ACFI workshop on Fundamental Symmetry Tests with Rare Isotopes Amherst, October 23-25 2014 Weak Decays: theoretical overview Vincenzo Cirigliano Los Alamos National Laboratory
Outline • Introduction: beta decays and new physics • Theoretical framework: from TeV to nuclear scales • (Quick) overview of probes and opportunities • Connection with high-energy landscape • Conclusions
Beta decays and new physics
β -decays and the making of the SM Fermi, 1934 Lee and Yang, 1956 Feynman & Gell-Mann + Marshak & Sudarshan Glashow, 1958 Salam, Weinberg p ν p ν e n ? e n Current-current, parity conserving u ν It’s (V-A)*(V-A) !! Parity conserving: W VV, AA, SS, TT ... Parity violating: VA, SP , ... d e Embed in non-abelian chiral gauge theory, predict neutral currents
β -decays and the making of the SM Fermi, 1934 Lee and Yang, 1956 Feynman & Gell-Mann + Marshak & Sudarshan Glashow, 1958 Salam, Weinberg p ν p ν e n ? e n Current-current, parity conserving u ν It’s (V-A)*(V-A) !! Parity conserving: W VV, AA, SS, TT ... Parity violating: VA, SP , ... d e Embed in non-abelian chiral gauge theory, ... of course with essential experimental input! predict neutral currents
β -decays and BSM physics • In the SM, W exchange (V-A, universality)
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
Theoretical framework
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
Theoretical Framework BSM dynamics involving E new particles with m > Λ Perturbative Λ matching (~TeV) W,Z Λ H (~GeV) • At scale E~M BSM > M W “integrate out” new heavy particles: generate operators of dim > 4 (this can be done for any model) Nuclear scale
Theoretical Framework BSM dynamics involving E new particles with m > Λ Perturbative Λ matching (~TeV) W,Z Λ H Non-perturbative matching (~GeV) H = π , n, p • At hadronic scale E ~ 1 GeV match to description in terms Nuclear of pions, nucleons (+ e, γ ) ⇔ take hadronic matrix elements scale
Theoretical Framework BSM dynamics involving E new particles with m > Λ Perturbative Λ matching (~TeV) W,Z Λ H Non-perturbative matching (~GeV) H = π , n, p Non-perturbative e ν Nuclear matrix Nuclear elements ⇒ scale (A,Z) observables
Quark-level interactions • Any new physics encoded in ten leading (dim6) quark-level couplings Linear sensitivity to ε i (interference with SM) Quadratic ~ sensitivity to ε i (interference suppressed by m ν /E) function of new model-parameters
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
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/m n • At what order do we stop? Work to 1st order in α / π ~10 -3 ε L,R,S,P q/m n ~10 -3 ,T ~ 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
Weinberg 1958 • A closer look at V, A matrix elements (SM operators):
Weinberg 1958 • A closer look at V, A matrix elements (SM operators): • Vanish in the isospin limit, hence are O(q/m n ) [calculable]. Since they multiply q/m n can neglect them • Pseudo-scalar bilinear is O(q/m n ): since it multiplies q/m n , 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
Nuclear matrix elements → Holstein 1974 lepton current • Correspondence with neutron decay:
Nuclear matrix elements → Holstein 1974 • Form factors a(q 2 ), c(q 2 ), ... can be expressed in terms of nucleon form factors g n (q 2 ) and nuclear matrix elements of appropriate operators (see extra slides)
Overview of probes
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(g A , ε α ), A(g A , ε α ) , B(g A , ε α ), ... isolated via suitable experimental asymmetries
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 V ud , V us ) Channel-dependent effective CKM element
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 ( Λ SM ≈ 0.2 TeV) VC, S.Gardner, B.Holstein 1303.6953 Gonzalez-Alonso & Naviliat-Cuncic 1304.1759
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 ( Λ SM ≈ 0.2 TeV) • Focus on probes that depend on the ε ‘s linearly VC, S.Gardner, B.Holstein 1303.6953 Gonzalez-Alonso & Naviliat-Cuncic 1304.1759
CKM unitarity: input V ud neutron Pion T=1/2 0 + → 0 + g A = 1..2701(25) beta decay mirror
CKM unitarity: input τ n = 880 s BOTTLE V ud V ud = 0.97417(21) Hardy-Towner 2014 τ n = 888 s BEAM neutron Pion T=1/2 0 + → 0 + g A = 1..2701(25) beta decay mirror • Extraction dominated by 0 + → 0 + transitions. Critical theoretical input: Marciano-Sirlin ‘06 Isospin breaking in the Nucleon-level nuclear matrix element: non-log-enhanced radiative correction
CKM unitarity: input τ n = 880 s BOTTLE V ud V ud = 0.97417(21) Hardy-Towner 2014 τ n = 888 s BEAM neutron Pion T=1/2 0 + → 0 + g A = 1..2701(25) beta decay mirror • Extraction dominated by 0 + → 0 + transitions. Critical theoretical input: • Neutron decay not yet competitive: Czarnecki, Marciano, Sirlin 2004
CKM unitarity: input CKM unitarity (from V ud ) V us τ→ s K → π ν K → μν τ→ K ν inclusive • V us from K → π ν Improved LQCD calculations have led to smaller f +K →π (0)= 0.959(5) → 0.970(3) V us = 0.2254(13) → 0.2232(9) F K /F π = 1.1960(25) [stable] V us / V ud = 0.2308(6) m π → m π phys , a → 0, dynamical charm FLAG 2013 + MILC 2014
CKM unitarity: test V us V us from K → μν Δ CKM = - (4 ± 5) ∗ 10 -4 0.9 σ K → μν Δ CKM = - (12 ± 6) ∗ 10 -4 2.1 σ V us from K → π l ν K → π l ν u n i t a r i t y V ud • No longer perfect agreement with SM. This could signal: • New physics in ε R,P(s) (Kl2 vs Kl3) and in ε L + ε R , ε L,R(s) ( Δ CKM ) • Systematics in data** or theory: δ C (A,Z), f + (0), F K /F π
CKM unitarity: opportunities • Given high stakes (0.05% EW test), compelling opportunities emerge: • Robustness of δ C and rad.corr: nucl. str. calculations + exp. validation • Pursue V ud through mirror nuclear transitions • Pursue V ud @ 0.02% through neutron decay δτ n ~ 0.35 s δ g A /g A ~ 0.025% δτ n / τ n ~ 0.04 % ( δ a/a , δ A/A ~ 0.1%) BL2, BL3 (cold beam), UCN τ , ... aCORN, Nab, UCNA+, ... • Impact on other phenomenology
Scalar and tensor couplings C U R R E N T • Current most sensitive probes**: π → e ν γ 0 + → 0 + (b F ) Towner-Hardyl, 2010 Bychkov et al, 2007 b F , π→ e νγ -1.0 × 10 -3 < g S ε S < 3.2 × 10 -3 -2.0 × 10 -4 < f T ε T < 2.6 × 10 -4 f T = 0.24(4) Quark model: 0.25 < g S < 1 ** For global analysis see Wauters et al, 1306.2608
Scalar and tensor couplings C U R R E N T • Current most sensitive probes**: π → e ν γ 0 + → 0 + (b F ) Towner-Hardyl, 2010 Bychkov et al, 2007 b F , π→ e νγ -1.0 × 10 -3 < g S ε S < 3.2 × 10 -3 -2.0 × 10 -4 < f T ε T < 2.6 × 10 -4 f T = 0.24(4) Lattice QCD: 0.91 < g S < 1.13 Impact of improved Quark model: 0.25 < g S < 1 theoretical calculations using lattice QCD Bhattacharya, et al 1110.6448 R. Gupta et al. 2014 ** For global analysis see Wauters et al, 1306.2608
Scalar and tensor couplings F U T U R E • Several precision measurements on the horizon (neutron & nuclei) • For definiteness, study impact of b n , B n @ 10 -3 ; b GT ( 6 He, ...) @10 -3 Nab, UCNB, b F , π→ e νγ 6 He, Quark model: ... 0.25 < g S < 1 0.6 < g T < 2.3 Additional studies at Herczeg 2001 FRIB? b n , B n b GT
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