1. Neutron Decay Electroweak Radiative Corrections Preliminary Update
(Implications for the neutron lifetime puzzle)
Czarnecki, WJM & A. Sirlin
Response to Dispersion Relations Results
Seng, Gorchtein, Patel & Ramsey-Musolf PRL
Hardy Fest 2019
William J. Marciano
January 7, 2019

2. John Hardy Celebration
More than 50 years of Research and Leadership
Distinguished Professor
Famous Collaboration with Ian Towner
Experimentalist + Theorist Combo
Champions of Superallowed Beta Decays
Many Honors: Bonner Prize etc.
Authority on Vud = (21) (2018 PDG)
Will it Survive?
“I come to praise Caesar, not to bury him”

3. Beta decay npeν Wγ Box Seng, Gorchtein, Patel & Ramsey-Musolf Dispersion Relations come to beta decay Congratulations: Major Development ΔRV= (38)  (22) Vud= (21)  (15) lasting?

4. Seng, Gorchtein, Patel & Ramsey–Musolf PRL (2018)
“Reduced Hadronic Uncertainties in the determination of Vud” Radiative Corrections: Axial Induced part via Dispersion Relation. Claim our RC= (38)  (22) |Vud|= (21)  (14) |Vud|2+|Vus|2 =0.9994(4)(2)0.9984(3)(2) 4 sigma deviation from unitarity

5. Work in Progress with A. Czarnecki & A. Sirlin
Radiative Corrections to Neutron Decay
Preliminary Unsanctioned Update
MS(2006) SGPR-M(2018) CMS(2019)
RC = 3.89(4)% (2)% (3)%
Vud = (21) (14) (18)
( )* ( )*
*Seng, Gorchtein, Ramsey-Musolf Nuclear Quenching
My Guess Vud= (13), n = 878.2(7)sec
Based on Vus via Kμ2/πμ2 (very clean theory)

6. Electroweak Radiative Corrections to Neutron Beta Decay
Include Virtual Corrections + Inclusive Bremsstrahlung
Normalize using G from the muon lifetime
Absorbs Ultraviolet Divergences & some finite parts
1/n= fG2|Vud|2me5(1+3gA2)(1+RC)/23
f=1.6887(1) (Includes Fermi Function etc. not Rad. Corr.)
RC calculated for (Conserved) Vector Current.
Same RC used to define gA: [A(gA)=(1.001)Aexp]
RC=/2[<g(Em)>+3ln(mZ/mp)+ln(mZ/mA)+2C+AQCD]
+ higher order O(/)2
g(Ee)=Universal Sirlin Function from Vector Current
A. Sirlin, PRD 164, 1767 (1967).

7. Next to leading short distance logs ~ -0.0001,
/2 <g(Em= MeV)>= long distance loops and brem.
averaged over the decay spectrum. Independent of Strong Int. up to O(Ee/mP)
g(Ee) also applies to Nuclei A. Sirlin (1967) Uncertainty < 10-5
3/2ln(mZ/mp) short-distance (Vector) log not renormalized by strong int.
[/2[ln(mZ/mA)+2C+AQCD] Induced by axial-current loop
Includes hadronic uncertainty
mA=1.2GeV long/short distance matching scale (factor 2 mA unc.)
C=0.8gA(N+P)=0.891 (long distance W Box diagram) WJM&A.Sirlin(1986)
AQCD= -s/(ln(mZ/mA)+cons)= QCD Correction
[/ln(mZ/m)]n leading logs summed via renormalization group, ( )
Next to leading short distance logs ~ ,
and -2ln(mp/me)= estimated (for neutron decay)
Czarnecki, WJM, Sirlin (2004) 1+RC=1.0390(8) main unc. from mA
matching short and long distance W (VA) Box. Unc*. ±8x10-4
vs future (±0.1sec goal) n ±1.1x10-4 goal.
* Note, unc. cancels in neutron vs nuclear beta decays eg Vud

8. The Infamous W Box Diagram

9. 2006 Improvement WJM & A. Sirlin
1.) Use large NQCD Interpolator to connect long-short distances
3 Resonances & 3 Matching Conditions
2.) Relate neutron beta decay to Bjorken Sum Rule (NF=3)
1-s/ 1-s(Q2)/-3.583(s(Q2)/) (s(Q2)/)3
The extra QCD corrections lead to a matching between
short and long distance Born corrections at about Q2=(0.8GeV)2
Very little change in size of RC, but uncertainties reduced by a
factor of 2.!
(Both Prescriptions Agree)
1+RC= (8) (39) for Neutron Beta Decay
Reduction by 1.4x10-4 (Same for 0+0+ beta decays) .

10. RC Error Budget 1) Neglected Two Loop Effects: 0.0001 conservative
2) Long Distance /C~/ (0.75gA(N+P))=0.0020
Assumed Uncertainty 10% reasonable?
3) Long-Short Distance Loop Matching: 0.8GeV<Q<1.5GeV
100%   conservative?
Total RC Error  Vud=±
More Aggressive Analysis Vud=±
(1/2 conservative)
 only about 2xn goal of ±0.1sec. (well matched)

11. M&S2006(xα/π) S,G.P&R-M2018(xα/π)
Dispersion Relation Approach to Box Diagram Seng, Gorchtein, Patel & Ramsey-Musolf PRL
M&S2006(xα/π) S,G.P&R-M2018(xα/π)
Perturbation
Born (8) (5)
Interpolator (14) (7)
Total (16) (9)
1+RC (38) (22)
Universal RC (38) (22)

12. From: S,G,P,R-M

13. 2019 Update Czarnecki, WJM & Sirlin
1.) Relate neutron beta decay to Bjorken Sum Rule (NF=3)
1-s/ 1-s(Q2)/-3.583(s(Q2)/) (s(Q2)/)3
(s(Q2)/)4 (Baikov,Chetyrkin,Kuhn) 4 loops!
= 1 - αBj(Q2)/π physical coupling
perturbative
F(Q2) = 1/Q2( 1-Bj(Q2)/) for Q2>Q20 =1.125GeV2
non-perturbative Light Front Holography (LFH)
Bj(Q2)/ =exp(-Q2/Q20) Q2≤Q20 Bj(0)/ = 1 AdS
F(0)=1/Q20 =0.89GeV-2
The extra QCD correction leads to a matching between
short and long distance couplings at about Q2=1.125GeV2

14. Running QCD Coupling from Bj sum rule data Brodsky, Duer et al.

15. Running QCD Bj coupling

16. γW Box RC: Bj Function Approach 1
Q2 Domain Integral (xα/π)
0<Q2<Q New Effect
Q20<Q2<2.25GeV
2.25GeV2<Q2<∞
ZW Box
Born
Σ not Q0 sensitive Midway Total (New)
DR (2018)
MS (2006)

17. From: S,G,P,R-M

18. Integrand: Bj Function (red) vs DR(blue)

19. 2. Large Nc QCD Approach (new)
Infinite sum of Vector and Axial-Vector Resonances
Use 3 Resonances + 3 Matching Conditions
F(Q2) = __ A__ B C____
Q2+m2ρ Q2+m2A Q2+m2ρ’
mρ =0.776GeV mA =1.230GeV mρ’ =1.465GeV
1. Integral m2c- ∞ equals Bj Function Integral
2. No 1/Q4 terms in large Q2 limit
3. F(0) =3/4gA(κ2n/mn2-κ2p/mp2) GDH Sum Rule
≈ 0.30GeV (1/Nc0 large Nc limit)?

20. 3 Resonance Solution for F(0)=0.3GeV-2
B =
C =
Integral 0 –m2c=0.23α/π
Total =2.98α/π (close to 2006)
Average of 2 Approaches=3.02α/π
DR=3.26α/π

21. Update Summary and Implications
DR: 1 + RC= (38)  (22)
“New Physics” Hint or something else?
CMS Preliminary Update
Based on 4 loop Bj Function & Q2 integration to 0
Bj function F(0)=0.89GeV-2
1+RC = (30)
Large N 3 Resonances F(0)=0.30GeV-2
1+RC= (30)
Average (30) Vud=0.9740(11)(15)

22. 1. Difference with CMS only ~ 0.05%
Comments on DR Results
1. Difference with CMS only ~ 0.05%
2. Is ZW Box included? Added 0.01%
3. Validity of GLS sum rule low Q2 data
4. Possible Double Counting?
5. Born Uncertainty?
Alternative Issues with Bj & Interpolator?
Try method elsewhere
More complicated low Q2 behavior

24. Fornal-Grinstein Solution BR(ndark particles) ~ 1%
BR(npeν)=0.9999(7) (gA )
Total exotic n decay BR < 0.27% at 95%CL
For Fornal-Grinstein Solution to be valid, post
2002 gA asymmetry values from PERKEOII and
UCNA must be wrong (significant tension)
PerkeoIII BR(n”new physics”) < 0.10% 95%CL

25. Recent gA =1.2764(6) Perkeo III Result
Post 2002 gAave=1.2762(5)  n = 878.2(7)s Neutron Lifetime Problem nbeam =888.0(2.0)s ntrap=879.4(6)s Could Both Be Right? ntrap (ave)=879.4(6) good agreement BR(any exotic n decay)< 0.10% (95% C.L.) Requires “Creative” Theorists