2 pb
4.59±0.19 pb
LHC pp @8 TeV( N. Kidonakis
87.1±2.8 pb
22.2±1.5 pb
5.55±0.22 pb
054018 (2010) and arxiv:0909.0037
Phys. arXiv:1205.3453)
arXiv:1205.3453)
Alberto Orso Maria Iorio
Shahram Rahatlou, Roma Sapienza & INFN
7
53
LEPTONIC
S
INGLE
T
OP
IN
T
W
Single-top t-channel:
leptonic events topology
Signature
“Light” jet j' with high
pseudorapidity |ηj'|
q'
µ or e
l
t
νl
t
Missing energy
b-jet:
central, high pT
b
2nd b-jet:
broad |η|, low pT
b
Main backgrounds:
∘ tt : both semileptonic and di-leptonic topologies
∘ W(→ lν )+jets : with contribution from W+(u,s,d,g) and W+(c,b)
∘ Multijet QCD → l + jets : reduced to extreme kinematic regions by selection cuts
Alberto Orso Maria Iorio
Shahram Rahatlou, Roma Sapienza & INFN
9
54
T HE C HALLENGE
EXPERIMENTALCHALLENGE
• Not very distinct signature with
many sources of background
• S : B ∼ 1 : 20 after final
selection
• No “golden” variable
CDF Preliminary 3.2 fb
CDF Data
Single Top
Normalized to Prediction
• S : B ∼ 1 : 109 before trigger
4000
Candidate Events
• Rare process at the Tevatron
-1
All Channels
tt
W+HF
W+LF
Other
Uncertainty
3000
2000
1000
• Large systematics uncertainties
0
1J
2J
3J
4J
Jet Multiplicity
• Sophisticated analysis methods needed
• Current approaches at CDF: Likelihood Function, Matrix Element,
Neural Network, Boosted Decision Trees
• S : B > 1 : 1 in most significant bins
ShahramBruno
Rahatlou,
Roma Sapienza
Casal
(IFCA)& INFN
Single Top Observation at CDF
16/7/2009
5 / 55
14
S
T CDF
INGLEAT CDF
OP AT
S INGLE T OP S ELECTION
• Top decays most of the times to Wb
• W + 2 or 3 jets with ET > 20 GeV
• One lepton (electron or muon) with
pT > 20 GeV
• Mainly from standard high pT lepton triggers
• Extended muon coverage from missing ET
dedicated triggers (30% gain in signal
acceptance)
• Missing transverse energy from neutrino,
/ T > 25 GeV
E
• Veto “non-W”, Z, dilepton, conversion,
cosmics
• At least one b-tagged jet (displaced
secondary vertex algorithm)
• Main backgrounds: W+Heavy Flavor,
W+Mistags, t t̄,...
Shahram
Rahatlou,
Roma(IFCA)
Sapienza & INFN
Bruno
Casal
Single Top Observation at CDF
Number of Events in 3.2 fb−1
W + 2 jets
W + 3 jets
s-channel
58.1 ± 8.4
19.2 ± 2.8
t-channel
87.6 ± 13.0
26.2 ± 3.9
W bb̄
656.9 ± 198.0 201.3 ± 60.8
292.2 ± 90.1
98.1 ± 30.2
W cc̄
250.4 ± 77.2
52.1 ± 16.0
W cj
Mistags
501.3 ± 69.6 151.9 ± 21.4
89.6 ± 35.8
35.1 ± 14.0
non-W
58.5 ± 6.6
21.2 ± 2.4
WW
WZ
28.9 ± 2.4
8.5 ± 0.7
0.9 ± 0.1
0.4 ± 0.0
ZZ
36.5 ± 5.6
15.6 ± 2.4
Z + jets
69.2 ± 10.0
60.2 ± 8.7
tt̄ dilepton
tt̄ non-dilepton
134.9 ± 19.6 421.8 ± 61.1
Total signal
145.7 ± 21.4
45.4 ± 6.7
Total prediction 2265.0 ± 375.4 1111.5 ± 129.5
Observed in data
2229
1086
Process
16/7/2009
6 / 1456
t-channel Cross Section σt [pb]
OBSERVATIONATTEVATRON
5
is ∂σs+t /∂mt = +
|Vtb | = 0.91 ± 0.11
confidence level lo
diction of [9, 10] fo
ing that |Vtb |2 ≫ |
fit for σs and σt , u
as the one-dimens
σt = 0.8+0.4
−0.4 pb.
SD + MJ Combination
CDF Data
68.3% CL
95.5% CL
99.7% CL
SM (NLO)
SM (NNNLO)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
s-channel Cross Section σs [pb]
FIG. 40: The results of the two-dimensional fit for σs and
σt . &The
Shahram Rahatlou, Roma Sapienza
INFN black point shows the best fit value, and the 68.3%,
We thank the F
of the participatin
tions. This work w
of Energy and Na
Istituto Nazionale
Education, Cultu
Japan; the Natur
Council of Canad
Republic of China
tion; the A.P. Sloa
57
OBSERVATIONOFSINGLETOP@CDFANDD0
• First Observation of Electroweak Single Top Quark Production (CDF)
– http://arxiv.org/abs/0903.0885
• Observation of Single Top-Quark Production (D0)
– http://arxiv.org/abs/0903.0850
• Analysis underway at both ATLAS and CMS but will be a challenging
measurement also at LHC
– Expect measurement by end of 2011 with 1 fb-1 of accumulated data
2010
• Measurement of the t-channel single top quark at CMS
– arXiv:1106.3052v1, published in Phys. Rev. Lett. 107 (2011) 091802
• Measurement of single top at ATLAS
– W+t channel (ATLAS-CONF-2011-104), t-channel (ATLAS-CONF-2011-101), s-channel (ATLAS-CONF-2011-118)
Shahram Rahatlou, Roma Sapienza & INFN
58
L=
W
+ ~pT,µ · ~ETmiss .
(4)
Δφ(l1,E
SINGLETOPATLHC
)
T
2
nt approaches are proposed to determine pz,n if two real solutions exist [3, 4]. The
so- 5: Cuts to suppress tt and Drell-Yan background in
Fig.
with less absolute value is taken in this analysis. For events with imaginary solutions,
therealATLAS [9] and CMS [8] Wt-channel analyses. Left:
smeared within its width (80.4 ± 2.1) according to a Breit-Wigner distribution so as
system
ns can be found.
Transverse momentum of the (jlE/t )-system PT
. Right:
2 (a, b) illustrates the reconstructed top quark mass for data and simulation. The detecTriangle cut in the ∆φ(l1,2 , E/t ) plane.
ects, specially uncertainties in pz,n solutions, result in the broadness of the distribution as
s the change in the mean mass value. The distribution of reconstructed cos ql⇤ in data is
600
500
data
t-channel
tW-channel
s-channel
tt
Di-boson
W+Jets
*
γ /Z+Jets
QCD
Stat. Unc.
900
800
700
600
400
500
300
400
1200
CMS Preliminary, s = 7 TeV
2.1 fb-1, ee/eµ/ µµ
data
tW
tt
Z/ γ *+jets
1000
Other
events / 2.1 fb-1
data
t-channel
tW-channel
s-channel
tt
Di-boson
W+Jets
*
γ /Z+Jets
QCD
Stat. Unc.
800
Number of Events
-1
CMS preliminary, 5.3 fb at s = 8 TeV
Number of events
Number of events
-1
CMS preliminary, 1.14 fb at s = 7 TeV
700
600
ATLAS Preliminary
500
Dilepton Combined
Data
Wt
Fake leptons
Z(→ ee/µµ)+jets
Z(→ ττ)+jets
∫ L dt = 0.70 fb
-1
400
Diboson
tt
300
600
200
400
300
200
200
100
200
100
100
100
150
200
250
300
350
400 450 500
mbµν (GeV)
50
100
(a)
250
300
350
400 450 500
mµν b (GeV)
-1
CMS preliminary, 1.14 fb at s = 7 TeV
500
Number of events
600
CMS preliminary, 5.3 fb at s = 8 TeV
data
t-channel
tW-channel
s-channel
tt
Di-boson
W+Jets
*
γ /Z+Jets
QCD
Stat. Unc.
700
Candidate Events
Number of events
200
(b)
-1
800
150
data
t-channel
tW-channel
s-channel
tt
Di-boson
W+Jets
*
γ /Z+Jets
QCD
Stat. Unc.
600
500
ATLAS Preliminary
2 jets 2-tag
0.70 fb-1 @ 7 TeV
400
60
1 jet 1 tag
2 jet 1 tag
2 jet 2 tag
1
2
3
4
5
6
7
8
9
EPJ Web of Confer
Number of Jets
Fig. 6: Results of the Wt-channel analyses for ee, µµ and
eµ channels combined. Left: CMS
[8] fits the three jet
arXiv:1205.5764
bins
indicated simultaneously to constrain signal and back2
grounds.
Right:
ATLAS [9] uses the first bin as signal bin,
1.8
ATLAS
Preliminary
the
1.6 tt background is estimated from the ≥ 2-jets sideband.
-log likelihood
0
50
0 0
6C
Ana
40
−1
ATLAS has analyzed the full 2010 dataset of 35 pbby
[5]t
and updated this analysis with 700 pb−1 of 2011 data
[9].
and
20
Both collaborations select the dilepton signatures only (ee,
been
µµ, eµ) where both the associated W and the W stemming
(c)
(d)
0
0 (a, b) and200
400of reconstructed
600 cosfrom
intwo
a
2: The reconstructed top quark mass
the distribution
q (c, the top decay leptonically. Due to that, exactly
m
[GeV/c
/σ
data and simulation at 7 TeV (a, c) and 8 TeV (b, d) center-of-mass
energies.] Corrections
opposite-sign leptonsσare required.
ATLAS cuts on E/t > 50
sure
different sources
are
considered
in
simulation.
The
shape
and
normalization
for
QCD
p
GeV in all three signatures. CMS cuts on E/t > 30 GeV in
400
300
200
100
0
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
300
1.4
1.2
200
1
100
0.4
0.6
0.8
1
cos(θl*)
0
-1
0.8
0.6
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
cos(θl*)
0.4
0.2
2
top, b−jet1
Roma
Sapienza
& INFN
ets andShahram
at s =Rahatlou,
8 TeV for
W+jets
events
are obtained from data [18, 19].
⇤0
l 0
1
2
3
4 obs 5
6
(s−channel)
t
7
8
(s−channel)
SM
t
59
SINGLETOP@LHC
Shahram Rahatlou, Roma Sapienza & INFN
60
MEASUREMENTOFCROSSSECTION
Shahram Rahatlou, Roma Sapienza & INFN
61
Vbar+X
Shahram Rahatlou, Roma Sapienza & INFN
64
Vbar+W/Z
Shahram Rahatlou, Roma Sapienza & INFN
65
new physics searches.
•
TTW
How to look for such a rare and complex final state? Same sign leptons!
W
Università
Roma-INFN
Roma
1
• rare SM process andSapienza
background
fordinew
physics
events
Fabrizio Margaroli
Shahram Rahatlou, Roma Sapienza & INFN
53
66
Vbar+W/ZCROSSSECTION
Shahram Rahatlou, Roma Sapienza & INFN
67
Vbar+HIGGS
Dominant background if H → bb
Shahram Rahatlou, Roma Sapienza & INFN
68
Where do we stand
•
Vbar+H➞γγ
ttH is difficult: cross section 130±20fb (@8TeV) approx 1/100 of gg→H
•
•
?
CDF/CMS/ATLAS
investigated semileptonic
and dileptonic decays of
ttbar, and bbar decays of H
Limits ranging from
4.5xSM(CMS) to
10.5xSM(ATLAS) using 5fb
@7TeV
?
• Rare but useful process to measure
Higgs
coupling
constants
Ttbar in lepton+jets,
Plus dilepton
– to be discussed in detail after Higgs
• Experimentally challenging due to very small cross section
Fabrizio
Margarolifb
– 130±20
!
Shahram Rahatlou, Roma Sapienza & INFN
Sapienza Università di Roma-INFN Roma 1
54
69