Flavourful Axion Phenomenology Eung Jin Chun`
Flavourful AxionPhenomenology
Eung Jin Chun`
Introduction
• Strong CP problem and PQ symmetry “Axion”
• It may be identified with a flavour symmetry.
• Signatures and constraints on flavour violating axion couplings.
• An (approximate) PQ symmetry as an accidental symmetry in a Pati-Salam unification model with A-to-Z flavour group correlated flavour observables.
Yonsei 190226 EJ Chun "Flavourful Axion" 2
Wilczek, ’82; … ; Ema, et.al.; Calibbi, et.al., ‘16
F. Bjoerkeroth, EJC, S. King, 1711.05741
1806.00660
Strong CP problem
• Gauge-invariance allows QCD 𝜃 term:
• It is a CP-odd 𝐸 ⋅ 𝐵 term inducing nucleon EDM.
• Why is 𝜃 so small? Symmetry origin: Peccei-Quinn ‘77.
Yonsei 190226 3EJ Chun "Flavourful Axion"
𝑑𝑛 ∼1
4𝜋2𝑒
𝑚𝑁𝑔𝜋𝑁𝑁𝜃 𝑔𝜋 𝑁𝑁 log
𝑚𝑁𝑚𝜋
< 10−26ecm ⇒ 𝜃 < 10−10
PQ mechanism
• Introduce a QCD anomalous global U(1) symmetry which is spontaneously broken at a high scale 𝐹𝑎 axion.
• QCD anomaly induces an axion-gluon-gluon coupling:
• QCD condensation generates axion potential driving the theta value to vanish:
• Axion mass is predicted to be
Yonsei 190226 4EJ Chun "Flavourful Axion"
Axion models• Kim-Shifman-Vainshtein-Zakharov:
• Dine-Fischler-Srednicki-Zhitinitski:
• Flavourful PQ symmetry: each generation has different PQ charges
Yonsei 190226 5EJ Chun "Flavourful Axion"
0 1 − 1 1 0 − 1
1 0 − 1
𝑖
𝑋 𝑞𝑖 + 𝑋 𝑢𝑖𝑐 + 𝑋 𝑑𝑖
𝑐 ≠ 0
PQ charges:
Axion is a Goldstone boson:
𝑆 = 𝐹𝑎𝑒𝑖𝑎𝐹𝑎
Constraints on Fa
• Lower bound from star cooling: low Fa efficient axionemission fast star cooling.
• Upper bound from axion dark matter density: axion potential generated after Λ𝑄𝐶𝐷 drives a coherent axion oscillation starting from a initial misaligned field value.
Yonsei 190226 6EJ Chun "Flavourful Axion"
Flavourful axion phenomenology
• PQ charges may be generation-dependent: QCD axion = phase field of flavons
• Fermion Yukawa couplings take a general form:
Yonsei 190226 EJ Chun "Flavourful Axion" 7
𝜙𝑖 =𝑣𝑖
2𝑒𝑖𝑥𝑖 𝑎𝑣𝑃𝑄
𝑎 =
𝑖
𝑥𝑖𝑣𝑖𝑎𝑖𝑣𝑃𝑄
; 𝑣𝑃𝑄2 =
𝑖
𝑥𝑖2𝑣𝑖
2
−ℒYuk = 𝑒𝑖𝑎𝑣𝑃𝑄
𝑥𝑓𝐿𝑖−𝑥𝑓𝑅𝑗 𝑀𝑖𝑗𝑓𝑓𝐿𝑖𝑓𝑅𝑗
Feng, et.al., ‘98
General flavourful axion couplings
• Take the transformation and then go to the mass basis:
Yonsei 190226 EJ Chun "Flavourful Axion" 8
−ℒ =𝜕𝜇𝑎
𝑣𝑃𝑄ഥ𝑓𝑖𝛾
𝜇 𝑉𝑖𝑗𝑓− 𝐴𝑖𝑗
𝑓𝛾5 𝑓𝑗 +
𝑎
𝑓𝑎
𝛼𝑠8𝜋
𝐺 ෨𝐺 + 𝑐𝑎𝛾𝛼
8𝜋𝐹 ෨𝐹 +𝑚𝑖
𝑓𝑓𝐿𝑖𝑓𝑅𝑗
𝑓𝐿/𝑅 → 𝑈𝑓𝐿/𝑅 𝑓𝐿/𝑅 , 𝑀𝑓→ 𝑈𝑓𝐿
† 𝑀𝑓𝑈𝑓𝑅 = 𝑚𝑓
𝑓𝑎 = 𝑣𝑃𝑄 /𝑁𝐷𝑊 (𝑁𝐷𝑊 = QCD anomaly)
𝑉𝑓 =1
2(𝑈𝑓𝐿
† 𝑥𝑓𝐿𝑈𝑓𝐿 + 𝑈𝑓𝑅† 𝑥𝑓𝑅𝑈𝑓𝑅)
𝐴𝑓 =1
2(𝑈𝑓𝐿
† 𝑥𝑓𝐿𝑈𝑓𝐿 − 𝑈𝑓𝑅† 𝑥𝑓𝑅𝑈𝑓𝑅)
𝑓𝐿/𝑅𝑖 → 𝑒𝑖𝑎𝑣𝑃𝑄
𝑥𝑓𝐿/𝑅𝑖 𝑓𝐿/𝑅𝑖
Lepton decays to axion
• LFV decays 𝑙𝑖 → 𝑙𝑗𝑎 with the couplings (𝑉𝑖𝑗𝑒 , 𝐴𝑖𝑗
𝑒 ):
• Angular distribution:
Yonsei 190226 EJ Chun "Flavourful Axion" 9
𝐵 𝑙𝑖 → 𝑙𝑗𝑎 ≡ ǁ𝑐𝑙𝑖→𝑙𝑗 𝐶𝑖𝑗𝑒 2 10
12𝐺𝑒𝑉
𝑣𝑃𝑄
2
𝐶𝑖𝑗𝑒 2 = 𝑉𝑖𝑗
𝑒 2 + 𝐴𝑖𝑗𝑒 2ǁ𝑐𝑙𝑖→𝑙𝑗 ≈
1
16𝜋Γ 𝑙𝑖
𝑚𝑙𝑖3
1012𝐺𝑒𝑉 2
𝑑Γ
𝑑cos𝜃=
𝐶𝑖𝑗𝑒 2
32𝜋
𝑚𝑙𝑖3
𝑣𝑃𝑄2 1 − 𝐴 𝑃𝑙𝑖cos𝜃 𝐴 =
2ℜ 𝐴𝑖𝑗𝑒 𝑉𝑖𝑗
𝑒∗
𝐶𝑖𝑗𝑒 2
=
𝐴 = 0 isotropy
𝐴 = −1 𝑉 − 𝐴: SM
𝐴 = +1 𝑉 + 𝐴: our model
Yonsei 190226 EJ Chun "Flavourful Axion" 10
Radiative LFV decay: 𝑙1 → 𝑙2𝑎𝛾
• Cristal Box:
• Future search?
Yonsei 190226 EJ Chun "Flavourful Axion" 11
𝐵𝑟 𝜇 → 𝑒𝑎𝛾 < 1.1 × 10−9 ⇒ 𝑣𝑃𝑄 > 9.4 × 108 𝐶21
𝑒 𝐺𝑒𝑉
𝐵𝑟 𝜇 → 𝑒𝛾 < 4.9 × 10−11
??
Meson decay to axion
• Meson decays 𝑃 → 𝑃′𝑎 from flavourful vector couplings:
Yonsei 190226 EJ Chun "Flavourful Axion" 12
≡ ǁ𝑐𝑃→𝑃′ 𝑉𝑖𝑗𝑞2 1012𝐺𝑒𝑉
𝑣𝑃𝑄
2
𝐵 𝑃 𝑞𝑖 → 𝑃′ 𝑞𝑗 𝑎 =
1
16𝜋Γ(𝑃)𝑉𝑖𝑗𝑞2𝑓+ 0
2𝑚𝑃3
𝑣𝑃𝑄2 1 −
𝑚𝑃′2
𝑚𝑃2
3
Yonsei 190226 EJ Chun "Flavourful Axion" 13
Axion-meson mixing
• After QCD condensation,
• Kinetic mixing diagonalization & mass re-diagonalizaton:
Yonsei 190226 EJ Chun "Flavourful Axion" 14
𝑐𝑖𝑗𝑣𝑃𝑄
𝜕𝜇𝑎 ഥ𝑓𝑖𝛾𝜇𝛾5𝑓𝑗 ⇒ 𝑐𝑃
𝑓𝑃𝑓𝑎𝜕𝜇𝑎𝜕
𝜇𝑃
𝑎 → 𝑎 + 𝑐𝑃𝑓𝑃𝑓𝑎
𝑚𝑃2
𝑚𝑃2 −𝑚𝑎
2 𝑃 , 𝑃 → 𝑃 − 𝑐𝑃𝑓𝑃𝑓𝑎
𝑚𝑎2
𝑚𝑃2 −𝑚𝑎
2 𝑎
mass-dependent mixing
Axion-pion mixing
• For QCD axion, the mixing is negligible (𝑓𝑃 ≪ 𝑓𝑎, 𝑚𝑎 ≪ 𝑚𝜋).
• For ALP, it can lead to sizable contribution to 𝐾+ → 𝜋+𝑎 & 𝑎 → 𝛾𝛾induced from 𝐾+ → 𝜋+𝜋0 & 𝜋0 → 𝛾𝛾:
• B 𝐾+ → 𝜋+𝑎 < 10−10 puts a limit:
Yonsei 190226 EJ Chun "Flavourful Axion" 15
Γ 𝐾+ → 𝜋+𝑎 ≈ 𝑐𝜋𝑓𝜋𝑓𝑎
𝑚𝑎2
𝑚𝜋2 −𝑚𝑎
2
2
Γ 𝐾+ → 𝜋+𝜋0
Γ 𝑎 → 𝛾𝛾 ≈ 𝑐𝜋𝑓𝜋𝑓𝑎
𝑚𝑎2
𝑚𝜋2 −𝑚𝑎
2
2𝑚𝑎𝑚𝜋
3
Γ 𝜋0 → 𝛾𝛾 ⇒ 𝑔𝑎𝛾 𝑚𝑖𝑥 =𝛼
𝜋
𝑐𝜋𝑚𝑎2
𝑚𝜋2 −𝑚𝑎
2
1
𝑓𝑎
𝑓𝑎 > 4𝑐𝜋𝑚𝑎
2
𝑚𝜋2−𝑚𝑎
2 𝑇𝑒𝑉 ⇒ 𝑔𝑎𝛾 𝑚𝑖𝑥 < 5.8 × 10−7 𝐺𝑒𝑉−1 for 𝑚𝑎 < 110𝑀𝑒𝑉
Yonsei 190226 EJ Chun "Flavourful Axion" 16
1702.02964
Impact on neutral meson mass splitting
• Flavourful axion couplings (𝐴12,23𝑢,𝑑 ) induces mixing with heavy
mesons (𝐾,𝐷, 𝐵) contributing to their mass splitting:
Yonsei 190226 EJ Chun "Flavourful Axion" 17
Δ𝑚𝑃 ≈ 𝜂𝑃2𝑚𝑃 = 𝑐𝑃
2𝑓𝑃2
𝑣𝑃𝑄2 𝑚𝑃
𝑎
A-to-Z flavour Pati-Salam Model
• A Pati-Salam unification model where an approximate PQ symmetry, arises accidentally from discrete flavour symmetry 𝐴4 × 𝑍5 × 𝑍3 × 𝑍5
′ :
Yonsei 190226 EJ Chun "Flavourful Axion" 18
King, ’14
Yonsei 190226 EJ Chun "Flavourful Axion" 19
𝑥𝑓𝐿 = 0,0,0
𝑥𝑓𝑅 = 2,1,0
NDW = 6
Fermions
Higgses
Flavons
Messengers
“Family-dependent DFSZ”
Protection up to D=10
Axion-dependent Yukawa
Yonsei 190226 EJ Chun "Flavourful Axion" 20
𝑥𝜑2𝑢,𝑑 = 1
𝑥𝜑1𝑢,𝑑 = 2
• Flavon fields 𝜙1,2𝑢,𝑑 and right-handed fermions 𝐹1,2,3
𝑐 are charged under the PQ symmetry:
Fitting fermion masses and mixing
• Fermion mass matrices from 15 input parameters:
• Best-fit:
Yonsei 190226 EJ Chun "Flavourful Axion" 21
Specific flavour prediction for axion
Our model Predictions
• Best-fit values for axion-fermion couplings:
• Rare decays to axion:
• Correlated probes:
Yonsei 190226 EJ Chun "Flavourful Axion" 22
Conclusion
• Axion solves the strong CP and dark matter problem.
• A specific Pati-Salam unified model is worked out to show an automatic PQ symmetry guaranteed by a flavour symmetry.
• It leads to interesting flavourful axion phenomenology.
• Rare Kaon and muon decays, 𝐾+ → 𝜋+𝑎 & 𝜇 → 𝑒 𝑎, provide sensitive probes for QCD axion.
• More numerous flavour observables can be looked for axion-like particles.
Yonsei 190226 EJ Chun "Flavourful Axion" 23