Lepton Flavour LHC?

m_{ν ⇒} (charged) lepton flavour change happens, and the LHC exists ...so look for

Lepton Flavour Violation @ LHC?

Sacha Davidson , P Gambino, G Grenier, S Lacroix , ML Mangano, S Perries, V Sordini, P Verdier IPN de Lyon/CNRS

(1412.xxxx,1207.4894,1001.0434, 1211.1248,1008.0280)

1. LHC is a discovery machine: look for LFV decays of theoretically motivated new particles (sleptons, N_R,...)

2. SM external legs exist _⇒ look for LFV interactions of SM particles?

Lepton Flavour Violation @ LHC?

Sacha Davidson , P Gambino, G Grenier, S Lacroix , ML Mangano, S Perries, V Sordini, P Verdier IPN de Lyon/CNRS

(1412.xxxx,1207.4894,1001.0434, 1211.1248,1008.0280)

1. LHC a discovery machine: look for LFV in decays of theoretically motivated new particles (sleptons, N_R,...)

2. SM external legs exist _⇒ LHC look for LFV interactions of SM particles?

with a heavy leg, to complement lower energy searches

µ, e τ Z τ µ, e h e q τ, µ t

Parametrise LFV vertices as contact interactions Bounds from low energy and LEP?

What about the Z?

LHC? low energy?

Dimension six operators for LFV Z decays

Mass dimension of Z and two lepton external legs = 4

⇒ Z _→ τ±µ∓ operators contains two Higgs and/or Derivatives

Three options among gauge invariant operators at dimension 6:

O(∂2) : µγ_βD_ατ Bαβ , ...

O(H2) : [H†D_αH]µγατ , ...

O(yH∂) dipole : ℓµHσβατ Bαβ , ...

Dimension six operators for LFV Z decays

Need two powers of a vev/momentum in operator.

Three options among gauge invariant operators at dimension 6.

Suppose operator coefficients such that:

Rossi+Brignole ..., µγ_βD_ατ Bαβ _→ g_ZC p 2 Z 16π2_Λ2µγατ Z α ..., [H†DαH]µγατ → gZA m2_Z 16π2_Λ2µγαZ α_τ ..., ℓµHσβατ Bαβ → gZD mτ 16π2_Λ2[µσαβτ]Z αβ

LEP and the LHC

1. LEP1 was a clean Z machine, with 17 _× 106 Zs

BR(Z → e±µ∓) < 1.7×10−6 , BR(Z → e±τ∓) < 9.8×10−6 , BR(Z → µ±τ∓) < 1.2×10−5 2. at LHC8, σ(pp _→ Z _→ µµ)¯ _∼ nb, _{L ∼} 20 fb−1, BR(Z _→ µµ)¯ _≃ 0.0366 #Zs _≃ σ(pp → Z → µµ¯) × L BR(Z _→ µµ¯) ∼ 5 × 10 7_Zs ∼ 25 _× LEP ATLAS 1408.5774: BR(Z → e∓µ±) < 7.5 × 10−7 95% C.L..

Low energy: the Z contributes too?

decades of rare decay/precision data?... BR(τ _→ µµµ¯ ) < 2.1 _× 10−8

µ_L τ_L Z µ τ µ µ Z

Low energy: the Z contributes too?

decades of rare decay/precision data?... BR(τ _→ µµµ¯ ) < 2.1 _× 10−8

µ_L τ_L Z µ τ µ µ Z

But gradient operators better constrained at high energy. Consider (∂αZβ−∂βZα = Zαβ)

gZC 1 16π2_Λ2Z αβ_µγα_∂β_τ → gZC p2_Z 16π2_Λ2µγαZ α_τ on the Z : vertex =g_Z Cm 2 Z 16π2_Λ2µZ/ τ in τ _→ µµµ¯ :vertex < g_Z Cm 2 τ 16π2_Λ2µZ/ τ (negligeable) ? But, am I allowed gradient operators? Yes, more later ...

The gradient2 Z → τ±µ∓ operators: are they important in loops?

τ

γ µ Z

and can I calculate that?

1. assume NP scale Λ _≫ m_Z

2. assume NP generates only ∂2 operator (no other LFV; not τ →µγ), so “interaction”:

gZCµτ

p2_Z

16π2_Λ2µγατ Z

α

3. in RG running between Λ and mZ, Z → τ±µ∓ will mix to τ → µγ operator

(...estimate the coefficient of 1/ǫ in dim reg...)

g BR(τ _→ µγ) _≃ 3α 4π g_Z4 G2_FΛ4 C_µτ log 32π2 2 ∼ 4 _× 10−8C 2 µτv4 Λ4 ⇒ no constraint on Cµτ from BRg(τ → ℓγ) <∼ 2 × 10−7

but µ _→ eγ constrains C_eµ: BR(Z _→ e±µ∓) <_∼ 10−10.

Derivative Operators, Eqns of Motion and the Operator Basis

Simma EJPC

equations of motion (EoM) for the hypercharge boson (B _≃ Z)

∂_µBµν ₋ g₂′(H†DνH ₋ [DνH]†H) ₋ g′ P_f Qf_Yf γνf = 0

Derivative Operators, Eqns of Motion and the Operator Basis

Simma EJPC

On-shell S-matrix elements induced by an operator containing EoM vanish. This is used to reduce the operator basis.

Eg, the equations of motion (EoM) for the hypercharge boson (B _≃ Z)

∂_µBµν ₋ g₂′(H†DνH ₋ [DνH]†H) ₋ g′ P_f Qf_Yf γνf = 0 so the operator: O = τ γ_νµ(∂_µBµν ₋ ig′2H†HBν ₋ g′ P_f Qf_Yf γνf) induces vertices τ γνµf γνf , ∝ Qf_Y Bντ γ_νµ, _∝ p2_{B −} m2_B (_mB = g′hHi).

These vertices cancel in on-shell S-matrix elements :

h

µτ

¯

_|O|

f

f

¯

_i

=

Q

Q

Derivative Operators, Eqns of Motion and the Operator Basis

Simma EJPC

On-shell S-matrix elements induced by an operator containing EoM vanish. This is used to reduce the operator basis.

Eg, the equations of motion (EoM) for the hypercharge boson (B _≃ Z)

∂_µBµν ₋ g₂′(H†DνH ₋ [DνH]†H) ₋ g′ P_f Qf_Yf γνf = 0 so the operator: O = τ γ_νµ(∂_µBµν ₋ ig′2H†HBν ₋ g′ P_f Qf_Yf γνf) induces vertices τ γνµf γνf , ∝ Qf_Y Bντ γ_νµ, _∝ p2_{B −} m2_B (_mB = g′hHi).

These vertices cancel in on-shell S-matrix elements :

h

µτ

¯

_|O|

f

f

¯

_i

=

Q

Q

Getting the same constraints on NP in either basis?

1. four fermion operator and ∂2 LFV Z operator: (τ γαµ)(µγαµ) , p2_Zτ Z/ µ

• on the Z, LFV Z coupling contributes, 4-f operator not.

• in τ _→ µµµ¯ , only 4-f operator contributes

2. four fermion operator and penguin=H†DνH LFV Z operator:

(τ γαµ)(µγαµ) , m2_Zτ Z/ µ

• on the Z, LFV Z coupling contributes, 4-f operator not.

• in τ _→ µµµ, both operators contribute in the amplitude, cancellations possible.¯

(formally: below _mZ, must “match out” Z so the coeff of 4 ferm op changes)

Choose derivative operators to parametrise Z contact interactions, because these contribute at LHC (where Z is propagating particle), but not at low energy:

Summary about the Z: LHC has interesting sensitivity to Z _→ µ±τ∓, Z _→ e±τ∓.

h

→

τ

±

ℓ

∓

low energy bounds h _→ τµ¯ selon CMS?

Operators and Models for LFV Higgs decays

LFV could appear in Higgs decays:

1. if have Y₁ℓHτ¯ , plus dim 6 operator Y₂H†HℓHτ¯

Giudice-Lebedev, Babu-Nandi

2. also two Higgs doublets of “ type III” = flavour changing couplings

+ keep two neutral light scalars ...Davidson-Grenier

Low energy constraints

LFV could appear in Higgs decays:

1. due to effective dim 6 operator H†HℓHτ¯ Giudice-Lebedev, Babu-Nandi 2. also two Higgs doublets of “ type III” = flavour changing couplings

+ keep two neutral light scalars

... Aristizabal,Vicente

allowed by low energy LFV searches:

Diaz-Cruz,Toscana Kanemura-Ota-Tsumura Davidson-Grenier ... Goudelis-Lebedev-Park Harnik-Kopp-Zupan Blankenburg,Ellis,Isidori • tree exchange of h :τ _→ ηµ, τ _→ µµµ¯ : y_{τ µ ∼}< _O(1) ok

• loops : τ _→ µγ, EW precision, b _→ sγ, etc

Tree level Higgs exchange (diff from Z! h is much narrower)

in low energy rare decays:

µ τ µ µ h Γ(τ→3µ) Γ(τ→µνν¯) ∼ y_{τ µy}2 2_µ m4 h g4 m4 W ∼ y 2 τ µyµ2 g4 so feeble bounds on yτ µ

on the narrow resonance ( Γ_{h ∼} 3y_b2/16π):

µL τL h Γ(h→τ µ) Γ(h→b¯b) ∼ y_{τ µ}2 y_b2

Bounds on LFV Higgs couplings from loops?

Recall perturbation theory expands in couplings and loops, and m_µ/m_t < 1/16π2

one-loop amplitudes _∝ (y_{LF V}y_µ)/16π2 can be smaller than...

τ µ γ h ek < τ µ γ t γ _h ...two-loop amplitudes _∝ g2(y_{LF V} y_t)/(16π2)2

Most restrictive bound y_{τ µ} <

∼ .1 from 2-loop τ → µγ

(model-dep; what else in loops?)

CMS: h _→ τ±µ∓ ), % τ µ → Best Fit to Br(h -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 % -0.37 +0.40 0.89 τ µ → h % -0.97 +1.58 0.05 , 2 Jets e τ µ % -0.78 +0.85 0.81 , 1 Jet e τ µ % -0.62 +0.66 0.87 , 0 Jets e τ µ % -0.88 +1.09 1.24 , 2 Jets had τ µ % -1.12 +1.07 0.03 , 1 Jet had τ µ % -1.15 +1.18 0.72 , 0 Jets had τ µ = 8 TeV s , -1 19.7 fb CMS preliminary BR(h _→ τ±µ∓) < 1.57% (95% C.L.) |y_{τ µ| ≤} 3.6 _× 10−3 BR(h _→ τ±µ∓) = 0.89 +0.40 −0.37 %(2.46σ) |yτ µ| ≃ 2.7 × 10−3 ∼ √yτyµ = 2.48 × 10−3

t

→

e

±

µ

∓

q

(

t

→

τ

±

ℓ

∓

q

)

Contact interactions mediating LFV top decays O_lq(1) = (l_iγαl_j)(q_rγαq_t) O_lq(3) = (l_iγατal_j)(q_rγατaqt) Oeq = (eiγαej)(qrγαqt) Olu = (liγαlj)(urγαut) Oeu = (eiγαej)(urγαut) O_lequ(1) = (l_ie_j)ǫ(q_ru_t) = ₋(ν_ie_j)(d_ru_t) + (e_iP_Re_j)(u_rP_Ru_t) Olequ(3) = (liσαβej)(qrσαβut)

l, q are doublets, e, u are singlets

i ₆= j lepton flavour indices, t = third generation quark index, r = first or second

BRs for LFV top decays is small...

Standard model top decay is 2-body, by enhanced equivalence thm :

Γ(t _→ bW) = g

2_m3

t

64πm2_W .

Three body decay, due to contact interaction _Λ12(tγαPRq)(ℓiγαℓj)

(guess from Γ =G2_{F m}5_µ/(192π3)): Γ(t _→ ℓ+ℓ− + j)_V±A = m 5 t 8 _× 192π3_Λ4 So BR(t _→ ℓ+ℓ− + j) = m 4 t 48π2_Λ4 <∼ 2 × 10 −3m4t Λ4

Low energy: LFV B and K decays?

focus on t_R (because what _tL does, _bL does too...)

exchange a W between the quark legs of _Λ1₂(cγαP_Rt)(eγ_αP_Lµ) gives

∼ g 2_m tmcVtsVcd 16π2_Λ2_(m2 t − m2W) log m 2 t m2_W (dγ α_P Rs)(eγαPLµ) which contributes to K+ _→ π+e−µ+. compare to SM K+ _→ π+ℓ−ℓ+ ∼ g 2 32π2_m2 t V_ts∗Vtd(dγαPRs)(ℓγαPLℓ)

Low energy: LFV B and K decays? B+ _→ K+ℓ+ℓ−, e+e−, µ+µ− 4.5,4.5,5.5 _× 10−7 K+ _→ π+µ+µ−, e+e− 9.4,3.0 _× 10−8 B+ _→ π+e±µ∓ < 1.7 _× 10−7 B+ _→ π+ℓ±τ∓ < 7.2 _× 10−5 B+ _→ K+e±µ∓ < 9.1 _× 10−8 B+ _→ K+ℓ±τ∓ < 3 ₋ 4.8 _× 10−5 K+ _→ π+e−µ+ < 1.3 _× 10−11

constrain coefficient of LFV top operator by normalising with SM:

m4_t Λ4 < ∼ BR(K _→ πe+µ−) BR(K _→ πℓ+_ℓ−₎ m2_t|V_td|2 14.5m2 r|Vrd|2 < ∼ 2 _× 10−4 r = c .12 r = u

Also restrictive bounds from K_{L →} µe.¯

Summary: for one operator, BR(t _→ eµ¯ + jet) <_∼ few _×10−4 (for other operators,

LHC sensitivity to LFV top decays? CMS and ATLAS search for t _→ Zc, Zu:

t ¯ t ℓ1 ¯ ν ¯_b c ℓ2 ¯ ℓ2

Find BR(t _→ Z+jet) <∼ 5×10−4 (assuming Z → ee, µ¯ µ¯, BR(Z → ℓ+ℓ−) ∼ .036)).

Equivalently BR(t _→ ℓ+ℓ− + jet) ∼< 4 × 10−6.

Summary

The LHC could produce New particles with LFV decays.

If New particles are beyond the mass reach of the LHC, they could nonetheless have effects parametrised by contact interactions, involving kinematically accessible particles. The LHC is the only place where the t, h and Z are kinematically accessible, so it (?is the only place which ?) can probe their LFV contact interactions.

ATLAS : BR(Z _→ eµ¯) _≤ 7.5 _× 10−7

CMS BR(h _→ τµ¯) _≤ 1.57 _× 10−2 (with _∼ 2σ excess:BR _≃ .89 _× 10−2) to do: the top?

Unlikely to see h _→ e±µ∓, Z _→ e±µ∓, due to µ _→ eγ bound. But maybe LFV top decays: t _→ e±µ∓+ accessible to LHC?