Wilkinsons Corrections and Role of Pseudoscalar Interactions in - PowerPoint PPT Presentation

Wilkinson’s Corrections and Role of Pseudoscalar Interactions in Neutron Beta Decays Andrey N. Ivanov TU Wien Atominstitut, Austria Amhest Center for Fundamental Interactions 17 May 2019 /USA A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Wilkinson’s Corrections to Neutron Beta Decay D. H. Wilkinson, NPA 377, 474 (1982) Electron-energy and angular distribution d 5 λ ( W ) ( E e ,� k e ,� ν , � ξ n , � k ¯ ξ e ) n = dE e d Ω e d Ω ¯ ν = Q ( E e ,� k e ,� k ¯ ν , Z = 1 ) L ( E e , Z = 1 ) C ( E e , Z = 1 ) J ( Z = 1 ) K ( α ) × d 5 λ ( JTW ) ( E e ,� k e ,� ν , � ξ n , � ξ e ) k ¯ n dE e d Ω e d Ω ¯ ν J. D. Jackson, S. B. Treiman, and H. W. Wyld,Jr., PR 106, 517 (1957) A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Q ( E e ,� k e ,� k ¯ ν , Z = 1 ) - proton recoil correction to Fermi function F ( E e , Z = 1 ) Fermi function F ( E e , Z = 1 ) � 4 ( 2 r p m e β ) 2 γ e πα/β 1 + 1 1 + γ + i α 2 � � � �� F ( E e , Z = 1 ) = 2 γ � Γ � � Γ 2 ( 3 + 2 γ ) ( 1 − β 2 ) γ β � � 1 − α 2 − 1 γ = , r p = 0 . 841 fm Q ( E e , Z = 1 ) of order O ( α ) k e · � � Q ( E e , Z = 1 ) = 1 − πα M − πα E 0 − E e E e k ¯ ν β β 3 M E e E ¯ ν D. H. Wilkinson, NPA 377, 474 (1982) A. N. Ivanov, M. Pitschmann, and N. I. Troitskaya, PRD 88, 073002 (2013); arXiv: 1212.0332 [hep-ph], Appendix H A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Corrections for correlation coefficients caused by proton recoil contribution to Fermi function E e = 0 . 761 MeV δ X ( E e ) / X ( E e ) E e = 0 . 966 MeV − 2 . 5 × 10 − 5 − 2 . 8 × 10 − 5 ≥ δζ ( E e ) /ζ ( E e ) ≥ + 3 . 0 × 10 − 4 + 1 . 1 × 10 − 4 ≥ δ a ( E e ) / a ( E e ) ≥ − 6 . 3 × 10 − 7 − 3 . 5 × 10 − 7 ≤ δ A ( E e ) / A ( E e ) ≤ − 6 . 3 × 10 − 7 − 3 . 5 × 10 − 7 ≤ δ B ( E e ) / B ( E e ) ≤ + 9 . 0 × 10 − 5 + 3 . 5 × 10 − 5 ≥ δ A W ( E e ) / A W ( E e ) ≥ + 5 . 1 × 10 − 7 + 1 . 3 × 10 − 7 ≥ δ G ( E e ) / G ( E e ) ≥ − 6 . 3 × 10 − 7 − 3 . 5 × 10 − 7 ≤ δ N ( E e ) / N ( E e ) ≤ − 6 . 2 × 10 − 7 − 3 . 3 × 10 − 7 ≤ δ H ( E e ) / H ( E e ) ≤ + 5 . 0 × 10 − 4 + 1 . 9 × 10 − 4 ≥ δ K e ( E e ) / K e ( E e ) ≥ Table: Analytical expressions one may find in our papers: PRD88, 073002 (2013); arXiv: 1212.0332 [hep-ph], Appendix H; PRC95, 055502 (2017); arXiv:1705.07330 [hep-ph]; PRD99, 053004 (2019); arXiv:1905.01178 [hep-ph]. Correction to the neutron decay rate � ( 1 + δζ ( E e ) /ζ ( E e )) � = 1 − 2 . 7 × 10 − 5 . A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

L ( E e , Z = 1 ) - correction caused by a finite proton radius, r p = 0 . 841 fm : Pohl et al. , Nature466,213(2010) m 2 L ( E e , Z = 1 ) = 1 + 13 1 − 1 60 α 2 − α r p E e � � e = 2 E 2 e = 1 + 1 . 154 × 10 − 5 − 4 . 183 × 10 − 5 E e + 0 . 827 × 10 − 5 m e E 0 E e Correction to the neutron decay rate � L ( E e , Z = 1 ) � = 1 − 0 . 85 × 10 − 5 Correction to correlation coefficients δ X ( E e ) X ( E e ) = 1 − L ( E e , Z = 1 ) The correction, caused by the finite proton radius, is the same for all correlation coefficients and, correspondingly, is not important for asymmetries of the neutron beta decay. A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

C ( E e , Z = 1 ) - correction caused by lepton - nucleon convolution through a finite nucleon volume C ( E e , Z = 1 ) = 1 − 2 . 854 × 10 − 5 − 1 . 361 × 10 − 5 E 2 − 1 . 238 × 10 − 5 E e − 0 . 018 × 10 − 5 m e e E 2 E 0 E e 0 Correction to the neutron decay rate � C ( E e , Z = 1 ) � = 1 − 4 . 09 × 10 − 5 Correction to correlation coefficients δ X ( E e ) X ( E e ) = 1 − C ( E e , Z = 1 ) The correction, caused by the lepton–nucleon convolution, is the same for all correlation coefficients and is not important for asymmetries of the neutron beta decay The analytical expression for C ( E e , Z = 1 ) is given in our paper PRC95, 055502 (2017); arXiv:1705.07330 [hep-ph] A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

J ( Z = 1 ) - correction caused by outer radiative corrections of higher order in α J ( Z = 1 ) = + α 3 2 + π 2 + α 3 α 2 ℓ n M 3 ℓ n 2 − 3 ℓ n M 2 π ℓ n 2 M � � � � = 1 + m e π 3 m e m e 1 + α � − 1 � = = 1 + 3 . 5 × 10 − 4 2 π ¯ × g ( E 0 ) Correction to the neutron decay rate � J ( Z = 1 ) � = 1 + 3 . 5 × 10 − 4 Correction to correlation coefficients δ X ( E e ) X ( E e ) = 1 − J ( Z = 1 ) The correction, caused by the outer radiative corrections of higher order in α , is the same for all correlation coefficients and, correspondingly, is not important for asymmetries of the neutron beta decay. A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

K ( α ) represents various further electromagnetic corrections of order O ( α ) (H. D. Wilkinson) Wilkinson did not calculate K ( α ) . However, according to Wilkinson NPA377, 474 (1982), one may expect that K ( α ) should contain, for example, the radiative correction ∆ V R , i.e. K ( α ) = 1 + ∆ V R , calculated by W. J. Marciano and A. Sirlin, PRL56, 22 (1986) A. Czarnecki, W. J. Marciano, and A. Sirlin, PRD70, 093006 (2004) W. J. Marciano and A. Sirlin, PRL96, 032002 (2006) Ch.-Y. Seng, M. Gorchtein, H. H. Patel, and M. J. Ramsey-Musolf, PRL121, 241804 (2018) Ch.-Y. Seng, M. Gorchtein, and M. J. Ramsey-Musolf, arXiv:1812.03352 [nucl-th] A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Wilkinson’s Correction to Neutron Decay Rate Wilkinson’s total correction to the neutron decay rate � Q ( E e ,� k e ,� k ¯ ν , Z = 1 ) L ( E e , Z = 1 ) C ( E e , Z = 1 ) J ( Z = 1 ) � = = 1 + 2 . 7 × 10 − 4 Thus, one may assert that Wilkinson’s total correction to the neutron decay rate can, in principle, change a digit at the fourth decimal place of the value of the neutron decay rate A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Role of Pseudoscalar SM and beyond the SM Interactions in Neutron Beta Decay Amplitude of the neutron beta decay with contributions of pseudoscalar SM and beyond the SM interactions M ( n → pe − ¯ ν e ) = = − G F γ µ ( 1 + λγ 5 ) + κ 2 M λ q µ �� � 2 M i σ µν q ν + π − q 2 − i 0 γ 5 � � ¯ √ V ud u p u n m 2 2 �� u e ( C p + ¯ u e γ µ ( 1 − γ 5 ) v ¯ u p γ 5 u n C P γ 5 ) v ¯ � ¯ � � ¯ � � ¯ × + ν ν The contribution of the one-pion-pole exchange is required by conservation of the charged axial-vector hadronic current in the chiral limit m π → 0: Y. Nambu, PRL 4, 380 (1960). The last term is given by J. D. Jackson, S. B. Treiman, and H. W. Wyld,Jr., PR 106, 517 (1957) A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Corrections to Electron-Energy and Angular Distribution: Ivanov et al. ; arXiv:1905.04147 [hep-ph] d 5 δλ n ( E e ,� k e ,� ν , � ξ n , � k ¯ ξ e ) = dE e d Ω e d Ω ¯ ν = ( 1 + 3 λ 2 ) G 2 F | V ud | 2 � ( E 0 − E e ) 2 E 2 e − m 2 e E e F ( E e , Z = 1 ) 32 π 5 � k e · � � ξ e · � λ E 0 − E e m e + λ m e k ¯ − λ m e k e � � � � ν × C ps + . . . + . . . E 0 E e E 0 E e E ¯ E 0 E e ν ξ e · ( � k e × � ξ n · � � ν )( � − E e k ¯ k e ) � �� + C ′ + . . . ps E 0 E 2 e E ¯ ν 2 λ m e E 0 − E 0 � � 4 M Re ( C P − ¯ C ps = C P ) = 1 + 3 λ 2 m 2 π = − 1 . 47 × 10 − 5 − 1 . 17 × 10 − 4 Re ( C P − ¯ C P ) 1 E 0 2 M Im ( C P − ¯ C P ) = − 1 . 17 × 10 − 4 Im ( C P − ¯ C ′ ps = − C P ) 1 + 3 λ 2 A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

Contribution of Pseudoscalar SM and Beyond the SM Interactions to Neutron Decay Rate Fierz-like interference term E 0 − E e m e �� �� 1 + λ C ps = 1 − 0 . 33 C ps E 0 E e C ps = − 1 . 47 × 10 − 5 − 1 . 17 × 10 − 4 Re ( C P − ¯ C P ) λ = − 1 . 27641 ( 56 ) , B. Märkisch et al. : arXiv: 1812.04666 [nucl-ex] The Fierz-like interference term, caused by the contribution of the pseudoscalar interaction beyond the SM only, was calculated by M. González-Alonso and J. M. Camalich, PRL112, 042501 (2014); arXiv: 1309.4434 [hep-ph]. A complete set of corrections to all correlation coefficients and the electron-energy and angular distribution one may find in our paper arXiv:1905.04147 [hep-ph] A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity

CKM Matrix Element V ud from Neutron Beta Decay V ud from the neutron beta decay � 5099 . 81 | V ud | = τ n ( 1 + ∆ R )( 1 + 2 . 7 × 10 − 4 ) W ( 1 − 0 . 33 C ps ) ∆ R = α g ( E 0 ) + ∆ V 2 π ¯ R 0 . 127 + Re ( C P − ¯ 0 . 33 C ps = − 3 . 86 × 10 − 5 � � C P ) Neutron beta decay: V ud = 0 . 97370 ( 14 ) Ch.-Y. Seng, M. Gorchtein, H. H. Patel, and M. J. Ramsey-Musolf, PRL121, 241804 (2018) Ch.-Y. Seng, M. Gorchtein, and M. J. Ramsey-Musolf, arXiv:1812.03352 [nucl-th] Thus, one may assert that Wilkinson’s corrections and pseudoscalar interactions can, in principle, change digits at the fourth and fifth decimal places of the V ud value A. N. Ivanov Current and Future Status of the First-Row CKM Unitarity