The Majoron in rare decays
Julian Heeck
CERN - Physics Beyond Colliders meets theory
6/11/2020 Majoronic seesaw
● SM + 3 singlets NR + new scalar
B−L breaking scale Heavy scalar Majoron [Chikashige, Mohapatra, Peccei, ‘81; Schechter, Valle, ‘82]
● Break U(1)B−L spontaneously:
● For
CERN 2020 Julian Heeck - The Majoron in rare decays 2 Majoron couplings
● Tree-level coupling only to neutrinos:
CERN 2020 Julian Heeck - The Majoron in rare decays 3 Majoron couplings
● Tree-level coupling only to neutrinos:
● One loop:
[JH, Garcia-Cely, JHEP ‘17; see also Pilaftsis ‘94] Off-diagonal!
CERN 2020 Julian Heeck - The Majoron in rare decays 4 Properties
● Crucial observation: the two matrices are independent!
[Davidson, Ibarra, JHEP ‘01]
● Jℓℓ’ coupling can be large and of arbitrary structure.
● Similar couplings arise for familons or flavor Z’. [Wilczek, ‘82; Reiss, ‘82; Grinstein, Preskill, Wise, 85; ...]
● Boson not necessarily massless, e.g. pseudo-Goldstone.
● Experimental signature depends on J decay channel:
[JH, Rodejohann, PLB ‘18; Bauer et al., PRL ‘20; Cornella et al., JHEP ‘20] [μ→e J, J→γγ: MEG, 2005.00339] CERN 2020 Julian Heeck - The Majoron in rare decays 5 Limit on effective coupling ARGUS ‘95
[JH, Garcia-Cely, JHEP ‘17]
CERN 2020 Julian Heeck - The Majoron in rare decays 6 ● Comparison of Majoron and non-Majoron limits. [from Coy & Frigerio, PRD ‘19]
● vs.
● Sterile neutrinos modify EWPD & LFV.
●
● Majoron wins for f ~ MR.
● ℓ→ℓ’ + J possible!
● Together with LFV in μ?
[JH, Patel, PRD ‘19] CERN 2020 Julian Heeck - The Majoron in rare decays 7 ● Comparison of Majoron and non-Majoron limits. [from Coy & Frigerio, PRD ‘19]
● vs.
● Sterile neutrinos modify EWPD & LFV.
●
● Majoron wins for f ~ MR.
● ℓ→ℓ’ + J possible!
● Together with LFV in μ?
[JH, Patel, PRD ‘19] CERN 2020 Julian Heeck - The Majoron in rare decays 8 Limit on effective coupling ARGUS ‘95
[JH, Garcia-Cely, JHEP ‘17]
CERN 2020 Julian Heeck - The Majoron in rare decays 9 Limit on effective coupling
[JH, Patel, PRD ‘19]
CERN 2020 Julian Heeck - The Majoron in rare decays 10 [JH, Patel, PRD ‘19]
CERN 2020 Julian Heeck - The Majoron in rare decays 11 Limit on effective coupling
[JH, Patel, PRD ‘19]
CERN 2020 Julian Heeck - The Majoron in rare decays 12 Summary
● Majoron = simple axion-like particle connected to seesaw.
● Seesaw parameters encoded in Jff couplings.
● Search via rare flavor-violating decays.
● One loop: ℓ→ℓ’ + J. – MEG, Mu3e, Belle II.
● Two loops: q→q’ + J, e.g. K→π J, B→K J. – NA62, Belle II, LHCb.
● Next step: add prompt/displaced/delayed vertices, J→SM.
● State-of-the-art review: Calibbi, Redigolo, Ziegler, Zupan, 2006.04795.
CERN 2020 Julian Heeck - The Majoron in rare decays 13 Backup
CERN 2020 Julian Heeck - The Majoron in rare decays 14 Pseudo-Goldstone
● Spontaneous global U(1) breaking gives mJ = 0. ● Non-zero mass from: – Breaking by gravity, e.g. wormholes,
[Alonso, Urbano, 1706.07415]
– Anomalies, e.g. if U(1)B-L = U(1)PQ. [Mohapatra, Senjanovic ‘83; Langacker, Peccei, Yanagida ‘86; SMASH ‘16]
– Explicit breaking, e.g.
CERN 2020 Julian Heeck - The Majoron in rare decays 15 μ→e J with J→ invisible
● TWIST, ‘15: limits on different anisotropies.
● Chiral coupling μPLeJ suppresses sensitivity! [JH, Garcia-Cely, 1701.07209]
● Bremsstrahlung is competitive: μ→e J γ. [Goldman et al, ‘87]
● Approximate limit
CERN 2020 Julian Heeck - The Majoron in rare decays 16 μ→e J with Mu3e
CERN 2020 Julian Heeck - The Majoron in rare decays 17 τ → ℓ J with J→ invisible
● ARGUS, ‘95; 5e5 taus. ● Belle, ‘16 prelim.; 1e9 taus.
τ → μ J
O(20) times better than ARGUS! τ → e J
m (GeV) mJ (GeV) J
● Also interesting for LFV Z’. [JH, 1602.03810; Altmannshofer et al, 1607.06832]
● Improvement with Belle II.
CERN 2020 Julian Heeck - The Majoron in rare decays 18 μ→e X with X→ visible
● Take Xeγ5e me/Λee.
● Decay length determines signature.
● Displaced vertex gives new observable. [JH, Rodejohann, PLB ‘18]
● Muon at rest:
Sub-GeV X with ee coupling allowed?
CERN 2020 Julian Heeck - The Majoron in rare decays 19 μ→e X with X→ ee [JH, Rodejohann, PLB ‘18]
● Decay length typically below cm. ⇒ looks prompt.
● Below beam dump:
Λee > 30 TeV; mostly invisible, but some DV!
Possible in Mu3e!
CERN 2020 Julian Heeck - The Majoron in rare decays 20 μ→e X with X→ γγ [JH, Rodejohann, PLB ‘18]
● Decay length always below cm. ⇒ looks prompt.
● Below beam dump: supernova constraints!
● Prompt channel still interesting, maybe MEG(II) or Mu3e extension? [Limits: Dolan et al, JHEP ‘17]
Muons difficult, taus easier.
CERN 2020 Julian Heeck - The Majoron in rare decays 21 τ→e X with X→ visible [JH, Rodejohann, PLB ‘18]
● Tau at rest, higher X boost.
● Arbitrary decay lengths possible.
● Similar for X → ee, μμ, μe.
● Worthwhile in LHCb
and Belle (II). [Limits: Dolan et al, JHEP ‘17]
New signatures from light physics!
CERN 2020 Julian Heeck - The Majoron in rare decays 22 Quark Flavor Phenomenology of the QCD Axion
[Camalich, Pospelov, Vuong, Ziegler, Zupan, 2002.04623]
CERN 2020 Julian Heeck - The Majoron in rare decays 23