SLIDE 1 Theory perspective on future electroweak measurements
University of Pittsburgh
Lepton-Photon 2017
- 1. Electroweak precision observables
- 2. Electroweak showers
- 3. X-plosion
SLIDE 2
Electroweak precision observables:
Going after large masses with one weak boson
SLIDE 3 Weak scale observables
1/19
Indirect sensitivity to top, Higgs, and new physics through quantum corrections W-boson mass MW (from τµ) Z-boson width ΓZ Z-pole cross-section σ0[e+e− → (Z) → f ¯ f] Effective weak mixing angle sin2 θf
eff
from Z asymmetries (ALR, Af
FB)
sin2 θf
eff =
1 2|Qf| Re
R
geff
R − geff L
f f H Z b b t W W
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
SLIDE 4 Current uncertainties
2/19
Most important quantities:
MW 15 MeV 4 MeV ΓZ 2.3 MeV 0.5 MeV σ0
had = σ[e+e− → Z → had.]
37 pb 6 pb Rb = Γ[Z → b¯ b]/Γ[Z → had.] 6.6 × 10−4 1.5 × 10−4 sin2 θℓ
eff (from ALR and AFB)
1.6 × 10−4 0.5 × 10−4 Complete NNLO or fermionic NNLO corrections known
Freitas, Hollik, Walter, Weiglein ’00; Awramik, Czakon ’02; Onishchenko, Veretin ’02 Awramik, Czakon, Freitas, Weiglein ’04; Awramik, Czakon, Freitas ’06 Hollik, Meier, Uccirati ’05,07; Freitas ’13,14; Dubovyk, Freitas, Gluza, Riemann, Usovitsch ’16
Partial 3/4-loop corrections
Chetyrkin, K¨ uhn, Steinhauser ’95 Faisst, K¨ uhn, Seidensticker, Veretin ’03 Boughezal, Tausk, v. d. Bij ’05; Schr¨
Chetyrkin et al. ’06; Boughezal, Czakon ’06
SLIDE 5
Constraints on new physics in effective theory framework
3/19
Assuming flavor universality: L =
i ci Λ2Oi + O(Λ−3)
(Λ ≫ MZ)
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) OF
L = i(Φ† ↔
Dµ Φ)( ¯ FLγµFL) O(3)F
L
= i(Φ†
↔
Da
µ Φ)( ¯
FLσaγµFL) Pomaral, Riva ’13 Ellis, Sanz, You ’14
SLIDE 6
Low-energy electroweak observables
4/19
Polarized ee, ep, ed scattering (QW(e), QW (p), eDIS)
E158 ’05; Qweak ’13; JLab Hall A ’13
νN/¯ νN scattering
NuTeV ’02
Atomic parity violation (QW(133Cs))
Wood et al. ’97 Gu´ ena, Lintz, Bouchiat ’05
→ Test of running MS weak mixing
angle sin2 ¯ θ(µ) e ν/¯ ν e ν/¯ ν e, p, N e, p, N Z gef
AV [¯
eγµγ5e] [ ¯ fγµf] gef
VA [¯
eγµe] [ ¯ fγµγ5f] gef
AV = 1 2 − 2|Qf|sin2 ¯
θ(µ) gef
VA = 1 2 − 2sin2 ¯
θ(µ)
SLIDE 7 Low-energy electroweak observables
5/19
Polarized ee, ep, ed scattering (QW(e), QW (p), eDIS)
E158 ’05; Qweak ’13; JLab Hall A ’13
νN/¯ νN scattering
NuTeV ’02
Atomic parity violation (QW(133Cs))
Wood et al. ’97 Gu´ ena, Lintz, Bouchiat ’05
→ Test of running MS weak mixing
angle sin2 ¯ θ(µ)
0.001 0.01 0.1 1 10 100 1000 10000
µ [GeV]
0.225 0.230 0.235 0.240 0.245
sin
2θW(µ)
QW(Cs) QW(e) LHC Tevatron LEP 1 SLD NuTeV JLab QW(p) QW(Ra) QW(e) SLAC SoLID JLab
antiscreening s c r e e n i n g
eDIS QW(p) JLab JLab KVI Mainz SM published planned
JE 201 14
Erler ’14
SLIDE 8 Low-energy electroweak observables
5/19
Polarized ee, ep, ed scattering (QW(e), QW (p), eDIS)
E158 ’05; Qweak ’13; JLab Hall A ’13
νN/¯ νN scattering
NuTeV ’02
Atomic parity violation (QW(133Cs))
Wood et al. ’97 Gu´ ena, Lintz, Bouchiat ’05
Future experiments: MOLLER (ee), P2, SoLID (ep), Atomic PV in radium
0.001 0.01 0.1 1 10 100 1000 10000
µ [GeV]
0.225 0.230 0.235 0.240 0.245
sin
2θW(µ)
QW(Cs) QW(e) LHC Tevatron LEP 1 SLD NuTeV JLab QW(p) QW(Ra) QW(e) SLAC SoLID JLab
antiscreening s c r e e n i n g
eDIS QW(p) JLab JLab KVI Mainz SM published planned
JE 201 14
Erler ’14
SLIDE 9 Future high-energy e+e− colliders
6/19
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
SLIDE 10
Future projections
7/19
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 θℓ
eff [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(αα2 s), O(Nfα2αs), O(N2 f α2αs)
(Nn
f = at least n closed fermion loops)
SLIDE 11
Future projections
8/19
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 θℓ
eff [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
SLIDE 12
Sensitivity to new physics
9/19
Heavy new physics: (one op. at a time)
de Blas et al. ’16
Light new physics: sterile neutrinos
Antusch, Gazzato, Fischer ’16 Drewes, Garbrecht, Gueter, Klaric ’16
SLIDE 13 Probes of EWPO with high-mass DY @ 100 TeV
10/19 Farina et al. ’16
- J. Ruderman, FCC physics wshop ’17
- M. Mangano, FCC week ’17
SLIDE 14
Electroweak showers:
Large scales obscured by many weak bosons
SLIDE 15 Electroweak showers: massless
11/19
EW physics at future pp collider: W/Z bosons can be copiously produced at multi-TeV pp collider Enhancement ∼ log2(E/MW) for near-collinear emission Approximate description through parton shower
Ciafaloni, Ciafaloni, Comelli ’00 Ciafaloni, Comelli ’05; Bell, K¨ uhn, Rittinger ’10 Christensen, Sj¨
- strand ’14; Krauss, Petrov, Schoenherr, Spannowsky ’14
Bauer, Ferland ’16; Chen, Han, Tweedie ’16
Presence of scalar fields (Higgs/longitudinal gauge bosons):
Chen, Han, Tweedie ’16
SLIDE 16 Electroweak showers: massive
12/19
Effect of masses / EWSB:
k2
T → k2 T + ¯
zm2
B + zm2 C − z¯
zm2
A
- Helicity-flipping (“ultra-collinear”)
splitting functions
- Complication from gauge artifacts ∝ E/MW
→ Remove with convenient gauge choice
Lgf = − 1 2ξ
nµ = (1, −ˆ k)
→ Smoothly interpolates to Goldstone equivalence
- f unbroken gauge at high energies
Chen, Han, Tweedie ’16
SLIDE 17 Electroweak showers: massive
12/19
Effect of masses / EWSB:
k2
T → k2 T + ¯
zm2
B + zm2 C − z¯
zm2
A
- Helicity-flipping (“ultra-collinear”)
splitting functions
- Complication from gauge artifacts ∝ E/MW
→ Remove with convenient gauge choice
Lgf = − 1 2ξ
nµ = (1, −ˆ k)
→ Smoothly interpolates to Goldstone equivalence
- f unbroken gauge at high energies
(GeV)
T
k 100 200 300 400 500 per GeV
0.0005 0.001 0.0015 0.002
(z=0.2)
T
vs k
T
dz dk ’)
L
f
±
W →
L
dP(f (massless)
T
W
T
W
L
W
SLIDE 18 Electroweak showers: mixing and PDFs
13/19
γ/ZT and h/ZL mixing: Sudakov evolution with density matrix
) (GeV) f M(f
200 400 600 800 1000 1200 1400
fraction of events (per 50 GeV)
10
10 R +
µ
L
+
R +
e
L
→ /Z γ
coherent
γ/Z incoherent
B0/W0 incoherent
Electroweak PDFs:
fV (z) ≈
T
dz′
z′ dPq→V q(′) dz′dk2
T
fq(z/z′)
Kane, Repko, Rolnick ’84; Dawson ’85
s/S = τ 0.05 0.1
τ dL/d
5 −
10
3 −
10
1 −
10 10
3
10
5
10
7
10 100 TeV q q γ q
T ±
qW
± L
qW
T
T +
W γ
± T
W
W
+ L
W
(TeV) s
2 4 6 8 10 12
Chen, Han, Tweedie ’16
SLIDE 19 Electroweak showers: phenomenology
14/19
Decay of W ′ with mW ′ = 20 TeV into heavy quarks: with EW shower: with EW+QCD shower:
) (TeV) Q M(Q
2 4 6 8 10 12 14 16 18 20 22
fraction of events (per 200 GeV)
10
10
10
10 1
+X b t +X t t +X b b +X t b , with EW FSR b t → 20 TeV W’
) (TeV) Q M(Q
2 4 6 8 10 12 14 16 18 20 22
fraction of events (per 200 GeV)
10
10
10
10 1
, with EW+QCD FSR b t → 20 TeV W’ +X b t +X t t +X b b +X t b
Chen, Han, Tweedie ’16
SLIDE 20
X-plosion:
Strength in numbers
SLIDE 21 Weak amplitudes at high energies
15/19
Higgs-plosion: φ∗ → nφ in φ4 theory: number of diagrams grows factorially Result at threshold: An = n!
2m2
(n−1)/2
1 + n(n − 1) √ 3λ 8π
- Voloshin ’92; Argyres, Kleiss, Papadopoulos ’92; Brown ’92; Smith ’92
n! eventually overcomes λn/2 yielding large cross-section
Libanov, Rubakov, Son, Troitsky ’94; Son ’95 Khoze ’15
SLIDE 22 Weak amplitudes at high energies
15/19
Higgs-plosion: φ∗ → nφ in φ4 theory: number of diagrams grows factorially Result at threshold: An = n!
2m2
(n−1)/2
1 + n(n − 1) √ 3λ 8π
- Voloshin ’92; Argyres, Kleiss, Papadopoulos ’92; Brown ’92; Smith ’92
n! eventually overcomes λn/2 yielding large cross-section
Libanov, Rubakov, Son, Troitsky ’94; Son ’95
W/Z-plosion:
Khoze ’14,15
Similar effect in SM for (longitudinal) SU(2) gauge bosons: A[nh + mZL] ∼ n!m! Techniques:
- recursion relations
- classical solutions
- extrapolation from MadGraph
SLIDE 23
Cross-sections at high energies
16/19
Partonic cross-section: pp cross-section: Unitarity limit: √spart 800 TeV Non-perturbative limit: √spart 300 TeV
Khoze, Jaeckel ’14
SLIDE 24
X-plosion: Observation
17/19
Experimental search is simple (background free) √ S = 100 TeV pT,j > 50 GeV ∆R > 0.4
Gainer ’17
SLIDE 25
X-plosion: Interpretation
18/19
Large cross-section σn for n > 100 H/W/Z bosons at 100-TeV collider? σn may be tamed by higher-order corrections n > 100 corresponds to O(αn) amplitude
→ Perturbative expansion diverges, but non-perturbative σn ≪ unitarity limit
Imaginary part of self-energies will dominate propagators for p2 ≫ m2
→ Damping of cross-section
Khoze, Spannowsky ’17
Fermion loops can cancel boson loops
Voloshin ’17
Higgs self-coupling runs to zero at large energies
Degrassi et al. ’12
SLIDE 26
Summary: Electroweak physics at future colliders
Multi-faceted and possibly surprising insights: Indirect sensitivity to high scales at high-lumi e+e− colliders Direct access to multi-boson interactions at pp colliders
SLIDE 27 Summary: Electroweak physics at future colliders
Multi-faceted and possibly surprising insights: Indirect sensitivity to high scales at high-lumi e+e− colliders Direct access to multi-boson interactions at pp colliders Theory description is challenging and requires new methods: Multi-loop (3,4,...) corrections for EWPO Electroweak parton showers, matching and merging Non-perturbative (?) description
SLIDE 28
Backup slides
SLIDE 29
Current status of electroweak precision tests
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 MH precision data (90%)
Direct measurements: MH = 125.6 ± 0.4 GeV mt = 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
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 Current status of SM loop results
γ,Z,W W W W γ,Z H Z γ,Z,W
- Complete NNLO corrections (∆r, sin2 θf
eff) Freitas, Hollik, Walter, Weiglein ’00 Awramik, Czakon ’02; Onishchenko, Veretin ’02 Awramik, Czakon, Freitas, Weiglein ’04; Awramik, Czakon, Freitas ’06 Hollik, Meier, Uccirati ’05,07; Degrassi, Gambino, Giardino ’14 Dubovyk, Freitas, Gluza, Riemann, Usovitsch ’16
- “Fermionic” NNLO corrections (ΓZ, σ0
had, Rf) Czarnecki, K¨ uhn ’96 Harlander, Seidensticker, Steinhauser ’98 Freitas ’13,14
- Partial 3/4-loop corrections to ρ/T-parameter
O(αtα2
s), O(α2 t αs), O(αtα3 s) Chetyrkin, K¨ uhn, Steinhauser ’95 Faisst, K¨ uhn, Seidensticker, Veretin ’03 Boughezal, Tausk, v. d. Bij ’05 Schr¨
- der, Steinhauser ’05; Chetyrkin et al. ’06
(αt ≡ y2
t
4π)
Boughezal, Czakon ’06
SLIDE 32 Electroweak showers vs. fixed order
Phase-space population for WZ + j production: (pp,
√ S = 100 TeV)
R(W,Z) ∆ 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
T
(W) / H
T
2p 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 500 1000 1500 2000 2500 3000
3 → Fixed-order 2
R(W,Z) ∆ 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
T
(W) / H
T
2p 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 500 1000 1500 2000 2500 3000
2 + full EW FSR shower → 2
Chen, Han, Tweedie ’16
