Theoretical Review on Lepton Universality and LFV

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1 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion Theoretical Review on Lepton Universality and LFV P. Paradisi Università di Valencia and IFIC KAON 007 Frascati, 4 May 007

2 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion General Considerations Flavor Physics in the LHC era High energy experiments are the key tool to determine the energy scale Λ by direct production of NP particles. Low energy experiments are a fundamental ingredient to determine the symmetry properties of the new d.o.f. via their virtual effects in precision observables.

3 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion NP search strategies Where to look for New Physics? Processes very suppressed or even forbidden in the SM FCNC processes (µ eγ, τ µγ, B 0 s,d µ+ µ, K πν ν) CPV effects (electron/neutron EDMs, d e,n...) Processes predicted with high precision in the SM EWPO as ρ, (g ) µ... LU in R e/µ M = Γ(M eν)/γ(m µν) (M = π, K) Marriage of LFV and LU in R e/µ M

4 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion NP search strategies Where to look for New Physics? Processes very suppressed or even forbidden in the SM FCNC processes (µ eγ, τ µγ, B 0 s,d µ+ µ, K πν ν) CPV effects (electron/neutron EDMs, d e,n...) Processes predicted with high precision in the SM EWPO as ρ, (g ) µ... LU in R e/µ M = Γ(M eν)/γ(m µν) (M = π, K) Marriage of LFV and LU in R e/µ M

5 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion NP search strategies Where to look for New Physics? Processes very suppressed or even forbidden in the SM FCNC processes (µ eγ, τ µγ, B 0 s,d µ+ µ, K πν ν) CPV effects (electron/neutron EDMs, d e,n...) Processes predicted with high precision in the SM EWPO as ρ, (g ) µ... LU in R e/µ M = Γ(M eν)/γ(m µν) (M = π, K) Marriage of LFV and LU in R e/µ M

6 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion NP search strategies Where to look for New Physics? Processes very suppressed or even forbidden in the SM FCNC processes (µ eγ, τ µγ, B 0 s,d µ+ µ, K πν ν) CPV effects (electron/neutron EDMs, d e,n...) Processes predicted with high precision in the SM EWPO as ρ, (g ) µ... LU in R e/µ M = Γ(M eν)/γ(m µν) (M = π, K) Marriage of LFV and LU in R e/µ M

7 General Considerations NP search strategies K πν ν and NP µ e universality in M lν Conclusion K πν ν and NP FCNC processes as K πνν offers a unique possibility in probing the underlying flavour mixing mechanism of NP No SM tree-level contributions (FCNC decays) One-loop SM contributions CKM-suppressed (V tsv td λ 5 ) Dominance of short distance (e.w.) effects SM uncertainties at % Great sensitivity to NP effects of many theories as SUSY, LHT, Z models... A(s d) FCNC c SM y t V tsv td 16π M W + c NP δ 1 16π Λ NP Large departures from the SM only if δ 1 VtsV td (beyond MFV) see talks of Haisch, Smith and Tarantino

8 µ e universality in M lν µ e universality in R K = Γ(K eν e )/Γ(K µν µ ) R exp. K = (.416 ± stat. ± 0.04 syst. ) 10 5 NA48/ 05 R exp. K = (.44 ± 0.11) 10 5 PDG R SM K = (.47 ± 0.001) 10 5 SM µ e universality in R π = Γ(π eν e )/Γ(π µν µ ) R exp. π = (1.30 ± 0.004) 10 4 PDG R SM π = (1.354 ± 0.000) 10 4 SM

9 µ e universality in M lν µ e universality in R K = Γ(K eν e )/Γ(K µν µ ) R exp. K = (.416 ± stat. ± 0.04 syst. ) 10 5 NA48/ 05 R exp. K = (.44 ± 0.11) 10 5 PDG R SM K = (.47 ± 0.001) 10 5 SM µ e universality in R π = Γ(π eν e )/Γ(π µν µ ) R exp. π = (1.30 ± 0.004) 10 4 PDG R SM π = (1.354 ± 0.000) 10 4 SM

10 µ e universality in M lν Denoting by r e µ NP the deviation from µ e universality in R K,π due to new physics, i.e.: ( ) R K,π = RK,π SM 1 + r e µ K,π NP, we get at the σ level: r e µ K NP NA48/ r e µ π NP 0.00 PDG The total errors are dominated by the EXP. ERRORS!!!

11 µ e universality in M lν Denoting by r e µ NP the deviation from µ e universality in R K,π due to new physics, i.e.: ( ) R K,π = RK,π SM 1 + r e µ K,π NP, we get at the σ level: r e µ K NP NA48/ r e µ π NP 0.00 PDG The total errors are dominated by the EXP. ERRORS!!!

12 New Generation of Experiments Bryman at this conference

13 µ e universality in M lν In the SM M lν is induced by a tree level W ± exchange In a HDM (including SUSY) also H ± provides tree level effects to M lν Four-Fermi interaction for M lν induced by W ±, H ± 4G F V ud [(uγ µ P L d)(lγ µ P L ν l ) tan β ( md m l m H ± ) ] (up R d)(lp L ν l ) PCAC s < 0 uγ µ γ 5 d M >= if M p µ M < 0 uγ 5 d M >= if M m M m d +m u

14 µ e universality in M lν H ± (W ± ) amplitude is proportional to m l because of the Yukawa coupling (helicity suppression) M M lν = G ( ) ] F V ud,s f M [m l m l tan md m β M m d +m u mh l(1 γ 5 )ν. ± Including H ± and W ± effects, the decay rates for M lν is Γ(M lν) = G F 8π V ud fm m Mml [ r M = 1 tan β ( md m u +m d ( 1 m l ) m M m M m H ± ) r M ]. Tree level H ± effects (r M ) are lepton flavour blind

15 µ e universality in M lν H ± (W ± ) amplitude is proportional to m l because of the Yukawa coupling (helicity suppression) M M lν = G ( ) ] F V ud,s f M [m l m l tan md m β M m d +m u mh l(1 γ 5 )ν. ± Including H ± and W ± effects, the decay rates for M lν is Γ(M lν) = G F 8π V ud fm m Mml [ r M = 1 tan β ( md m u +m d ( 1 m l ) m M m M m H ± ) r M ]. Tree level H ± effects (r M ) are lepton flavour blind

16 µ e universality in M lν e µ non universal effects in R M arise from the one loop l W ± ν l vertex corrections through the exchange of H 0 (A 0 ) H ± l (with l=e, µ) leading to (for m H 300GeV and t β 50) ( ) r e µ SUSY α m µ me 4π mh tβ 10 6 χ ± χ 0 l e,µ leading to (with δ m/ m 0.1) r e µ SUSY α 4π well below the r e µ π NP ( m µ m e m µ + m e ) m W M SUSY e µ 0.00 and r bounds K NP exp.

17 µ e universality in M lν e µ non universal effects in R M arise from the one loop l W ± ν l vertex corrections through the exchange of H 0 (A 0 ) H ± l (with l=e, µ) leading to (for m H 300GeV and t β 50) ( ) r e µ SUSY α m µ me 4π mh tβ 10 6 χ ± χ 0 l e,µ leading to (with δ m/ m 0.1) r e µ SUSY α 4π well below the r e µ π NP ( m µ m e m µ + m e ) m W M SUSY e µ 0.00 and r bounds K NP exp.

18 µ e universality in M lν WHAT ARE WE MISSING?... R EXP. K = Γ(K eν e) + Γ(K eν µ ) + Γ(K eν τ ) Γ(K µν µ ) + Γ(K µν e ) + Γ(K µν τ )...EXPERIMENTALLY THE NEUTRINO FLAVOUR IS UNDETERMINED!! Masiero, Paradisi, Petronzio, 06

19 µ e universality in M lν WHAT ARE WE MISSING?... R EXP. K = Γ(K eν e) + Γ(K eν µ ) + Γ(K eν τ ) Γ(K µν µ ) + Γ(K µν e ) + Γ(K µν τ )...EXPERIMENTALLY THE NEUTRINO FLAVOUR IS UNDETERMINED!! Masiero, Paradisi, Petronzio, 06

20 µ e universality in M lν WHAT ARE WE MISSING?... R EXP. K = Γ(K eν e) + Γ(K eν µ ) + Γ(K eν τ ) Γ(K µν µ ) + Γ(K µν e ) + Γ(K µν τ )...EXPERIMENTALLY THE NEUTRINO FLAVOUR IS UNDETERMINED!! Masiero, Paradisi, Petronzio, 06

21 Higgs Mediated LFV LFV Yukawa Int. (if δ ij = m ij / m 0) Babu & Kolda, 0: L (G F ) (8G F ) 1 4 m τ c β m τ c β ( ) 3j L τ Rl j L + 3j R τ Ll j (cβ α R h 0 s β α H 0 ia 0) ( ) 3j L τ Rν j L + 3j R ντ L l j R H ± + h.c. 3j α 4π δ 3j Higgs (gaugino) mediated LFV effects decouple as m H (m SUSY ), Key ingredients in the Higgs mediated LFV: large tan β 50 large slepton mixings, δ 3j O(1), ( m SUSY >1TeV)

22 µ e universality in M lν R LFV K = i K eν i i K µν i Γ SM(K eν e ) + Γ(K eν τ ) Γ SM (K µν µ ), i = e, µ, τ s R u L H + r e µ K SUSY r e µ π SUSY ( ( e R,µ R m 4 K M 4 H ± md ν τ m u + m d eh ± ν τ g m τ M W 31 R tan β 31 R α 4π δ31 RR 31 R t β =40 M H ± =500GeV ) (m ) τ 31 R tan 6 β 10 m e ) ( m 4 π m 4 k ) r e µ K SUSY 10 4

23 µ e universality in M lν R LFV K = i K eν i i K µν i Γ SM(K eν e ) + Γ(K eν τ ) Γ SM (K µν µ ), i = e, µ, τ s R u L H + r e µ K SUSY r e µ π SUSY ( ( e R,µ R m 4 K M 4 H ± md ν τ m u + m d eh ± ν τ g m τ M W 31 R tan β 31 R α 4π δ31 RR 31 R t β =40 M H ± =500GeV ) (m ) τ 31 R tan 6 β 10 m e ) ( m 4 π m 4 k ) r e µ K SUSY 10 4

24 µ e universality in M lν R LFV K = i K eν i i K µν i Γ SM(K eν e ) + Γ(K eν τ ) Γ SM (K µν µ ), i = e, µ, τ s R u L H + r e µ K SUSY r e µ π SUSY ( ( e R,µ R m 4 K M 4 H ± md ν τ m u + m d eh ± ν τ g m τ M W 31 R tan β 31 R α 4π δ31 RR 31 R t β =40 M H ± =500GeV ) (m ) τ 31 R tan 6 β 10 m e ) ( m 4 π m 4 k ) r e µ K SUSY 10 4

25 µ e universality in M lν Which is the sign of r e µ NP? LFV effects to LFC channels in R M lh ± ν l g ( m l tanβ 1 + m ) τ ll RL M W m tanβ l (l = e, µ) R LFV K,π R SM K,π ll RL α 1 4π δl3 RR δ3l LL f loop 10 4 Deviations from µ e universality in K l and π l [( 1 m τ m ) K,π m e MH 11 RL tan3 β + m τ ± m e m 4 K,π M 4 H ± 31 R tan 6 β ] R LFV K RK SM (1 0.03), RLFV π Rπ SM ( )

26 µ e universality in M lν Which is the sign of r e µ NP? LFV effects to LFC channels in R M lh ± ν l g ( m l tanβ 1 + m ) τ ll RL M W m tanβ l (l = e, µ) R LFV K,π R SM K,π ll RL α 1 4π δl3 RR δ3l LL f loop 10 4 Deviations from µ e universality in K l and π l [( 1 m τ m ) K,π m e MH 11 RL tan3 β + m τ ± m e m 4 K,π M 4 H ± 31 R tan 6 β ] R LFV K RK SM (1 0.03), RLFV π Rπ SM ( )

27 Phenomenology: τ l j X (X = γ, η, l j l j (l k l k )) P. P, hep-ph/ r e µ K SUSY 10 = Br th.(exp.) (τ ex ) 10 10( 7)

28 Phenomenology: τ l j X (X = γ, η, l j l j (l k l k )) P. P, hep-ph/ r e µ K SUSY 10 = Br th.(exp.) (τ ex ) 10 10( 7)

29 LFV channels in B lν Including LFV channels in B lν, with l = e, µ [ ( R l/τ m LFV Rl/τ SM 1 + r 1 4 )( ) ] B m τ H 3l R tan 6 β M 4 H ± m l Imposing the τ l j X (X = γ, η, l j l j (l k l k )) constraints R µ/τ LFV µ/τ 1.5R SM, R e/τ LFV 104 R e/τ SM [G.Isidori, P.P., 06] Imposing the µ e universality constraints in R K R e/τ LFV R e/τ SM [ 1 + r 1 H mb 4 mk 4 ] r e µ K Susy 4 10

30 Lepton Universality in τ decays Tree level H ± effects to R τ = Γ(τ µν ν)/γ(µ eν ν) R τ /R τ SM 1 m µt β M H ± ( ) ( tβ 00GeV 50 M H ± Tree level H ± effects to R τ = Γ(τ K(π)ν)/Γ(K(π) µν) cancel Tree level H ± effects to B(B X τν) ) B(B X τν) 1 m τ t ( β tβ B(B X τν) SM MH ± ) ( 00GeV ) M H ±

31 The large tan β scenario Key ingredients for the LU breaking: M l (M = π, K, B) physics: Large tan β, M H < 1TeV Large LFV slepton minxings, δ 3j O(1), ( m SUSY 1TeV) τ physics: Large tan β, M H < 1TeV No LFV effects How natural is the large tan β scenario? Top-Bottom Yukawa unification in GUT (SO(10)) tan β = (m t /m b ) Correlations between (B τν) and (B X s γ), M Bs, (B s,d l + l ), (g ) µ and m h 0 [G.Isidori, P.P., 06]

32 Phenomenology of MFV at large tan β tan β (30 50), M H ( )GeV, M q (1 )TeV (10 30)% suppression up to 10 enhancement

33 Phenomenology of MFV at large tan β t β (30 50), M H ( )GeV, M q (1 )TeV (0 10)% suppression up (0 0)% enhancement

34 Phenomenology of MFV at large tan β MFV at large tan β predicts a suppression of B τν and M s with respect to the SM ( ( M Bs ) ( M Bs ) SM µa U m q ) ( tβ 50 ( ) ( 400GeV 4 Br(B s µ + µ ) M H ) 4 ( ) 400GeV. µa U m q M H ) ( ) 6 tβ 50 ( ( ) Br(B lν) ( ) ) Br(B lν) SM tβ 400GeV m H ± Br(B τν) ( M Bd ) (V ub /V td ) /ˆB d much better then V ub f B!

35 Lightest Higgs boson mass G.Isidori, P.P., 06

36 WMAP large tan β µ=500 GeV M coannihilation Dark Matter constraint satisfied for M H Coannihilation Processes: 1 M NLSP M LSP 1.1 Resonant Processes: M A M LSP t β = 0 (green), 30 (red), 50 (black) Isidori, Mescia, P.P., Temes, 07

37 Constraints/Reference-Ranges Constraints/Reference-Ranges under WMAP constraints B X s γ: [1.01 < R Bsγ < 1.4] a µ : [ < 10 9 (a exp µ a SM µ ) < 4] B µ + µ : [B exp < ] M Bs : [ M Bs = ± 0.5 ps 1 ] B τν : [0.8 < R Bτν < 0.9]

38 B-physics, (g ) µ under WMAP constraints M H M 1 Isidori, Mescia, P.P., Temes, 07

39 General Considerations NP search strategies K πν ν and NP Conclusion µ e universality in M lν Conclusion Conclusion Where to look for New Physics? LU % in R e/µ K = Γ(K eν)/γ(k µν) can be generated by the LFV LU 0.1% in Rπ e/µ generated by the LFV = Γ(π eν)/γ(π µν) can be LFV SUSY effects can greatly enhance also R l/τ B, l = e, µ. The relevant SUSY parameter space for large LU breaking effects is allowed by the constraints of rare LFV decays, B-physics observables and Dark Matter Charged meson decays offer a great chance to probe LFV in New Physics.

Rare B decay searches with BABAR using hadronic tag reconstruction

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