NEUTRINO AND HUBBLE TENSION VIA A MAJORON IN MFV

Based on: 2009.01848, FAA, E. Fernández-Martínez, M. González-López, L. Merlo.

Fernando Arias Aragón [email protected] Outline

• Introduction

• The Majoron Mechanism

• The Majoron and from a MFV Setup

• Phenomenological Signatures

• Conclusions

2 Introduction

• The Hubble Tension: L. Verde, T. Treu, and A. Riess, 1907.10625 • Early Universe vs local measurements of 퐻 differ up to 4 − 6 휎 0 K. C. Wong et. al., H0LiCOW XIII, 1907.04869 • This may be solved by:

• Systematics

• New cosmological model

• physics. E.g.: a Majoron M. Escudero and S. J. Witte, 1909.04044

• Study its compatibility with solutions to other SM problems

• Light masses → Type-I Seesaw

• Flavour puzzle → flavour continuous global symmetries

• Strong CP Problem → Axion 3 Introduction

• The Majoron, 휔, is the NGB associated to the breaking of LN

• For it to alleviate the 퐻0 tension it needs:

• A in the range of

푚휔 ∈ 0.1, 1 eV • Coupling to of order −14 −12 휆휔휈휈 ∈ [5 × 10 , 10 ]

• Phenomenology of this Majoron in a Type-I Seesaw

• Collider signatures: 푁푅, Higgs invisible decay, new scalar • Astrophysical effects: CAST and Red Giant observations

• Majoron emission in 0휈훽훽 decays

4 The Majoron Mechanism

• SM extended with 3 RH neutrinos and a singlet scalar 휒, with LN −푳푵 and 푳흌 respectively

1+퐿푁 2퐿푁−퐿휒 휔 휒 퐿휒 1 휒 퐿휒 휎 + 푣휒 𝑖 푣휒 ҧ 푐 푣휒 −ℒ휈 = 푙퐿퐻෩풴휈푁푅 + 휒푁ഥ푅풴푁푁푅 + h. c., 휒 = 푒 , 휀휒 = Λ휒 2 Λ휒 2 2Λ휒

• Heavy and light neutrino masses generated after LN SSB

2+퐿휒 퐿 2퐿푁−퐿휒 휀 휒 푣2 푣 휒 −1 푇 퐿휒 휒 푚휈 = 풴휈풴푁 풴휈 , 푚푁 = 휀휒 풴푁 2푣휒 2

• Axion coupling to light neutrinos:

푙표푤−푒푛푒푟𝑔푦 휆휔휈휈 푐 푚휈 ℒ휔 ⊃ 𝑖 휔휈ҧ퐿휈퐿, 휆휔휈휈 = 2 2 퐿휒푣휒 5 The Majoron Mechanism

• Combining those expressions with the bound on 휆휔휈휈 2+퐿휒 퐿휒 −1 푇 −13 −12 퐿휒 휀휒 풴휈풴푁 풴휈 ∈ 1.2 × 10 , 2.4 × 10 2퐿푁−퐿휒 퐿 휀 휒 휒 −14 풴푁 ≫ 3.5 × 10 퐿휒

• A renormalizable scenario is possible, but it is very fine-tuned

퐿푁 = −1, 퐿휒 = −2 −1 푇 −13 −12 풴휈풴푁 풴휈 ∈ 1.2 × 10 , 2.4 × 10

• Can fine-tuning be avoided exploiting 휀휒?

6 The Majoron Mechanism

• Two phenomenologically interesting non-renormalizable scenarios:

7 The Majoron Mechanism

• Apart from a small coupling to neutrinos, the Majoron needs a specific mass

• Wormhole effects fall short R. Alonso and A. Urbano, 1706.07415

• Planck-suppressed operators provide a mass too large E. K. Akhmedov et al., hep-ph/9209285

• Explicit breaking of LN via a Majorana mass term

• Additional scalar d.o.f. to the Majoron: the radial part of 휒, 휎

• Through the quartic coupling 푔퐻†퐻휒∗휒, ℎ and 휎 mix with an angle 휗

푀2 − 푀2 푔 = 휎 ℎ sin 2휗 2푣푣휒 sin2 휗 ≲ 0.11 ATLAS Collaboration, 1909.02845

8 The Majoron and Axion from a MFV setup

R. S. Chivukula and H. Georgi, PLB 188, 99-104 (1987) • Minimal Flavour Violation assumption: only Yukawas violate flavour symmetry

D’Ambrosio et al., 020736 • Flavour Symmetry Group identified in the limit of vanishing Yukawas Cirigliano et al., 0507001

풢퐹 = 푈 3 푞퐿 × 푈 3 푢푅 × 푈 3 푑푅 × 푈 3 푙퐿 × 푈 3 푁푅 × 푈 3 푒푅 퐴 풢퐹 ⊃ 풢퐹 = 푈 1 퐵 × 푈 1 퐿 × 푈 1 푌 × 푈 1 푃푄 × 푈 1 푒푅 × 푈 1 푁푅

• The PQ charges are chosen to explain 푚푏Τ푚푡 and 푚휏Τ푚푡

FAA & Merlo, 1709.07039 푥푞퐿 = 푥푙퐿 = 푥푢푅 = 푥푁푅 = 0, 푥푑푅 = 푥푒푅 = 3

• As with LN, PQ is made an exact symmetry by the addition of a scalar field Φ with 푥Φ = −1

푎 휌 + 푣Φ 𝑖 Φ = 푒 푣Φ 2

9 The Majoron and Axion from a MFV setup

3 3 Φ Φ −ℒ푌 = 푞ത퐿퐻෩풴푢푢푅 + 푞ത퐿퐻풴푑푑푅 + 푙퐿ҧ 퐻풴푒푒푅 ΛΦ ΛΦ 1+퐿푁 2퐿푁−퐿휒 휒 퐿휒 1 휒 퐿휒 ҧ 푐 + 푙퐿퐻෩풴휈푁푅 + 휒푁ഥ푅풴푁푁푅 + h. c. Λ휒 2 Λ휒

• The matrices 풴푢,푑,푒,휈,푁 must become spurions transforming under the non-Abelian part of 풢퐹

† 푚푢 푚푐 푚푑 푚푑 푚푒 푚푒 풴푢 = 푐푡푉 diag , , 1 , 풴푑 = 푐푏diag , , 1 , 풴푒 = 푐휏diag , , 1 푚푡 푚푡 푚푏 푚푏 푚휏 푚휏

• The PQ SSB explains the 푚푏Τ푚푡 and 푚휏Τ푚푡 ratios assuming 푣 Φ ≃ 0.23 2ΛΦ • Non-renormalizable flavour violating operators are Yukawa suppressed: 1 − 10 TeV scale, accessible at colliders 10 The Majoron and Axion from a MFV setup

• MFV in the sector: 풴휈 and 풴푁 cannot be directly identified in terms of neutrino masses or the PMNS elements. • Two possible ways out: Cirigliano et al., 0507001 푁퐴 • 풢퐿 = 푆푈 3 푙퐿 × 푆푈 3 푒푅 × 푆푂 3 푁푅 × 퐶푃 ⇒ 풴푁 ∝ ퟙ, 풴휈 ∈ ℝ S. Davidson and F. Palorini, hep-ph/0607329 2+퐿휒 퐿 휀 휒 푣2 휒 푇 푚휈 = 풴휈풴휈 2푣휒 푁퐴 R. Alonso et al., 1103.5461 • 풢퐿 = 푆푈 3 푙퐿+푁푅 × 푆푈 3 푒푅 ⇒ 풴휈 ∝ ퟙ 2+퐿휒 퐿 휀 휒 푣2 휒 −1 푚휈 = 풴푁 2푣휒 • The axion arising from the PQ SSB couples to and behaves as the usual QCD Axion solving the Strong CP Problem N. Viaux et al., 1311.1669 12 O. Straniero et al., 1802.10357 10 GeV 푣Φ 8 푚푎 ∼ 6 μeV , 푓푎 = ≳ 8 × 10 GeV S. A. Díaz et al., 1910.10568 푓푎 9 11 Phenomenological Signatures

• Coupling to

푙표푤−푒푛푒푟𝑔푦 1 휇휈 −10 −1 ℒ ⊃ 휆 휔퐹 퐹෨ , 휆 ≲ 10 GeV CAST Collaboration, 1705.02290 휔 4 휔훾훾 휇휈 휔훾훾

• Matching the effective coupling with the 2 loop explicit expression yields C. García-Cely and J. Heeck, 1701.07209

2 2+2퐿푁 훼푚 퐿 휆 = 휔 휀 휒 Tr(풴 풴†) 휔훾훾 3 2 휒 휈 휈 384 2휋 푚푒푣휒

• Coupling to

푙표푤−푒푛푒푟𝑔푦 −13 N. Viaux et al., 1311.1669 ℒ휔 ⊃ 𝑖휆휔푒푒휔푒ҧ푒, 휆휔푒푒 ≲ 4.3 × 10

• The explicit expression can be found at the 1 loop level C. García-Cely and J. Heeck, 1701.07209

2+2퐿푁 1 푚 퐿 휆 = 푒 휀 휒 풴 풴† − Tr 풴 풴† 휔푒푒 2 휒 휈 휈 11 휈 휈 12 16휋 푣휒 Phenomenological Signatures

• Coupling to neutrinos

• Constrained by Majoron emission in 0휈훽훽 decays −5 휆휔휈휈 < 10 R. Cepedello et al., 1811.00031

13 Phenomenological Signatures

• Coupling with the Higgs • Apart from the ℎ − 휎 mixing angle 휗, the Higgs invisible decay ℎ → 휔휔 is constrained sin2 휗 푀3 푣 CMS collaboration, 1809.05937 ℎ 휒 Γℎ→휔휔 = 2 ≲ 0.8 MeV ⇒ ≳ 5 TeV 32휋푣휒 sin 휗

14 Phenomenological Signatures

• Heavy neutrinos • Case NR1 testable at beam dump experiments or near detectors at oscillation experiments like DUNE or SHiP • Case NR2 interesting for production at LHC or future colliders

• 푁 → 3휈 in the early universe may disfavour some scenarios

• If it happens after BBN, as it may happen in Case NR1 with 푀푁 ∈ 3.5, 200 MeV, the light-heavy neutrino mixing

휃푠 is bound by

2 푚휈 −15 −17 sin 휃푠 ≡ ≲ 10 − 10 A. C. Vincent et al., 1408.1956 푀푁 • The heavier masses in Case NR2 allow for decay before BBN, evading that cosmological bound

15 Conclusions

• Majorons can alleviate the Hubble tension

• The smallness of neutrino masses was addressed here with a Majoron

• This Majoron can easily be embedded in MFV, where also a QCD axion can arise

• Cosmology sets strong bounds

• Colliders may see several signals: “Light” Heavy neutrinos, new scalar or Higgs invisible decay

16 THANK YOU FOR YOUR ATTENTION

17 BACKUP SLIDES

18 Phenomenological Signatures

Plot from A. C. Vincent, E. F. Martínez, P. Hernández, M. Lattanzi, and O. Mena, 1408.1956

19 The Majoron Mechanism

• Two phenomenologically interesting non-renormalizable scenarios:

• Other possibilities

† • 퐿푁 > 0, 퐿휒 < 0 ⇒ 휒 ↔ 휒

• 퐿푁 < 0, 퐿휒 > 0 ⇒ non-local

−1 • 퐿푁 = 퐿휒 = −1 ⇒ 푚휈 ∝ 휀휒 , highly fine-tuned 20