Majorons in the Sky and in the Lab
Julian Heeck
Oklahoma State University
9/17/2020 Neutrinos have masses and mix
● Mass splittings ✔
● Angles ✔
● Phase(s) ✘
● Ordering ✘
● Mass scale ✘
● Dirac vs. Majorana ✘
● Mass origin ✘
OSU 2020 Julian Heeck - Majorons 2 Majoronic seesaw
● SM + 3 singlets NR + new scalar
Lepton number breaking scale Heavy scalar Majoron [Chikashige, Mohapatra, Peccei, ‘81; Schechter, Valle, ‘82]
● Break U(1)L spontaneously:
● For
OSU 2020 Julian Heeck - Majorons 3 Majoron couplings
● Tree-level coupling only to neutrinos:
OSU 2020 Julian Heeck - Majorons 4 Majoron couplings
● Tree-level coupling only to neutrinos:
● Assume Pseudo-Goldstone Majoron: mJ ≠ 0. [Rothstein, Babu, Seckel, ‘93] ● Long lifetime → Dark matter! [Berezinsky, Valle ‘93; Lattanzi, Valle ‘07; Bazzocchi et al, ‘08; Queiroz, Sinha, ‘14]
OSU 2020 Julian Heeck - Majorons 5 Dark matter abundance
● Freeze out via λ JJHH: – mJ ~ mh/2, – mJ > 400 GeV.
OSU 2020 Julian Heeck - Majorons 6 Dark matter abundance
● Freeze out via λ JJHH: – mJ ~ mh/2, – mJ > 400 GeV.
● Freeze in:
Stephen West
Lyman-α excludes mJ< 12 keV! [McDonald, ‘02; Hall, Jedamzik, March-Russell, Use different mechanism: West ‘10; Frigerio, Hambye, Masso, ‘11] JH, Teresi, 1706.09909, 1709.07283.
OSU 2020 Julian Heeck - Majorons 7 Indirect detection
● General limit from DM → invisible: [Audren, Lesgourgues, Mangano, Serpico, Tram, ‘14]
● Can we observe the neutrino lines? – mJ > 10 TeV: No. Dominant decay is J →ννh(h). ► no line! [Dudas, Mambrini, Olive, ‘15] – Also want to avoid electroweak Bremsstrahlung. [Kachelriess, Serpico, ‘07; Bell, Dent, Jacques, Weiler, ‘08; Queiroz, Yaguna, Weniger, ‘16]
– For MeV < mJ < 100 GeV: Yes!
OSU 2020 Julian Heeck - Majorons 8 Flavor of J → νk νk
Mass eigenstates → no oscillations!
Flavor ratios:
[JH, Garcia-Cely, 1701.07209, JHEP ‘17]
OSU 2020 Julian Heeck - Majorons 9
] 7 ) 1 ‘
V e P E G ( H f J
, e 9 l 0 a 2 c 7 s
0 . g 1 n i 0 k 7 1 a
, e y r l b e
C n - o a
i t i c r m a i l G
r , e ed! H w ud J cl [ o Ex L
OSU 2020 Julian Heeck - Majorons 10 mJ (GeV) = 2 Eν
] 7 ) 1 ‘
V e P E G ( H f J
, e 9 l 0 a 2 c 7 s
0 . g 1 n i 0 k 7 1 a
, e y r l b e
C n - o a
i t i c r m a i l G
r , e + ed! H w Threshold for ν p → n e . ud J e cl [ o Ex L
OSU 2020 Julian Heeck - Majorons 11 mJ (GeV) = 2 Eν
] 7 ) 1 ‘
V e P E G ( H f J
, e 9 l 0 a 2 c 7 s
0 . g 1 n i Reinterpreted Super-K data. 0 k 7 1 a
[Palomares-Ruiz, 0712.1937, updated in , e y r Argüelles++, 1912.09486] l b e
C n - o a
i t i c r m a i l G
r , e + ed! H w Threshold for ν p → n e . ud J e cl [ o Ex L
OSU 2020 Julian Heeck - Majorons 12 mJ (GeV) = 2 Eν
] 7 ) 1 ‘
V e P E G ( H f J
, e 9 l 0 a 2 c 7 s
0 . g 1 n i 0 k 7 1 a
, e y r l b e
C n - o a
i t i c r m a i l G
r , e ed! H w ud J cl [ o Ex L
OSU 2020 Julian Heeck - Majorons 13 mJ (GeV) = 2 Eν Look for neutrinos from light DM!
● ν lines detectable down to MeV.
● For free in searches for diffuse supernova neutrino background.
● Borexino = indirect DM detector! ν ● Darwin, Hyper-K, JUNO,… = indirect DM detectors.
● DM → ν easily dominant channel, no SU(2) argument as for multi-TeV DM. [El Aisati, Garcia-Cely, Hambye, Vanderheyden, 1706.06600]
OSU 2020 Julian Heeck - Majorons 14 Majoron couplings
● Tree-level coupling only to neutrinos:
● One loop:
[JH, Garcia-Cely, JHEP ‘17; see also Pilaftsis ‘94] Off-diagonal!
OSU 2020 Julian Heeck - Majorons 15 [JH, Patel, PRD ‘19]
OSU 2020 Julian Heeck - Majorons 16 Loop induced J→γγ, qq, ℓℓ’
● Tree-level J couplings ∝ Mν while loop level ∝
● One-to-one mapping: [Davidson, Ibarra, hep-ph/0104076]
● Loop couplings contain unknown seesaw parameters!
J→γγ, qq, ℓℓ’ are complementary to νν channel!
● One generation:
[Chikashige, Mohapatra, Peccei, ‘81; Pilaftsis ‘94]
OSU 2020 Julian Heeck - Majorons 17 Indirect detection II
● DM → ττ, bb, tt, … give – continuous γ spectrum: Integral, Fermi-LAT. – anti-protons and positrons: e,p,γ PAMELA, AMS-02.
● DM decay around z ~ 1000: – modification of CMB. [Slatyer, Wu, 1610.06933] – independent of DM profile.
● DM→ γγ gives lines.
OSU 2020 Julian Heeck - Majorons 18 Indirect detection II [Slatyer, Wu, 1610.06933]
● DM → ττ, bb, tt, … give – continuous γ spectrum: Integral, Fermi-LAT. – anti-protons and positrons: e,p,γ PAMELA, AMS-02.
● DM decay around z ~ 1000: – modification of CMB. [Slatyer, Wu, 1610.06933] – independent of DM profile.
● DM→ γγ gives lines.
OSU 2020 Julian Heeck - Majorons 19 Gamma line plot ] 7 1 ‘
P E H J
, 9 0 2 7 0 . 1 0 7 1
, y l e C - a i c r a G
, H J [
mJ (GeV) OSU 2020 JulianmJ (GeV) Heeck - Majorons 20 Gamma line plot ] 7 1 ‘
P E H J
, 9 0 2 7 0 . 1 0 7 1
, y Strong CMB limits. l e
[Slatyer, Wu, 1610.06933] C - a i c r a G
, H J [
mJ (GeV) OSU 2020 JulianmJ (GeV) Heeck - Majorons 21 Gamma line plot ] 7 1 ‘
P E H J
, 9 0 2 7 0 . 1 0 7 1
, y l e C - a “MeV gap”, γ limits will improve a i c r
lot with e-ASTROGAM, AdEPT. a G
, H J [
mJ (GeV) OSU 2020 JulianmJ (GeV) Heeck - Majorons 22 Is it possible to detect dark matter via neutrinos and not gamma-rays or anti-matter? Yes!
depends on depends on
Independent / Complementary!
OSU 2020 Julian Heeck - Majorons 23 Majoron = DM
● Naturally light, long-lived DM candidate.
● Indirect detection possible: – MeV < mJ: J → νν, γγ, ff. – keV < mJ < MeV: J →γγ. Maybe warm DM. [JH, Teresi, 1706.09909, 1709.07283]
Majoron ≠ DM
● Increase couplings to produce J in lab.
● Measure seesaw parameters.
OSU 2020 Julian Heeck - Majorons 24 Majoron couplings
● Tree-level coupling only to neutrinos:
● One loop: Too small for lab
[JH, Garcia-Cely, JHEP ‘17; see also Pilaftsis ‘94] Off-diagonal!
OSU 2020 Julian Heeck - Majorons 25 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; ...]
● 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]
OSU 2020 Julian Heeck - Majorons 26 [Perrevoort, 1812.00741] μ→e J
● Electron line on top of Michel spectrum.
● Good prospects @ Mu3e.
● In progress: signal in μ→e conversion exps. COMET, Mu2e(-II). – Many muons! – Nuclear recoil: Ee up to mμ. – Suppression of tail... [Garcia i Tormo++, PRD ‘11; Uesaka, 2005.07894] [JH++, Mu2e-II Snowmass LOI]
OSU 2020 Julian Heeck - Majorons 27 Limit on effective coupling ARGUS ‘95
[JH, Garcia-Cely, JHEP ‘17]
OSU 2020 Julian Heeck - Majorons 28 ● 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] OSU 2020 Julian Heeck - Majorons 29 ● 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] OSU 2020 Julian Heeck - Majorons 30 Limit on effective coupling ARGUS ‘95
[JH, Garcia-Cely, JHEP ‘17]
OSU 2020 Julian Heeck - Majorons 31 Limit on effective coupling
[JH, Patel, PRD ‘19]
OSU 2020 Julian Heeck - Majorons 32 Limit on effective coupling
[JH, Patel, PRD ‘19]
OSU 2020 Julian Heeck - Majorons 33 Summary
● Majoron = simple axion-like particle connected to seesaw.
● Seesaw parameters encoded in loop couplings (Jff & Jγγ).
● In the sky: – DM→νν @ JUNO, DUNE, Hyper-K, DARWIN,... – DM→γγ, ℓℓ’, qq @ Fermi, CTA, e-ASTROGAM,...
● In the lab: – One loop: ℓ→ℓ’ + J @ MEG, Mu3e, Mu2e, Belle II,… – Two loops: K→π J, B→K J @ NA62, Belle II, LHCb.
● Next step: add prompt/displaced/delayed vertices, J→SM.
Always look out for lines! OSU 2020 Julian Heeck - Majorons 34 Backup
OSU 2020 Julian Heeck - Majorons 35 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.
OSU 2020 Julian Heeck - Majorons 36 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
OSU 2020 Julian Heeck - Majorons 37 μ→e J with Mu3e
OSU 2020 Julian Heeck - Majorons 38 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.
OSU 2020 Julian Heeck - Majorons 39 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?
OSU 2020 Julian Heeck - Majorons 40 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!
OSU 2020 Julian Heeck - Majorons 41 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.
OSU 2020 Julian Heeck - Majorons 42 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!
OSU 2020 Julian Heeck - Majorons 43 Quark Flavor Phenomenology of the QCD Axion
[Camalich, Pospelov, Vuong, Ziegler, Zupan, 2002.04623]
OSU 2020 Julian Heeck - Majorons 44