Standard Model Theory of Neutron Beta Decay

Transcription

1 Standard Model Theory of Neutron Beta Decay The Utility of a Δτ n/ τ n measurement to ±0.01%! (Electroweak Radiative Corrections) William J. Marciano November 9, 2012 Santa Fe, NM

2 Neutron Decay Master Relations 1) V ud 2 = (1.9)sec Unc. Radiative Corrections τ n (1+3g A2 ) Same as in Nuclear β Decay 2) τ n = (1.9)sec Radiative Corrections Cancel! V ud 2 (1+3g A2 ) 3) (1+3g A2 ) = (1.9)sec Radiative Corrections Cancel! V ud 2 τ n Current Δ V ud 2 / V ud 2 = ±0.02% NP = ±0.04% RC Superallowed β Δτ n/ τ n = ±0.12% Δg A2 /g A 2 ±0.20% τ n PDG =880.1(1.1)sec. Recent g A = (13) Perkeo II ±0.01% Outstanding/Appropriate Goals for τ n and g A 2

3 Refs: A. Sirlin RMP 50, 573 (1978) + earlier work WJM & A. Sirlin, PRL 56, 22 (1986); ibid 96, (2006) A. Czarnecki, WJM, A. Sirlin, PRD 70, (2004) Also see the classic: D. Wilkinson, NP SU(2) L xu(1) Y Standard Model Electroweak Radiative Corrections to µ eν e ν µ and n peν e both Infinite but renormalized using (G F0 G µ ) Quark mixing divergences absorbed in V 0 ud V ud maintaining Unitarity The CKM Quark Mixing Matrix: V ud V us V ub V CKM = V cd V cs V cb V td V ts V tb 3x3 Unitary Matrix Unitarity V ud 2 + V us 2 + V ub 2 =1 Any Apparent Deviation from 1 Implies New Physics at the tree or quantum loop level

4 Short-distance behavior of µ and β decays differ due to weak hypercharges of µ L (Y=-1) and d L. (Y=+1/3). Different anomalous dimensions! Muon Decay Γ 0 (µ eνν)=f(m e2 /m µ2 )G 0 F 2 m µ5 /192π 3 = 1/τ µ 0 Neutron Decay Γ 0 (n peν)=fg 0 F 2 V 0 ud 2 m e5 (1+3g A2 )/2π 3 =1/τ n 0 F(x)=1-8x+8x 3 -x 4-12x 2 lnx Phase Space Factor f= phase space factor, including Fermi function proton recoil, finite nucleon size Uncertainty O(few x10-5 ) Other Effects: Weak Magnetism, Induced Pseudoscalar etc. negligible g A and τ n important for: Unitarity test, solar neutrino flux, reactor neutrino flux, primordial abundances, spin content of proton, Goldberger-Treiman/Muon Capture, Bjorken Sum Rule, lattice benchmark Must be precisely determined!

5 Electroweak Radiative Corrections to Muon Decay Virtual One Loop Corrections + Inclusive Bremsstrahlung Absorb Ultraviolet divergences and some finite parts in G 0 F =g 0 2 /4 2m 2 W0 G µ τ µ -1 = Γ(µ + e + ν e ν µ (γ)) F(m e2 /m µ2 )G µ2 m µ5 [1+RC]/192π 3 RC =α/2π(25/4-π 2 )(1+α/π[2/3ln(m µ /m e )-3.7) ] Fermi Th. Defines G µ Other SM and New Physics radiative corrections absorbed into G µ. Eg. Top Mass, Higgs Mass, Technicolor, Susy,W* MuLAN experiment at PSI (Complete) World Ave. τ µ+ = (22)x10-6 sec 1ppm! Most precise lifetime ever measured gives: G µ = (6)x10-5 GeV -2 precise & important

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7 Electroweak Radiative Corrections to Neutron Beta Decay Include Virtual Corrections + Inclusive Bremsstrahlung Normalize using G µ from the muon lifetime Absorbs Ultraviolet Divergences & some finite parts 1/τ n = fg µ2 V ud 2 m e5 (1+3g A2 )(1+RC)/2π 3 f= (Includes Fermi Function etc. not Rad. Corr.) RC calculated for (Conserved) Vector Current since it is not renormalized by strong interaction at zero momentum transfer. Same RC used to define g A : [A(g A )=(1.001)Aexp ] RC=α/2π[<g(E m )>+3ln(m Z /m p )+ln(m Z /m A )+2C+A QCD ] + higher order O(α/π) 2 g(e e )=Universal Sirlin Function (1967) from Vector Current A. Sirlin, PRD 164, 1767 (1967).

8 α/2π <g(e m = MeV)>= long distance loops and brem. averaged over the decay spectrum. Independent of Strong Int. up to O(E e /m P ) g(e e ) also applies to Nuclei A. Sirlin (1967) Uncertainty < α/2πln(m Z /m p ) short-distance (Vector) log not renormalized by strong int. [α/2π[ln(m Z /m A )+2C+A QCD ] Induced by axial-current loop Includes hadronic uncertainty m A =1.2GeV long/short distance matching scale (factor 2 m A unc.) C=0.8g A (µ N +µ P )=0.891 (long distance γw Box diagram) WJM&A.Sirlin(1986) A QCD = -α s /π(ln(m Z /m A )+cons)=-0.34 QCD Correction [α/πln(m Z /m)] n leading logs summed via renormalization group, ( ) Next to leading short distance logs ~ , and -α 2 ln(m p /m e )= estimated (for neutron decay) Czarnecki, WJM, Sirlin (2004) 1+RC=1.0390(8) main unc. from m A matching short and long distance γw (VA) Box. Unc*. ±8x10-4 vs future (discussed here ±0.1sec) τ n ±1.1x10-4 goal. * Note, unc. cancels in neutron vs nuclear beta decays eg V ud

9 γw Box Diagram

10 2006 Improvement WJM & A. Sirlin 1.) Use large N QCD Interpolator to connect long-short distances 2.) Relate neutron beta decay to Bjorken Sum Rule (N F =3) 1-α s /π 1-α s (Q 2 )/π-3.583(α s (Q 2 )/π) (α s (Q 2 )/π) (α s (Q 2 )/π) 4 (Baikov,Chetyrkin and Kuhn) Negligible Effect The extra QCD corrections lead to a matching between short and long distance corrections at about Q 2 =(0.8GeV) 2 Very little change in size of RC, but uncertainties reduced by a factor of 2 (perhaps 3)! (Both Prescriptions Agree) 1+RC= (8) (39) for Neutron Beta Decay Reduction by 1.4x10-4 (Same for beta decays) Unc. Reduced to ±3.9x10-4 (about 3x τ n goal).

11 RC Error Budget 1) Neglected Two Loop Effects: ± conservative 2) Long Distance α/πc~α/π (0.75g A (µ N +µ P ))= Assumed Uncertainty ±10% ± reasonable? 3) Long-Short Distance Loop Matching: 0.8GeV<Q<1.5GeV ±100% ± conservative Total RC Error ± ΔV ud =± More Aggressive Analysis ΔV ud =± (1/2 conservative) only about 2xτ n goal of ±0.1sec. (well matched)

12 Superallowed ( ) Beta Decays & V ud RC same as in Neutron Decay but with <g(e m )> averaged Nuclear decay spectrum, C modified by Nucleon-Nucleon Interactions and +Z α 2 ln(m p /m e ) corrections (opposite sign from neutron) ft= V ud 2 (2984.5s)(1+RC)(1+NP corr.) Nuclear Physics (NP) isospin breaking effects (Hardy & Towner Calculations: See later critique) ft values + RC for 13 precisely measured nuclei found to be consistent with CVC: Average V ud

13 Superallowed Nuclear Beta Decays RC Uncertainty-Same as Neutron Decay Nuclear Unc. - Significantly Reduced ( ) Nuclear Coulomb Corrections Improved V ud = (11) Nuc (19) RC (2008 Hardy and Towner Update) ( ((13)(14)(19) in PDG08) ( (11)(15)(19) in PDG06) ( (80) in 2004) Factor of 3 worse

14 The Kaon Revolution of (Starting with BNL E865) +FNAL, Frascati & CERN BR(K πeν) increased by 6%! All Major K L BRs Changed! ε K changed by 3.7σ! Now Based on: Γ(K πlν) exp & Γ(K µν)/γ(π µν) exp + Lattice Matrix Elements f + (0)=0.960(5) & f K /f π =1.193(6) 2010 Flavianet Analysis Currently: V us =0.2253(13) from K πlν Vector V us =0.2252(13) from K µν Axial-Vector V us =0.2253(9) Kaon Average (was ~0.220 pre 2004) (Watch for lattice updates)

15 CURRENT STATUS of CKM Unitarity V ud 2 + V us 2 + V ub 2 =0.9999(4) Vud (4) Vus =0.9999(6) Outstanding Agreement With Unitarity Confirms CVC & SM Radiative Corrections: 2αln(m Z /m p )/π+ +3.6% at 60 sigma level! Naively Fits m Z =90(7)GeV vs GeV (Direct) Comparison of G µ with other measurements (normalization) constrains or unveils New Physics New Physics Constraints-Implications: Exotic Muon Decays, W*bosons, SUSY, Technicolor, Z Bosons, H ±, Heavy Quark/Lepton Mixing

16 Comparisons can be viewed as a probe of differences among Fermi Constants µ e Decay G µ = (6)x10-5 GeV -2 τ µ Decay G F = (26000)x10-5 GeV -2 τ e Decay G F = (26000)x10-5 GeV -2 Tests e-µ-τ Universality Agreement Constrains Heavy Lepton Mixing CKM Unitarity: G F CKM = (3000)x10-5 GeV -2 Best After τ µ! Agreement Constrains: Exotic Muon Decays, Heavy Quark Mixing, W* (extra dim., Sequential ),SUSY Loops, H -, (Squarks vs Sleptons), Z,

17 Exotic Muon Decays: µ eν e ν µ wrong neutrinos! BR (95%CL) Potential Background Uncertainty For Neutrino Oscillations At Neutrino Factory Heavy Quark Mixing (e.g. E6 D L singlets) V ud 0.03 Similar Heavy Lepton Constraint Seems unlikely, since V ub =0.003

18 W* Excited KK Bosons or sequential W (different µ & β) 4(m W /m W* ) 2 =0.0001(6), m W* >6TeV? Unless Cancellation with muon decay? (1TeV extra dim. Unlikely?) LHC sequential W? 2 Higgs Doublets Charged Higgs H ± m H± 5.6tanβ (From K µν)

19 Superallowed Beta Decay Issue Isospin Breaking Coulomb Corrections of Hardy and Towner questioned by: G. Miller & A. Schwenk N. Auerbach H. Liang et al. Hardy and Towner (1-δ C ) correction increases V ud δ C ~ % Correction Recent Claims δ C is smaller due to nuclear radial excitations smaller V ud = (Liang, Giai, Meng) V ud 2 + V us 2 + V ub 2 reduced to (roughly) ? Unitarity Lost? Issue needs complete quantitative resolution ( Experimentally Addressed by Hardy & Towner)

20 Neutron Decay (n peν) & V ud V ud 2 = (1.9)sec Master Relation τ n (1+3g A2 ) Measure τ n and g A G A /G V (decay asymmetries) 2008 PDG τ n ave =885.7(8)sec, g A ave =1.2695(29) V ud ave =0.9746(4) τn (18) ga (2) RC reasonable but 2012 τ n PDG 880.1(1.1)sec? & g A (13) Perkeo II V ud =0.9739(6) τn (8) ga (2) RC Agrees with superallowed! Nuclear Beta V ud = (22) (Are τ n & g A both shifting?) History g A = ? Many New τ n & g A Experiments Planned

21 2012 PDG (Confusion) 2010 PDG τ n ave =885.7(8)sec, g A ave =1.2695(28) 2012 PDG τ n ave =880.1(1.1)sec, g A ave =Deferred (1.275?) Should expect g A =1.275 Independent of Radiative Corrections! Experimental measurements of g A and τ n will test Nuclear Coulombic corrections.

22 Conclusion

23 Goals 1) Extraction of g A from τ n &V ud (nuclear) independent of radiative corrections unc! τ n to±0.1 sec + V ud = (11) Nuc Δg A to ±0.0001! 2) V ud comparison of neutron and nuclear beta decays ( V ud = (11) Nuc (19) RC ) suggests τ n should be measured to ±0.1sec ΔV ud ± ! Good Luck