Lepton flavor violation at future (lepton) colliders: induced by - - PowerPoint PPT Presentation

Lepton flavor violation at future (lepton) colliders: induced by neutral and doubly-charged scalars

Yongchao Zhang

Washington University in St. Louis January 11, 2019 Mini-Workshop: Theory - Physics Opportunities and Advanced Tools IAS, HKUST

based on

• P. S. B. Dev, R. N. Mohapatra & YCZ, PRL120(2018)221804 [1711.08430]
• P. S. B. Dev, R. N. Mohapatra & YCZ, PRD98(2018)075028 [1803.11167]
• P. S. B. Dev & YCZ, JHEP1810(2018)199 [1808.00943]

(see also P. S. B. Dev, M. J Ramsey-Musolf & YCZ, PRD98(2018)055013 [1806.08499]) see also CEPC CDR [1811.10545] & CLIC Yellow Book [1812.02093]

Outline

Motivations of the LFV processes Beyond SM neutral scalar H at future lepton colliders

◮ On-shell production ◮ Off-shell production ◮ Prospects at ILC and CEPC (CLIC in backup slides)

Doubly-charged scalar H±± at future lepton colliders

◮ On-shell production through the (LFV) Yukawa couplings ◮ Off-shell production ◮ Prospects at ILC and CEPC (CLIC in backup slides)

Displaced LFV signals at future colliders

◮ Long-lived H±±

L

in type-II seesaw

◮ DV prospects at HL-LHC, FCC-hh & ILC ◮ DV from H±±

R

in left-right models

Conclusion

Yongchao Zhang (Wustl) LFV Jan 11, 2019 2 / 31

Why lepton-flavor violation (LFV) at future lepton colliders?

Neutrino oscillations ⇒ lepton flavor violation why not in the charged lepton sector??? “Smoking-gun” signal beyond the SM; Clean SM background at lepton colliders, compared to the hadron colliders. ...Connection to neutrino mass generation (and other pheno)

◮ Beyond SM neutral scalar H from e.g. left-right model, sneutrino in RPV

SUSY models;

◮ Doubly-charged scalar H±± in type-II seesaw and its extensions like left-right

model;

◮ Might also be connected to the heavy neutrino searches, effective 4-fermion

interactions, or even DM pheno at future lepton colliders. (See the talks by R. Franceschini, J. Zupan,

• M. Ramsey-Musolf, O. Fischer, M. Mitra)

Yongchao Zhang (Wustl) LFV Jan 11, 2019 3 / 31

Beyond SM neutral scalar H @ future lepton colliders

Well-motivated underlying models

RPV SUSY: sneutrinos (˜ ν)

[Aulakh, Mohapatra ’82; Hall,Suzuki ’84; Ross, Valle ’85, Barbier+ ’04; Duggan, Evans, Hirschauer ’13]

LRPV = 1 2λαβγ Lα Lβ E c

γ

Left-right symmetric models: the SU(2)R-breaking scalar H3

[Dev, Mohapatra, YCZ ’16; ’16; ’17; Maiezza, Senjanovi´ c, Vasquez ’16]

LFV couplings are generated at tree and loop level 2HDM: CP-even or odd (heavy) scalars from the 2nd doublet

[Branco+ ’11; Crivellin, Heeck, Stoffer ’15]

LFV couplings are induced from small deviation from the lepton-specific structure. Mirror models: singlet scalar connecting the SM leptons to heavy mirror leptons [Hung ’06, ’07; Bu, Liao, Liu ’08; Chang, Chang, Nugroho+ ’16; Hung, Le,

Tran+ ’17]

LFV couplings arise from the SM-heavy lepton mixing

Yongchao Zhang (Wustl) LFV Jan 11, 2019 5 / 31

Effective LFV couplings

Model-independent effective LFV couplings of H LY = hαβ ¯ ℓα, LHℓβ, R + H.c. . For simplicity, we assume hαβ are real, symmetric, H is CP-even, hadrophobic and the mixing with the SM Higgs h is small.

H might originate from a isospin singlet, doublet or triplet, depending on specific underlying models.

Effective Dim-4 couplings = Effective 4-fermion couplings like

1 Λ2 (¯

ee)(¯ eµ)

[Kabachenko, Pirogov ’97; Ferreira, Guedes, Santos ’06; Aranda, Flores-Tlalpa, Ramirez-Zavaleta+ ’09; Murakami, Tait ’14; Cho, Shimo ’14]

mH < √s ⇒ on-shell production

Yongchao Zhang (Wustl) LFV Jan 11, 2019 6 / 31

On-shell production of H at lepton colliders

the e+e− process e+e− → ℓ±

α ℓ∓ β + H

e− e+ γ, Z ℓ+

α

H ℓ−

β

γ, Z ℓ− ℓ− e+ H e+ e− γ, Z ℓ− e− e+ H e+ e−

involving the charged-currents [H decaying into visible particles] e+e− → να¯ νe + H

W ℓ− να ¯ νe H e+ e−

Yongchao Zhang (Wustl) LFV Jan 11, 2019 7 / 31

Laser photon in future lepton colliders

In future lepton colliders, high luminosity photon beams can be obtained by Compton backscattering of low energy, high intensity laser beam off the high energy electron beam [Ginzburg et al ’83, ’84]. The effective photon luminosity distribution (x = ω/Ee 0.83 the fraction of electron energy carried away by the scattered photon,

ξ = 4ω0Ee/m2

e)

fγ/e(x) =

1 D(ξ)

• (1 − x) +

1 (1−x) − 4x ξ(1−x) + 4x2 ξ2(1−x)2

• ,

with D(ξ) =

• 1 − 4

ξ − 8 ξ2

• log(1 + ξ) + 1

2 + 8 ξ − 1 2(1+ξ)2 ,

Yongchao Zhang (Wustl) LFV Jan 11, 2019 8 / 31

On-shell production of H at lepton colliders

involving the laser photon(s) e±γ → ℓ± + H , γγ → ℓ±

α ℓ∓ β + H

e− γ H ℓ− H ℓ+

α

ℓ−

β

γ γ

Yongchao Zhang (Wustl) LFV Jan 11, 2019 9 / 31

Constraints on the LFV couplings: on-shell

On-shell production amplitudes depend linearly on the LFV couplings muonium anti-muonium oscillation: (¯ µe) ↔ (µ¯ e) (heµ)

[Clark, Love ’03]

e− µ+ H µ− e+ e− µ+ H µ− e+

Electron and muon g − 2 (heℓ, hµℓ)

[Lindner, Platscher, Queiroz ’16]

Bhabha scattering, LEP ee → ℓℓ data (heℓ)

[OPAL ’03; L3 ’03; DELPHI ’05]

e e γ H µ heµ heµ

e− e+ H ℓ− ℓ+

Yongchao Zhang (Wustl) LFV Jan 11, 2019 10 / 31

Prospects of H: on-shell production

5 10 50 100 500 10-5 10-4 10-3 10-2 0.1 1

mH [GeV] |heμ|

s = 240 GeV 5 ab-1 eγ → μ H e+e- → eμ H γ γ → e μ H e+e- → νeνμ H ee → μμ ( g

• 2

)μ m u

• n

i u m

• s

c i l l a t i

• n

( g

• 2

)e 10 100 1000 10-4 10-3 10-2 0.1 1

mH [GeV] |heμ|

s = 1 TeV 1 ab-1 eγ → μ H e+ e- → e μ H γ γ → e μ H e+e- → νeνμ H ee → μμ (g-2)μ m u

• n

i u m

• s

c i l l a t i

• n

(g-2)e

γγ (eγ) channel: laser photon collision. Green bands: muon g − 2 anomaly (excluded). Assuming the dominant decay mode H → e±µ∓.

Very sadly, “Japanese science committee questions the project’s (ILC) multibillion-dollar price tag...” [https://www.nature.com/articles/d41586-018-07833-9] CLIC could do better!

Yongchao Zhang (Wustl) LFV Jan 11, 2019 11 / 31

Prospects of H: on-shell production

5 10 50 100 500 10-4 10-3 10-2 0.1 1

mH [GeV] |heτ|

s = 240 GeV 5 ab-1 eγ → τ H e+e- → eτ H γγ → eτ H e+e- → νeντ H ee → ττ (g-2)e 10 100 1000 10-4 10-3 10-2 0.1 1

mH [GeV] |heτ|

s = 1 TeV 1 ab-1 e γ → τ H e+e- → eτ H γ γ → e τ H e+e- → νeντ H

→

ee → ττ ( g

• 2

)e

γγ (eγ) channel: laser photon collision. Assuming the dominant decay mode H → e±τ ∓.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 12 / 31

Prospects of H: on-shell production

5 10 50 100 500 10-3 10-2 0.1 1

mH [GeV] |hμτ|

s = 240 GeV 5 ab-1 (g-2)

μ

( g

• 2

)μ e x c l u d e d e+ e- → μ τ H γ γ → μ τ H 10 100 1000 10-2 0.05 0.10 0.50 1

mH [GeV] |hμτ|

s = 1 GeV 1 ab-1 (g-2)μ (g-2)μ excluded e

+

e

• → μτ H

γ γ → μ τ H

◮ γγ (eγ) channel: laser photon collision. ◮ Assuming the dominant decay mode H → µ±τ ∓. ◮ The muon g − 2 discrepancy can be directly tested at CEPC & ILC via the searches

e+e−, γγ → µτ + H.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 13 / 31

Off-shell production of H at lepton colliders

Off-shell production (at resonance when mH ≃ √s)

might also be mediated by a (light) gauge boson Z ′ with LFV couplings [Heeck ’16]

e+e− → ℓ±

α ℓ∓ β

e− e+ H ℓ−

α

ℓ+

β

e− e+ H ℓ−

α

ℓ+

β Yongchao Zhang (Wustl) LFV Jan 11, 2019 14 / 31

Constraints on the LFV couplings: off-shell

Off-shell production amplitudes depend quadratically on the LFV couplings process current data constraints [GeV−2] µ− → e−e+e− < 10−12 |h†

eeheµ|/m2 H < 6.6 × 10−11

τ − → e−e+e− < 2.7 × 10−8 |h†

eeheτ|/m2 H < 2.6 × 10−8

τ − → µ−e+e− < 1.8 × 10−8 |h†

eehµτ|/m2 H < 1.5 × 10−8

τ − → µ+e−e− < 1.5 × 10−8 |h†

eµheτ|/m2 H < 1.9 × 10−8

τ − → e−γ < 3.3 × 10−8 |h†

eeheτ|/m2 H < 1.0 × 10−6

τ − → µ−γ < 4.4 × 10−8 |h†

eµheτ|/m2 H < 1.2 × 10−6

(g − 2)e < 5.0 × 10−13 |h†

eeheτ|/m2 H < 1.1 × 10−7

|h†

eµheτ|/m2 H < 1.0 × 10−8

ee → ee, ττ Λ > 5.7 & 6.3 TeV |h†

eeheτ|/m2 H < 1.4 × 10−7

ee → µµ, ττ Λ > 5.7 & 7.9 TeV |h†

eµheτ|/m2 H < 1.3 × 10−7

The µ → 3e limit is so strong that the it leaves no hope to see any signal in the ee → eµ channel at future lepton colliders.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 15 / 31

Prospects of H: off-shell production

e+e− → e±τ ∓

e− e+ hee H heτ e− τ + 10 50 100 500 1000 10-6 10-5 10-4 10-3 10-2

mH [GeV] |hee

† heτ|

τ- → e-e+e- τ- → e-γ ( g

• 2

)e ee → ℓℓ CEPC ILC

◮ Resonance effect at mH ≃ √s with width ΓH = 10 (30) GeV at CEPC (ILC). ◮ The off-shell scalar could be probed well beyond 10 TeV scale for couplings hαβ of

• rder one.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 16 / 31

Prospects of H: off-shell production

e+e− → µ±τ ∓

e− e+ hee H hµτ µ− τ + e− e+ heµ H heτ µ− τ +

Figure: The s and t channels depend on different h†h couplings.

10 50 100 500 1000 10-6 10-5 10-4 10-3 10-2

mH [GeV] |hee

† hμτ|

τ- → μ-e+e- CEPC ILC 10 50 100 500 1000 10-6 10-5 10-4 10-3 10-2

mH [GeV] |heμ

† heτ|

τ- → μ+e-e- τ- → μ-γ (g-2)e ee → ℓℓ CEPC ILC

Yongchao Zhang (Wustl) LFV Jan 11, 2019 17 / 31

Doubly-charged scalar H±± @ future lepton colliders

H±± at lepton (and hadron) colliders

The (left- and right-handed) H±± can be pair produced from the gauge interactions to the γ/Z bosons. The Drell-Yan production channels can not be used to measure directly the (LFV) Yukawa couplings fαβ of H±± to charged leptons, unless H±± is long-lived. The current LHC same-sign dilepton limits depend largely on the branching fractions BR(H±± → ℓ±

α ℓ± β ).

ee eμ μμ eτ μτ ττ ee+eμ+μμ 10-2 0.1 1 200 300 400 500 600 700 800

BR (H±± → ℓi

±ℓj ±)

Limits on M±± [GeV]

Solid lines: ATLAS'17 Dashed lines: CMS '17

Figure: LHC dilepton limits on the right-handed H±±.

[Dev, Mohapara & YCZ, 1803.11167]

Yongchao Zhang (Wustl) LFV Jan 11, 2019 19 / 31

On-shell Production of H±± at lepton colliders through the (LFV) Yukawa couplings fαβ

Model-independent effective couplings of (right-handed) H±± LY = fαβH++ℓC

αℓβ + H.c.

Pair production through the gauge and Yukawa couplings

[Chakrabarti+, hep-ph/9804297]

e− e+ γ/Z H−− H++ γ γ H++ H−− H++ e− e+ ℓ− H−− H++

The Drell-Yan processes dominate the pair production if the Yukawa couplings feℓ are very small.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 20 / 31

On/off-shell production of H±± at lepton colliders

Single production through the Yukawa couplings

[Kuze & Sirois, hep-ex/0211048; Barenboim, Huitu, Maalampi & Raidal, hep-ph/9611362; Lusignoli & Petrarca, PLB226, 397; Yue & Zhao, hep-ph/0701017; Godfrey, Kalyniak, Romanenko, hep-ph/0108258; hep-ph/0207240; Rizzo, PRD25, 1355; Yue, Zhao & Ma, 0706.0232]

e− e+ γ, Z ℓ+

α

H−− ℓ−

i

ℓ+

β

e− γ e ℓ+ H−− γ γ H−− ℓ+

α

ℓ+

β

Off-shell production

[Godfrey, Kalyniak, Romanenko, hep-ph/0108258; hep-ph/0207240; Rizzo, PRD25, 1355

e− e+ ℓ− H−− H++ e− e+ H−− ℓ+

α

ℓ−

β

γ e− ℓ−

γ

H−− ℓ−

β

ℓ+

α Yongchao Zhang (Wustl) LFV Jan 11, 2019 21 / 31

Prospects of H±± @ ILC 1TeV: single production

200 400 600 800 1000 10-4 0.001 0.010 0.100 1

M±± [GeV] feμ

s = 1 TeV 1 ab-1 ee → μμ e+e- → H++H-- (Yukawa) e±γ → H±±μ∓ e+e- → H±±e∓μ∓ γγ → H±±e∓μ∓

pair production BR(eμ) = 100%

◮ Assuming the dominant decay mode H±± → e±µ±. ◮ Below √s/2 ≃ 500 GeV, the process e+e− → H±±ℓ∓

α ℓ∓ β is dominated by the

Drell-Yan pair production e+e− → H++H−− with the subsequent decay H∓∓ → ℓ∓

α ℓ∓ β .

◮ The electron and muon g − 2 limits are highly suppressed by the charge lepton

masses and are not shown in the plot. CLIC could probe higher mass ranges.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 22 / 31

Prospects of H±± @ ILC 1TeV: single production

200 400 600 800 1000 10-4 0.001 0.010 0.100 1

M±± [GeV] feτ

s = 1 TeV 1 ab-1 e e → τ τ e+e- → H++H-- (Yukawa) e

±

γ → H

± ±

τ

∓

e+e- → H±±e∓τ∓ γγ → H±±e∓τ∓ pair production BR(eτ) = 100% fμμ [γγ] fμτ [γγ] fττ [γγ] fμμ [e+e-] fμτ [e+e-] fττ [e+e-] 500 550 600 650 700 750 800 10-2 0.1 1

M±± [GeV] fαβ

s = 1 TeV 1 ab-1

BR(μμ) = 100%

◮ Assuming the dominant decay mode H±± → e±τ ± (left), ℓ±

α ℓ± β (right).

◮ Below √s/2 ≃ 500 GeV, the process e+e− → H±±ℓ∓

α ℓ∓ β is dominated by the

Drell-Yan pair production e+e− → H++H−− with the subsequent decay H∓∓ → ℓ∓

α ℓ∓ β .

◮ The electron and muon g − 2 limits are highly suppressed by the charge lepton

masses and are not shown in the plots. CLIC could probe higher mass ranges.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 23 / 31

Prospects of H±± @ CEPC & ILC: off-shell production

ee → eτ [CEPC] ee → eτ [ILC] eγ → eeτ + τee [CEPC] eγ → eeτ + τee [ILC] 500 1000 5000 104 10-4 0.001 0.010 0.100 1

M±± [GeV] |fee

† feτ|

τ- → e-e+e- τ- → e- γ e e → ℓ ℓ ee → μτ [CEPC] ee → μτ [ILC] eγ → μeτ + τeμ [CEPC] eγ → μeτ + τeμ [ILC] 500 1000 5000 104 10-4 0.001 0.010 0.100 1

M±± [GeV] |feμ

† feτ|

τ- → μ-e+e- τ- → μ- γ e e → ℓ ℓ

◮ Suppressed by the three-body phase space, the sensitivities in the eγ processes are

comparatively much weaker.

◮ As in the neutral scalar case, the limit from µ → eee are so stringent that it has

precluded the H±±-mediated signal ee → eµ at CEPC & ILC.

◮ The effective cutoff scale Λ ≃ M±±/|f | can be probed at CEPC & ILC 1TeV up to

few 10 TeV (even higher at CLIC).

◮ The sensitivities for more flavor combinations α, β, γ in e±γ → ℓ∓

α ℓ± β ℓ± γ can be

found in our paper 1803.11167.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 24 / 31

the LFV signals might be displaced...

One example: H±±

L

in type-II seesaw (and its right-handed partner H±±

R

in left-right models)

Konetschny & Kummer ’77; Magg & Wetterich ’80; Schechter & Valle ’80; Cheng & Li ’80; Mohapatra & Senjanovic ’81; Lazarides, Shafi & Wetterich ’81

One of the simplest seesaw frameworks to generate the tiny neutrino masses L = − (fL)αβ ψT

LαCiσ2∆LψLβ + µHTiσ2∆† LH + H.c.,

∆L = δ+

L /

√ 2 δ++

L

= H++

L

δ0

L

−δ+

L /

√ 2

• Neutrino masses are given by

mν = √ 2 fLvL = U mνUT (with the VEV δ0

L = vL/

√ 2) The coupling matrix fL is fixed by neutrino oscillation data, up to the unknown lightest neutrino mass m0, the neutrino mass hierarchy, and the Dirac & Majorana CP violating phases. ⇒ VERY PREDICTIVE

Yongchao Zhang (Wustl) LFV Jan 11, 2019 26 / 31

Long-lived H±±

L Decay through the Yukawa couplings (suppressed by m2

ν/v 2 L)

Γ(H±±

L

→ ℓ±

α ℓ± β ) =

MH±±

L

8π(1 + δαβ) |(mν)αβ|2 v 2

L

, Decay through the gauge interactions (suppressed by v 2

L and potentially the phase-space)

Γ(H±±

L

→ W ±W ±) = G2

Fv 2 LM3 H±±

L

2π √ 1 − 4xW (1 − 4xW + 12x2

W ) ,

(with xW ≡ m2

W /M2 H±±

L

) Four-body decay for off-shell W -boson pairs H±±

L

→ W ± ∗W ± ∗ → f ¯ f ′f ′′¯ f ′′′ Neglecting the cascade decays H±± → H±(∗)W ±(∗), H±(∗)H±(∗) (small scalar mass splitting)

Yongchao Zhang (Wustl) LFV Jan 11, 2019 27 / 31

Proper lifetime of H±±

L

BR(ℓℓ) 1% 10% 50% 90% 99% 60 80 100 120 140 160 10-10 10-9 10-8 10-7 105 106 107 108 109

MHL

±± [GeV]

|fL

max

vL [eV] 1 mm 1 cm 10 cm 1 m NH (m1 = 0)

BR(ℓℓ) 1% 10% 50% 90% 99% 60 80 100 120 140 160 10-10 10-9 10-8 10-7 105 106 107 108 109

MHL

±± [GeV]

|fL

max

vL [eV] 1 m m 1 c m 1 c m 1 m IH (m3 = 0)

Γtotal(H±±

L

) = Γ(H±±

L

→ ℓαℓβ) + Γ(H±±

L

→ W ± (∗)W ± (∗)) . Assuming lightest neutrino mass m0 = 0. vL|fL|max ≃

• 0.027 eV ,

for NH with m1 = 0 , 0.048 eV , for IH with m3 = 0 .

Yongchao Zhang (Wustl) LFV Jan 11, 2019 28 / 31

Sensitivities of displaced vertices

Dev & YCZ, 1808.00943

50 100 500 1000 10-11 10-8 10-5 10-2 101 104 107

MHL

±± [GeV]

|fL

max

vL [eV] NH (m1 = 0)

Z width μ → e γ LEP LHC7 LHC8 LHC13 HSCP ILC H L

• L

H C FCC-hh 50 100 500 1000 10-11 10-8 10-5 10-2 101 104 107

MHL

±± [GeV]

|fL

max

vL [eV] IH (m3 = 0)

Z width μ → eee LEP LHC7 LHC8 LHC13 HSCP ILC H L- L H C FCC-hh

Assuming at least 100 events for the DV sensitivities of H±±

L

→ e±e±, e±µ±, µ±µ±. The low-energy high-precision LFV measurements (such as µ → eee and µ → eγ), the prompt same-sign dilepton searches of H±±

L

and the DV searches of H±±

L

are largely complementary to each other in the type-II seesaw.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 29 / 31

H±±

R

in left-right symmetric model

Dev, Ramsey-Musolf & YCZ, 1806.08499 Dev & YCZ, 1808.00943

50 100 500 1000 10-10 10-7 10-4 10-1

MHR

±± [GeV]

|(fR)ee| parity-violating

Z width ee → ee ν β β [ N H ] [ I H ] MOLLER LEP LHC7 LHC8 LHC13 HSCP ILC HL-LHC FCC-hh

Considering the simple scenario H±±

R

→ e±e±, W ±∗

R W ±∗ R .

We do not have the LFV constraints e.g. µ → eγ, and MOLLER pops out... The low-energy high-precision LFV measurements (MOLLER and 0νββ), the prompt same-sign dilepton searches of H±±

R

and the DV searches of H±±

R

are largely complementary to each other in the LRSM.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 30 / 31

Conclusion

A large variety of well-motivated models accommodate a beyond SM neutral scalar H and/or doubly-charged scalar H±±, with LFV couplings to the SM charged leptons. These LFV couplings can be studied in a model-independent way at future lepton colliders, which strengthens the physics case for future lepton colliders. The neutral scalar H can be produced on-shell via e±γ → ℓ± + H and e+e−, γγ → ℓ±

α ℓ∓ β + H or off-shell via e+e− → ℓ± α ℓ∓ β .

The doubly-charged scalar H±± can be (doubly & singly) on-shell and

• ff-shell produced from the (LFV) Yukawa couplings to the charged leptons.

It is promising that future lepton colliders could probe a broad region of mass and coupling parameters for both H and H±±, which go well beyond the existing low-energy LFV constraints like τ → eee. The neutral scalar explanation of the muon g − 2 anomaly can be directly tested at future lepton colliders in the e+e−, γγ → µ±τ ∓ + H processes. It might also be possible that the LFV signals are displaced, like H±± → e±µ± in type-II seesaw and left-right models.

Thank you for your attention!

Yongchao Zhang (Wustl) LFV Jan 11, 2019 31 / 31

backup slides

Constraints on the LFV couplings hαβ

On-shell production amplitudes depend linearly on the LFV couplings muonium anti-muonium oscillation: (¯ µe) ↔ (µ¯ e) (heµ)

e− µ+ H µ− e+ e− µ+ H µ− e+

Oscillation probablity [Clark, Love ’03] P = 2(∆M)2 Γ2

µ + 4(∆M)2

with the H-induced mass splitting ∆M = 2α3

EMh2 eµµ3

πm2

H

, µ = memµ me + mµ

Yongchao Zhang (Wustl) LFV Jan 11, 2019 33 / 31

Constraints on the LFV couplings hαβ

Electron and muon g − 2 (heℓ, hµℓ)

[Lindner, Platscher, Queiroz ’16]

e e γ H µ heµ heµ

∆ae ≃ h2

eµmemµ

16π2m2

H

• 2 log

m2

H

m2

µ

• − 3
• .

The value of heµ to explain (g − 2)µ discrepancy is excluded by the (g − 2)e constraint. ∆aµ ≡ ∆aexp

µ

− ∆ath

µ = (2.87 ± 0.80) × 10−9

Yongchao Zhang (Wustl) LFV Jan 11, 2019 34 / 31

Constraints on the LFV couplings hαβ

Bhabha scattering, LEP ee → ℓℓ data (heℓ)

[OPAL ’03; L3 ’03; DELPHI ’05]

e− e+ H ℓ− ℓ+

Effective 4-fermion interaction h2

eℓ

m2

H

(¯ eℓ)(¯ eℓ)

Fierz transf.

= = = = = = = ⇒ 1 Λ2 (¯ eγµe)(¯ ℓγµℓ) If mH √s, the LEP limits on the cut-off scale Λ do not apply, and we have to consider the kinetic dependence 1 m2

H

→ 1 q2 − m2

H

≃ 1 −s cos θ/2 − m2

H

Yongchao Zhang (Wustl) LFV Jan 11, 2019 35 / 31

Constraints on the LFV couplings hαβ

Off-shell production amplitudes depend quadratically on the LFV couplings 3-body LFV decays of muon and tauon, e.g. [Sher, Yuan ’91] Γ(τ − → e+e−e−) ≃ 1 δ |h†

eeheτ|2 m5 τ

3072π3m4

H

, (δ = 2) 2-body LFV decays of muon and tauon, e.g. [Harnik, Kopp, Zupan ’12] Γ(τ → eγ) = αEMm5

τ

64π4

• |cL|2 + |cR|2

, cL = cR ≃ h†

eeheτ

24m2

H

. hee, eµ, eτ contribute to (g − 2)e & LEP ee → ℓℓ data,

[DELPHI ’05; Hou, Wong ’95]

|h†

eeheτ|

⇒ ee → eτ |h†

eµheτ|

⇒ ee → µτ (t-channel)

Yongchao Zhang (Wustl) LFV Jan 11, 2019 36 / 31

SM backgrounds for on-shell production of H

Main SM backgronds are particle misidentification for e+e− → ℓ+

αℓ− β + X ,

(α = β) The mis-identification rate is expected to be small, of order 10−3

[Milstene, Fisk, Para ’06; Hammad, Khalil, Un ’16; Yu, Ruan, Boudry+ ’17]

Examle: e+e− → Zh → (e+e−/µ+µ−)h e±µ∓ + h

background signal 50 100 150 200 0.1 1 10 100 1000

meμ [GeV] Number of Events

s = 240 GeV 5 ab-1 mH = 50 GeV heμ = 0.003

background signal 200 400 600 800 1000 0.01 0.05 0.10 0.50 1 5 10

meμ [GeV] Number of Events

s = 1 TeV 1 ab-1 mH = 300 GeV heμ = 0.01

S/

• S + B = 55

S/

• S + B = 61

Yongchao Zhang (Wustl) LFV Jan 11, 2019 37 / 31

SM backgrounds for off-shell production of H

Main SM backgrounds: e+e− → W +W − → ℓ+

αℓ− β ν¯

ν The backgrounds can be well controlled by

[Kabachenko, Pirogov ’97; Cho, Shimo ’16; Bian, Shu, YCZ ’15]

requiring that the constructed energy Eℓ ≃ √s/2 , kinetic distribution analysis of the backgrounds and signals

Yongchao Zhang (Wustl) LFV Jan 11, 2019 38 / 31

CLIC prospects of H and H±±

CLIC prospects of H: on-shell production

10 50 100 500 1000 5000 10-4 10-3 10-2 0.1 1

mH [GeV] |heμ|

s = 3 TeV 2 ab-1 e γ → μ H e+e- → eμ H γ γ → e μ H ee → μμ muonium oscillation ( g

• 2

)e 10 50 100 500 1000 5000 10-4 10-3 10-2 0.1 1

mH [GeV] |heτ|

s = 3 TeV 2 ab-1 e γ → τ H e

+

e

• →

e τ H γ γ → e τ H ee → ττ ( g

• 2

)e

γγ (eγ) channel: laser photon collision. Shaded regions are excluded. Assuming the dominant decay mode H → e±µ∓ (left), e±τ ∓ (right).

Yongchao Zhang (Wustl) LFV Jan 11, 2019 40 / 31

CLIC prospects of H: on-shell production

10 50 100 500 1000 5000 10-2 0.1 1

mH [GeV] |hμτ|

s = 3 TeV 2 ab-1 ( g

• 2

)

μ

( g

• 2

)

μ

e x c l u d e d e+ e- → μ τ H γ γ → μ τ H

γγ (eγ) channel: laser photon collision. Shaded regions are excluded. Assuming the dominant decay mode H → µ±τ ∓. Dotted brown line: central values of muon g − 2 anomaly, green and yellow bands: the 1σ and 2σ regions.

The muon g − 2 discrepancy can be directly tested at CLIC via the searches of γγ → µτ + H.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 41 / 31

CLIC prospects of H: off-shell production

e+e− → e±τ ∓

e− e+ hee H heτ e− τ + 10 100 1000 104 10-6 10-5 10-4 10-3 10-2 10-1

mH [GeV] |hee

† heτ|

s = 3 TeV 2 ab-1 τ- → e-e+e- τ- → e-γ (g-2)e ee → ℓℓ CLIC

Resonance effect at mH ≃ √s with width ΓH = 30 GeV The off-shell scalar could be probed well beyond 10 TeV scale (or even up to 100 TeV).

Yongchao Zhang (Wustl) LFV Jan 11, 2019 42 / 31

CLIC prospects of H: off-shell production

e+e− → µ±τ ∓

e− e+ hee H hµτ µ− τ + e− e+ heµ H heτ µ− τ +

Figure: The s and t channels depend on different h†h couplings.

10 100 1000 104 10-6 10-5 10-4 10-3 10-2 10-1

mH [GeV] |hee

† hμτ|

s = 3 TeV 2 ab-1 τ

• → μ
• e

+

e

• CLIC

10 100 1000 104 10-6 10-5 10-4 10-3 10-2 10-1

mH [GeV] |heμ

† heτ|

s = 3 TeV 2 ab-1 τ- → μ+e-e- τ- → μ-γ ( g

• 2

)e ee → ℓℓ CLIC

Yongchao Zhang (Wustl) LFV Jan 11, 2019 43 / 31

CLIC prospects of H±±: single production

500 1000 1500 2000 2500 3000 10-3 10-2 0.1 1

M±± [GeV] |feμ|

s = 3 TeV 2 ab-1 ee → μμ e±γ → H±±μ∓ e

+

e

• → H

± ±

e

∓

μ

∓

pair production dilepton limit BR(eμ) = 100%

Assuming the dominant decay mode H±± → e±µ±. Below √s/2 = 1.5 TeV, the process e+e− → H±±ℓ∓

α ℓ∓ β is dominated by the Drell-Yan

pair production e+e− → H++H−− with the subsequent decay H∓∓ → ℓ∓

α ℓ∓ β .

The γγ → H±±ℓ∓

α ℓ∓ β sensitivity is weaker than the e+e− process.

The electron and muon g − 2 limits are highly suppressed by the charge lepton masses and are not shown in the plot.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 44 / 31

CLIC prospects of H±±: single production

500 1000 1500 2000 2500 3000 10-3 10-2 0.1 1

M±± [GeV] |feτ|

s = 3 TeV 2 ab-1 e e → τ τ e±γ → H±±τ∓ e

+

e

• → H

± ±

e

∓

τ

∓

pair production dilepton limit BR(eτ) = 100% 1600 1800 2000 2200 2400 0.05 0.10 0.50 1

M±± [GeV] |fμτ|

s = 3 TeV 2 ab-1 γγ → H±±μ∓τ∓ e+e- → H±±μ∓τ∓

Assuming the dominant decay mode H±± → e±τ ± (left), µ±τ ± (right). Below √s/2 = 1.5 TeV, the process e+e− → H±±ℓ∓

α ℓ∓ β is dominated by the Drell-Yan

pair production e+e− → H++H−− with the subsequent decay H∓∓ → ℓ∓

α ℓ∓ β .

The γγ → H±±ℓ∓

α ℓ∓ β sensitivity is weaker than the e+e− process.

The electron and muon g − 2 limits are highly suppressed by the charge lepton masses and are not shown in the plots.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 45 / 31

CLIC prospects of H±±: off-shell production

e+e− → e±τ ∓ e+e− → µ±τ ∓

1000 104 105 10-4 10-3 10-2 0.1 1

M±± [GeV] |fee

† feτ|

s = 3 TeV 2 ab-1 τ- → e-e+e- τ- → e-γ ee → ℓℓ CLIC 1000 104 105 10-4 10-3 10-2 0.1 1

M±± [GeV] |feμ

† feτ|

s = 3 TeV 2 ab-1 τ- → μ-e+e- τ- → μ-γ ee → ℓℓ CLIC

Suppressed by the three-body phase space, the sensitivities in the eγ processes are comparatively much weaker. As in the neutral scalar case, the limit from µ → eee are so stringent that it has precluded the H±±-mediated signal ee → eµ at CLIC. The effective cutoff scale Λ ≃ M±±/|f | can be probed at CLIC up to few 10 TeV.

Yongchao Zhang (Wustl) LFV Jan 11, 2019 46 / 31