NUCLEAR STRUCTURE AND THEORY FOR PRECISION BETA DECAY EXPERIMENTS: - PowerPoint PPT Presentation

1 “Beta Decay as a Probe of New Physics” DORON GAZIT RACAH INSTITUTE OF PHYSICS HEBREW UNIVERSITY OF JERUSALEM NUCLEAR STRUCTURE AND THEORY FOR PRECISION BETA DECAY EXPERIMENTS: NUCLEAR SHAPE CORRECTIONS

2 COLLABORATORS COLLABORATORS IN THIS WORK Ayala Glick Magid Expt: Guy Ron, Yonatan Mishnayot, Ben Ohayon Michael Hass, Sergey Vaintraub, Ish Mukul

3 INTRODUCTION INTRODUCTION ▸ The standard model is incomplete: dark sector, neutrino masses. ▸ Finding signatures of beyond the standard model physics in quantum phenomena is one of the heralds of modern physics. ▸ LHC is the energy frontier. ▸ Nuclear phenomena are a precision frontier: ▸ New t tech chniques a allow u unprece cedented e experimental a accu ccuracy cy. ▸ Need a an a acco ccompanying t theoretica cal e effort t to a analyze cs . experimental r results a and p pinpoint n new p physics ▸ It’s not a very rewarding job…

4 INTRODUCTION BSM EFFORTS USING NUCLEAR BETA DECAYS b decays Precision spectrum studies Precision Correlation Studies Neutrino hypothesized Parity breaking KATRIN V-A structure

5 INTRODUCTION BSM EFFORTS USING NUCLEAR BETA DECAYS b decays Precision spectrum studies Precision Correlation Studies Neutrino hypothesized Parity breaking KATRIN V-A structure

6 INTRODUCTION BSM EFFORTS USING NUCLEAR BETA DECAYS b decays Precision spectrum studies Precision Correlation Studies ”New Physics” searches using beta decays have been moving back and forth, from ▸ spectrum to correlation studies. Atomic traps acted as the catalyst for precision correlation studies, and many ▸ experiments have been constructed since ~2005. In the last couple of years, the seesaw seems to tilt towards precision spectrum ▸ studies again, based on theoretical expectations for the size of the effect.

7 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS d 5 ω β ∓ Differential b decay rate d � k / 4 π d � ν / 4 π d ϵ = � ( ϵ ) · � ( q , ⃗ β · ˆ ν ). ⃗ = $ Momentum transfer ⃗ neutrino momentum % , 𝛾 particle momentum to energy ratio 𝜉 𝛾 � ( ϵ ) = 2 G 2 2 � J + 1 ×(𝑑𝑝𝑠𝑠𝑓𝑑𝑢𝑗𝑝𝑜𝑡) Nuclear independent part � J ( 2 J i + 1 )( ϵ 0 − ϵ ) 2 k ϵ F ( ± ) ( Z f , ϵ ), π 2 Classification of b decays Δ𝐾 ) = 0 + (Super)allowed - Fermi transition ∝ 𝑟 2 Δ𝐾 ) = 0,1 + Allowed – Fermi/Gamow-Teller Δ𝐾 ) = 0,1,2 / ∝ 𝑟 3 Unique First forbidden transition

8 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS WHERE DOES NUCLEAR STRUCTURE ENTER? NUCLEAR STRUCTURE DEPENDENT NUCLEAR STRUCTURE DEPENDENT

9 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS d 5 ω β ∓ Differential b decay rate d � k / 4 π d � ν / 4 π d ϵ = � ( ϵ ) · � ( q , ⃗ β · ˆ ν ). ⃗ = $ Momentum transfer ⃗ neutrino momentum % , 𝛾 particle momentum to energy ratio 𝜉 𝛾 ∝ 𝑟 ? � ˆ x ) ˆ d ⃗ J 0 ( ⃗ C J M ( q ) = x j J ( qx ) Y J M ( ˆ x ) Nuclear dependent part ∝ 𝑟 ?/3 E J M ( q ) = 1 � x ) ] · ˆ x ⃗ ∇ × [ j J ( qx ) ⃗ ⃗ ˆ d ⃗ J ( ⃗ Y J J M ( ˆ x ) q Assuming V-A structure � ∝ 𝑟 ? x ) · ˆ � ( q , ⃗ x j J ( qx ) ⃗ ˆ ⃗ β · ˆ ν ) d ⃗ J ( ⃗ Y J J M ( ˆ M J M ( q ) = x ) ⎧ �� ⃗ � J ⎨ A ?B � ��� E J ∥⟩ | 2 + | ⟨∥ ˆ L J M ( q ) = i � | ⟨∥ ˆ M J ∥⟩ | 2 � x ) ] · ˆ ∝ 𝐹 � ˆ � 1 − ν · ˆ β · ˆ = q q x ⃗ ⃗ ˆ d ⃗ J ( ⃗ ∇ [ j J ( qx ) Y J M ( ˆ x ), 2 � J + 1 q ⎩ J ≥ 1 � �� M J ∥⟩ ∗ ν − ⃗ 2 ℜ⟨∥ ˆ E J ∥⟩⟨∥ ˆ ± ˆ q · ˆ β J ≥ 1 �� ⃗ �� �� � ν · ⃗ L J ∥⟩ | 2 | ⟨∥ ˆ � ˆ 1 − ˆ ν · ˆ β · ˆ + β + 2 q q J ≥ 0 � � ν · ⃗ | ⟨∥ ˆ C J ∥⟩ | 2 + 1 + ˆ β � � L J ∥⟩ ∗ �� ν + ⃗ ℜ⟨∥ ˆ C J ∥⟩⟨∥ ˆ − 2 ˆ ˆ q · (4) β , We have similar expressions for Tensor and Scalar structures, and interferences.[Glick-Magid, Gazit, unpublished]

10 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS d 5 ω β ∓ Differential b decay rate d � k / 4 π d � ν / 4 π d ϵ = � ( ϵ ) · � ( q , ⃗ β · ˆ ν ). ⃗ = $ Momentum transfer ⃗ neutrino momentum % , 𝛾 particle momentum to energy ratio 𝜉 𝛾 ∝ 𝑟 ? � ˆ x ) ˆ d ⃗ J 0 ( ⃗ C J M ( q ) = x j J ( qx ) Y J M ( ˆ x ) Nuclear dependent part ∝ 𝑟 ?/3 E J M ( q ) = 1 � x ) ] · ˆ x ⃗ ∇ × [ j J ( qx ) ⃗ ⃗ ˆ d ⃗ J ( ⃗ Y J J M ( ˆ x ) q Assuming V-A structure � ∝ 𝑟 ? x ) · ˆ � ( q , ⃗ x j J ( qx ) ⃗ ˆ ⃗ β · ˆ ν ) d ⃗ J ( ⃗ Y J J M ( ˆ M J M ( q ) = x ) ⎧ �� ⃗ � J ⎨ A ?B � ��� E J ∥⟩ | 2 + | ⟨∥ ˆ L J M ( q ) = i � | ⟨∥ ˆ M J ∥⟩ | 2 � x ) ] · ˆ ∝ 𝐹 � ˆ � 1 − ν · ˆ β · ˆ = q q x ⃗ ⃗ ˆ d ⃗ J ( ⃗ ∇ [ j J ( qx ) Y J M ( ˆ x ), 2 � J + 1 q ⎩ J ≥ 1 � �� M J ∥⟩ ∗ ν − ⃗ 2 ℜ⟨∥ ˆ E J ∥⟩⟨∥ ˆ ± ˆ q · ˆ β J ≥ 1 �� ⃗ �� �� � ν · ⃗ L J ∥⟩ | 2 | ⟨∥ ˆ � ˆ 1 − ˆ ν · ˆ β · ˆ + β + 2 q q J ≥ 0 � � ν · ⃗ | ⟨∥ ˆ C J ∥⟩ | 2 + 1 + ˆ β � � L J ∥⟩ ∗ �� ν + ⃗ ℜ⟨∥ ˆ C J ∥⟩⟨∥ ˆ − 2 ˆ ˆ q · (4) β , We have similar expressions for Tensor and Scalar structures, and interferences.[Glick-Magid, Gazit, unpublished]

11 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS Δ𝐾 ) = 0,1 + e.g., allowed transitions d ! V − A = 4 1 ⇡ 2 k ✏ ( W 0 − ✏ ) 2 d ✏ d Ω k d Ω ⌫ 2 J i + 1 · 4 ⇡ 4 ⇡ Fermi 2 8 | C V | 2 + � � 0 � C � � > 2 V < ⌘ � � � E� ⇣ D � � ˆ ⌫ · ~ C V · 1 + ˆ � J f � J i � � � � 0 2 � � > : Gamow-Teller 2 9 | C A | 2 + � � 0 � C � � > ✓ 1 − 1 ◆ � 2 A � � E� = D � ⌫ · ~ � ˆ L A + 3 3 ˆ + O ( q ) � J f � J i � � � � 1 2 � � > ; Correlation coefficient ⇣ Assumptions: vanishing momentum transfer (q=0).

12 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS Δ𝐾 ) = 0,1 + e.g., allowed transitions V+T d ! V − A = 4 1 ⇡ 2 k ✏ ( W 0 − ✏ ) 2 d ✏ d Ω k d Ω ⌫ 2 J i + 1 · 4 ⇡ 4 ⇡ 2 8 | C V | 2 + � � 0 � C � � > 2 V < ⌘ � � � E� ⇣ D � � ˆ ⌫ · ~ C V · 1 + ˆ � J f � J i � � � � 0 2 Assuming V+T structure � � > : 2 9 + 𝐷 E F + 𝐷 E | C A | 2 + � � G F 0 � C � � > ✓ 1 − 1 ◆ � 2 A � � E� = D � ⌫ · ~ � ˆ L A + + 3 3 ˆ + O ( q ) � J f � J i � � � � 2 1 2 � � > ; ⇣

13 PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS e.g., allowed transitions V-A WITH T CORRECTIONS: (Gamow–Teller decays), � ∝ ( 1 + bm e ϵ + a β ν ⃗ ν ) ⟨∥ β · ˆ where m is the electron 1 − | C T | 2 +| C ′ C T + C ′ T | 2 − 1 a β ν ≈ � � T , and b = 2 3 | C A | 2 C A the relative strength of the tensor (pseudo-t Caveats: a) Sensitive to combination of tensor couplings, with spectrum averaging of energy, thus in a specific nucleus – the sensitivity to BSM couplings is QUADRATIC… b) Spectrum, i.e., integration over angle, sensitive to Fierz term, i.e., insensitive to fully right handed couplings. [14] M. González-Alonso, O. Naviliat-Cuncic, Kinematic sensitivity to the Fierz term of β -decay differential spectra, Phys. Rev. C 94 (2016) 035503. [15] B.R.

� PRECISION B -DECAY STUDIES TO PINPOINT BSM EFFECTS Unique first forbidden Δ𝐾 ) = 2 / � ( q , ⃗ β · ˆ ν ) ⎧ �� ⃗ � J ⎨ � ��� E J ∥⟩ | 2 + | ⟨∥ ˆ M J ∥⟩ | 2 � | ⟨∥ ˆ � ˆ � 1 − ν · ˆ β · ˆ ∝ 𝑟 ? = q q � 2 � J + 1 ˆ x ) ˆ d ⃗ J 0 ( ⃗ x j J ( qx ) Y J M ( ˆ C J M ( q ) = x ) 14 ⎩ J ≥ 1 � �� M J ∥⟩ ∗ ν − ⃗ 2 ℜ⟨∥ ˆ E J ∥⟩⟨∥ ˆ ∝ 𝑟 ?/3 ± ˆ E J M ( q ) = 1 � q · ˆ β x ) ] · ˆ x ⃗ ∇ × [ j J ( qx ) ⃗ ⃗ ˆ d ⃗ J ( ⃗ Y J J M ( ˆ x ) J ≥ 1 q �� ⃗ �� �� � ν · ⃗ � | ⟨∥ ˆ L J ∥⟩ | 2 � ˆ ∝ 𝑟 ? 1 − ˆ + β + 2 ν · ˆ β · ˆ x ) · ˆ q q x j J ( qx ) ⃗ ⃗ ˆ d ⃗ J ( ⃗ M J M ( q ) = Y J J M ( ˆ x ) J ≥ 0 L J M ( q ) = i � � � 𝑲 ν · ⃗ x ) ] · ˆ | ⟨∥ ˆ C J ∥⟩ | 2 1 + ˆ x ⃗ ⃗ + ˆ β M 𝑲𝑵 d ⃗ J ( ⃗ ∇ [ j J ( qx ) Y J M ( ˆ ≈ 𝑭 x ), 𝑲 + 𝟐 q � � L J ∥⟩ ∗ �� ν + ⃗ ℜ⟨∥ ˆ C J ∥⟩⟨∥ ˆ − 2 ˆ q · ˆ (4) β , C T + C ′ m e � ( q , ⃗ T ν ) ∝ 1 ± 2 γ 0 β · ˆ ϵ C A 1 − | C T | 2 + | C ′ T | 2 �� ⃗ − 1 ν · ⃗ � � ˆ � � ˆ ��� � − ν · ˆ β · ˆ 2 β q q . | C A | 2 5 (11) Glick-Magid, DG, et al, Beta spectrum of unique first forbidden decays as a novel test for fundamental symmetries, Phys. Lett. B767, 285 (2017)