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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.

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SLIDE 1

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, PRD101, 075014 [1911.12334]
  • P. S. B. Dev, R. N. Mohapatra & YCZ, 2005.00490
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SLIDE 2

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

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SLIDE 3

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 KL → π0ν¯ 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

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SLIDE 4

Production of S in supernova core

N1 N2 π N3 N4 S × × × × (c) (d) (a) (b) (e) N1 N2 π N4 N3 S × × × × (c′) (d′) (a′) (b′) (e′)

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 + Sππ coupling L = sin θS

  • yhNNNN + Aπ(π0π0 + π+π−)
  • ,

yhNN ∼ 10−3 , Aπ = 2 9vEW

  • m2

S + 11

2 m2

π

  • ∼ 10−3mπ ,

Neglecting the contributions from Se+e− and Sγγ couplings, which are both very small.

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 4 / 16

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SLIDE 5

Emission rate of S

Energy emission rate per unit volume in the supernova core: Q =

  • dΠ5S
  • spins

|M|2(2π)4δ4(p1 + p2 − p3 − p4 − kS)ESf1f2PdecayPabs , dΠ5 : 5-body phase space S : symmetry factor for (non-)identical particles f (p) : non-relativistic Maxwell-Boltzmann distribution Pdecay = exp{−RcΓS} : decay factor, Pabs = exp{−Rc/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

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Cancellation at the leading order

To the LO of m2

S/mNES:

Ma + Mb + Mc + Md ≃ 0 , Ma′ + Mb′ + Mc′ + Md′ ≃ 0 . Expand to the NLO of m2

S/mNES:

1 (pi ± kS)2 − m2

N

≃ 1 ±2mNES + m2

S

≃ 1 ±2mNES

  • 1 ∓

m2

S

2mNES

  • The contributions of the SNN diagrams to production rate will be suppressed

by the ratio of (mS/ES)4 in the limit of small mS.

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 6 / 16

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SLIDE 7

Comparison of different contributions

1 5 10 50 100 500 1000 1049 1050 1051 1052 1053 1054 1055

mS [MeV] energy loss [erg/sec]

ℐA ℐC ℐB total

Figure: T = 30 MeV, nB = 1.2 × 1038 cm−3, sin θ = 10−6

IA: SNN diagrams: ∝ y 2

hNN

mS ES 4 ⇐ = cancellation IB: Sππ diagrams: ∝ mN vEW 2 mS T 2 T mN

  • + 11

2 m2

π

mNT 2 IC: always in between IA and IB.

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 7 / 16

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SLIDE 8

Decay of S

1 5 10 50 100 500 1000 10-30 10-27 10-24 10-21 10-18 104 107 1010 1013 1016

mS [MeV] ΓS [MeV] cτS [meter]

e+e- μ+μ- γγ

S decays mostly into e+e− or µ+µ− (for mS 2mµ) Not include S → π+π−, π0π0 as S decays so fast for mS 2mπ that it can not escape from the core.

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 8 / 16

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SLIDE 9

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]: λ−1(ES) ≡ 1 2ES dNS(−kS) dΠS = 1 2ES

  • dΠ4S
  • spins

|M′|2(2π)4δ4(p1 + p2 − p3 − p4 + kS)f1f2 , Effective energy-independent inverse MFP [Ishizuka & Yoshimura ’90]: λ−1 ≡

  • dES

E 3

S

eES /T −1λ−1(ES)

  • dES

E 3

S

eES /T −1

=

  • dx

x3 ex−1λ−1(x)

  • dx

x3 ex−1

.

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 9 / 16

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SLIDE 10

MFP of S

1 5 10 50 100 500 1000 10-7 10-6 10-5 10-4 0.001 0.010

mS [MeV] sin θ

. 1 k m 1 k m 1 k m 1 k m

Figure: T = 30 MeV, nB = 1.2 × 1038 cm−3

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 10 / 16

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SLIDE 11

Supernova luminosity limits on S

1 5 10 50 100 500

  • 5. ×10-7
  • 1. ×10-6
  • 5. ×10-6
  • 1. ×10-5
  • 5. ×10-5

mS [MeV] sin θ

limit from Krnjaic

Figure: T = 30 MeV, nB = 1.2 × 1038 cm−3, Rc = 10 km

Purple (orange) regions: luminosity limit of 5 (3) × 1053 erg/sec; Limit from Krnjaic [’15]: not consider the cancellation & the Sππ 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

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SLIDE 12

Complementarity to other limits

1 10 100 1000 10-7 10-6 10-5 10-4 0.001 0.010

mS [MeV] sin θ supernova

B B N meson decay C H A R M D U N E

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 mS 100 MeV [Berryman,

de Gouvˆ ea, Fox, Kayser, Kelly & Raaf ’19; Dev, Mohapatra & YCZ ’19 PRD].

Yongchao Zhang (Wustl) supernova & KOTO May 4, 2020 12 / 16

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SLIDE 13

”KOTO anomaly”

The SM prediction: BR(KL → π0ν¯ ν)SM =

  • 3.4 ± 0.6
  • × 10−11

3 ”signal events” are observed at KOTO:

[Kitahara, Okui, Perez, Soreq & Tobioka ’19 PRL]

BR(KL → π0ν¯ ν)KOTO = 2.1+2.0(+4.1)

−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

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SLIDE 14

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]

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SLIDE 15

One simplest explanation: light long-lived scalar S

50 100 150 200 250

  • 1. ×10-4
  • 5. ×10-4

0.001 0.005

mS [MeV] sin θ generic singlet model

K O T O a n

  • m

a l y KOTO E 9 4 9 NA62 CHARM

Limits from (LLP = long-lived particle): E949 [′09] : K + → π+ + LLP , NA62 [′19] : K + → π+ν¯ ν , KOTO [′18] : KL → π0ν¯ ν , CHARM [′85] : K → π + LLP 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

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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 2mπ, 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