Weak Decays: theoretical overview

Transcription

1 ACFI workshop on Fundamental Symmetry Tests with Rare Isotopes Amherst, October Weak Decays: theoretical overview Vincenzo Cirigliano Los Alamos National Laboratory

2 Outline Introduction: beta decays and new physics Connection with high-energy landscape Theoretical framework: from TeV to nuclear scales (Quick) overview of probes and opportunities Conclusions

3 Beta decays and new physics

4 β-decays and the making of the SM Fermi, 1934 Lee and Yang, 1956 p ν Feynman & Gell-Mann + Marshak & Sudarshan 1958 Glashow, Salam, Weinberg n e p? ν Current-current, parity conserving n e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,... It s (V-A)*(V-A)!! u d W ν e Embed in non-abelian chiral gauge theory, predict neutral currents

5 β-decays and the making of the SM Fermi, 1934 Lee and Yang, 1956 p ν Feynman & Gell-Mann + Marshak & Sudarshan 1958 Glashow, Salam, Weinberg n e p? ν Current-current, parity conserving n e Parity conserving: VV, AA, SS, TT... Parity violating: VA, SP,... It s (V-A)*(V-A)!! u d W ν e... of course with essential experimental input! Embed in non-abelian chiral gauge theory, predict neutral currents

6 β-decays and BSM physics In the SM, W exchange (V-A, universality)

7 β-decays and BSM physics In the SM, W exchange (V-A, universality) BSM: sensitive to tree-level and loop corrections from large class of models broad band probe of new physics Name of the game: precision! To probe BSM physics at scale Λ, need expt. & th. at the level of (v /Λ) 2 : 10-3 is a well motivated target

8 Theoretical framework

9 Theoretical Framework How do we connect neutron and nuclear beta-decay observables to short-distance physics (W exchange + BSM-induced interactions)? This is a multi-scale problem! Best tackled within Effective Field Theory

10 Theoretical Framework E BSM dynamics involving new particles with m > Λ Λ (~TeV) W,Z Perturbative matching ΛH (~GeV) At scale E~MBSM > MW integrate out new heavy particles: generate operators of dim > 4 (this can be done for any model) Nuclear scale

11 Theoretical Framework E BSM dynamics involving new particles with m > Λ Λ (~TeV) W,Z Perturbative matching ΛH (~GeV) H = π, n, p Non-perturbative matching Nuclear scale At hadronic scale E ~ 1 GeV match to description in terms of pions, nucleons (+ e,γ) take hadronic matrix elements

12 Theoretical Framework E BSM dynamics involving new particles with m > Λ Λ (~TeV) W,Z Perturbative matching ΛH (~GeV) H = π, n, p Non-perturbative matching Non-perturbative Nuclear scale (A,Z) e ν Nuclear matrix elements observables

13 Quark-level interactions Any new physics encoded in ten leading (dim6) quark-level couplings Linear sensitivity to εi (interference with SM) Quadratic sensitivity to ~ εi (interference suppressed by mν/e) function of new model-parameters

14 Matrix elements To disentangle short-distance physics, need hadronic and nuclear matrix elements of SM (at <10-3 level) and BSM operators Tools (for nucleons and nuclei): symmetries of QCD lattice QCD nuclear structure

15 Nucleon matrix elements Need the matrix elements of quark bilinears between nucleons Given the small momentum transfer in the decays q/m n ~10-3, can organize matching according to power counting in q/mn At what order do we stop? Work to 1st order in εl,r,s,p,t ~ 10-3 q/mn ~10-3 α/π ~10-3 Include O(q/m n) and radiative corrections only for SM operator S. Weinberg 1958, B. Holstein 70s,... Gudkov et al 2000 s

16 A closer look at V, A matrix elements (SM operators): Weinberg 1958

17 A closer look at V, A matrix elements (SM operators): Weinberg 1958 Vanish in the isospin limit, hence are O(q/m n) [calculable]. Since they multiply q/mn can neglect them Pseudo-scalar bilinear is O(q/m n): since it multiplies q/mn, can neglect it (but form factor is known, so this can be included) The weak magnetism form factor is related to the difference of proton and neutron magnetic moments, up to isospin-breaking corrections

18 Nuclear matrix elements Holstein 1974 lepton current Correspondence with neutron decay:

19 Nuclear matrix elements Holstein 1974 Form factors a(q2 ), c(q 2 ),... can be expressed in terms of nucleon form factors gn(q 2 ) and nuclear matrix elements of appropriate operators (see extra slides)

20 Overview of probes

21 How do we probe the ε s? Rich phenomenology, two classes of observables: 1. Differential decay rates (probe non V-A via b and correlations) Lee-Yang, Jackson-Treiman-Wyld a(ga, εα), A(gA, εα), B(gA, εα),... isolated via suitable experimental asymmetries

22 How do we probe the ε s? Rich phenomenology, two classes of observables: 1. Differential decay rates (probe non V-A via b and correlations) 2. Total decay rates (probe mostly V, A via extraction of Vud, Vus) Channel-dependent effective CKM element

23 Snapshot of the field This table summarizes a large number of measurements and th. input Already quite impressive. Effective scales in the range Λ= 1-10 TeV (ΛSM 0.2 TeV) VC, S.Gardner, B.Holstein Gonzalez-Alonso & Naviliat-Cuncic

24 Snapshot of the field This table summarizes a large number of measurements and th. input Already quite impressive. Effective scales in the range Λ= 1-10 TeV (ΛSM 0.2 TeV) Focus on probes that depend on the ε s linearly VC, S.Gardner, B.Holstein Gonzalez-Alonso & Naviliat-Cuncic

25 CKM unitarity: input Vud neutron ga = (25) T=1/2 mirror Pion beta decay

26 CKM unitarity: input Vud τn= 880 s BOTTLE τn= 888 s BEAM Vud = (21) Hardy-Towner neutron ga = (25) T=1/2 mirror Pion beta decay Extraction dominated by transitions. Critical theoretical input: Marciano-Sirlin 06 Isospin breaking in the nuclear matrix element: Nucleon-level non-log-enhanced radiative correction

27 CKM unitarity: input Vud τn= 880 s BOTTLE τn= 888 s BEAM Vud = (21) Hardy-Towner neutron ga = (25) T=1/2 mirror Pion beta decay Extraction dominated by transitions. Critical theoretical input: Neutron decay not yet competitive: Czarnecki, Marciano, Sirlin 2004

28 CKM unitarity: input CKM unitarity (from Vud) V us K π ν K μν τ Kν τ s inclusive Improved LQCD calculations have led to smaller V us from K π ν f+ K π (0)= 0.959(5) 0.970(3) Vus = (13) (9) FK/Fπ = (25) [stable] Vus / Vud = (6) mπ mπ phys, a 0, dynamical charm FLAG MILC 2014

29 CKM unitarity: test Vus from K μν ΔCKM = - (4 ± 5) σ V us K μν ΔCKM = - (12 ± 6) 10-4 Vus from K πlν 2.1 σ K πlν unitarity No longer perfect agreement with SM. This could signal: New physics in εr,p (s) (Kl2 vs Kl3) and in εl+εr, εl,r (s) V ud (ΔCKM) Systematics in data** or theory: δc (A,Z), f+(0), FK/Fπ

30 CKM unitarity: opportunities Given high stakes (0.05% EW test), compelling opportunities emerge: Robustness of δc and rad.corr: nucl. str. calculations + exp. validation Pursue V ud through mirror nuclear transitions Pursue V 0.02% through neutron decay δτ n ~ 0.35 s δτ n /τ n ~ 0.04 % BL2, BL3 (cold beam), UCNτ,... δg A /g A ~ 0.025% (δa/a, δa/a ~ 0.1%) acorn, Nab, UCNA+,...

31 Scalar and tensor couplings CURRENT Current most sensitive probes**: (bf) π e ν γ Towner-Hardyl, 2010 Bychkov et al, 2007 bf, π eνγ < gs εs < < ft εt < ft = 0.24(4) Quark model: 0.25 < gs < 1 ** For global analysis see Wauters et al,

32 Scalar and tensor couplings CURRENT Current most sensitive probes**: (bf) π e ν γ Towner-Hardyl, 2010 Bychkov et al, 2007 bf, π eνγ < gs εs < < ft εt < Lattice QCD: 0.91 < gs < 1.13 ft = 0.24(4) Quark model: 0.25 < gs < 1 Impact of improved theoretical calculations using lattice QCD Bhattacharya, et al R. Gupta et al ** For global analysis see Wauters et al,

33 Scalar and tensor couplings FUTURE Several precision measurements on the horizon (neutron & nuclei) For definiteness, study impact of b n, 10-3 ; bgt ( 6 Nab, UCNB, 6 He,... Additional studies at FRIB? bf, π eνγ Quark model: 0.25 < gs < < gt < 2.3 Herczeg 2001 bn, Bn bgt

34 Scalar and tensor couplings FUTURE Several precision measurements on the horizon (neutron & nuclei) For definiteness, study impact of b n, 10-3 ; bgt ( 6 Nab, UCNB, 6 He,... Lattice QCD < gs < 1.13 Additional studies at FRIB? bf, π eνγ ΛS = 5 TeV 1.0 < gt < 1.1 R. Gupta et al bn, Bn bgt Can dramatically improve existing limits on εt, probing ΛT ~ 10 TeV

35 Connection with highenergy landscape

36 Connection with landscape The new physics that contributes to εα affects other observables! Relative constraining power depends on specific model Model-independent statements possible in heavy BSM benchmark: MBSM > TeV new physics looks point-like at the weak scale u i u i d j d j Vertex corrections strongly constrained by Z-pole observables (ΔCKM is at the same level) Four-fermion interactions poorly constrained: σhad at LEP would allow ΔCKM ~0.01 and non V-A structures at εi ~ 5%. What about LHC? VC, Gonzalez-Alonso, Jenkins

37 Heavy BSM benchmark: all εα couplings contribute to the process p p e ν + X LHC constraints T. Bhattacharya, VC, et al, No excess events at high mt bounds on εα (at the 0.3% -1% level)

38 β decays vs LHC reach β decays_ LHC All ε s in μ = 2 GeV LHC: s = 7 TeV L = 5 fb % 1.2% 0.9% 0.6% 0.3% 0% 15.0% 12.0% 9.0% 6.0% 3.0% x x _ 0% Unmatched lowenergy sensitivity and future reach LHC limits close to low-energy. Interesting interplay in the future LHC reach already stronger than low-energy VC, Gonzalez-Alonso, Graesser,

39 β-decays 0.1% can be more constraining than LHC! FUTURE Quark model vs LQCD matrix elements Bhattacharya, et al Updated with 2014 lattice input LHC: s = 14 TeV L = 10, 300 fb -1

40 Connection to models Model set overall size and pattern of effective couplings Beta decays can play very useful diagnosing role Qualitative picture: DNA matrix WR Can be made quantitative u d LQ H + e ν YOUR FAVORITE MODEL......

41 MSSM: Distinctive correlation between Cabibbo universality (CKM) and lepton universality, controlled by sfermion spectrum Light selectrons, heavy squarks & smuons Light squarks, heavy sleptons Bauman, Erler, Ramsey- Musolf, arxiv: After LHC constraints Present 1-sigma Light smuons, heavy squarks & selectrons Future 1-sigma Post-LHC effects are at the few*10-4 level

42 MSSM: Light but compressed SUSY spectrum? invisible at the LHC Can lead to ΔCKM > 10-4 Bauman, Pitschmann, Erler, Ramsey-Musolf, preliminary! CKM > 10-4 CMS: SUS pas

43 Leptoquarks: ΔCKM constraint vs direct searches at HERA and LHC Pair production at LHC 95% CL limits Single production at HERA (depends on λ) λ λ S0 (3,1,1/3)

44 Leptoquarks: ΔCKM constraint vs direct searches at HERA and LHC ΔCKM constraint is stronger (for all four LQ that contribute to ΔCKM) 95% CL limits λ λ S0 (3,1,1/3)

45 Conclusions Precise (<0.1%) beta decays: broad band probe of new physics. Discovery potential depends on the underlying model Both in the heavy BSM benchmark and within specific models, a discovery window exists well into the LHC era! Currently, nuclear decays provide strongest constraints on nonstandard couplings (εl+εr, εs, εt) General guideline for selection of future FRIB: experimental feasibility theoretical feasibility : need reliable calculations of recoil order effects and structure-dependent radiative corrections

46 Future prospects for ΔCKM Lowering error on ΔCKM to 10-4 requires factor of 3-4 improvement in Vud and Vus Need to overcome following issues: V ud : radiative corrections and IB in matrix element V us : K matrix elements from lattice QCD need to improve by factor of ~3 (may be doable in next 5 years). However, experimental input from K decays currently implies δ(δckm) ~ Seems more realistic goal

47 Extra slides

48 V ud from nuclear β decays Coulomb distortion of wave-functions Nucleus-dependent rad. corr. (Z, E max,nuclear structure) Nucleus-independent short distance rad. corr. Towner-Hardy Ormand-Brown Sirlin-Zucchini 86 Jaus-Rasche 87 Marciano-Sirlin 06

49

50 Scalar and tensor couplings FUTURE Fit to decay parameters must include g A (correlations!), and must account for theory uncertainties at recoil order Lattice QCD (n) and nuclear calculations can reduce recoil-order uncertainty to negligible level S. Gardner, B. Plaster 2013 Fit to Monte Carlo pseudo-data of a and A with εt at its current limit ga

51 More on matrix elements

52 Nucleon matrix elements Need the matrix elements of quark bilinears between nucleons Given the small momentum transfer in the decays q/m n ~10-3, can organize matching according to power counting in q/mn At what order do we stop? Work to 1st order in εl,r,s,p,t ~ 10-3 q/mn ~10-3 α/π ~10-3 Include O(q/m n) and radiative corrections only for SM operator B. Holstein 70s,... Gudkov et al 2000 s

53 General matching Weinberg 1958

54 General matching Weinberg 1958 Need all other form-factors at q2 = 0

55 A closer look at V, A matrix elements (SM operators): Weinberg 1958 Vanish in the isospin limit, hence are O(q/m n). Since they multiply q/mn can neglect them Pseudo-scalar bilinear is O(q/m n): since it multiplies q/mn, can neglect it The weak magnetism form factor is related to the difference of proton and neutron magnetic moments, up to isospin-breaking corrections

56 What do we know about gv,a,s,t? g V = 1 (CVC) up to 2nd order corrections in (mu - md) Ademollo-Gatto Berhends-Sirlin (1-2εR)*gA can be extracted from neutron decay measurement. LQCD calculation of ga are at the ~10-15% level No phenomenological handle on g S; some (quite uncertain yet) info on gt, from polarized structure function of nucleon: need LQCD!

57 Connection to Lee-Yang Ignoring recoil order corrections, one recovers Lee-Yang effective Lagrangian The couplings are expressed in terms of gi and εi

58 Nuclear matrix elements Holstein 1974 Correspondence with neutron decay:

59 Nuclear form factors can be expressed in terms of nucleon form factors gn(q 2 ) and nuclear matrix elements of appropriate operators Holstein 1974

60 Nuclear form factors can be expressed in terms of nucleon form factors gn(q 2 ) and nuclear matrix elements of appropriate operators Holstein 1974

61 Nuclear matrix elements: