1. overview of electroweak precision tests 2. constraints...
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Electroweak precision tests & constraints on neutrino models
A. Freitas
University of Pittsburgh
39th International School of Nuclear Physics, Erice-Silicy
1. Overview of electroweak precision tests
2. Constraints on neutrino models
3. Future e+e− colliders
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Overview of electroweak precision tests 1/21
W mass
µ decay in Fermi Model
µ−νµ
νe
e−
GF
µ−νµ
νe
e−γQED corr.(2-loop)
Γµ =G2Fm
5µ
192π3F
(m2em2µ
)
(1 + ∆q)
Ritbergen, Stuart ’98Pak, Czarnecki ’08
µ decay in Standard Model
µ−νµ
νe
e−
W−µ−
νµ
νe
e−
W−
Z
G2F√2
=e2
8s2wM2W
(1 + ∆r)
electroweak corrections
-
Z-pole observables 2/21
Indirect sensitivity to top, Higgs, andnew physics through quantum corrections
Z-pole cross-sectionσ0[e+e− → (Z) → ff̄ ]
Z-boson width ΓZ
Partial widths Γf = Γ[Z → ff̄ ]s=M2ZBranching ratios:Rq = Γq/Γhad (q = b, c)
Rℓ = Γhad/Γℓ (ℓ = e, µ, τ )
Z
f
fHZ
b
b
t
W
W
LEP EWWG ’05
Ecm [GeV]
σ had
[nb]
σ from fitQED corrected
measurements (error barsincreased by factor 10)
ALEPHDELPHIL3OPAL
σ0
ΓZ
MZ
10
20
30
40
86 88 90 92 94
-
Z-pole observables 3/21
Z-pole asymmetries:
AfFB ≡
σ(θ < π2) − σ(θ >π2)
σ(θ < π2) + σ(θ >π2)
=3
4AeAf
ALR ≡σ(Pe > 0) − σ(Pe < 0)σ(Pe > 0) + σ(Pe < 0)
= Ae
Af = 2gV f/gAf
1 + (gV f/gAf)2
=1 − 4|Qf | sin2 θfeff
1 − 4|Qf |sin2 θfeff + 8(|Qf |sin2 θfeff)
2
sin2 θfeff = “effective weak mixing angle”
sin2 θfeff = sw ≡ 1 − M2W/M2Z at tree-level
Most precisely measured for f = ℓ
-
Current status of electroweak precision tests 4/21
Standard Model after Higgs discovery:
Good agreement between measured mass and indirect prediction
Very good agreement over large number of observables
Erler ’13
150 155 160 165 170 175 180 185
mt [GeV]
10
20
30
50
100
200
300
500
1000
MH [
GeV
]
ΓZ, σhad, Rl, Rq (1σ)Z pole asymmetries (1σ)MW (1σ)direct mt (1σ)direct MHprecision data (90%)
Direct measurements:MH = 125.6 ± 0.4 GeVmt = 173.24 ± 0.95 GeV
Indirect prediction:MH = 123.7 ± 2.3 GeV
(with LHC BRs)MH = 89
+22−18 GeV
(w/o LHC data)
mt = 177.0 ± 2.1 GeV
-
Current status of SM loop results 5/21
Known corrections to ∆r, sin2 θfeff , gV f , gAf :
γ,Z,WW
W
W
γ,Z
H
Z
γ,Z,W
•• Complete NNLO corrections (∆r, sin2 θℓeff) Freitas, Hollik, Walter, Weiglein ’00Awramik, Czakon ’02; Onishchenko, Veretin ’02
Awramik, Czakon, Freitas, Weiglein ’04; Awramik, Czakon, Freitas ’06Hollik, Meier, Uccirati ’05,07; Degrassi, Gambino, Giardino ’14
•• “Fermionic” NNLO corrections (gV f , gAf ) Czarnecki, Kühn ’96Harlander, Seidensticker, Steinhauser ’98
Freitas ’13,14
•• Partial 3/4-loop corrections to ρ/T -parameterO(αtα2s), O(α2tαs), O(αtα3s) Chetyrkin, Kühn, Steinhauser ’95
Faisst, Kühn, Seidensticker, Veretin ’03Boughezal, Tausk, v. d. Bij ’05
Schröder, Steinhauser ’05; Chetyrkin et al. ’06(αt ≡
y2t4π
) Boughezal, Czakon ’06
-
Current uncertainties 6/21
Experiment Theory error Main source
MW 80.385 ± 0.015 MeV 4 MeV α3, α2αsΓZ 2495.2 ± 2.3 MeV 0.5 MeV α2bos, α3, α2αs, αα2sσ0had 41540 ± 37 pb 6 pb α2bos, α3, α2αsRb ≡ ΓbZ/ΓhadZ 0.21629 ± 0.00066 0.00015 α2bos, α3, α2αssin2 θℓeff 0.23153 ± 0.00016 4.5 × 10−5 α3, α2αs
Theory error estimate is not well defined, ideally ∆th ≪ ∆expCommon methods: •• Count prefactors (α, Nc, Nf , ...)
•• Extrapolation of perturbative series•• Renormalization scale dependence•• Renormalization scheme dependence
Also parametric error from external inputs (mt, mb, αs, ∆αhad, ...)
-
Constraints on new physics 7/21
Oblique parameters:
αT =ΣWW(0)
MW− ΣZZ(0)
MZ
α
4s2c2S =
ΣZZ(M2Z) − ΣZZ(0)MZ
+s2 − c2
sc
ΣZγ(M2Z)
MZ− Σγγ(M
2Z)
MZ
-1.5 -1.0 -0.5 0 0.5 1.0 1.5
S
-1.0
-0.5
0
0.5
1.0
T
all (90% CL)ΓΖ, σhad, Rl, RqasymmetriesMW, ΓWe & ν scatteringAPV
Erler ’16
-
General parametrization of new physics 8/21
→
“Integrate out” heavy praticles with mass m ∼ Λ(expand full result in MZ/Λ)
Generate higher-dimensional operators, leading dimension 6L = ∑i ciΛ2Oi + O(Λ
−3) (Λ ≫ MZ)
Possible operators restricted by SM field content and gauge invarianceBuchmüller, Wyler ’86
Grzadkowski, Iskrzynski, Misiak, J. Rosiek ’10
-
General parametrization of new physics 9/21
Effective field theory: L = ∑i ciΛ2Oi + O(Λ−3) (Λ ≫ MZ)
OT = (DµΦ)†ΦΦ†(DµΦ) α∆T = −v2
2cTΛ2
OBW = Φ†BµνWµνΦ α∆S = −e2v2cBWΛ2
O(3)eLL = (L̄
eLσ
aγµLeL)(L̄eLσ
aγµLeL) ∆GF = −√
2c(3)eLLΛ2
OfR = i(Φ
† ↔Dµ Φ)(f̄RγµfR) f = e, µ τ, b, lq
OFL = i(Φ† ↔Dµ Φ)(F̄LγµFL) F =
(
νe
e
)
,
(
νµ
µ
)
,
(
ντ
τ
)
,
(
u, c
d, s
)
,
(
t
b
)
O(3)FL = i(Φ
† ↔Daµ Φ)(F̄LσaγµFL)
In general more operators than EWPOs→ Some can be constrained by W → ℓν, had., e+e− → W+W−
-
Current constraints on some dim-6 operators 10/21
Assuming flavor universality: L = ∑i ciΛ2Oi + O(Λ−3) (Λ ≫ MZ)
OT = (DµΦ)†ΦΦ†(DµΦ)OBW = Φ†BµνW µνΦ
O(3)eLL = (L̄eLσ
aγµLeL)(L̄eLσ
aγµLeL)
OfR = i(Φ† ↔Dµ Φ)(f̄RγµfR)
OFL = i(Φ†
↔Dµ Φ)(F̄Lγ
µFL)
O(3)FL = i(Φ†
↔Daµ Φ)(F̄Lσaγ
µFL)
Pomaral, Riva ’13Ellis, Sanz, You ’14
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Constraints on neutrino models 11/21
Heavy sterile neutrinos
Extend SM with one (several) sterile neutrinosLoinaz, Okamura, Rayyan, Takeuchi, Wijewardhana ’02,04Akhmedov, Kartavtsev, Lindner, Michaels, Smirnov ’13
Mass matrix in (νe, νµ, ντ , νs) basis:
0 0 0 yes
0 0 0 yµs
0 0 0 yτs
y∗es y∗µs y
∗τs M
, M ≫ MZ
→ Heavy neutrino mass eigenstate ν4 with m4 ≈ M ,small mixing with SM leptons ǫi = |Ui4|2, (i = e, µ, τ)
Impact on Z → νν̄: Γν/ΓSMν = 1 − 13(ǫe + ǫµ + ǫτ)
Impact on Fermi constant: G2F → G2F(1 − ǫe)(1 − ǫµ)µ−
νµ
νe
e−
GF
Impact on S/T parameter
ν
ℓ±
W± W±
ν
ν̄
Z Z
ℓ̄
ℓ
Z Z
-
Heavy sterile neutrinos 12/21
Cancellation between tree-level and loop corrections possible→ Relatively large mixing angles allowed by EWPOs
ǫe + ǫµ + ǫτ (color coded)
1 10 102
mi (TeV)
4
5
6
7
χ2
0
10−3
2·10−3
3·10−3
4·10−3
5·10−3
6·10−3
7·10−3
-3 -2 -1 0 1 2 3
Γlept
Γinv/Γlept
sin2 θW
g2L
g2R
M2W
0νββ
µ → eγ
Akhmedov, Kartavtsev, Lindner, Michaels, Smirnov ’13
-
Heavy sterile neutrinos 13/21
Additonal constraint: lepton number universality de Gouvea, Kobach ’15
-
Lighter sterile neutrinos 14/21
For m4 < MZ: Decay Z → νiν4 possible
If ν4 does not decay in detector:→ Lesser suppression of Γν
de Gouvea, Kobach ’15
only for Uµ4 = Uτ4 = 0
-
Lighter sterile neutrinos 15/21
For m4 < MZ: Decay Z → νiν4 possible
If ν4 does decay in detector:→ Direct search limits Antusch, Fischer ’15
e+Z
N
ν
ν, ℓ
Z, W
e−
ÈΘΤ2
ÈΘe2
ÈΘΜ2
DELPHI
20 40 60 80 100 120
10-1
10-2
10-3
10-4
10-5
10-6
M @GeVD
ÈΘΑ
2
-
Future e+e− colliders 16/21
International Linear Collider (ILC)Int. lumi at
√s ∼ MZ: 50–100 fb−1
Circular Electron-Positron Collider (CEPC)Int. lumi at
√s ∼ MZ: 2 × 150 fb−1
Future Circular Collider (FCC-ee)Int. lumi at
√s ∼ MZ: > 2 × 30 ab−1
-
Future projections 17/21
Measurement error Intrinsic theory
Current ILC CEPC FCC-ee Current Future†
MW [MeV] 15 3–4 3 1 4 1
ΓZ [MeV] 2.3 0.8 0.5 0.1 0.5 0.2
Rb [10−5] 66 14 17 6 15 7
sin2 θℓeff [10−5] 16 1 2.3 0.6 4.5 1.5
→ Existing theoretical calculations adequate for LEP/SLC/LHC,but not ILC/CEPC/FCC-ee!
† Theory scenario: O(αα2s), O(Nfα2αs), O(N2f α2αs)(Nnf = at least n closed fermion loops)
-
Future projections 18/21
Measurement Intrinsic theory Parametric
ILC FCC-ee Current Future ILC FCC-ee
MW [MeV] 3–4 1 4 1 2.6 0.6–1
ΓZ [MeV] 0.8 0.1 0.5 0.2 0.5 0.1
Rb [10−5] 14 6 15 7 < 1 < 1
sin2 θℓeff [10−5] 1 2.3 4.5 1.5 2 1–2
Projected parameter measurements:
δmt δαs δMZ δ(∆α)
ILC: 50 MeV 0.001 2.1 MeV 5 × 10−5
FCC-ee: 50 MeV 0.0002 0.1 MeV 3–5 × 10−5
-
Projected bounds on neutrino models 19/21
Improved bounds both from EWPOs and direct searchesAntusch, Fischer ’15
ILC
50 100 150 200 250
10-1
10-2
10-3
10-4
10-5
10-6
10-7
M @GeVD
Q2
L>10m CEPC
50 100 150 200 250
10-2
10-4
10-6
10-8
10-10
10-12
M @GeVD
Q2
L>10m FCC-ee
50 100 150 200 250
10-2
10-4
10-6
10-8
10-10
10-12
M @GeVD
Q2
Direct searchesZ pole search 2Σ: ÈyÈ= ÚΑ yΝΑ
2 , Q2=ÚΑÈΘΑ2
Higgs ®WW 1Σ: ÈyÈ= ÚΑ yΝΑ2 , Q2=ÚΑÈΘΑ
2
e+e-® h +MEHTL 1Σ: ÈyÈ=ÈyΝe È, Q2=ÈΘe
2
e+e-® lΝlΝ* 1Σ: ÈyÈ=ÈyΝe È, Q2=ÈΘe
2
OtherPrecision constraints: ÈyÈ= yΝe
2 + yΝΜ2 , Q2=ÈΘe 2+ÈΘΜ 2
Precision constraints: ÈyÈ=ÈyΝΤ È, Q2=ÈΘΤ
2
’’Unprotected’’ type-I seesaw
-
Displaced vertex search 20/21
For small mixing |θ|2 = ∑i ǫi and small m4,ν4 propagates in detector before decaying
Antusch, Cazzato, Fischer ’16
-
Displaced vertex search 20/21
For small mixing |θ|2 = ∑i ǫi and small m4,ν4 propagates in detector before decaying
Drewes, Garbrecht, Gueter, Klaric ’16
→ see talk by J. Klaric
-
Summary 21/21
W/Z precision data provides trong constraints on multi-TeV new physics→ Non-trivial test for low-scale seesaw / left-right symmetric models, etc.
For some neutrino models and regions of parameter space, EWPOs are themost important constraints
Future e+e− colliders will probe new, theoretically motivated parameter space
-
Backup slides
-
Theory challenges
Full SM corrections at ≥2-loop:Large number of diagrams and tensor integrals, O(100) −O(10000)Many different scales (masses and ext. momenta)
Computer algebra methods:
Generation of diagrams with FeynArts, QGraf, ...Küblbeck, Eck, Mertig ’92, Hahn ’01
Nogueira ’93
Dirac/Lorentz algebra with Form, FeynCalc, ... Vermaseren ’89,00Mertig ’93
Evaluation of loop integrals:
In general not possible analytically
Numerical methods must be automizable, stable, fastly converging
Need procedure for isolating divergent pieces
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