Supernova limits on a light CP-even scalar and implications for the KOTO anomaly Yongchao Zhang Washington University in St. Louis yongchao.zhang@physics.wustl.edu May 4, 2020 Phenomenology 2020 Symposium based on P. S. B. Dev, R. N. Mohapatra & YCZ, PRD 101 , 075014 [1911.12334] P. S. B. Dev, R. N. Mohapatra & YCZ, 2005.00490
Supernova limits on light particles Supernovae provide a unique environment to produce copiously light hypothetical particles: axion/ALP [Iwamoto ’84; Pantziris & Kang ’86; Turner ’88; Raffelt & Seckel, ’88; Mayle, Wilson, Ellis, Olive, Schramm & Steigman ’88; Brinkmann & Turner ’88; Burrows, Turner & Brinkmann ’89; more recent papers...] dark photon [Bjorken, Essig, Schuster, & Toro ’09; Dent, Ferrer & Krauss ’12; Kazanas, Mohapatra, Nussinov, Teplitz & YCZ ’14; ...] sterile neutrino [Kainulainen, Maalampi & Peltoniemi ’91; Kuflik, McDermott & Zurek ’12...] compact extra dimensions [Hanhart, Phillips, Reddy & Savage ’00; Hanhart, Pons, Phillips & Reddy ’01...] CP-even scalar [Ishizuka & Yoshimura ’90; Diener & Burgess ’13; Krnjaic ’15; Lee ’18; Arndt & Fox (saxion) ’02] Raffelt criterion: the energy loss due to these exotic particles can not exceed that from neutrino emission [Raffelt criterion ’96] . Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 2 / 16
Supernova limits on light CP-even scalar S Very limited supernova limits in the literature on light CP-even scalar (compared to axion/ALP & dark photon) Motivations: natural DM candidate [Silveira & Zee ’85; McDonald ’94; Burgess, Pospelov & ter Veldhuis ’00; Cline, Kainulainen, Scott & Weniger ’13] dark force mediator [Pospelov, Ritz & Voloshin ’07; Kainulainen, Tuominen & Vaskonen ’15; Bell, Busoni Sanderson ’16; Knapen, Lin & Zurek ’17; Matsumoto, Tsai & Tseng ’18; Batell, Freitas, Ismail & Mckeen ’18] baryogenesis [Espinosa & Quiros ’93; Profumo, Ramsey-Musolf & Shaughnessy ’07; Espinosa, Konstandin & Riva ’11; Croon, Howard, Ipek & Tait ’19] KOTO anomaly in K L → π 0 ν ¯ ν [Kitahara, Okui, Perez, Soreq & Tobioka ’19 PRL; Egana-Ugrinovic, Homiller, and Meade ’19; Dev, Mohapatra & YCZ ’19 PRD; Liu, McGinnis, Wagner & Wang ’20; Cline, Puel & Toma, ’20] Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 3 / 16
Production of S in supernova core N 1 × × N 3 N 1 × × N 4 ( c ) ( a ) ( c ′ ) ( a ′ ) π ( e ) π ( e ′ ) S S ( d ) ( b ) ( d ′ ) ( b ′ ) N 2 × × N 4 N 2 × × N 3 Figure: N + N + S → N + N The couplings of S to SM particles are all from mixing with the SM Higgs. Two contributions: SNN coupling + S ππ coupling y hNN NN + A π ( π 0 π 0 + π + π − ) � � L = sin θ S , 2 � S + 11 � y hNN ∼ 10 − 3 , m 2 2 m 2 ∼ 10 − 3 m π , A π = 9 v EW π Neglecting the contributions from Se + e − and S γγ couplings, which are both very small. Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 4 / 16
Emission rate of S Energy emission rate per unit volume in the supernova core: � � |M| 2 (2 π ) 4 δ 4 ( p 1 + p 2 − p 3 − p 4 − k S ) E S f 1 f 2 P decay P abs , d Π 5 S Q = spins d Π 5 : 5-body phase space S : symmetry factor for (non-)identical particles f ( p ) : non-relativistic Maxwell-Boltzmann distribution P decay = exp {− R c Γ S } : decay factor , P abs = exp {− R c /λ } : re-absorption factor due to N + N + S → N + N [ λ : mean free path (MFP)] Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 5 / 16
Cancellation at the leading order To the LO of m 2 S / m N E S : M a + M b + M c + M d ≃ 0 , M a ′ + M b ′ + M c ′ + M d ′ ≃ 0 . Expand to the NLO of m 2 S / m N E S : m 2 1 1 1 � � S ≃ ≃ 1 ∓ ( p i ± k S ) 2 − m 2 ± 2 m N E S + m 2 ± 2 m N E S 2 m N E S N S The contributions of the SNN diagrams to production rate will be suppressed by the ratio of ( m S / E S ) 4 in the limit of small m S . Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 6 / 16
Comparison of different contributions 10 55 10 54 energy loss [ erg / sec ] ℐ A 10 53 total ℐ C 10 52 ℐ B 10 51 10 50 10 49 1 5 10 50 100 500 1000 m S [ MeV ] Figure: T = 30 MeV, n B = 1 . 2 × 10 38 cm − 3 , sin θ = 10 − 6 I A : SNN diagrams: � 4 � m S ∝ y 2 ⇐ = cancellation hNN E S I B : S ππ diagrams: � m N � 2 � T � 2 � 2 �� m S m 2 � + 11 ∝ π 2 v EW T m N m N T I C : always in between I A and I B . Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 7 / 16
Decay of S 10 4 10 - 18 μ + μ - 10 7 10 - 21 c τ S [ meter ] Γ S [ MeV ] 10 10 e + e - 10 - 24 10 13 γγ 10 - 27 10 16 10 - 30 1 5 10 50 100 500 1000 m S [ MeV ] S decays mostly into e + e − or µ + µ − (for m S � 2 m µ ) Not include S → π + π − , π 0 π 0 as S decays so fast for m S � 2 m π that it can not escape from the core. Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 8 / 16
Re-absorption of S Re-absorption of S via the process N + N + S → N + N Inverse MFP [Giannotti & Nesti ’05; Burrows, Ressell & Turner ’90] : 1 d N S ( − k S ) λ − 1 ( E S ) ≡ 2 E S d Π S 1 � � |M ′ | 2 (2 π ) 4 δ 4 ( p 1 + p 2 − p 3 − p 4 + k S ) f 1 f 2 , = d Π 4 S 2 E S spins Effective energy-independent inverse MFP [Ishizuka & Yoshimura ’90] : E 3 � � x 3 e ES / T − 1 λ − 1 ( E S ) e x − 1 λ − 1 ( x ) d E S S d x � λ − 1 � ≡ = . E 3 � x 3 � d x d E S S e x − 1 e ES / T − 1 Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 9 / 16
MFP of S 0.010 0.001 10 - 4 sin θ 0 . 1 k m 10 - 5 1 k m 1 0 k m 10 - 6 1 0 0 k m 10 - 7 1 5 10 50 100 500 1000 m S [ MeV ] Figure: T = 30 MeV, n B = 1 . 2 × 10 38 cm − 3 Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 10 / 16
Supernova luminosity limits on S 5. × 10 - 5 1. × 10 - 5 limit from Krnjaic sin θ 5. × 10 - 6 1. × 10 - 6 5. × 10 - 7 1 5 10 50 100 500 m S [ MeV ] Figure: T = 30 MeV, n B = 1 . 2 × 10 38 cm − 3 , R c = 10 km Purple (orange) regions: luminosity limit of 5 (3) × 10 53 erg/sec; Limit from Krnjaic [’15]: not consider the cancellation & the S ππ diagrams; The supernova limits can be improved at IceCube-DeepCore, Hype-K & DUNE; More limits from neutron star mergers [Harris, Fortin, Sinha & Alford ’20] Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 11 / 16
Complementarity to other limits 0.010 C H A R M 0.001 meson decay 10 - 4 sin θ D U N E B B N 10 - 5 supernova 10 - 6 10 - 7 1 10 100 1000 m S [ MeV ] Meson decay: FCNC decays K → π + X , B → K ( π ) + X , with X = ee , µµ, γγ , missing energy; DUNE could probe the supernova excluded regions m S � 100 MeV [Berryman, ea, Fox, Kayser, Kelly & Raaf ’19; Dev, Mohapatra & YCZ ’19 PRD] . de Gouvˆ Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 12 / 16
”KOTO anomaly” The SM prediction: BR ( K L → π 0 ν ¯ × 10 − 11 � � ν ) SM = 3 . 4 ± 0 . 6 3 ”signal events” are observed at KOTO: [Kitahara, Okui, Perez, Soreq & Tobioka ’19 PRL] ν ) KOTO = 2 . 1 +2 . 0(+4 . 1) BR ( K L → π 0 ν ¯ − 1 . 1( − 1 . 7) × 10 − 9 CAUTION [Shinohara, Talk given at KAON2019]: The 3 events are beyond the reasonable expectation. The KOTO collaboration is checking the events, detector status, and background estimations. The KOTO collaboration did NOT claim the observed events as signals, or give any numbers on the branching ratio or physics results. Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 13 / 16
If the 3 events are a signal of BSM... heavy mediators (effective operators) long-lived light mediators or dark particles light mediator decaying off-axis into photons .... Kitahara, Okui, Perez, Soreq & Tobioka ’19 PRL; Egana-Ugrinovic, Homiller, and Meade ’19; Dev, Mohapatra & YCZ ’19 PRD; Fabbrichesi † & Gabrielli ’19; Liu, McGinnis, Wagner & Wang ’20; Cline, Puel & Toma ’20; Jho, Lee, Park, Park & Tseng ’20; Camalich, Pospelov, Vuong, Ziegler & Zupan ’20; He, Ma, Tandean, Valencia ’20; Ziegler, Zupan, Zwicky ’20 [see also the talks by J. Liu, S. Homiller & B. Lehmann]
One simplest explanation: light long-lived scalar S 0.005 9 4 9 E 0.001 KOTO sin θ NA62 5. × 10 - 4 l y K O T O a n o m a CHARM 1. × 10 - 4 generic singlet model 50 100 150 200 250 m S [ MeV ] Limits from (LLP = long-lived particle): E949 [ ′ 09] : K + → π + + LLP , NA62 [ ′ 19] : K + → π + ν ¯ ν , KOTO [ ′ 18] : K L → π 0 ν ¯ CHARM [ ′ 85] : K → π + LLP ν , The supernova limits are roughly two orders of magnitude lower than the KOTO signal region. Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 15 / 16
Conclusion We have performed the first full calculation of supernova limits on the light CP-even scalar S . Different from the axion/ALP and dark photon cases, there is a cancellation for the production of S . We have taken into consideration the decay and re-absorption of S in the supernova core. Depending on the scalar mass up to the 2 m π , the mixing angle of S with the SM Higgs is excluded in the range of 3 . 5 × 10 − 7 to 2 . 5 × 10 − 5 . The light scalar S is a good explanation for the “KOTO anomaly”. Thank you very much! Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 16 / 16
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