Lepton Flavour LHC?

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1 m ν (charged) lepton flavour change happens, and the LHC exists...so look for Lepton Flavour LHC? Sacha Davidson, P Gambino, G Grenier, S Lacroix, ML Mangano, S Perries, V Sordini, P Verdier IPN de Lyon/CNRS (1412.xxxx, , , , ) 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? with a heavy SM leg, so LHC complements lower energy searches

2 Lepton Flavour LHC? Sacha Davidson, P Gambino, G Grenier, S Lacroix, ML Mangano, S Perries, V Sordini, P Verdier IPN de Lyon/CNRS (1412.xxxx, , , , ) 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 τ µ,e τ,µ Z µ,e h τ t e q Parametrise LFV vertices as contact interactions Bounds from low energy and LEP? LHC sensitivity?

3 What about the Z? LEP? LHC? low energy?

4 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 β D α τb αβ,... O(H 2 ) : [H D α H]µγ α τ,... O(yH ) dipole : l µ Hσ βα τb αβ,... (where B αβ = α B β β B α, B hypercharge gauge boson).

5 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 β D α τb αβ g Z C p2 Z 16π 2 Λ 2µγ ατz α..., [H D α H]µγ α τ g Z A m2 Z 16π 2 Λ 2µγ αz α τ..., l µ Hσ βα τb αβ g Z D m τ 16π 2 Λ 2[µσ αβτ]z αβ NP of mass Λ > m Z in a loop, A,C,D dimless

6 LEP and the LHC 1. LEP1 was a clean Z machine, with Zs BR(Z e ± µ ) < , BR(Z e ± τ ) < , BR(Z µ ± τ ) < at LHC8, σ(pp Z µ µ) nb, L 20 fb 1, BR(Z µ µ) #Zs σ(pp Z µ µ) L BR(Z µ µ) Zs 25 LEP ATLAS : BR(Z e µ ± ) < % C.L.. LHC has more Zs than LEP, and better sensitivity

7 Low energy: the Z contributes too? decades of rare decay/precision data?... BR(τ µ µµ) < τ L τ µ Z µ L µ Z µ

8 Low energy: the Z contributes too? decades of rare decay/precision data?... BR(τ µ µµ) < τ L τ µ Z µ L µ Z µ But gradient operators better constrained at high energy. Consider ( α Z β β Z α = Z αβ ) g Z C on the Z : vertex =g Z Cm 2 Z 16π 2 Λ 2µZ/ τ 1 16π 2 Λ 2Zαβ µγ α β τ g Z C p2 Z 16π 2 Λ 2µγ αz α τ in τ µ µµ :vertex < g Z Cm 2 τ 16π 2 Λ 2µZ/ τ (negligeable)? But, am I allowed gradient operators? Yes, more later...

9 The gradient 2 Z τ ± µ operators: are they important in loops? and can I calculate that? τ Z µ 1. assume NP scale Λ m Z γ 2. assume NP generates only 2 operator (no other LFV; not τ µγ), so interaction : g Z C µτ p 2 Z 16π 2 Λ 2µγ ατz α 3. in RG running between Λ and m Z, Z τ ± µ will mix to τ µγ operator (...estimate the coefficient of 1/ǫ in dim reg...) BR(τ µγ) 3α gz 4 4πG 2 F Λ4 ( ) 2 Cµτ log C2 µτv 4 32π 2 no constraint on C µτ from BR(τ lγ) < but µ eγ constrains C eµ : BR(Z e ± µ ) < (BR(µ eγ) < ) Λ 4

10 Simma EJPC Derivative Operators, Eqns of Motion and the Operator Basis equations of motion (EoM) for the hypercharge boson (B Z) µ B µν g 2 (H D ν H [D ν H] H) g f Qf Y fγν f = 0 p 2 Z ν m 2 Z Zν g J ν

11 Simma EJPC Derivative Operators, Eqns of Motion and the Operator Basis 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) µ B µν g 2 (H D ν H [D ν H] H) g f Qf Y fγν f = 0 so the operator: O = τγ ν µ( µ B µν ig 2 H HB ν g f Qf Y fγν f) induces vertices τγ ν µfγ ν f, Q f Y B ν τγ ν µ, p 2 B m2 B (m B = g H ). These vertices cancel in on-shell S-matrix elements : f µ µτ O f f = Q f Y f τ Q f Y p 2 m 2 B p 2 m 2 B f f µ τ

12 Simma EJPC Derivative Operators, Eqns of Motion and the Operator Basis 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) µ B µν g 2 (H D ν H [D ν H] H) g f Qf Y fγν f = 0 so the operator: O = τγ ν µ( µ B µν ig 2 H HB ν g f Qf Y fγν f) induces vertices τγ ν µfγ ν f, Q f Y B ν τγ ν µ, p 2 B m2 B (m B = g H ). These vertices cancel in on-shell S-matrix elements : f µ µτ O f f = Q f Y Q f Y p 2 m 2 B p 2 m 2 B f τ f so only keep one dim 6 Zτµ operator: HD ν H, or 2 Z ν τγ ν µ f µ τ

13 Getting the same constraints on NP in either basis? 1. four fermion operator and 2 LFV Z operator: (τγ α µ)(µγ α µ), p 2 Z τz/ µ on the Z, LFV Z coupling contributes, 4-f operator not. in τ µ µµ, only 4-f operator contributes 2. four fermion operator and penguin=h D ν H LFV Z operator: (τγ α µ)(µγ α µ), m 2 Z τz/ µ on the Z, LFV Z coupling contributes, 4-f operator not. in τ µ µµ, both operators contribute in the amplitude, cancellations possible. (formally: below m Z, 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:

14 Summary about the Z: LHC has interesting sensitivity to Z µ ± τ, Z e ± τ. h τ ± l low energy bounds h τ µ selon CMS?

15 Operators and Models for LFV Higgs decays LFV could appear in Higgs decays: 1. if have Y 1 lhτ, plus dim 6 operator Y2 H H lhτ Giudice-Lebedev, Babu-Nandi 2. also two Higgs doublets of type III = flavour changing couplings + keep two neutral light scalars...davidson-grenier Aristizabal,Vicente

16 Low energy constraints LFV could appear in Higgs decays: 1. due to effective dim 6 operator H H lhτ 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: tree exchange of h :τ ηµ, τ µ µµ : y τµ < O(1) ok Diaz-Cruz,Toscana Kanemura-Ota-Tsumura Davidson-Grenier... Goudelis-Lebedev-Park Harnik-Kopp-Zupan Blankenburg,Ellis,Isidori loops : τ µγ, EW precision, b sγ, etc : y τµ < O(y τ ) ok

17 Tree level Higgs exchange (diff from Z! h is much narrower) in low energy rare decays: τ µ y 2 τµ y2 µ µ h µ Γ(τ 3µ) Γ(τ µν ν) m 4 h g 4 m 4 W y 2 τµ y2 µ g 4 so feeble bounds on y τµ on the narrow resonance ( Γ h 3y 2 b /16π): τ L h Γ(h τ µ) Γ(h b b) y 2 τµ y 2 b µ L right place to look for small couplings: BR(h τµ) y τµ 2 /y 2 b

18 Bounds on LFV Higgs couplings from loops? Recall perturbation theory expands in couplings and loops, and m µ /m t < 1/16π 2 one-loop amplitudes (y LFV y µ )/16π 2 can be smaller than... h e k τ µ < γ γ t γ h τ µ...two-loop amplitudes g 2 (y LFV y t )/(16π 2 ) 2 Most restrictive bound y τµ <.1 from 2-loop τ µγ (model-dep; what else in loops?) And not see h e ± µ at LHC because BR(h e ± µ ) < 10 8 from µ eγ...

19 CMS: h τ ± µ µτ, 0 Jets had % µτ, 1 Jet had % µτ, 2 Jets had % CMS preliminary fb, s = 8 TeV BR(h τ ± µ ) < 1.57% (95% C.L.) y τµ BR(h τ ± µ ) = %(2.46σ) y τµ y τ y µ = µτ, 0 Jets e % µτ, 1 Jet e % µτ, 2 Jets e % h µτ % Best Fit to Br(h µτ), %

20 t e ± µ q (t τ ± l q) Low Energy? LHC?

21 Contact interactions mediating LFV top decays O (1) lq O (3) lq = (l i γ α l j )(q r γ α q t ) = (l i γ α τ a l j )(q r γ α τ a q t ) O eq = (e i γ α e j )(q r γ α q t ) O lu = (l i γ α l j )(u r γ α u t ) O eu = (e i γ α e j )(u r γ α u t ) O (1) lequ = (l i e j )ǫ(q r u t ) = (ν i e j )(d r u t )+(e i P R e j )(u r P R u t ) O (3) lequ = (l i σ αβ e j )(q r σ αβ u t ) l,q are doublets, e,u are singlets i j lepton flavour indices, t = third generation quark index, r = first or second generation quark index.

22 BRs for LFV top decays is small... Standard model top decay is 2-body, by enhanced equivalence thm : Γ(t bw) = g2 m 3 t 64πm 2 W. Three body decay, due to contact interaction 1 Λ 2 (tγ α P R q)(l i γ α l j ) (guess from Γ = G 2 F m5 µ /(192π3 )): Γ(t l + l +j) V±A = m 5 t 8 192π 3 Λ 4 So BR(t l + l +j) = m4 t 48π 2 Λ 4 < m4 t Λ 4

23 Low energy: LFV B and K decays? focus on t R (because what t L does, b L does too...) exchange a W between the quark legs of 1 Λ 2 (cγ α P R t)(eγ α P L µ) gives g2 m t m c V ts V cd m2 t 16π 2 Λ 2 (m 2 t m 2 W )log m 2 (dγ α P R s)(eγ α P L µ) W which contributes to K + π + e µ +. compare to SM K + π + l l + g2 32π 2 m 2 t V tsv td (dγ α P R s)(lγ α P L l)

24 Low energy: LFV B and K decays? B + K + l + l,e + e,µ + µ K + π + µ + µ,e + e B + π + e ± µ B + π + l ± τ B + K + e ± µ B + K + l ± τ K + π + e µ + 4.5,4.5, , < < < < < constrain coefficient of LFV top operator by normalising with SM: m 4 t BR(K πe + µ ) m 2 < t V td 2 < Λ 4 BR(K πl + l ) 14.5m 2 r V rd 2 { r = c.12 r = u Also restrictive bounds from K L µē. Summary: for one operator, BR(t e µ+jet) < few 10 4 (for other operators, BR(t e µ+jet) < few 10 7 ). t l τ +jet unconstrained by B decays.

25 LHC sensitivity to LFV top decays? CMS and ATLAS search for t Zc,Zu: t t c l1 ν l 2 l 2 b FindBR(t Z+jet) < (assumingz eē,µ µ,br(z l + l ).036)). Equivalently BR(t l + l +jet) < ?? sensitive to BR(t eµ+jet) < few 10 6??

26 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 e µ) CMS BR(h τ µ) (with 2σ excess:br ) 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?