SLIDE 1 Electroweak precision data and Higgs physics
University of Pittsburgh
HEFT 2017
- 1. Overview of electroweak precision tests
- 2. Effective operator description
- 3. Connection between EWPO and HEFT
SLIDE 2 Overview of electroweak precision tests
1/20
W mass
µ decay in Fermi Model
µ− νµ νe e− GF µ− νµ νe e− γ
QED corr. (2-loop) Γµ = G2
Fm5 µ
192π3 F
m2
e
m2
µ
Ritbergen, Stuart ’98 Pak, Czarnecki ’08
µ decay in Standard Model
µ− νµ νe e− W−
µ− νµ νe e− W− Z
G2
F
√ 2 = e2 8s2
wM2
W
(1 + ∆r) electroweak corrections
SLIDE 3 Z-pole observables
2/20
Deconvolution of initial-state QED radiation: σ[e+e− → f ¯ f] = Rini(s, s′) ⊗ σhard(s′)
Kureav, Fadin ’85 Berends, Burgers, v. Neerven ’88 Kniehl, Krawczyk, K¨ uhn, Stuart ’88 Beenakker, Berends, v. Neerven ’89 Skrzypek ’92 Montagna, Nicrosini, Piccinini ’97 LEP EWWG ’05
Ecm [GeV] σhad [nb]
σ from fit QED corrected measurements (error bars increased by factor 10) ALEPH DELPHI L3 OPAL
σ0 ΓZ MZ
10 20 30 40 86 88 90 92 94
e− e+ f f γ
SLIDE 4 Z-pole observables
2/20
Deconvolution of initial-state QED radiation: σ[e+e− → f ¯ f] = Rini(s, s′) ⊗ σhard(s′) Subtraction of γ-exchange, γ–Z interference, box contributions: σhard = σZ + σγ + σγZ + σbox
LEP EWWG ’05
Ecm [GeV] σhad [nb]
σ from fit QED corrected measurements (error bars increased by factor 10) ALEPH DELPHI L3 OPAL
σ0 ΓZ MZ
10 20 30 40 86 88 90 92 94
e− e+ f f γ e− e+ f f γ
e− e+ f f W W
SLIDE 5 Z-pole observables
2/20
Deconvolution of initial-state QED radiation: σ[e+e− → f ¯ f] = Rini(s, s′) ⊗ σhard(s′) Subtraction of γ-exchange, γ–Z interference, box contributions: σhard = σZ + σγ + σγZ + σbox Z-pole contribution: σZ = R (s − M2
Z)2 + M2 ZΓ2 Z
+ σnon−res
LEP EWWG ’05
Ecm [GeV] σhad [nb]
σ from fit QED corrected measurements (error bars increased by factor 10) ALEPH DELPHI L3 OPAL
σ0 ΓZ MZ
10 20 30 40 86 88 90 92 94
e− e+ f f γ e− e+ f f γ
e− e+ f f W W
SLIDE 6 Z-pole observables
2/20
Deconvolution of initial-state QED radiation: σ[e+e− → f ¯ f] = Rini(s, s′) ⊗ σhard(s′) Subtraction of γ-exchange, γ–Z interference, box contributions: σhard = σZ + σγ + σγZ + σbox Z-pole contribution: σZ = R (s − M2
Z)2 + M2 ZΓ2 Z
+ σnon−res In experimental analyses: σ ∼ 1 (s − M2
Z)2 + s2Γ2 Z/M2 Z
MZ = MZ
Z/M2 Z ≈ MZ − 34 MeV
ΓZ = ΓZ
Z/M2 Z ≈ ΓZ − 0.9 MeV LEP EWWG ’05
Ecm [GeV] σhad [nb]
σ from fit QED corrected measurements (error bars increased by factor 10) ALEPH DELPHI L3 OPAL
σ0 ΓZ MZ
10 20 30 40 86 88 90 92 94
e− e+ f f γ e− e+ f f γ
e− e+ f f W W
SLIDE 7 Z-pole observables
3/20
Total and partial Z widths: Γf = Γ[Z → f ¯ f]s=M2
Z
ΓZ =
Γf Γf ≈ NcMZ 12π
V |gf V |2 + Rf A|gf A|2
1 1 + Re Σ′
Z
Z
Rf
V , Rf A: Final-state QED/QCD radiation;
gf
V , gf A, Σ′ Z: Electroweak corrections
e− e+ f f Z
Branching ratios: Rq = Γq/Γhad (q = b, c, probes heavy quark generations) Rℓ = Γhad/Γℓ (ℓ = e, µ, τ)
SLIDE 8 Z-pole observables
4/20
Peak cross section: σ0
had = σZ(s = M2 Z) = 12π
M2
Z
ΓeΓq Γ2
Z
(1 + δX) ⌊ → NNLO correction term Z-pole asymmetries / effective weak mixing angle: Af
FB ≡ σ(θ < π 2) − σ(θ > π 2)
σ(θ < π
2) + σ(θ > π 2) = 3
4AeAf ALR ≡ σ(Pe > 0) − σ(Pe < 0) σ(Pe > 0) + σ(Pe < 0) = Ae Af = 2 gV f/gAf 1 + (gV f/gAf)2 = 1 − 4|Qf| sin2 θf
eff
1 − 4|Qf|sin2 θf
eff + 8(|Qf|sin2 θf eff)2
Most precisely measured for f = ℓ (also f = b, c)
SLIDE 9
Current uncertainties
5/20
Experiment Theory error Main source MW 80385 ± 15 MeV 4 MeV α3, α2αs ΓZ 2495.2 ± 2.3 MeV 0.5 MeV α2
bos, α3, α2αs, αα2 s
σ0
had
41540 ± 37 pb 6 pb α2
bos, α3, α2αs
Rb 0.21629 ± 0.00066 0.00015 α2
bos, α3, α2αs
sin2 θℓ
eff
0.23153 ± 0.00016 4.5 × 10−5 α3, α2αs
SLIDE 10
Impact on Higgs physics
6/20
Standard Model: Good agreement between measured mass and indirect prediction Very good agreement over large number of observables
Erler ’16
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 MH precision data (90%)
Direct measurements: MH = 125.09±0.24 GeV mt = 173.34 ± 0.81 GeV Indirect prediction: MH = 126.1 ± 1.9 GeV (with LHC BRs) MH = 96+22
−19 GeV
(w/o LHC data) mt = 176.7 ± 2.1 GeV
SLIDE 11 Impact on Higgs physics
7/20
Higgs singlet extension:
Robens, Stefaniak ’13
Constraints on singlet mass and mixing angle Two-Higgs-Doublet Model:
Eberhardt, Nierste, Wiebusch ’13
Constraints on couplings of SM-like Higgs
0.3 1 10 30 tan β 0.2π 0.3π 0.4π 0.5π 0.6π β − α
hV V
gSM
hV V
hff
gSM
hff
sin α or sin α cos α
SLIDE 12 Impact on Higgs physics
8/20
Oblique parameters:
S
0.1 0.2 0.3
T
0.1 0.2 0.3
68% and 95% CL fit contours for U=0 =173 GeV)
t
=126 GeV, m
H
: H
ref
(SM Present fit Present uncertainties SM Prediction 0.4 GeV ± = 125.7
H
M 0.76 GeV ± = 173.34
t
m
G fitter SM
Jun '14
Gfitter coll. ’14
αT = ΣWW(0) MW − ΣZZ(0) MZ α 4s2c2S = ΣZZ(M2
Z) − ΣZZ(0)
MZ + s2 − c2 sc ΣZγ(M2
Z)
MZ − Σγγ(M2
Z)
MZ
SLIDE 13 Impact on Higgs physics
8/20
Oblique parameters:
S
0.1 0.2 0.3
T
0.1 0.2 0.3
68% and 95% CL fit contours for U=0 =173 GeV)
t
=126 GeV, m
H
: H
ref
(SM Present fit Present uncertainties SM Prediction 0.4 GeV ± = 125.7
H
M 0.76 GeV ± = 173.34
t
m
G fitter SM
Jun '14
Gfitter coll. ’14
αT = ΣWW(0) MW − ΣZZ(0) MZ α 4s2c2S = ΣZZ(M2
Z) − ΣZZ(0)
MZ + s2 − c2 sc ΣZγ(M2
Z)
MZ − Σγγ(M2
Z)
MZ Not adequate for new physics that affects flavor (Z → ℓℓ, Z → bb, ...)
SLIDE 14 Effective operator description
9/20
Effective field theory: L =
i ci Λ2Oi + O(Λ−3)
(Λ ≫ MZ) Contributions at tree-level:
e− e+ f f Z
Oφ1 = (DµΦ)†Φ Φ†(DµΦ) OBW = Φ†BµνW µνΦ O(3)e
LL
= (¯ Le
LσaγµLe L)(¯
Le
LσaγµLe L)
Of
R = i(Φ† ↔
Dµ Φ)( ¯ fRγµfR) f = e, µ τ, b, lq OF
L = i(Φ† ↔
Dµ Φ)( ¯ FLγµFL) F =
νe
e
νµ
µ
ντ
τ
u, c
d, s
t
b
L
= i(Φ† ↔ Da
µ Φ)( ¯
FLσaγµFL)
SLIDE 15
Effective operator description
9/20
Effective field theory: L =
i ci Λ2Oi + O(Λ−3)
(Λ ≫ MZ) Contributions at tree-level: Oφ1 = (DµΦ)†Φ Φ†(DµΦ) α∆T = −v2
2 cφ1 Λ2
OBW = Φ†BµνW µνΦ α∆S = −e2v2cBW
Λ2
O(3)e
LL
= (¯ Le
LσaγµLe L)(¯
Le
LσaγµLe L)
∆GF = − √ 2c(3)e
LL
Λ2
Of
R = i(Φ† ↔
Dµ Φ)( ¯ fRγµfR)
effect on Z → f ¯ f OF
L = i(Φ† ↔
Dµ Φ)( ¯ FLγµFL) O(3)F
L
= i(Φ† ↔ Da
µ Φ)( ¯
FLσaγµFL)
SLIDE 16
Effective operator description
9/20
Effective field theory: L =
i ci Λ2Oi + O(Λ−3)
(Λ ≫ MZ) Contributions at tree-level: Oφ1 = (DµΦ)†Φ Φ†(DµΦ)
relevant for Higgs physics, but strongly bounded from EWPO OBW = Φ†BµνW µνΦ O(3)e
LL
= (¯ Le
LσaγµLe L)(¯
Le
LσaγµLe L)
irrelevant for Higgs physics Of
R = i(Φ† ↔
Dµ Φ)( ¯ fRγµfR) OF
L = i(Φ† ↔
Dµ Φ)( ¯ FLγµFL) O(3)F
L
= i(Φ† ↔ Da
µ Φ)( ¯
FLσaγµFL)
SLIDE 17
Current constraints on some dim-6 operators
10/20
Assuming flavor universality: Significant correlation/ degeneracy between different operators
Pomaral, Riva ’13 Ellis, Sanz, You ’14
SLIDE 18
Effective operator description
11/20
Contributions at 1-loop-level: OH = 1
2∂µ(Φ†Φ) ∂µ(Φ†Φ)
OB = i(DµΦ)†Bµν(DνΦ) OW = i(DµΦ)†W µν(DνΦ) OBB = −Φ†BµνBµνΦ OWW = −Φ†W µνWµνΦ + few more
→ Direct correlation with Higgs production and decay rates
Chen, Dawson, Zhang ’13 Hartmann, Shephard, Trott ’16
SLIDE 19 Impact of one-loop operator insertions
12/20 Chen, Dawson, Zhang ’13
400 200 200 400 400 200 200 400 f WW 2 TeV 2 f W 2 TeV 2 400 200 200 400 400 200 200 400 f WW f BB 2 TeV 2 f WW f BB 2 TeV 2
Assumptions: Tree-level EWPO operators are zero Loop contributions are UV-divergent → must choose renormalization scheme
SLIDE 20
Connection between EWPO and HEFT
13/20
Competetive and complementary senstivity to HEFT operators from Higgs physics and EWPO @ NLO SMEFT @ NLO requires (model-dependent) assumptions More operators than EWPOs a) 1-loop contributions from OH, OB, OW, OBB, OWW can be absorbed into tree-level contributions from Oφ1, OBW, ...
→ No sensitivity on OH, OB, ... since Oφ1, OBW, ... dominate
b) Assume some operators (Oφ1, OBW, ...) vanish
→ Depends on renormalization scheme and scale → Compatible with some UV-completions, but not all
SLIDE 21 Connection between EWPO and HEFT
14/20
Renormalization Loop diagrams with HEFT operator insertions are in general UV-divergent [Exceptions e.g. O6 = (Φ†Φ)3 in 2-loop diagrams
Z Z h h h h
Kribs, Maier, Rzehak, Spannowsky, Waite ’17]
Divergencies absorbed in oparators entering at tree-level (Oφ1, OBW, ...)
- Ambiguity due to choice of renormalization
(MS, MS with BFM, ...)
Mebane, Greiner, Zhang, Willenbrock ’13 Hartmann, Trott ’15
- Ambiguity due to choice of scale:
Oφ1, OBW, ... can only be zero at one scale µ0
SLIDE 22
Connection between EWPO and HEFT
15/20
RG running and mixing Operators in loops and renormalization can be treated through RG evolution (as well as resummation of log Λ
µ terms) Shiftman, Vainshtein, Zakharov ’77; Floratos, Ross, Sachrajda ’77; Gilman, Wise ’79 Morozov ’84; Hagiwara, Ishihara, Szalapski, Zeppenfeld ’93; Han, Skiba ’04 Grojean, Jenkins, Manohar, Trott ’13; Jenkins, Manohar, Trott ’13 Alonso, Jenkins, Manohar, Trott ’13; Elias-Miro, Espinosa, Masso, Pomarol ’13
... Currently only leading-log (LL) approximation known; for Higgs physics today Λ/µ < 10
Englert et al. ’14
SLIDE 23 Example: Higgs singlet extension
16/20
SM + singlet scalar S V (Φ, S) = µ2
1Φ†Φ + λ1(Φ†Φ)2 + µ2 2S2 + λ2S4 + λ3(Φ†Φ)S2
Φ =
1 √ 2
⊤
S = vs/ √ 2 For vs ≫ v: m2
H ≈ Λ2 ≡ 2λ2v2 s
sin2 α ≈ λ2
3
2λ2 v2 Λ2 Oblique parameters: S ≈ λ2
3
24πλ2 v2 m2
H
ln m2
H
m2
h
+ . . . T ≈ − 3λ2
3
32πc2
wλ2
v2 m2
H
ln m2
H
m2
h
+ . . .
SLIDE 24 Example: Higgs singlet extension
17/20
EFT description: LO: αT = −cφ1 v2 Λ2 Oφ1 = (DµΦ)†Φ Φ†(DµΦ) NLO: αT = 3αcH 16πs2
wM2
W
v2 Λ2
M2
Zm2 h
m2
h − M2 Z
ln m2
h
M2
Z
2∂µ(Φ†Φ) ∂µ(Φ†Φ)
Note: NLO contribution is finite, so cannot be obtained through RG mixing
SLIDE 25 Example: Higgs singlet extension
18/20
Matching: (µ = MW)
Freitas, Lopez-Val, Plehn ’16
LL-L: cφ1 = 3αs2
wλ2
3
32πc2
wλ2
ln Λ2 µ2 cH = 0 LL-TL: cφ1 = 3αs2
wλ2
3
32πc2
wλ2
ln Λ2 µ2 cH = λ2
3/(2λ2)
BP-TL: cφ1 = αs2
wλ2
3
32πc2
wλ2
µ2 − 5 2
3/(2λ2)
v-improv.: Λ → mH,
λ2
3
2λ2 → sin2 α Λ2 v2 Brehmer, Freitas, Lopez-Val, Plehn ’15
SLIDE 26
Example: Higgs singlet extension
19/20
Sample benchmarks:
Freitas, Lopez-Val, Plehn ’16
LL approximation not adequate Full 1-loop matching (with v-induced terms) necessary to relate EWPO–HEFT “Phenomenological” operators to be defined at weak scale
SLIDE 27
Conclusions
20/20
Electroweak precision tests can probe Higgs physics beyond the Standard Model Model independent description of new physics through dim-6 operators Sensitivity of EWPO to HEFT operators mostly through loop contributions
→ Analysis depends on (model-dependent)
assumptions Full 1-loop matching important for connect- ing HEFT to UV-complete models
SLIDE 28
Conclusions
20/20
Electroweak precision tests can probe Higgs physics beyond the Standard Model Model independent description of new physics through dim-6 operators Sensitivity of EWPO to HEFT operators mostly through loop contributions
→ Analysis depends on (model-dependent)
assumptions Full 1-loop matching important for connect- ing HEFT to UV-complete models
SLIDE 29
Backup slides
SLIDE 30
Current status of electroweak precision tests
1.4σ 1.5σ 2.0σ 2.5σ Surprisingly good agreement: χ2/d.o.f. = 18.1/14 (p = 20%) Most quantities measured with 1%–0.1% precision A few interesting deviations: MW (∼ 1.4σ) σ0
had
(∼ 1.5σ) Aℓ(SLD) (∼ 2σ) Ab
FB
(∼ 2.5σ) (gµ − 2) (∼ 3σ)
GFitter coll. ’14
SLIDE 31
Future projections
ILC: High-energy e+e− linear collider, running at √s ≈ MZ with 30 fb−1 CEPC: Circular e+e− collider, running at √s ≈ MZ with 2 × 150 fb−1 FCC-ee: Circular e+e− collider, running at √s ≈ MZ with 4 × 3000 fb−1 Current exp. ILC CEPC FCC-ee Current perturb. MW [MeV] 15 3–4 3 1 4 ΓZ [MeV] 2.3 0.8 0.5 0.1 0.5 Rb [10−5] 66 14 17 6 15 sin2 θℓ
eff [10−5]
16 1 2.3 0.6 4.5
→ Existing theoretical calculations adequate for LEP/SLC/LHC,
but not ILC/CEPC/FCC-ee!
SLIDE 32 Theory and parametric uncertainties
ILC CEPC
with 3-loop†
ILC*
CEPC** MW [MeV] 3–4 3 1 2.6 2.1 ΓZ [MeV] 0.8 0.5 < ∼ 0.2 0.5 0.15 Rb [10−5] 14 17 5–10 < 1 < 1 sin2 θℓ
eff [10−5]
1 2.3 1.5 2 2
† Theory scenario: O(αα2 s), O(Nfα2αs), O(N2 f α2αs)
(Nn
f = at least n closed fermion loops)
Parametric inputs: * ILC: δmt = 100 MeV, δαs = 0.001, δMZ = 2.1 MeV **CEPC: δmt = 600 MeV, δαs = 0.0002, δMZ = 0.5 MeV also: δ(∆α) = 5 × 10−5
SLIDE 33 Theory uncertainties in extraction of pseudo-observables
Subtraction of QED radiation contributions
→ Known to O(α2), O(α3L3) for ISR,
O(α2) for FSR and O(α2L2) for AFB (L = log s
m2
e )
Berends, Burgers, v.Neerven ’88 Kniehl, Krawczyk, K¨ uhn, Stuart ’88 Beenakker, Berends, v.Neerven ’89 Skrzypek ’92; Montagna, Nicrosini, Piccinini ’97
→ O(0.1%) uncertainty on σZ, AFB → Improvement needed for ILC/CEPC/FCC-ee
Subtaction of non-resonant γ-exchange, γ–Z in- terf., box contributions, Bhabha scattering
see, e.g., Bardin, Gr¨ unewald, Passarino ’99
→ O(0.01%) uncertainty within SM
(improvements may be needed)
→ Sensitivity to some NP beyond EWPO
LEP EWWG ’05
Ecm [GeV] σhad [nb]
σ from fit QED corrected measurements (error bars increased by factor 10) ALEPH DELPHI L3 OPAL
σ0 ΓZ MZ
10 20 30 40 86 88 90 92 94
e− e+ f f γ e− e+ f f γ
e− e+ f f W W
