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Neutron Decay Electroweak Radiative Corrections Preliminary Update

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

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Neutron Decay Electroweak Radiative Corrections Preliminary Update

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  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 = 0.97420(21)(2018 PDG) Will it Survive? “I come to praise Caesar, not to bury him”

  3. Beta decay npeν Wγ BoxSeng, Gorchtein, Patel & Ramsey-MusolfDispersion Relations come to beta decayCongratulations: Major DevelopmentΔRV=0.02361(38)  0.02467(22)Vud=0.97420(21)  0.97370(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=0.02361(38)  0.02467(22) |Vud|=0.97420(21)  0.97370(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)% 3.99(2)% 3.93(3)% Vud = 0.97420(21) 0.97370(14) 0.97400(18) (0.97392)* (0.97422)* *Seng, Gorchtein, Ramsey-MusolfNuclear Quenching My Guess Vud=0.97425(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. /2 <g(Em=1.292579MeV)>=0.015056 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 notrenormalized 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)=-0.34 QCD Correction [/ln(mZ/m)]n leading logs summed via renormalization group, (+0.0016) Next to leading short distance logs ~ -0.0001, and -2ln(mp/me)=-0.00043 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)/)2-20.212(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= 1.0390(8)1.03886(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%0.0002 reasonable? 3) Long-Short Distance Loop Matching: 0.8GeV<Q<1.5GeV 100%  0.0003 conservative? Total RC Error 0.00038 Vud=±0.00019 More Aggressive Analysis Vud=±0.00013 (1/2 conservative)  only about 2xn goal of ±0.1sec. (well matched)

  11. Dispersion Relation Approach to Box DiagramSeng, Gorchtein, Patel & Ramsey-Musolf PRL M&S2006(xα/π) S,G.P&R-M2018(xα/π) Perturbation 1.85 1.87 Born 0.83(8) 0.91(5) Interpolator 0.14(14) 0.48(7) Total 2.82(16) 3.26(9) 1+RC 1.03886(38) 1.03992(22) Universal RC 0.02361(38) 0.02467(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)/)2-20.212(s(Q2)/)3 -175.7(s(Q2)/)4 (Baikov,Chetyrkin,Kuhn) 4 loops! = 1 - αBj(Q2)/πphysical 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<Q20 0.20 New Effect Q20<Q2<2.25GeV2 0.125 2.25GeV2<Q2<∞ 1.83 ZW Box 0.06 Born 0.856 Σ not Q0 sensitiveMidway 3.07 Total (New) 3.32 DR (2018) 2.82 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-2 (1/Nc0 large Nc limit)?

  20. 3 Resonance Solution for F(0)=0.3GeV-2 • A =-1.0603 • B =+5.7820 • C = -3.7783 • 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=1.03886(38) 1.03992(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 =1.03944(30) • Large N 3 Resonances F(0)=0.30GeV-2 1+RC= 1.03932(30) Average 1.03938(30) Vud=0.9740(11)(15)

  22. 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

  23. Fornal-Grinstein Solution BR(ndark particles) ~ 1% BR(npeν)=0.9999(7) + 1.30(gA-1.2755) 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

  24. 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

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