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

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

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