1. 1 Implications of Br(  e  ) and  a  on Muonic Lepton Flavor Violating Processes Chun-Khiang Chua Chung Yuan Christian University

2. 2 Motivation Charged lepton flavor violation decays are prohibited in the SM MEG set a tight bound on Br(  e  Muon g-2 remains an unsolved puzzle (3.x  ) (since 2001) Bounds on  e  3e, muon to electron conversions (  N  e N) are constantly improved (1-6 order of magnitude improvements are expected in future)

3. Current limits and future sensitivities “Ratios of current bounds” ~ O(1). Sensitivities will be improved by 1-6 orders of magnitudes in future 3

4. 4 We consider … Muon g-2 and LFV generated by  one-loop dig.s: Use a bottom up approach: data  couplings, masses Study the correlations among these processes

5. 5 Investigate Two Cases: Case I: Cancellations among diagrams are not effective (~order of magnitudes) Case II: Have some built-in cancellations, e.g. SGIM.

6. 6 Investigate Two Cases: Case I: Cancellations among diagrams are not effective (~order of magnitudes) Case II: Have some built-in cancellations, e.g. SGIM.

7. 7 Muon g-2 (case I) g R(L) : couplings of  R(L) -  -  int  g R g R (g L g L ) term:  From g 2 100GeV: m ,   300(200)GeV (tight)  g~e: m ,  =10-30GeV (disfavored) g R g L term: (chiral enh.)  From g 2 100GeV: m   TeV, m   000TeV  g~e: m   20 TeV  More sensitive than the RR case 10 -4 10 -5

8. 8  LFV (penguins) (case I) 10 -8 10 -9 Sensitive in RL is more than 3 orders of mag. better than the RR case  e  bound is most severe

9. 9  LFV (penguins) (case I) Exp. bound ratios ~ O(1)  e  constrains other processes

10. 10  LFV (Z-penguins) (case I) Consider vanishing mixing limit of  weak eigenstate. For m   GeV, Z-peng. has similar (better) sensitivity as the RR  -peng. Z-peng is less sensitive than the RL  -peng. unless m  is as heavy as O(100) TeV Br(Z   e) <10 -13~15 [Br UL (Z   e) ~10 -6 ] 10 -4 10 -8 Z-peg.  -peg.

11. 11  LFV (boxes) (case I) Dirac and Majorana cases have different sensitivities  e  +perturbativity (+  a  +edm) exclude some (most) parameter space.

12. Comparing Br(  e  ) and  a  The ratio is smaller than any known coupling ratio among 1 st and 2 nd generations. 12

13. 13 Investigate Two Cases: Case I: Cancellations among diagrams are not effective (~order of magnitudes) Case II: Have some built-in cancellations, e.g. SGIM.

14. 14 Muon g-2 (case II)  =(  m 2 /m 2 )   mixing angle g R(L) g R(L) term same as case I g R g L term: (chiral enh.)  Cancelation is working at the low m   m  mass ratio region  need larger couplings, smaller mass  From g 2 100GeV: m   100 TeV, m   few  TeV [m   TeV, m   000TeV (case I)]  For g~ e,  =1, m  =m   3 TeV Bend up Case I Case II

15. 15  LFV (penguins) (case II)  e  bound is not always the most stringent one Sensitivities are relaxed

16. 16  LFV (penguins) (case II)  e  bound is not always the most stringent one  e  enhanced relatively (B~10 -13 )

17. 17  LFV (Z-penguins) (case II) 10 -2 10 -7 Z-peng. sensitivity is relaxed in the low mass ratio region, for m   GeV, Z-peng. has similar (better) sensitivity as the RR  -peng. Z-peng. is less sensitive than the RL  -peng. unless m  is as heavy as O(10 3 ) TeV (not supported by g-2) Z-peng. Is subdominant. Br(Z   e) <10 -13~15 [Br UL (Z   e) ~10 -6 ] Z-peg.  -peg.

18. 18  LFV (boxes) (case II) Dirac and Majorana cases have different sensitivities  e  +perturbativity (+  a  +edm) exclude some (most) parameter space.

19. Comparing Br(  e  ) and  a  Can be easily satisfied with 19

20. 20 Conclusion Consider  -  loop-induced LFV muon decays. Bounds are translated to constraints on parameters (couplings and masses) Muon g-2 favors non-chiral interaction Z-penguin may play some role Box diagram contributions are highly constrained from other’s Comparing different cases, we found that:  Case I (no cancellation): Need fine-tune to satisfy Br(  e  ) and  a   3e,  e N bounded by  e  (2~3 orders below expt.)  Case II (built-in cancellation): Mixing angles soften the fine-tune in Br(  e  ) and  a   3e remains suppressed,  e N is enhanced (~ expt. sensitivity)