Radiative corrections to Gamow-Teller transitions Leendert Hayen - - PowerPoint PPT Presentation

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 Vud calculation

Neutron is extremely well-studied system, ideal system for Vud |Vud|2τn

• fV + 3fAλ2

= 2π3 G 2

Fm5 eg2 V

1 1 + RC

2

Neutron Vud calculation

Neutron is extremely well-studied system, ideal system for Vud |Vud|2τn

• fV + 3fAλ2

= 2π3 G 2

Fm5 eg2 V

1 1 + RC From β decay perspective, need 3 things

• Neutron lifetime

2

Neutron Vud calculation

Neutron is extremely well-studied system, ideal system for Vud |Vud|2τn

• fV + 3fAλ2

= 2π3 G 2

Fm5 eg2 V

1 1 + RC From β decay perspective, need 3 things

• Neutron lifetime
• λ

2

Neutron Vud calculation

Neutron is extremely well-studied system, ideal system for Vud |Vud|2τn

• fV + 3fAλ2

= 2π3 G 2

Fm5 eg2 V

1 1 + RC From β decay perspective, need 3 things

• Neutron lifetime
• λ
• Theory calculations for fV ,A and RC

2

Neutron Vud calculation

Neutron is extremely well-studied system, ideal system for Vud |Vud|2τn

• fV + 3fAλ2

= 2π3 G 2

Fm5 eg2 V

1 1 + RC From β decay perspective, need 3 things

• Neutron lifetime
• λ
• Theory calculations for fV ,A and RC

Clearly, all trivial things

2

Neutron Vud calculation

Major decades-long community efforts

UCNA, Phys Rev C 97 (2018) 035505 3

Neutron Vud calculation

Major decades-long community efforts

4

Radiative corrections to GT

Neutron Vud calculation

Well, at least fV ,A are well-known, right? RIGHT?

5

Neutron Vud calculation

Well, at least fV ,A are well-known, right? RIGHT? Seminal work by Wilkinson in 1982, exhaustively listed all corrections: found ∆fV ,A ≃ 10−6, fV = 1.6887(2)

5

Neutron Vud calculation

Well, at least fV ,A are well-known, right? RIGHT? Seminal work by Wilkinson in 1982, exhaustively listed all corrections: found ∆fV ,A ≃ 10−6, fV = 1.6887(2) One particular case appears forgotten, however...

5

Neutron Vud calculation

Recap: p|V µ|n = ¯ p

• gV γµ + gM − gV

2M σµνqν + i gS 2M qµ

• n

6

Neutron Vud calculation

Recap: p|V µ|n = ¯ p

• gV γµ + gM − gV

2M σµνqν + i gS 2M qµ

• n

gives rise to spectrum shape contribution dN dWe wm ∝ 4 3M gM gAMGT peWe(W0 − We)2 ×

• We − W0

2 − m2

e

2We

• represents vector-axial vector spacelike cross term

6

Neutron Vud calculation

Recap: p|V µ|n = ¯ p

• gV γµ + gM − gV

2M σµνqν + i gS 2M qµ

• n

gives rise to spectrum shape contribution dN dWe wm ∝ 4 3M gM gAMGT peWe(W0 − We)2 ×

• We − W0

2 − m2

e

2We

• represents vector-axial vector spacelike cross term

However cross terms do not contribute to decay rate!

6

Neutron Vud calculation

Recap: p|V µ|n = ¯ p

• gV γµ + gM − gV

2M σµνqν + i gS 2M qµ

• n

gives rise to spectrum shape contribution dN dWe wm ∝ 4 3M gM gAMGT peWe(W0 − We)2 ×

• We − W0

2 − m2

e

2We

• 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 Vud calculation

V -A cross terms contribute due to Coulomb interaction, i.e. O(αZ)

7

Neutron Vud calculation

V -A cross terms contribute due to Coulomb interaction, i.e. O(αZ) Leads to Wilkinson’s result, ∆fwm ∼ 10−6 for neutron

7

Neutron Vud calculation

V -A cross terms contribute due to Coulomb interaction, i.e. O(αZ) Leads to Wilkinson’s result, ∆fwm ∼ 10−6 for neutron There is one more thing: Coulomb corrections on weak magnetism gives non-negligible terms O(αZ/MR) besides expected O(αZ(q/M)qR) fA fV = 1 + 4 5 αZ MR gM gA = 1.0040(2) 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 5 αZ MR gM gA

8

Interpretation

Addition is constant term in spectrum shape ∆ dN dW ∝ 4 5 αZ MR gM gA Two observations:

• Almost constant for all Z

8

Interpretation

Addition is constant term in spectrum shape ∆ dN dW ∝ 4 5 αZ MR gM gA 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 |Vud|2τnfV

• 1 + 3λ2

eff

• =

2π3 G 2

Fm5 eg2 V

1 1 + RC

9

Usual theory & experiment analysis

Rewriting this in the usual way for the neutron |Vud|2τnfV

• 1 + 3λ2

eff

• =

2π3 G 2

Fm5 eg2 V

1 1 + RC Experiments measure λeff , difference in counting rates and “A′′

exp = −2(λ2 − |λ|)

1 + 3λ2

9

Usual theory & experiment analysis

Rewriting this in the usual way for the neutron |Vud|2τnfV

• 1 + 3λ2

eff

• =

2π3 G 2

Fm5 eg2 V

1 1 + RC Experiments measure λeff , difference in counting rates and “A′′

exp = −2(λ2 − |λ|)

1 + 3λ2 which is fine, however. . .

9

Consequences

Vud analysis in mirror systems

Use mirror T = 1/2 systems because MF = 1, mixed F-GT Ftmirror = 2Ft0+→0+ 1 + fA

fV ρ2 10

Vud analysis in mirror systems

Use mirror T = 1/2 systems because MF = 1, mixed F-GT Ftmirror = 2Ft0+→0+ 1 + fA

fV ρ2

where ρ = CAMGT CV MF (1 + δA)(1 + ∆A

R)

(1 + δV )(1 + ∆V

R )

1/2

10

Vud analysis in mirror systems

Use mirror T = 1/2 systems because MF = 1, mixed F-GT Ftmirror = 2Ft0+→0+ 1 + fA

fV ρ2

where ρ = CAMGT CV MF (1 + δA)(1 + ∆A

R)

(1 + δV )(1 + ∆V

R )

1/2

• ne assumes

ρ ≈ CAMGT CV MF and measured experimentally

Severijns et al., PRC 78 (2008) 055501 10

Vud analysis in mirror systems

Experimental measurement of ρ includes EM renormalization, but

11

Vud analysis in mirror systems

Experimental measurement of ρ includes EM renormalization, but for the mirror analysis, the EM renormalization is also included in fA/fV : double counting

11

Vud analysis in mirror systems

Experimental measurement of ρ includes EM renormalization, but for the mirror analysis, the EM renormalization is also included in fA/fV : double counting Direct consequence: fA/fV for mirrors will decrease, effect on Vud differs per transition (size of ρ)

11

Vud analysis in mirror systems

Experimental measurement of ρ includes EM renormalization, but for the mirror analysis, the EM renormalization is also included in fA/fV : double counting Direct consequence: fA/fV for mirrors will decrease, effect on Vud differs per transition (size of ρ) Generally: Vud from mirrors will increase O(0.1%), currently V 0+→0+

ud

= 0.9740(2) V mirror

ud

= 0.9727(14)

11

Comparison to lattice QCD

In the usual analysis, ∆V

R is assumed to encapsulate all E-indep RC

− → invites comparison to gLQCD

A 12

Comparison to lattice QCD

In the usual analysis, ∆V

R is assumed to encapsulate all E-indep RC

− → invites comparison to gLQCD

A

Used to put limits on RH currents via ˜ gA = gQCD

A

(1 − 2Re ǫR)

12

Comparison to lattice QCD

In the usual analysis, ∆V

R is assumed to encapsulate all E-indep RC

− → invites comparison to gLQCD

A

Used to put limits on RH currents via ˜ gA = gQCD

A

(1 − 2Re ǫR) Current precision of lattice O(1%) → uncertainty on ǫR ∼ O(0.5%)

12

Comparison to lattice QCD

Current status: Additional 0.4% RC causes nearly 100% shift!

13

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 ∆ dN dW ∝ ±2 5 αZ MRc1 (±2b + d) where b/Ac1 is weak magnetism, dAc1 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 ∆ dN dW ∝ ±2 5 αZ MRc1 (±2b + d) where b/Ac1 is weak magnetism, dAc1 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 gA, currently neutron Vud is insensitive

15

Conclusions

Additional RC to axial current only, O(0.4%) Renormalization of gA, currently neutron Vud is insensitive Double counting does occur in mirror V ud, result will go up → better agreement with superallowed

15

Conclusions

Additional RC to axial current only, O(0.4%) Renormalization of gA, currently neutron Vud is insensitive Double counting does occur in mirror V ud, result will go up → better agreement with superallowed Comparison of gA with lattice, expect 0.4% difference, strong consequences for ǫR

15

Conclusions

Additional RC to axial current only, O(0.4%) Renormalization of gA, currently neutron Vud is insensitive Double counting does occur in mirror V ud, result will go up → better agreement with superallowed Comparison of gA with lattice, expect 0.4% difference, strong consequences for ǫR Work being done to investigate further, better ab initio calculations

15