Radiative corrections to Gamow-Teller transitions Leendert Hayen ACFI Workshop, May 16th 2019 IKS, KU Leuven, Belgium
Introduction
Thanks Great thanks to Misha Gorshteyn and Vincenzo Cirigliano @ ECT* April 2019 1
Neutron V ud calculation Neutron is extremely well-studied system, ideal system for V ud 2 π 3 1 | V ud | 2 τ n f V + 3 f A λ 2 � � = G 2 F m 5 e g 2 1 + RC V 2
Neutron V ud calculation Neutron is extremely well-studied system, ideal system for V ud 2 π 3 1 | V ud | 2 τ n f V + 3 f A λ 2 � � = G 2 F m 5 e g 2 1 + RC V From β decay perspective, need 3 things • Neutron lifetime 2
Neutron V ud calculation Neutron is extremely well-studied system, ideal system for V ud 2 π 3 1 | V ud | 2 τ n f V + 3 f A λ 2 � � = G 2 F m 5 e g 2 1 + RC V From β decay perspective, need 3 things • Neutron lifetime • λ 2
Neutron V ud calculation Neutron is extremely well-studied system, ideal system for V ud 2 π 3 1 | V ud | 2 τ n f V + 3 f A λ 2 � � = G 2 F m 5 e g 2 1 + RC V From β decay perspective, need 3 things • Neutron lifetime • λ • Theory calculations for f V , A and RC 2
Neutron V ud calculation Neutron is extremely well-studied system, ideal system for V ud 2 π 3 1 | V ud | 2 τ n f V + 3 f A λ 2 � � = G 2 F m 5 e g 2 1 + RC V From β decay perspective, need 3 things • Neutron lifetime • λ • Theory calculations for f V , A and RC Clearly, all trivial things 2
Neutron V ud calculation Major decades-long community efforts UCNA, Phys Rev C 97 (2018) 035505 3
Neutron V ud calculation Major decades-long community efforts 4
Radiative corrections to GT
Neutron V ud calculation Well, at least f V , A are well-known, right? RIGHT? 5
Neutron V ud calculation Well, at least f V , A are well-known, right? RIGHT? Seminal work by Wilkinson in 1982, exhaustively listed all corrections: found ∆ f V , A ≃ 10 − 6 , f V = 1 . 6887(2) 5
Neutron V ud calculation Well, at least f V , A are well-known, right? RIGHT? Seminal work by Wilkinson in 1982, exhaustively listed all corrections: found ∆ f V , A ≃ 10 − 6 , f V = 1 . 6887(2) One particular case appears forgotten, however... 5
Neutron V ud calculation Recap: � g V γ µ + g M − g V σ µν q ν + i g S � � p | V µ | n � = ¯ 2 M q µ p n 2 M 6
Neutron V ud calculation Recap: � g V γ µ + g M − g V σ µν q ν + i g S � � p | V µ | n � = ¯ 2 M q µ p n 2 M gives rise to spectrum shape contribution � d N � wm 4 g M p e W e ( W 0 − W e ) 2 ∝ d W e 3 M g A M GT 2 − m 2 � W e − W 0 � e × 2 W e represents vector-axial vector spacelike cross term 6
Neutron V ud calculation Recap: � g V γ µ + g M − g V σ µν q ν + i g S � � p | V µ | n � = ¯ 2 M q µ p n 2 M gives rise to spectrum shape contribution � d N � wm 4 g M p e W e ( W 0 − W e ) 2 ∝ d W e 3 M g A M GT 2 − m 2 � W e − W 0 � e × 2 W e represents vector-axial vector spacelike cross term However cross terms do not contribute to decay rate! 6
Neutron V ud calculation Recap: � g V γ µ + g M − g V σ µν q ν + i g S � � p | V µ | n � = ¯ 2 M q µ p n 2 M gives rise to spectrum shape contribution � d N � wm 4 g M p e W e ( W 0 − W e ) 2 ∝ d W e 3 M g A M GT 2 − m 2 � W e − W 0 � e × 2 W e represents vector-axial vector spacelike cross term However cross terms do not contribute to decay rate! Except... Weinberg, Phys Rev 115 (1959) 481 6
Neutron V ud calculation V - A cross terms contribute due to Coulomb interaction, i.e. O ( α Z ) 7
Neutron V ud calculation V - A cross terms contribute due to Coulomb interaction, i.e. O ( α Z ) Leads to Wilkinson’s result, ∆ f wm ∼ 10 − 6 for neutron 7
Neutron V ud calculation V - A cross terms contribute due to Coulomb interaction, i.e. O ( α Z ) Leads to Wilkinson’s result, ∆ f wm ∼ 10 − 6 for neutron There is one more thing: Coulomb corrections on weak magnetism gives non-negligible terms O ( α Z / MR ) besides expected O ( α Z ( q / M ) qR ) = 1 + 4 α Z f A g M = 1 . 0040(2) 5 f V MR g A Plot twist! Wilkinson Nucl Phys A 377 (1982) 474; Bottino et al. Phys Rev C 9 (1974) 2052; Holstein Phys Rev C 10 (1974) 1215 7
Interpretation Addition is constant term in spectrum shape ∆ dN dW ∝ 4 α Z g M 5 MR g A 8
Interpretation Addition is constant term in spectrum shape ∆ dN dW ∝ 4 α Z g M 5 MR g A Two observations: • Almost constant for all Z 8
Interpretation Addition is constant term in spectrum shape ∆ dN dW ∝ 4 α Z g M 5 MR g A Two observations: • Almost constant for all Z • Implies EM renormalization specifically to Gamow-Teller decays which is so far not included 8
Usual theory & experiment analysis Rewriting this in the usual way for the neutron 2 π 3 1 | V ud | 2 τ n f V 1 + 3 λ 2 � � = eff G 2 e g 2 F m 5 1 + RC V 9
Usual theory & experiment analysis Rewriting this in the usual way for the neutron 2 π 3 1 | V ud | 2 τ n f V 1 + 3 λ 2 � � = eff G 2 e g 2 F m 5 1 + RC V Experiments measure λ eff , difference in counting rates and exp = − 2( λ 2 − | λ | ) “ A ′′ 1 + 3 λ 2 9
Usual theory & experiment analysis Rewriting this in the usual way for the neutron 2 π 3 1 | V ud | 2 τ n f V 1 + 3 λ 2 � � = eff G 2 e g 2 F m 5 1 + RC V Experiments measure λ eff , difference in counting rates and exp = − 2( λ 2 − | λ | ) “ A ′′ 1 + 3 λ 2 which is fine, however . . . 9
Consequences
V ud analysis in mirror systems Use mirror T = 1 / 2 systems because M F = 1, mixed F-GT F t mirror = 2 F t 0 + → 0 + 1 + f A f V ρ 2 10
V ud analysis in mirror systems Use mirror T = 1 / 2 systems because M F = 1, mixed F-GT F t mirror = 2 F t 0 + → 0 + 1 + f A f V ρ 2 where � (1 + δ A )(1 + ∆ A � 1 / 2 ρ = C A M GT R ) (1 + δ V )(1 + ∆ V C V M F R ) 10
V ud analysis in mirror systems Use mirror T = 1 / 2 systems because M F = 1, mixed F-GT F t mirror = 2 F t 0 + → 0 + 1 + f A f V ρ 2 where � (1 + δ A )(1 + ∆ A � 1 / 2 ρ = C A M GT R ) (1 + δ V )(1 + ∆ V C V M F R ) one assumes ρ ≈ C A M GT C V M F and measured experimentally Severijns et al. , PRC 78 (2008) 055501 10
V ud analysis in mirror systems Experimental measurement of ρ includes EM renormalization, but 11
V ud analysis in mirror systems Experimental measurement of ρ includes EM renormalization, but for the mirror analysis, the EM renormalization is also included in f A / f V : double counting 11
V ud analysis in mirror systems Experimental measurement of ρ includes EM renormalization, but for the mirror analysis, the EM renormalization is also included in f A / f V : double counting Direct consequence: f A / f V for mirrors will decrease, effect on V ud differs per transition (size of ρ ) 11
V ud analysis in mirror systems Experimental measurement of ρ includes EM renormalization, but for the mirror analysis, the EM renormalization is also included in f A / f V : double counting Direct consequence: f A / f V for mirrors will decrease, effect on V ud differs per transition (size of ρ ) Generally: V ud from mirrors will increase O (0 . 1%), currently V 0 + → 0 + = 0 . 9740(2) ud V mirror = 0 . 9727(14) ud 11
Comparison to lattice QCD In the usual analysis, ∆ V R is assumed to encapsulate all E-indep RC → invites comparison to g LQCD − A 12
Comparison to lattice QCD In the usual analysis, ∆ V R is assumed to encapsulate all E-indep RC → invites comparison to g LQCD − A Used to put limits on RH currents via g A = g QCD ˜ (1 − 2Re ǫ R ) A 12
Comparison to lattice QCD In the usual analysis, ∆ V R is assumed to encapsulate all E-indep RC → invites comparison to g LQCD − A Used to put limits on RH currents via g A = g QCD ˜ (1 − 2Re ǫ R ) A Current precision of lattice O (1%) → uncertainty on ǫ R ∼ O (0 . 5%) 12
Comparison to lattice QCD Current status: 13 Additional 0 . 4% RC causes nearly 100% shift!
Radiative GT corrections There is now an additional RC which is not included in ∆ R V for GT decays 14
Radiative GT corrections There is now an additional RC which is not included in ∆ R V for GT decays More generally, based on “old” approach dW ∝ ± 2 α Z ∆ dN ( ± 2 b + d ) 5 MRc 1 where b / Ac 1 is weak magnetism, d A c 1 is induced tensor (0 for isospin multiplet decays) 14
Radiative GT corrections There is now an additional RC which is not included in ∆ R V for GT decays More generally, based on “old” approach dW ∝ ± 2 α Z ∆ dN ( ± 2 b + d ) 5 MRc 1 where b / Ac 1 is weak magnetism, d A c 1 is induced tensor (0 for isospin multiplet decays) What else is missing? Interest & work together with Misha and Vincenzo 14
Conclusions
Conclusions Additional RC to axial current only , O (0 . 4%) 15
Conclusions Additional RC to axial current only , O (0 . 4%) Renormalization of g A , currently neutron V ud is insensitive 15
Conclusions Additional RC to axial current only , O (0 . 4%) Renormalization of g A , currently neutron V ud is insensitive Double counting does occur in mirror V ud , result will go up → better agreement with superallowed 15
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