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Implications of Br(e) and a on Muonic Lepton Flavor Violating Processes

Chun-Khiang Chua

Chung Yuan Christian University

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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 e3e, muon to electron conversions ( N e N) are constantly improved (1-6 order of magnitude improvements are expected in future)

Current limits and future sensitivities

“Ratios of current bounds” ~ O(1).

Sensitivities will be improved by 1-6 orders of magnitudes in future

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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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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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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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Muon g-2 (case I) gR(L): couplings of R(L)--int

gRgR (gLgL) term: From g2<4 and m, >100GeV:

m,300(200)GeV (tight) g~e: m,=10-30GeV (disfavored)

gRgL term: (chiral enh.) From g2<4 and m, >100GeV:

mTeV, m000TeV g~e: m 20 TeV More sensitive than the RR case

10-4

10-5

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LFV (penguins) (case I)

10-8

10-9

Sensitive in RL is more than 3 orders of mag. better than the RR case

ebound is most severe

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LFV (penguins) (case I)

Exp. bound ratios ~ O(1) econstrains other processes

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LFV (Z-penguins) (case I)

Consider vanishing mixing limit of weak eigenstate. For mGeV, Z-peng. has similar (better) sensitivity as the RR -

peng. Z-peng is less sensitive than the RL -peng. unless mis as heavy as O(100)

TeV Br(Z e) <10-13~15 [BrUL(Z e) ~10-6]

10-4

10-8

Z-peg. -peg.

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LFV (boxes) (case I)

Dirac and Majorana cases have different sensitivities

e +perturbativity (+a+edm) exclude some (most) parameter space.

Comparing Br(e) and a

The ratio is smaller than any known coupling ratio among 1st and 2nd generations.

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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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Muon g-2 (case II)

=(m2/m2)mixing angle

gR(L)gR(L) term same as case I

gRgL term: (chiral enh.) Cancelation is working at the low

mmmass ratio region need larger couplings, smaller mass From g2<4 and m, >100GeV:

m100 TeV, mfewTeV

[mTeV, m000TeV (case I)] For g~ e, =1, m=m3 TeV

Bend up

Case I

Case II

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LFV (penguins) (case II)

e bound is not always the most stringent one

Sensitivities are relaxed

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LFV (penguins) (case II)

e bound is not always the most stringent one

e enhanced relatively (B~10-13)

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LFV (Z-penguins) (case II)10-2

10-7

Z-peng. sensitivity is relaxed in the low mass ratio region, for mGeV, Z-peng. has similar (better) sensitivity as the RR -peng.

Z-peng. is less sensitive than the RL -peng. unless mis as heavy as O(103) TeV (not supported by g-2)

Z-peng. Is subdominant. Br(Z e) <10-13~15 [BrUL(Z e) ~10-6]

Z-peg. -peg.

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LFV (boxes) (case II)

Dirac and Majorana cases have different sensitivities

e +perturbativity (+a+edm) exclude some (most) parameter space.

Comparing Br(e) and a

Can be easily satisfied with

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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)