charged lepton flavour violation at collidersbased on work in collaboration with tong li 1809.07924,...

based on work in collaboration with

Tong Li 1809.07924, 1907.06963

Yi Cai 1510.02486; Yi Cai, German Valencia 1802.09822

Charged lepton flavour violation at colliders

Michael A. Schmidt

17 January 2020

3rd FCC Physics and Experiments Workshop

http://www.arxiv.org/abs/1809.07924http://www.arxiv.org/abs/1907.06963http://www.arxiv.org/abs/1510.02486http://www.arxiv.org/abs/1802.09822

Motivation

The Standard Model is very successful. . .

. . . but incomplete

In particular neutrinos are massive

many different possibilities – see Cai, Herrero-Garcia, MS, Vicente, Volkas 1706.08524

1

http://www.arxiv.org/abs/1706.08524

Motivation

The Standard Model is very successful. . .

. . . but incomplete

In particular neutrinos are massive

many different possibilities – see Cai, Herrero-Garcia, MS, Vicente, Volkas 1706.08524

→ need way to discriminate models

Lepton flavour is not conserved (← ν oscillations)• in SM+mν suppressed by unitarity, A ∼ GFm2ν ' 10−26• many neutrino mass models have large charged LFV

due to non-unitarity or new contributions,

e.g. inverse seesaw, radiative mass models

• LFV processes a good probe to discriminate mν models• could be completely unrelated to neutrino mass, e.g. SUSY

3


Motivation

Energy Frontier

Intensity

Frontier Cosmi

cFrontier

Origin of Mass

Neutrinos

Proton Decay

Dark Matter

Dark Energy

Origin of

Universe

Unification

of Forces

Charged

Lepton

Flavour

Violation

Can high-energy colliders compete with the intensity frontier?4

cLFV at colliders

Future lepton colliders: e+e− → ``′

Future lepton colliders: e+e− → ``′ + X

LHC: qq̄, gg → ``′

Conclusions

5

Future lepton colliders: e+e− → ``′

cLFV scattering processes at a future lepton collider

Consider simplified models with bileptons X

Off-shell production:

e+e− → ``′e+

e−

`′−

`+

X

e+

e−

`+

`′−X

On-shell production:

e+e− → ``′ + Xe+

e−

`′−

`+

X

`′+γ/Z

e+

e−

X

`+

e−

e+

γ/Z

3 2-body final state

7 depends on product of

couplings

7 phase space suppression

3 depends on single LFV

coupling

6

Bileptons - seven simplified models [Li,MS 1809.07924 1907.06963]

∆L = 0complex scalar H2 ∼ (2, 12 )

L = y ij2 H2L̄iPR`j + h.c .

LH singlet vector H1 ∼ (1, 0)

L = y ij1 H1µL̄iγµPLLj

LH triplet vector H3 ∼ (3, 0)

L = y ij3 L̄iγµ~σ · H3µPLLj

right-handed vector H ′1 ∼ (1, 0)

L = y ′ij1 H ′1µ ¯̀iγµPR`j

∆L = 2right-handed scalar ∆1 ∼ (1, 2)

L = λij1 ∆1`Ti CPR`j + h.c .

left-handed scalar ∆3 ∼ (3, 1)

L = − λij3√2LTi Ciσ2~σ · ~∆3PLLj + h.c .

vector ∆2 ∼ (2, 32 )

L = λij2 ∆2µαLTiβγµPR`j�αβ + h.c .

assumption: CP conservation,

symmetric Yukawa couplings (H2, ∆2)

related work: Dev, Mohapatra, Zhang 1711.08430, also 1712.03642, 1803.11167

7

http://www.arxiv.org/abs/1809.07924http://www.arxiv.org/abs/1907.06963http://www.arxiv.org/abs/1711.08430http://www.arxiv.org/abs/1712.03642http://www.arxiv.org/abs/1803.11167

Off-shell production H1µ: e+e− → e±µ∓(e±τ∓) [Li,MS 1809.07924]

L = y ij1 H1µL̄iγµPLLj

e+

e−

e−

`+

H1

e+

e−

`+

e−H1

Basic cuts: pT > 10 GeV and |η| < 2.5

Four collider configurations:

CEPC: 5 ab−1 at 240 GeV

FCC-ee: 16 ab−1 at 240 GeV

ILC500: 4 ab−1 at 500 GeV

CLIC: 5 ab−1 at 3 TeV

LFV trilepton decays, `− → `−1 `+2 `−3

10-6

10-5

10-4

10-3

10-2

10 102

103

CEPCFCC-eeILC500CLIC

µ→3e

µ→3e

pro

j.

τ→3e

τ→3e

pro

j.

|y1e

e y 1

eµ|,

|y1e

e y 1

eτ|

mH1 (GeV)same result for H ′1µ/H3µ

τ efficiency not included in figure

60% τ eff. ⇒ 77% sensitivity reduction for 1 τ8


H1µ: e+e− → µ±τ∓ [Li,MS 1809.07924]

10-6

10-5

10-4

10-3

10-2

10 102

103

CEPC

FCC-eeILC500CLIC

τ- →µ

- e+ e

-τ

- →µ

- e+ e

- pro

j.

mH1 (GeV)

|y1e

e y 1

µτ|

rel. couplings |y ee1 yµτ1 |e+

e−

µ±

τ∓H1

10-6

10-5

10-4

10-3

10-2

10 102

103


τ- →µ

+ e- e

-τ- →

µ+ e

- e- p

roj.

mH1 (GeV)

|y1e

µ y 1

eτ|

rel. couplings |y eµ1 y eτ1 |e+

e−

µ+

τ−H1

e+

e−τ+

µ−H1

9


Future lepton colliders:

e+e− → ``′ + X

Other observables [Li,MS 1907.06963]

• anomalous magnetic moments, a`

• Muonium antimuonium conversion,µ+e− → µ−e+

• lepton flavour universality, `→ `′νν̄

• shift of GF : sin2 θW , mW , CKM unitarity

• non-standard interactions, e.g. KARMEN:ν oscillation at L = 0: ν̄µ → ν̄e

• LEP/LHC searches

• neutrino trident prod’n: νµN → νµN`+`−

`− `′−`′′−

H02

γ

µ+

e−

µ−

e+

H02

`

ν

ν̄

`′

h+2

e+

e−

`+

`−H02

11


Anomalous magnetic moment [Li,MS 1907.06963]

`− `′−`′′−

H02

γ

∆aµ = (2.74± 0.73)× 10−9 → > 3σ∆ae = (−0.88± 0.36)× 10−12 → > 2σ

• definite signsH

(′0)1µ ,∆1,∆3 : ∆a` ≥ 0

∆2µ : ∆a` ≤ 0H3µ and H2 can have either sign

• generally suppressed by lepton masses: ∆a` ∼ O(1) y2

12π2m2`m2X

with exception of H2:

∆a`(H2) =−(y†2 y2 + y2y

†2 )``

96π2

(m2`m2h2

+m2`m2a2

)+

(y†2 y2)``

96π2m2`m2

H+2

+∑k

Re[y k`2 y`k2 ]

mkm`16π2

ln(

m2km2

h2

)+ 3

2

m2h2−

ln

(m2km2a2

)+ 3

2

m2a2

12


Muonium-antimuonium oscillation [Li,MS 1907.06963]

µ+

e−

µ−

e+

H02

P(B = 0.1T ) ≤ 8.3× 10−11Willmann et al hep-ex/9807011

factor > 100 improvement possibleBernstein, Schöning (2019)

• in QM muonium M = (µ+e−) described byH = H0 + Hhf + HZeeman → |↑↓〉 and |↓↑〉 states mix

• bileptons induce muonium-antimuonium mixing HMM̄

HMM̄ ∼1

πa3B

1

∗ ∗∗ ∗

1

using basis of energy eigen-

states of (anti)muonium

|λ1〉 ≡ |↑↑〉, |λ2,3〉, |λ4〉 ≡ |↓↓〉

• reevaluated under assumption of HMM̄ � H• magnetic fields suppress conversion probability by

0.36 (H(′)01µ , H3µ, ∆1,3),

0.79 (∆2, H2 : mh2 = ma2), and 0.5 (H2 : mh2 � ma2)13

http://www.arxiv.org/abs/1907.06963http://www.arxiv.org/abs/hep-ex/9807011

Muonium-antimuonium oscillation [Li,MS 1907.06963]

µ+

e−

µ−

e+

H02

P(B = 0.1T ) ≤ 8.3× 10−11Willmann et al hep-ex/9807011

factor > 100 improvement possibleBernstein, Schöning (2019)

• in QM muonium M = (µ+e−) described byH = H0 + Hhf + HZeeman → |↑↓〉 and |↓↑〉 states mix• bileptons induce muonium-antimuonium mixing HMM̄

HMM̄ ∼1

πa3B

1

∗ ∗∗ ∗

1

using basis of energy eigen-

states of (anti)muonium

|λ1〉 ≡ |↑↑〉, |λ2,3〉, |λ4〉 ≡ |↓↓〉

• reevaluated under assumption of HMM̄ � H• magnetic fields suppress conversion probability by

0.36 (H(′)01µ , H3µ, ∆1,3),

0.79 (∆2, H2 : mh2 = ma2), and 0.5 (H2 : mh2 � ma2)13

http://www.arxiv.org/abs/1907.06963http://www.arxiv.org/abs/hep-ex/9807011

Lepton flavour universality [Li,MS 1907.06963]

`

ν

ν̄

`′

h+2L = −2

√2GF [ν̄iγµPLνj ][¯̀kγ

µ(g ijklLL PL+gijklLR PR`)]

Consider LFU ratios

Rµe =Γ(τ → ντµν̄µ)Γ(τ → ντeν̄e)

RexpµeRSMµe

= 1.0034± 0.0032

Rτµ =Γ(τ → ντeν̄e)Γ(µ→ νµeν̄e)

RexpτµRSMτµ

= 1.0022± 0.0028

H1µ, H3µ and ∆3: Contribution to gLL,NP → interference with SMH2, ∆2: Contribution to gLR,NP → no interference

gijklLL,NP

= −yij1 y

kl1

2√

2GFm2H0

1

−ykj3 y

il3√

2GFm2

H+3

−λjl3λ

ik∗3

2√

2GFm2

∆+3

gijklLR,NP

=y il2 y

jk∗2

4√

2GFm2

H+2

−λil2λ

jk∗2

2√

2GFm2

∆+2

14


Lepton flavour universality [Li,MS 1907.06963]

`

ν

ν̄

`′ L = −2√

2GF [ν̄iγµPLνj ][¯̀kγµ(g ijklLL PL+g

ijklLR PR`)]

Consider LFU ratios

Rµe =Γ(τ → ντµν̄µ)Γ(τ → ντeν̄e)

RexpµeRSMµe

= 1.0034± 0.0032

Rτµ =Γ(τ → ντeν̄e)Γ(µ→ νµeν̄e)

RexpτµRSMτµ

= 1.0022± 0.0028

H1µ, H3µ and ∆3: Contribution to gLL,NP → interference with SMH2, ∆2: Contribution to gLR,NP → no interference

gijklLL,NP

= −yij1 y

kl1

2√

2GFm2H0

1

−ykj3 y

il3√

2GFm2

H+3

−λjl3λ

ik∗3

2√

2GFm2

∆+3

gijklLR,NP

=y il2 y

jk∗2

4√

2GFm2

H+2

−λil2λ

jk∗2

2√

2GFm2

∆+2

14


New contributions to muon decay and GF ,µ [Li,MS 1907.06963]

µ

ν

ν̄

eGF = GF ,µ(1 + δGF )

δGF = −Re(gµeeµLL,NP)−1

2

∑α,β

(|gαβeµLL,NP |2 + |gαβeµLR,NP |2)

A shift in the Fermi constant measured in muon decays induces

shifts in

• Weinberg angle δs2W

s2W=

c2Ws2W−c2W

δGF

• W boson mass δm2W

m2W=

s2Ws2W−c2W

δGF

• CKM unitarity |V expud |2 + |Vexpus |2 + |V expub |2 = 1 + 2δGF

Caveat: analysis based on PDG 2018, does not include the

recent determination of Vud and Vus

15


On-shell production H2: e+e− → e±µ∓ + h2/a2 [Li,MS 1907.06963]

L =y ij2 H2αL̄αi PR`j + h.c .

e+

e−

e−

`+

h2/a2

e+γ/Z

e+

e−

h2/a2

`+

e−

e+

γ/Z

Cuts: pT > 10 GeV and |η| < 2.5100% h/a reconstruction efficiency

Five collider configurations:



ILC (500 GeV): 4 ab−1 at 500 GeV

ILC (1TeV): 1 ab−1 at 1 TeV


CEPCFCC-eeILC (500 GeV)ILC (1 TeV)CLIC

5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mh2 (GeV)

|y 2eμ | a μ(mh 2=ma 2≪m

H 2+ )

a μ(mh 2=ma

2=mH 2+ )

ae(mh2≪ma2

,mH 2+ )

muoniumosc.

muoniumosc. (proj.)

LEP ee→μμDUNE

(H 2+ )

16


On-shell production H2: e+e− → e±µ∓ + h2/a2 [Li,MS 1907.06963]

L =y ij2 H2αL̄αi PR`j + h.c .

e+

e−

e−

`+

h2/a2

e+γ/Z

e+

e−

h2/a2

`+

e−

e+

γ/Z

Cuts: pT > 10 GeV and |η| < 2.510% h/a reconstruction efficiency

Five collider configurations:



ILC (500 GeV): 4 ab−1 at 500 GeV

ILC (1TeV): 1 ab−1 at 1 TeV



5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mh2 (GeV)


H 2+ )

a μ(mh 2=ma

2=mH 2+ )

ae(mh2≪ma2

,mH 2+ )

muoniumosc.

muoniumosc. (proj.)

LEP ee→μμDUNE

(H 2+ )

16


On-shell production H2: e+e− → `±`′∓ + H2 [Li,MS 1907.06963]


5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mh2 (GeV)


H 2+ )

a μ(mh 2=ma

2=mH 2+ )

ae(mh2≪ma2

,mH 2+ )

muoniumosc.

muoniumosc. (proj.)

LEP ee→μμDUNE

(H 2+ )

e+

e−

e−

`+

h2/a2

e+γ/Z

e+

e−

h2/a2

`+

e−

e+

γ/Z

L = y ij2 H2αL̄αi PR`j + h.c.


5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mh2 (GeV)

|y 2eτ |

a μ(mh 2=ma

2≪mH 2+ )

a μ(mh 2=ma

2=mH 2+ )

ae(mh2≪ma2

,mH 2+ )

LEP ee→ττ


5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mh2 (GeV)

|y 2μτ |a μ(mh 2=

ma2≪mH 2+ )

a μ(mh 2=ma

2=mH 2+ )

aμ(mh 2≪ma

2,mH 2

+ )

60% τ efficiency included 17


On-shell production H1,3µ: e+e− → `±`′∓ + H1,3 [Li,MS 1907.06963]


5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mH1 (3)(,)0 (GeV)

|y 1(3)

eμ|

a μ(mH 1,mH

3≪mH 3+ )

a μ(mH 3=mH

3+ )

muoniumosc.

muoniumosc. (proj.)LEP ee→μμ

DUNE

(H 3+ )

LFU(H 1)

GF(H 1)

e+

e−

e−

`+

H1,3

e+γ/Z

e+

e−

H1,3

`+

e−

e+

γ/Z

L = y ij1 H1µL̄iγµPLLj + y

ij3 L̄iγ

µ~σ · H3µPLLj


5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mH1 (3)(,)0 (GeV)

|y 1(3)

eτ|

a μ(mH 1,mH

3≪mH 3+ )

a μ(mH 3=mH

3+ )LEP ee→ττ

LFU(H 1)


5 10 50 100 500 100010-4

0.001

0.010

0.100

1

mH1 (3)(,)0 (GeV)

|y 1(3)μτ|

a μ(mH 1,mH

3≪mH 3+ )

a μ(mH 3=mH

3+ )

LFU(H 1)



On-shell production ∆1,3: e+e− → `±`′∓ + ∆1,3 [Li,MS 1907.06963]


5 10 50 100 500 100010-5

10-4

0.001

0.010

0.100

1

mΔ1 (3)++ (GeV)

|λ 1(3)

eμ|

aμ(mΔ 1++ ,mΔ 3++≪mΔ 3

+ )aμ(mΔ 3++ =

mΔ 3+ )

DUNE

(Δ 3+ )LEP ee→μμ

LFU(Δ 3+ )

GF(Δ 3+ )

e+

e−

e−

`−

∆++1,3

e+γ/Z

e+

e−

∆++1,3

`−

e−

e+

γ/Z

L = λij1 ∆++1 `

Ti CPR`j +

λij3√2LTi Ciσ2~σ · ~∆3PLLj + h.c.


5 10 50 100 500 100010-5

10-4

0.001

0.010

0.100

1

mΔ1 (3)++ (GeV)

|λ 1(3)

eτ|

aμ(mΔ 1++ ,mΔ 3++≪mΔ 3

+ )aμ(mΔ 3++ =

mΔ 3+ )

LEP ee→ττLFU

(Δ 3+ )


5 10 50 100 500 100010-5

10-4

0.001

0.010

0.100

1

mΔ1 (3)++ (GeV)

|λ 1(3)μτ|

aμ(mΔ1++,mΔ3++≪mΔ3+)

aμ(mΔ 3++ =mΔ 3+ ) LFU(Δ 3+ )



On-shell production ∆2µ: e+e− → `±`′∓ + ∆2 [Li,MS 1907.06963]


5 10 50 100 500 100010-6

10-5

10-4

0.001

0.010

0.100

1

mΔ2++ (GeV)

|λ 2eμ | aμ(mΔ2++≪mΔ2+ )

aμ(mΔ2++ =mΔ2+ )

DUNE(Δ 2+ )

e+

e−

e−

`−

∆++2

e+γ/Z

e+

e−

∆++2

`−

e−

e+

γ/Z

L = λij2 ∆2µαLTiβCγ

µPR`j�αβ + h.c.


5 10 50 100 500 100010-6

10-5

10-4

0.001

0.010

0.100

1

mΔ2++ (GeV)

|λ 2eτ |

aμ(mΔ2++≪mΔ2+ )

aμ(mΔ2++ =mΔ2+ )


5 10 50 100 500 100010-610-510-40.001

0.010

0.100

1

mΔ2++ (GeV)

|λ 2μτ |

aμ(mΔ2++≪mΔ2+ )

aμ(mΔ2++ =mΔ2+ )



LHC: qq̄, gg → ``′

cLFV at the Large Hadron Collider (LHC) [Cai, MS 1510.02486]

Processes at LHC: pp → ì`j + jets

q

q

ì

`j

q

q

ì

`j

g

g

q

q

ì

`j

qg

q

q

ì

`j

q

Signal: opposite-sign different flavour pair of leptons → existing searches:

• ATLAS 7 TeV: LFV heavy neutral particle decay to eµ ATLAS 1103.5559• CMS 8 TeV: LFV heavy neutral particle decay to eµ CMS-PAS-EXO-13-002• ATLAS 7 TeV, 2.1 fb−1, exclusive:

LFV in eµ continuum in�R SUSYATLAS 1205.0725

• ATLAS 8 TeV, 20.3 fb−1, inclusive:LFV heavy neutral particle decayATLAS 1503.04430

• CMS 8 TeV: LFV heavy neutral particle decay to eµ CMS 1604.05239• ATLAS 13 TeV, 3.2 fb−1: LFV heavy neutral particle decay ATLAS 1607.08079• ATLAS 13 TeV, 36.1 fb−1 ATLAS 1807.06573

21

http://www.arxiv.org/abs/1510.02486http://www.arxiv.org/abs/1103.5559http://www.arxiv.org/abs/1205.0725http://www.arxiv.org/abs/1503.04430http://www.arxiv.org/abs/1604.05239http://www.arxiv.org/abs/1607.08079http://www.arxiv.org/abs/1807.06573

cLFV at hadron colliders: quarks

ēµ µ̄e ēττ̄ e µ̄τ τ̄µ10−1

100

101

102

103

Λ[T

eV]

ūu, d̄d, s̄s, c̄c, b̄bτ → `Mτ → `f0

µ− eM → `ν

LHC8LHC14

Cai, MS 1510.02486

ATLAS 8TeV 1503.04430; ATLAS 14 TeV, 300 fb−1 projection

Qledq = (L̄α`)(d̄Qα) , Q(1)lequ = (L̄α`)�αβ(Q̄βu)LHC more interesting for vector operators with right-handed quark

currents due to weaker constraints from intensity frontier

[q̄γµPRq][¯̀γµPR,L`] 22

http://www.arxiv.org/abs/1510.02486http://www.arxiv.org/abs/1503.04430

cLFV at hadron colliders: gluons

OX , ŌX 2.541.631.17

O′X , Ō′X 1.631.17eµ

OY ,Z 1.640.98

OX , ŌX 1.030.610.42

O′X , Ō′X 1.030.610.44eτ

OY ,Z 1.060.47

OX , ŌX 1.230.900.43

O′X , Ō′X 1.230.900.46µτ

OY ,Z 1.230.67 low-energy

LHC

LHC (unitarised)

Λ [TeV]0.1 0.5 1 1.5 2 2.5 3

coupling → form factorC → C

1+ŝ

Λ2Baur, Zeppenfeld hep-ph/9309227

Cai, MS, Valencia 1802.09822

OijX = αsG aµνG aµν(ēRiLj · φ∗ + L̄j · φeRi

)O′ijX = i αsG aµνG̃ aµν

(ēRiLj · φ∗ − L̄j · φeRi

)ŌijX = i αsG aµνG aµν

(ēRiLj · φ∗ − L̄j · φeRi

)Ō′ijX = αsG aµνG̃ aµν

(ēRiLj · φ∗ + L̄j · φeRi

)OijY = i αsG aµρG aσνηρσL̄iγµDνLjOijZ = i αsG aµρG aσνηρσ ēRiγµDνeRj

OX , ŌX : µN → eN, τ → `M+M−O′X , Ō′X : τ → `M0

LHC searches: ATLAS 13 TeV, 3.2 fb−1 (eµ, eτ , µτ) 1607.08079, CMS 13 TeV, 35.9 fb−1 (eµ) 1802.01122

23

http://www.arxiv.org/abs/hep-ph/9309227http://www.arxiv.org/abs/1802.09822http://www.arxiv.org/abs/1607.08079http://www.arxiv.org/abs/1802.01122

Searches for cLFV in decays of Z and Higgs boson

Z→eµ

Z→eτ

Z→µτ

10−12

10−9

10−6

10−3

BR

(Z→` 1` 2

)

CEPC current

Z → eµ: ATLAS 1408.5774, CMS EXO-13-005Z → `τ : DELPHI (µτ), OPAL (eτ)similar sensitivity as LFV τ decays

→ complementary probe

| τµ

|Y5−10 4−10 3−10 2−10 1−10

|

µ τ|Y

5−10

4−10

3−10

2−10

1−10

(13 TeV)-136.0 fbCMS

B

Conclusions

Conclusions

colliders provide complementary way to search for charged LFV

Off-shell production/EFT

• µ↔ e flavour: stringent limits from low-energy precision exp.• τ ↔ ` flavour complementary sensitivity at colliders

On-shell production

• possibly no constraints from LFV decays• µ↔ τ flavour: constraints from LFU [H1,∆3] and aµ [H2]• e ↔ ` flavour complementary sensitivity at colliders

EFT

• colliders test more Lorentz structures• best for operators which are difficult to constrain at low energy

25

Conclusions cont.

Energ

y Frontier

IntensityFrontier Cosm

icFr

onti

er

Higgs physics

Neutrinos

Proton Decay

Dark Matter

Dark Energy

Unifica-tion ofForces

cLFV

Than

kyo

u!

26

Backup slides

26

cLFV Z boson decays

Z→eµ

Z→eτ

Z→µτ

10−12

10−9

10−6

10−3

BR

(Z→` 1` 2

)CEPC current

Z → eµ: ATLAS 1408.5774, CMS EXO-13-005Z → `τ : DELPHI (µτ), OPAL (eτ)ATLAS, 13 TeV, 36.1 fb−1 1804.09568

almost same sensitivity for µτ

No tree-level FCNC in SM

induced at 1 loop in SM +mν

Z

`−1

`+2

W

W

ν ∝ GFm2ν

16π2' 10−28

Observation clear sign of new physics

e.g. due to a leptoquark

Z

`−1

`+2

q

q′

φ

today typically less stringent as low-energy

precision experiments

but will be more interesting with new Z

boson factory

or if there is a signal to disentangle physics

27


cLFV Higgs decay

Dimension-6 SMEFT operators Grzadkowski et al 1008.4884

L =[Yij +

cijΛ2

(H†H)]L̄iPR`jH+h.c .→

[mijv

+cij√

2

v2

Λ2

]h ¯̀iPR`j+h.c .

9 Results

The best-fit branching ratios and upper limits are computed under the assumption of B(H → µτ) = 0for the H → eτ search and B(H → eτ) = 0 for the H → µτ search, respectively. The best-fit values ofthe LFV Higgs boson branching ratios are equal to 0.15+0.18−0.17% and −0.22 ± 0.19% for the H → eτ andH → µτ search, respectively. In the absence of any significant excess, upper limits on the LFV branchingratios are set for a Higgs boson with mH = 125GeV. The observed (median expected) 95% CL upper limitsare 0.47% (0.34+0.13−0.10 %) and 0.28% (0.37

+0.14−0.10 %) for the H → eτ and H → µτ searches, respectively.

These limits are significantly lower than the corresponding Run 1 limits of Refs. [7, 8]. The breakdown ofcontributions from different signal regions is shown in Fig. 4.

) in %τ e→ H(Β95% CL upper limit on 0 1 2 3 4 5 6

ATLAS Preliminary Observedσ 1±Expected

σ 2±Expected

-1 = 13 TeV, 36.1 fbs

VBFµτe

1.59 (exp)1.69 (obs)

-1.24

+1.72 = 0.07µ

µτe

0.58 (exp)0.81 (obs)

-0.31

+0.31 = 0.30µ

hadτe

0.54 (exp)0.72 (obs)

-0.26

+0.27 = 0.23µ

non-VBFhad

τe

0.65 (exp)1.00 (obs)

-0.32

+0.33 = 0.42µ

non-VBFµτe

0.61 (exp)0.80 (obs)

-0.31

+0.31 = 0.25µ

τe

0.34 (exp)0.47 (obs)

-0.17

+0.18 = 0.15µ

VBFhad

τe

0.97 (exp)0.84 (obs)

-0.58

+0.60 = -0.35µ

) in %τµ → H(Β95% CL upper limit on 0 1 2 3 4 5 6

ATLAS Preliminary Observedσ 1±Expected

σ 2±Expected

-1 = 13 TeV, 36.1 fbs

VBFe

τµ

1.64 (exp)1.08 (obs)

-0.89

+0.89 = -1.28µ

eτµ

0.66 (exp)0.44 (obs)

-0.31

+0.31 = -0.38µ

hadτµ

0.44 (exp)0.41 (obs)

-0.23

+0.23 = -0.07µ

non-VBFhad

τµ

0.57 (exp)0.49 (obs)

-0.32

+0.31 = -0.21µ

non-VBFe

τµ

0.72 (exp)0.57 (obs)

-0.35

+0.35 = -0.24µ

τµ

0.37 (exp)0.28 (obs)

-0.19

+0.19 = -0.22µ

VBFhad

τµ

0.96 (exp)0.94 (obs)

-0.58

+0.58 = -0.09µ

Figure 4: 95% CL upper limits on the LFV branching ratios of the Higgs boson, H → eτ (left) and H → µτ (right).Best-fit values of the branching ratios (µ̂) are also given, in %. The limits are computed under the assumption thateither B(H → µτ) = 0 (left) or B(H → eτ) = 0 (right). Results of the fit when only the data of an individualchannel or of an individual category are used, are also shown; in these cases the signal and control regions from allother channels/categories are removed from the fit.

The branching ratio of the LFV Higgs decay is related to the non-diagonal Yukawa coupling matrixelements [84] by the formula

√|Ỳ τ |2 + |Yτ` |2 = 8πmH

B(H → `τ)1 − B(H → `τ) ΓH (SM), (1)

where ΓH (SM) stands for the Higgs boson width as predicted by the Standard Model. Thus, theobserved limits on the branching ratio correspond to the following limits on the matrix elements:√|Yτe |2 + |Yeτ |2 < 0.00197, and

√|Yτµ |2 + |Yµτ |2 < 0.00152. Figure 5 shows the limits on the individual

matrix elements Yτ` and Ỳ τ together with the limits from the ATLAS Run 1 analysis and from τ → `γsearches [84, 85].

14

ATLAS-CONF-2019-013BR(h→ eτ) < 0.47% ), %τµ→(HΒ95% CL limit on

0 2 4 6 8 10 12 14

0.25% (0.25%)

τµ→H

1.79% (1.62%) , VBF

eτµ

2.27% (1.98%) , 2 Jets

eτµ

1.34% (1.19%) , 1 Jet

eτµ

1.30% (0.83%) , 0 Jets

eτµ

0.51% (0.58%) , VBF

hτµ

0.56% (0.94%) , 2 Jets

hτµ

0.53% (0.56%) , 1 Jet

hτµ

0.51% (0.43%) , 0 Jets

hτµ

: BDT fitτµ→h

Observed

Median expected

68% expected

95% expected


CMS 1712.07173BR(h→ µτ) < 0.25%

h

τ

`

28


cLFV Higgs decay cont.

√|Y`τ |2 + |Yτ`|2 =

8πΓH(SM)

mH

BR(H → `τ)1− BR(H → `τ)

4−10 3−10 2−10 1−10

|τe

|Y

4−10

3−10

2−10

1−10| e τ

|Y

γ e → τ

< 1

0%

Β

< 1

%Β

< 0

.1%

Β

< 0

.01%

Β

< 5

0%

Β

| < n.l.

eτ

Yτe

|Y

-1=13 TeV, 36.1 fbs

PreliminaryATLAS Observedσ 1±Expected

σ 2±Expected

ATLAS Run 1

4−10 3−10 2−10 1−10|

τ µ|Y

4−10

3−10

2−10

1−10| µ τ

|Y

γ µ → τ

< 1

0%

Β

< 1

%Β

< 0

.1%

Β

< 0

.01%

Β

< 5

0%

Β

| < n.l.

µ τ

Yτ µ

|Y

-1=13 TeV, 36.1 fbs

PreliminaryATLAS Observedσ 1±Expected

σ 2±Expected

ATLAS Run 1

Figure 5: Upper limits on the absolute value of the couplings Yτ` and Ỳ τ together with the limits from the ATLASRun 1 analysis (light grey line) and the most stringent indirect limits from τ → `γ searches (dark purple region).Indicated are also limits corresponding to different branching ratios (0.01%, 0.1%, 1%, 10% and 50%) and thenaturalness limit (denoted n.l.) |Yτ`Ỳ τ | . mτm`v [84] where v is the vacuum expectation value of the Higgs field.

10 Conclusions

Direct searches for H → eτ and H → µτ are performed with the pp collisions recorded by the ATLASdetector at the LHC corresponding to an integrated luminosity of 36.1 fb−1 at a centre-of-mass energy of√

s = 13TeV. No significant excess was observed above the expected background from SM processes. Theobserved (expected) 95% CL upper limits on the branching ratios of H → eτ and H → µτ are 0.47%(0.34+0.13−0.10 %) and 0.28% (0.37

+0.14−0.10 %), respectively. These limits represent an improvement by a factor 2

(5) over the corresponding Run 1 limits for the H → eτ (H → µτ) decay.

References

[1] ATLAS Collaboration, Observation of a new particle in the search for the Standard Model Higgsboson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1, arXiv: 1207.7214 [hep-ex](cit. on p. 2).

[2] CMS Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment atthe LHC, Phys. Lett. B 716 (2012) 30, arXiv: 1207.7235 [hep-ex] (cit. on p. 2).

[3] A. Arhrib, Y. Cheng and O. C. Kong, Comprehensive analysis on lepton flavor violating Higgsboson to µ∓τ± decay in supersymmetry without R parity, Phys. Rev. D 87 (2013) 015025, arXiv:1210.8241 [hep-ph] (cit. on p. 2).

[4] K. Agashe and R. Contino, Composite Higgs-mediated flavor-changing neutral current, Phys. Rev.D 80 (2009) 075016, arXiv: 0906.1542 [hep-ph] (cit. on p. 2).

15

ATLAS-CONF-2019-013

τ

h

ττ

γ

µY ∗ττPL + YττPR Y

∗τµPL + YµτPR

+µ

h

µτ

γ

µY ∗τµPL + YµτPR Y

∗µµPL + YµµPR

µ

h γ, Z

tt

τ

γ

µµ

h γ, Z

WW

τ

γ

µ

µ

h γ, Z

W W

τ

γ

µ

µ

h

µ

Z

µτ

γ

µHarnik et al 1209.1397

| τµ

|Y5−10 4−10 3−10 2−10 1−10

|

µ τ|Y

5−10

4−10

3−10

2−10

1−10


B

General (type-III) 2 Higgs doublet model

EFT

L =[mivδij +

cij√2

v 2

Λ2

]h ¯̀iPR`j

two neutral CP even Higgs

Φi = (vi + φi )/√

2v2v1

= tβ

SM Higgs: h = −sαφ1 + cαφ2with Yukawa couplings

Yij = −sαcβ

mivδij +

cos(β − α)cβ

√mimj

vχ`ij

Not suppressed by v 2/Λ2 → large contribution

BR(h→ µτ) ∝(|χ`23|2 + |χ`32|2

)cos2(β−α)(1+tan2 β)

Benbrik, Chen, Nomura 1511.08544

EWPO

Higgs decay channels

30


Example: Zee model

• Non-zero neutrino masses

• generated at loop level Zee 1980

• Simplest model with 2 Higgs doublets andcharged singlet scalar h+

L

Φi

Φi

L

h+ Φi

L ē

-10 -8 -6 -4 -2log10(Br(h→ τe))

-8

-6

-4

-2

log 1

0(Br(h→

τµ

))

2σ region

1σ region

Normal orderingm1 < m2 < m3

-10 -8 -6 -4 -2log10(Br(h→ τe))

-8

-6

-4

-2

log 1

0(Br(h→

τµ

))

2σ region

1σ region

Inverted orderingm3 < m1 < m2

Herrero-Garcia et al 1701.05345

[see Herrero-Garcia et al 1605.06091 for Higgs cLFV in other neutrino mass models] 31


Future lepton collider

e−

e+

Z

h

Z ∗

LHC

ILC

CEPC(FCC-ee)

yeμ yeτ yμτ

5.×10-5

1.×10-4

5.×10-4

10-3

Qin et al 1711.07243

LHC CMS-PAS-HIG-16-005, CMS 1607.03561

ILC√s = 250 GeV, 4 polarizations, L = 2 ab−1

CEPC√s = 240 GeV, L = 5 ab−1

32


Future lepton collider

e−

e+

Z

h

Z ∗

LHC

ILC

CEPC(FCC-ee)

yeμ yeτ yμτ

5.×10-5

1.×10-4

5.×10-4

10-3

Qin et al 1711.07243

LHC CMS-PAS-HIG-16-005, CMS 1607.03561

ILC√s = 250 GeV, 4 polarizations, L = 2 ab−1

CEPC√s = 240 GeV, L = 5 ab−1

LHCILCCEPC(FCC-ee)H→bb (λb=1)

-1.0 -0.5 0.0 0.5 1.00.10.5

1

5

10

50

cos(α-β)

λ μτ

Qin et al 1711.07243

LHCILCCEPC(FCC-ee)H→bb (λb=0.5)

-1.0 -0.5 0.0 0.5 1.00.10.5

1

5

10

50

cos(α-β)

λ μτ

32

http://www.arxiv.org/abs/1711.07243http://www.arxiv.org/abs/1607.03561http://www.arxiv.org/abs/1711.07243

Scalar Operators

Qledq = (L̄α`)(d̄Qα) Q(1)lequ = (L̄α`)�αβ(Q̄βu)

Relevant Wilson coefficients Ξu,d of SM EFT

− L = Ξdij ,kk (Qledq)ij ,kk + Ξuij ,kk(Q(1)lequ

)ij ,kk

+ h.c. .

Effective four fermion Lagrangian

L4f = ΞCdij ,kl(ν̄Li`Rj)(d̄RkuLl) + ΞNdij ,kl(¯̀Li`Rj)(d̄RkdLl)+ ΞCuij ,kl(ν̄Li`Rj)(d̄LkuRl) + Ξ

Nuij ,kl(¯̀Li`Rj)(ūLkuRl) .

We do not consider top quark because of different phenomenology.

33

Scalar Operators

Qledq = (L̄α`)(d̄Qα) Q(1)lequ = (L̄α`)�αβ(Q̄βu)

Relevant Wilson coefficients Ξu,d of SM EFT


)ij ,kk

+ h.c. .




Thus the most general four fermion coefficients are

ΞNdij ,kl = U`∗ii ′ V

dlk Ξ

dij ,kk Ξ

Cdij ,kl = U

ν∗ii ′ V

ulk Ξ

di ′j ,kk

ΞNuij ,kl = −U`∗ii ′ V u∗kl Ξuij ,ll ΞCuij ,kl = Uν∗ii ′ V d∗kl Ξui ′j ,llIn general there is quark flavour violation.

We do not consider top quark because of different phenomenology.33

Scalar Operators

Qledq = (L̄α`)(d̄Qα) Q(1)lequ = (L̄α`)�αβ(Q̄βu)Relevant Wilson coefficients Ξu,d of SM EFT


)ij ,kk

+ h.c. .




Choose basis in which charged lepton mass matrix is diagonal as

well as ΞN?ij ,kk

ΞNdij ,kl = δklΞdij ,kk Ξ

Cdij ,kl = U

∗ii ′ V

∗kl Ξ

di ′j ,kk

ΞNuij ,kl = −δklΞuij ,kk ΞCuij ,kl = U∗ii ′ V ∗kl Ξui ′j ,ll⇒ No tree-level FCNC processes.We do not consider top quark because of different phenomenology.

33

Renormalization Group Corrections

• Main effect are QCD corrections

q q

q

q

`i

`j

• Following the standard discussion at NLOBuchalla,Buras, Lautenbacher hep-ph/9512380

Ξ(µ) = Ξ(µ0)

(αs(µ)

αs(µ0)

) γ02β0

with coefficients

β0 = 11− 2nF/3 and γ0 = 6C2(3) = 8

• Wilson coefficients become larger at smaller scales.⇒ Increases reach of precision experiments

34

http://www.arxiv.org/abs/hep-ph/9512380

Precision Experiments

µ− e−

N N

µ− e conversion in nuclei

τ−

`−

M0

τ → `M0

`−j

`+i

M0

M0 → `+i `−j

ν

`+i

M+

M+ → `+i ν

35

µ− e Conversion

• Agnostic about mediation mechanism

• Following discussion inGonzalez, Gutsche, Helo, Kovalenko, Lyubovitskij, Schmidt 1303.0596

µ− e−

N N

Dimensionless µ− e conversion rate

R(A,Z)µe ≡

Γ(µ− + (A,Z )→ e− + (A,Z ))Γ(µ− + (A,Z )→ νµ + (A,Z − 1))

with muon conversion rate

Γ(µ−+(A,Z )→ e−+(A,Z )) =∣∣∣ΞNu,Ndij ,kl ∣∣∣2×F×peEe (Mp +Mn)22π

F depends on mediation mechanismNo dependence on phase of Ξ if there is only one operator.

Strongest limit for first generation quarks,

but non-negligible for other quarks if pure direct nuclear mediation36


µ− e Conversion

• Agnostic about mediation mechanism

• Following discussion inGonzalez, Gutsche, Helo, Kovalenko, Lyubovitskij, Schmidt 1303.0596

µ− e−

N N

48Ti 197Au 208Pb

Rmaxµe 4.3× 10−11 7.0× 10−13 4.6× 10−11

ūu 1100 [870] 2100 [1700] 760 [610]

d̄d 1100 [930] 2200 [1900] 780 [680]

s̄s 480 [-] 950 [-] 340 [-]

c̄c 150 [-] 290 [-] 110 [-]

b̄b 84 [-] 170 [-] 61 [-]

Direct nuclear mediation [Meson mediation]

Strongest limit for first generation quarks,

but non-negligible for other quarks if pure direct nuclear mediation36


LFV Semileptonic τ Decays

• Only light quarks u,d,s• Weak dependence on phase• f0: ϕm parameterises quark content• Quark FCNC parameterised by λ

Ξuij,kl = λΞuij,llVkl Ξ

dij,kl = λΞ

dij,kkVkl

τ−

`−

M0

decay Brmaxi cutoff scale Λ [TeV]

Ξuij ,uu Ξdij ,dd Ξ

dij ,ss

τ− → e−π0 8.0× 10−8 10 10 -τ− → e−η 9.2× 10−8 34 34 7.9τ− → e−η′ 1.6× 10−7 42 42 12τ− → e−K 0S 2.6× 10−8 - 7.8

√λ 7.8

√λ

τ− → e−(f0(980)→ π+π−) 3.2× 10−8 13√

sinϕm 13√

sinϕm 16√

cosϕm

τ− → µ−π0 1.1× 10−7 9.0− 9.6 9.0− 9.6 -τ− → µ−η 6.5× 10−8 36− 38 36− 38 8.4− 8.9τ− → µ−η′ 1.3× 10−7 42− 46 42− 46 12− 13τ− → µ−K 0S 2.3× 10−8 - (7.8− 8.3)

√λ (7.8− 8.3)

√λ

τ− → µ−(f0(980)→ π+π−) 3.4× 10−8 (12− 14)√

sinϕm (12− 14)√

sinϕm (15− 16)√

cosϕm

37

Leptonic Neutral Meson Decays M0 → `+i `−j

Quark FCNC parameterised by λ

Ξuij,kl = λΞuij,llVkl Ξ

dij,kl = λΞ

dij,kkVkl

For λ = 0 only constraints from π0, η(′) decays

decay Brmaxi cutoff scale Λ [TeV]

Ξuij ,uu Ξdij ,dd Ξ

dij ,ss Ξ

uij ,cc Ξ

dij ,bb

π0 → µ+e− 3.8× 10−10 2.2 2.2 - - -π0 → µ−e+ 3.4× 10−9 1.2 1.2 - - -π0 → µ+e− + µ−e+ 3.6× 10−10 2.6 2.6 - - -η → µ+e− + µ−e+ 6× 10−6 0.52 0.52 0.12 - -η′ → eµ 4.7× 10−4 0.091 0.091 0.026 - -

K 0L → e±µ∓ 4.7× 10−12 - 86√λ 86

√λ - -

D0 → e±µ∓ 2.6× 10−7 6.4√λ - - 6.4

√λ -

B0 → e±µ∓ 2.8× 10−9 - 10√λ - - 6.6

√λ

B0 → e±τ∓ 2.8× 10−5 - 0.97√λ - - 0.62

√λ

B0 → µ±τ∓ 2.2× 10−2 - 0.18√λ - - 0.12

√λ

`−j

`+i

M0

38

Leptonic Charged Meson Decays M+ → `+i ν

• RM = Br(M+→e+ν)

Br(M+→µ+ν)

• Theoretical error for Rπ (RK ) about 5%• Improvement by factor 20 (2) possible••X indicates constraints• Second index of Λ corresponds to charged lepton

decay constraint cutoff scale Λ [TeV] Wilson coefficients

Λµe,eµ,eτ Λτe,τµ,µτ Ξuij ,uu Ξ

dij ,dd Ξ

dij ,ss Ξ

uij ,cc Ξ

dij ,bb

Rπ Rexpπ ± 5% 25− 280 25− 260 •X •X - - -

RK RexpK ± 5% 24− 160 24− 150 X - •X - -

Br(D+ → e+ν) < 8.8× 10−6 2.8− 2.9 2.9 - X - X -Br(D+s → e+ν) < 8.3× 10−5 3.2− 3.3 3.2− 3.3 - - X •X -Br(B+ → e+ν) < 9.8× 10−7 2.0 2.0 X - - - •XBr(π+ → µ+ν) Brexp ± 5% 1.9− 7.4 1.9− 9.4 •X •X - - -Br(K+ → µ+ν) Brexp ± 5% 1.7− 5.8 1.7− 7.4 X - •X - -Br(D+ → µ+ν) (3.82± 0.33)× 10−4 1.1− 2.7 1.1− 3.4 - X - X -Br(D+s → µ+ν) (5.56± 0.25)× 10−3 1.3− 4.3 1.3− 5.3 - - X •X -Br(B+ → µ+ν) < 1.0× 10−6 1.9− 2.7 1.7− 3.0 X - - - •XBr(D+ → τ+ν) < 1.2× 10−3 0.21− 0.78 0.23− 0.73 - •X - X -Br(D+s → τ+ν) (5.54± 0.24)× 10−2 0.33− 1.2 0.33− 1.1 - - •X •X -Br(B+ → τ+ν) (1.14± 0.27)× 10−4 0.49− 1.3 0.49− 1.2 •X - - - •X

ν

`+i

M+

39

Invariant Mass Distribution of eµ Pair for Different Quarks

0 500 1000 1500 2000M(eµ) [GeV]

0

1000

2000

3000

4000

5000

Arb

itrar

yun

itsudscb

Production cross section normalised to same value for each quark.

• Sea quarks s, c, b peaked at low invariant mass

• Valence quarks u, d shifted towards larger invariant mass40

Interesting ATLAS searches [Cai, MS 1510.02486]

Recast limits of most sensitive previous searches

ATLAS 1503.04430 ATLAS 1205.0725

8 TeV 7 TeV

20.3 fb−1 2.1 fb−1

eµ, eτ , µτ eµ

inclusive exclusive

including arbitrary number of jets separated by number of jets

Projection to 14 TeV

• Assume 300 fb−1

• Follow searching strategy of exclusive 7 TeV search41


ATLAS Searches [Cai, MS 1510.02486]

0 100 200 300 400 500 600 700 800 900 1000

Eve

nts

/ 2

5 G

eV

1

10

210

310

0 100 200 300 400 500 600 700 800 900 1000

Eve

nts

/ 2

5 G

eV

1

10

210

310

= 95 GeV)t~Signal (m

Total Background

Top

τ τ →* γZ/Fake Background

Diboson

ATLAS

-1 Ldt = 2.1 fb∫

[GeV]µe m0 100 200 300 400 500 600 700 800 9001000D

ata

/ S

M

0.5

1

1.5

ATLAS 7TeV 1205.0725

Eve

nts

/ 20

GeV

1−10

1

10

210

310

410

510 Data (1 TeV)τν∼

ττ →Z Others

Z' (0.75 TeV)

Jet fake

tt

Total SM

-1 = 8 TeV, 20.3 fbs

ATLAS

µe

Dilepton Mass [GeV]0 200 400 600 800 1000 1200

Dat

a/S

M

12

Eve

nts

/ 20

GeV

1−10

1

10

210

310

410


ll→Z Others

Z' (0.75 TeV)

Jet fake

tt

Total SM

-1 = 8 TeV, 20.3 fbs

ATLAS

τe


Dat

a/S

M

12

ATLAS 8TeV 1503.04430

Eve

nts

/ 20

GeV

1−10

1

10

210

310

410


ll→Z Others

Z' (0.75 TeV)

Jet fake

tt

Total SM

-1 = 8 TeV, 20.3 fbsATLAS

τµ


Dat

a/S

M

12

ATLAS 8TeV 1503.04430 42

http://www.arxiv.org/abs/1510.02486http://www.arxiv.org/abs/1205.0725http://www.arxiv.org/abs/1503.04430http://www.arxiv.org/abs/1503.04430

ATLAS Searches [Cai, MS 1510.02486]

0 100 200 300 400 500 600 700 800 900 1000

Eve

nts

/ 2

5 G

eV

1

10

210

310

0 100 200 300 400 500 600 700 800 900 1000

Eve

nts

/ 2

5 G

eV

1

10

210

310


Total Background

Top


Diboson

ATLAS

-1 Ldt = 2.1 fb∫

[GeV]µe m0 100 200 300 400 500 600 700 800 9001000D

ata

/ S

M

0.5

1

1.5


Eve

nts

/ 20

GeV

1−10

1

10

210

310

410


ττ →Z Others

Z' (0.75 TeV)

Jet fake

tt

Total SM

-1 = 8 TeV, 20.3 fbs

ATLAS

µe


Dat

a/S

M

12

ATLAS 8TeV 1503.04430• Main backgrounds: tt̄, WW , Z/γ∗ → ττalso W /Z plus jets, WZ/ZZ , single top and W /Z + γ

⇒ Efficiently reduced in exclusive 7 TeV analysisby rejecting jets and EmissT < 20 GeV

• Modelling of main background agrees with ATLAS• Fake background estimated from data⇒ Use background from ATLAS publications

43


SM Background

0 100 200 300 400 500 600 700 800 900 1000

Eve

nts

/ 2

5 G

eV

1

10

210

310

0 100 200 300 400 500 600 700 800 900 1000

Eve

nts

/ 2

5 G

eV

1

10

210

310


Total Background

Top


Diboson

ATLAS

-1 Ldt = 2.1 fb∫

[GeV]µe m0 100 200 300 400 500 600 700 800 9001000D

ata

/ S

M

0.5

1

1.5


Eve

nts

/ 20

GeV

1−10

1

10

210

310

410


ττ →Z Others

Z' (0.75 TeV)

Jet fake

tt

Total SM

-1 = 8 TeV, 20.3 fbs

ATLAS

µe


Dat

a/S

M

12

ATLAS 8TeV 1503.04430• Main backgrounds: tt̄, WW , Z/γ∗ → ττalso W /Z plus jets, WZ/ZZ , single top and W /Z + γ

⇒ Efficiently reduced in exclusive 7 TeV analysisby rejecting jets and EmissT < 20 GeV

• Modelling of main background agrees with ATLAS• Fake background estimated from data⇒ Use background from ATLAS publications

44


Selection Criteria

Same selection criteria as in ATLAS 7 and 8 TeV analyses.

• oppositely charged leptons

• Electrons: ET > 25 GeV, |η| < 1.37 or 1.52 < |η| < 2.47, tightidentification criteria

• Muons: pT > 25 GeV, |η| < 2.4

• Tau: ET > 25 GeV, 0.03 < |η| < 2.47

• Lepton isolation: scalar sum of lepton pT within cone of ∆R = 0.2(0.4)is less than 10% (6%) of lepton pT for 7 (8) TeV search

• Jets reconstructed anti-kT algorithm with radius parameter 0.4

• 7 TeV analysis: jets rejected if pT > 30 GeV or EmissT < 25 GeV

• Invariant mass of lepton pair: > 100(200) GeV in 7(8) TeV analysis

• azimuthal angle difference ∆φ > 3(2.7) in 7 (8) TeV analysis

14 TeV projection

Same as 7 TeV exclusive analysis and pT (`) > 300 GeV and EmissT < 20 GeV

45

Limits from LHC on Cutoff Scale in TeV

HHHH

HHHq̄q

¯̀i`j

ēµ ēτ µ̄τ

7 TeV 8 TeV 14 TeV 8 TeV 8 TeV

ūu 2.6 2.9 8.9 2.4 2.2

d̄d 2.3 2.3 8.0 2.1 1.9

s̄s 1.1 1.4 4.0 0.95 0.88

c̄c 0.97 1.3 3.6 0.82 0.78

b̄b 0.74 1.0 2.7 0.63 0.61

• 8 TeV analysis gives only a slight improvement compared to 7 TeVdespite 10 times more data because of large background

• eτ and µτ limits weaker than eµ because of low τ -tagging rate andhigher fake background

• 14 TeV projection: same search strategy as 7 TeV exclusive search46

cLFV D8 operator with 2 gluons and 2 leptons

process exp. limit operator Λ [TeV]

eµ

Br(µ− 4822Ti→ e− 4822Ti) < 4.3× 10−12 OX , ŌX 2.11Br(µ− 19779Au→ e− 19779Au) < 7× 10−13 OX , ŌX 2.54

eτ

Br(τ+ → e+π+π−) < 2.3× 10−8 OX , ŌX 0.42Br(τ− → e−K+K−) < 3.4× 10−8 OX , ŌX 0.37Br(τ− → e−η) < 9.2× 10−8 O′X , Ō′X 0.40Br(τ− → e−η′) < 1.6× 10−7 O′X , Ō′X 0.44

µτ

Br(τ− → µ−π+π−) < 2.1× 10−8 OX , ŌX 0.43Br(τ− → µ−K+K−) < 4.4× 10−8 OX , ŌX 0.36Br(τ− → µ−η) < 6.5× 10−8 O′X , Ō′X 0.42Br(τ− → µ−η′) < 1.3× 10−7 O′X , Ō′X 0.46

47

cLFV at the Large Hadron Collider (LHC): gluons [Cai, MS, Valencia 1802.09822]

Processes at LHC: pp → `i`jg

g

`i

¯̀j

Signal:

opposite-sign different flavour pair of leptons

Most sensitive searches

ATLAS 1607.08079 CMS-PAS-EXO-16-058 1802.01122

13 TeV 13 TeV

3.2 fb−1 35.9 fb−1

eµ, eτ , µτ eµ

inclusive inclusive

newer ATLAS search: 13 TeV, 36.1 fb−1 1807.06573

EFT scattering amplitudes

A(s) ' sΛ2

s→∞−→ ∞

Solutions:

• UV-complete models/simplified models

• apply unitarization procedure, e.g.K-matrix unitarization

Wigner 1964; Wigner, Eisenbud 1947; Gupta 1950

Recent application to monojets: Bell, Busoni, Kobakhidze, Long, MS 1606.02722

• couplings → form factorBaur, Zeppenfeld hep-ph/9309227

C → C1 + ŝ

Λ2⇒ Violation of perturbative unitarity48

http://www.arxiv.org/abs/1802.09822http://www.arxiv.org/abs/1607.08079http://www.arxiv.org/abs/1802.01122http://www.arxiv.org/abs/1807.06573http://www.arxiv.org/abs/1606.02722http://www.arxiv.org/abs/hep-ph/9309227

H1µ: e+e− → e±µ∓(e±τ∓)

10-6

10-5

10-4

10-3

10-2

10 102

103


µ→3e

µ→3e

pro

j.

τ→3e

τ→3e

pro

j.

|y1e

e y 1

eµ|,

|y1e

e y 1

eτ|

mH1 (GeV)

L = y ij1 H1µ ¯̀iγµPL`j

e+

e−

e−

`+

H1

e+

e−

`+

e−H1

same result for

right-handed H ′1µ

τ efficiency not included in figure60% τ eff. ⇒ 77% (60%) sensitivity reduction for 1 (2) τ leptons

49

H2: e+e− → e±µ∓(e±τ∓)

10-6

10-5

10-4

10-3

10-2

10 102

103

CEPC

FCC-ee

ILC500

CLIC

µ→3e

µ→3e

pro

j.

τ→3e

τ→3e

pro

j.

|y2e

e y 2

eµ|,

|y2e

e y 2

eτ|

mh2=ma2 (GeV)

L = y ij2 H02 ¯̀iPR`j + h.c .

e+

e−

e−

`+

H2

e+

e−

`+

e−H2

50

H1µ,H2: e+e− → µ±τ∓

e+

e−

µ±

τ∓X 0

rel. couplings

|y eeyµτ |10

-6

10-5

10-4

10-3

10-2

10 102

103

CEPC

FCC-eeILC500CLIC

τ- →µ

- e+ e

-τ

- →µ

- e+ e

- pro

j.

mH1 (GeV)

|y1e

e y 1

µτ|

10-6

10-5

10-4

10-3

10-2

10 102

103

CEPC

FCC-eeILC500CLIC

τ- →µ

- e+ e

-τ- →

µ- e

+ e- p

roj.

mh2=ma2 (GeV)

|y2e

e y 2

µτ|

e+

e−

µ+

τ−X 0

e+

e−τ+

µ−X 0

rel. couplings

|y eµy eτ |10

-6

10-5

10-4

10-3

10-2

10 102

103


τ- →µ

+ e- e

-τ- →

µ+ e

- e- p

roj.

mH1 (GeV)

|y1e

µ y 1

eτ|

10-6

10-5

10-4

10-3

10-2

10 102

103

CEPCFCC-eeILC500

CLIC

τ- →µ

+ e- e

-

τ- →µ

+ e- e

- pro

j.

mh2=ma2 (GeV)

|y2e

µ y 2

eτ|

51

charged lepton flavour violation at collidersbased on work in collaboration with tong li 1809.07924,...

Documents