E FFECTIVE L AGRANGIAN FOR H IGGS I NTERACTIONS Concha Gonzalez-Garcia (YITP Stony Brook & ICREA U. Barcelona ) MPIK Heidelberg, July 24th 2013 T. Corbett, O. Eboli and J. Gonzalez-Fraile arXiv:1207.1344, 1211.4580, 1304.1151 http://hep.if.usp.br/Higgs
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Concha Gonzalez-Garcia · EFFECTIVE LAGRANGIAN FOR HIGGS INTERACTIONS Concha Gonzalez-Garcia (YITP Stony Brook & ICREA U. Barcelona ) MPIK Heidelberg, July 24th 2013 T. Corbett, O.
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EFFECTIVE LAGRANGIAN FOR
HIGGS INTERACTIONS
Concha Gonzalez-Garcia(YITP Stony Brook & ICREA U. Barcelona )
MPIK Heidelberg, July 24th 2013
T. Corbett, O. Eboli and J. Gonzalez-Fraile
arXiv:1207.1344, 1211.4580, 1304.1151
http://hep.if.usp.br/Higgs
EFFECTIVE LAGRANGIAN FOR
HIGGS INTERACTIONS
Concha Gonzalez-Garcia(ICREA-U Barcelona & YITP-Stony Brook)
MPKI Heidelberg, July 24th, 2013
OUTLINE
Introduction: the SM Higgs Boson
Effective Lagrangian for SM-like Higgs Boson
Data Driven Choice of Operator Basis
Application to Present Analysis of Higgs Data
Summary
Introduction: the Standard Model
Introduction: the Standard Model• The SM is a gauge theory based on the symmetry group
SU(3)C × SU(2)L × U(1)Y
Introduction: the Standard Model• The SM is a gauge theory based on the symmetry group
SU(3)C × SU(2)L × U(1)Y
With matter made of3 fermion generationswith quantum numbers
(1, 2)− 12
(3, 2) 16
(1, 1)−1 (3, 1) 23
(3, 1)− 13
(
νe
e
)
L
(
ui
di
)
LeR ui
R diR
(
νµ
µ
)
L
(
ci
si
)
LµR ci
R siR
(
ντ
τ
)
L
(
ti
bi
)
LτR tiR bi
R
And the gauge bosonscarriersof thestrong, weakandelectromagneticinteractions
g W± Z0 γ
Introduction: the Standard Model• The SM is a gauge theory based on the symmetry group
SU(3)C × SU(2)L × U(1)Y
With matter made of3 fermion generationswith quantum numbers
(1, 2)− 12
(3, 2) 16
(1, 1)−1 (3, 1) 23
(3, 1)− 13
(
νe
e
)
L
(
ui
di
)
LeR ui
R diR
(
νµ
µ
)
L
(
ci
si
)
LµR ci
R siR
(
ντ
τ
)
L
(
ti
bi
)
LτR tiR bi
R
And the gauge bosonscarriersof thestrong, weakandelectromagneticinteractions
g W± Z0 γ
• In a gauge theory the Lagrangian is fully determined by symmetry• In 90’s we tested fermion-GB interactions to better than 1%• Also we have tested GB self-interactions to 5-10%
Introduction: SM• Plus: Gauge Theories are renormalizable (theoretically sound)
• Minus: GS forbids mass for gauge-bosons (for SM group also for fermions)
VµV µ or fRfL are not Gauge Invariant
• But we know that many particles have mass:
Most fermionshave masses
W± andZ0 have mass (weak interaction is short range)
Introduction: SM• Plus: Gauge Theories are renormalizable (theoretically sound)
• Minus: GS forbids mass for gauge-bosons (for SM group also for fermions)
VµV µ or fRfL are not Gauge Invariant
• But we know that many particles have mass:
Most fermionshave masses
W± andZ0 have mass (weak interaction is short range)
• To give mass to these states without spoiling renormalizability:
⇒ Spontaneous Symmetry Breaking
≡ It is the ground state (vacuum) which breaks the symmetry
≡ Vacuum is invariant only under a subgroup of the GS
⇒ There will be massless excitations
⇒ In presence of long range forces massless excitations disappear
and the force becomes short ranged
≡ Generation of mass for the Gauge Bosons
Introduction: SM• Plus: Gauge Theories are renormalizable (theoretically sound)
• Minus: GS forbids mass for gauge-bosons (for SM group also for fermions)
VµV µ or fRfL are not Gauge Invariant
• But we know that many particles have mass:
Most fermionshave masses
W± andZ0 have mass (weak interaction is short range)
• To give mass to these states without spoiling renormalizability:
⇒ Spontaneous Symmetry Breaking
≡ It is the ground state (vacuum) which breaks the symmetry
≡ Vacuum is invariant only under a subgroup of the GS
⇒ There will be massless excitations
⇒ In presence of long range forces massless excitations disappear
and the force becomes short ranged
≡ Generation of mass for the Gauge Bosons
• In SM EWSSB: SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM
Introduction: Higgs Mechanism of EWSB
• To allow for EWSB we need to addsomethingto parametrize this non-trivial vacuum
Lorentz Invariance⇒ somethingcannot have spin≡ scalar
EWSB⇒ somethingmust benon-singletSU(2)L but colorlessandelec neutral
Introduction: Higgs Mechanism of EWSB
• To allow for EWSB we need to addsomethingto parametrize this non-trivial vacuum
Lorentz Invariance⇒ somethingcannot have spin≡ scalar
EWSB⇒ somethingmust benon-singletSU(2)L but colorlessandelec neutral
• Most minimal choice:
something≡ fundamental scalarSU(2) doublet: Φ(1, 2) 12
=
(
φ+
φ0
)
With particular form of the potential[Englert& Brout;Higgs:Guralnik&Hagen&Kibble]
LΦ = (DµΦ)(DµΦ)† − (µ2|Φ|2 + λ|Φ|4)with µ2 < 0
Introduction: Higgs Mechanism of EWSB
• To allow for EWSB we need to addsomethingto parametrize this non-trivial vacuum
Lorentz Invariance⇒ somethingcannot have spin≡ scalar
EWSB⇒ somethingmust benon-singletSU(2)L but colorlessandelec neutral
• Most minimal choice:
something≡ fundamental scalarSU(2) doublet: Φ(1, 2) 12
=
(
φ+
φ0
)
With particular form of the potential[Englert& Brout;Higgs:Guralnik&Hagen&Kibble]
LΦ = (DµΦ)(DµΦ)† − (µ2|Φ|2 + λ|Φ|4)with µ2 < 0
• SSB≡ choice of vacuum:Φ0 = 1√2
(
0
v
)
About this vacuum
⇒ W andZ become massive
⇒ fermionscan acquire a mass via Yukawa interactionsλf ffΦ
⇒ Physical scalar excitationh(x): Φ(x) = 1√2
(
0
v + h(x)
)
The Higgs Boson
Intro: The Higgs Boson
• A few properties of the Higgs Boson
∗ Neutral Scalar with CP=+10+
∗ Its mass is the only free parametermH =√
2λ v
∗ Interactions with GBand fermionsproportional to their masses
Intro: Higgs Decay Modes
Γ(h → ff) =GF m2
f (Nc)
4√
2πMh (1 − rf )
32 ri ≡ 4M2
i
M2h
Γ(h → W+W−) =GF M3
h
8π√
2
√1 − rW (1 − rW + 3
4r2
W )
Γ(h → ZZ) =GF M3
h
8π√
2
√1 − rZ(1 − rZ + 3
4r2
Z)
Γ0(h → gg) =GF α2
sM3h
64√
2π3 |X
q
F1/2(rq) |2 Γ(h → γγ) = α2GF
128√
2π3 gV M3h |
X
q,W
NciQ2i Fi(ri) |2
F1/2(rq) ≡ −2rq [1 + (1 − rq)f(rq)] f(x) =
8
>
>
>
>
>
<
>
>
>
>
>
:
sin−2(p
1/x), if x ≥ 1
− 14
2
6
6
4
log
0
B
B
@
1+√
1−x1−
√1−x
1
C
C
A
− iπ
3
7
7
5
2
, if x < 1,FW (rW ) = 2 + 3rW [1 + (2 − rW )f(rW )]
50.0 100.0 150.0 200.0Mh (GeV)
10-4
10-3
10-2
10-1
100
Hig
gs B
ranc
hing
Rat
ios
Higgs Branching Ratios to Fermion Pairs
bb
τ+τ-
cc
ss
µ+µ-
50.0 100.0 150.0 200.0Mh (GeV)
10-6
10-5
10-4
10-3
10-2
10-1
100
Hig
gs B
ranc
hing
Rat
ios
Higgs Branching Ratios to Gauge Boson Pairs
gg
γγ
ZγZZ*
WW*
50 100 200 500 100010
-3
10-2
10-1
1
10
102
Γ (H
)
(G
eV)
MH (GeV)
H→tt
140
H→ZZ
H→WW
Intro: Higgs at e+e−
σ(e+e− → Zh) =πα2λ
1/2Zh [λZh + 12
M2Z
s][1 + (1 − 4 sin2 θW )2]
192s sin4 θW cos4 θW (1 − M2Z/s)2
λZh ≡ (1 − M2h+M2
Zs
)2 − 4M2hM2
Zs2 s = (pe+ + pe−)2
180.0 190.0 200.0 210.0ECM (GeV)
0.0
0.2
0.4
0.6
σ (p
b)
Mh=90 GeVMh=100 GeVMh=110 GeV
e+e
- -> Zh
Searches at LEP (e+e−√
s = 90 − 210 GeV) ⇒ MH ≥ 114.4 GeV
Intro: Higgs at Hadron Collidersgg t H�pp (a) �pp �q0q W WH(b) �pp �qq Zf gZf gH(c) W;Zf gW;Zf gH�pp (d)Tevatron (pp