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1 Implications of Br( e ) and a on Muonic Lepton Flavor Violating Processes Chun-Khiang Chua Chung Yuan Christian University
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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)
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Current limits and future sensitivities “Ratios of current bounds” ~ O(1). Sensitivities will be improved by 1-6 orders of magnitudes in future 3
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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
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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.
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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.
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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
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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
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9 LFV (penguins) (case I) Exp. bound ratios ~ O(1) e constrains other processes
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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.
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11 LFV (boxes) (case I) Dirac and Majorana cases have different sensitivities e +perturbativity (+ a +edm) exclude some (most) parameter space.
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Comparing Br( e ) and a The ratio is smaller than any known coupling ratio among 1 st and 2 nd generations. 12
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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.
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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
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15 LFV (penguins) (case II) e bound is not always the most stringent one Sensitivities are relaxed
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16 LFV (penguins) (case II) e bound is not always the most stringent one e enhanced relatively (B~10 -13 )
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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.
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18 LFV (boxes) (case II) Dirac and Majorana cases have different sensitivities e +perturbativity (+ a +edm) exclude some (most) parameter space.
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Comparing Br( e ) and a Can be easily satisfied with 19
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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)
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