V ud Outlook : Experiment & Theory M.J. Ramsey-Musolf U Mass Amherst http://www.physics.umass.edu/acfi/ My pronouns: he/him/his Collaborators : All workshop participants CKM Workshop ACFI May 2019 1
Workshop Goals • Review recent theoretical developments in the extraction of V ud and V us from experimental measurements • Seek a consensus on the current values of theoretical inputs and associated theoretical uncertainties • Develop a roadmap for future, improved theoretical evaluations and experimental tests 2
Precision ~ BSM Mass Scale Precision Goal: δ Δ CKM ~ O(10 -4 ) Heavy BSM Physics: Λ ∼ 10 TeV (tree) Δ CKM ~ C ( v/ Λ ) 2 Λ < 1 TeV (loop) Ultralight BSM Physics: Δ CKM ~ ε 2 ( α /4 π ) ε < 1 (loop) 3
Questions for This Discussion • How robust is the quoted uncertainty on the new value of Δ R V ? • What additional tests (theory, experiment) are available ? • What is the roadmap to refined computation of δ NS ? • How important are contributions from other region of the low-E nuclear response ? How to compute & how to test computations ? 4
Dispersion Relations Radiative Correction: ν 0 + (f) 0 + (f) e 1 1 W W dQ 2 M 2 Z Z d ⌫ ( ⌫ + 2 q ) ↵ ⇤ V A (0) ⌫ ( ⌫ + q ) 2 F (0) ( ⌫ , Q 2 ) , W = 3 γ W M 2 W + Q 2 ⇡ M 0 0 γ γ Z 1 dQ 2 M 2 = 3 ↵ W + Q 2 ] M (0) W 3 (1 , Q 2 ) − 0 + (i) 0 + (i) e Q 2 [ M 2 2 ⇡ 0 • Relate F 3 (0) and M 3 (0) to data and/or • Compute F 3 (0) and M 3 (0) using same methods used to describe semi- leptonic scattering processes with nucleon & nuclear targets 5
Leptoproduction: Had & Nuc Response Free nucleons Nuclei � Elastic Hadronic Elastic Resonances Regge/ Quasi- Deep Inelastic Hadronic Elastic Resonances Regge/ Deep Inelastic Discrete GDR Levels � Pion Production 6
Recent Results: Single Nucleon 7
Leptoproduction: Had & Nuc Response Free nucleons Nuclei � Elastic Hadronic Elastic Resonances Regge/ Quasi- Deep Inelastic Hadronic Elastic Resonances Regge/ Deep Inelastic Discrete GDR Levels � Pion Production “CMS” Preliminary Single nucleon: PRL 121 (2008) 241804 V = 0.02361(38) � Δ R V = 0.02361(38) � 0.02467 (22) Δ R 0.02433(32) 8 W. Marciano: this workshop
Dispersion Relations Refinements (WJM): - • Compute contributions to M 3 ν p+ ν p at each Q 2 from different ω regions • Implement 4 loop BjSR for pQCD region • Isospin rotate to M 3 (0) 9
Large N C Interpolator Marciano DR: C.-Y. Seng Neutrino data ? # of resonances ? Q 0 2 = 1.08 GeV 2 10
Recent Results: Nuclei 11
Leptoproduction: Had & Nuc Response Free nucleons Nuclei � Elastic Hadronic Elastic Resonances Regge/ Quasi- Deep Inelastic Hadronic Elastic Resonances Regge/ Deep Inelastic Discrete GDR Levels � Pion Production Quasielastic response Part of δ NS : “ C B Nucl ” 12 New work
Impact on δ NS Gorshteyn 13
Implications: “Conventional Analysis” Hardy 14
Implications Hardy final nucleus 15
Implications + New “CMS” Δ R ? Hardy 16
Tests & Improvements: Single Nucleon 17
Future Tests • Lattice computation of M 3 (0) (Q 2 ) • PV electron scattering Isospin relation 4 F (0) = F p 3 , γ Z − F n 3 , γ Z . 3 • SoLID ? • EIC ? • More neutrino data for M 3 (0) (Q 2 ) 18
Lattice QCD & M 3 (0) (Q 2 ) Feynman-Hellmann Theorem Seng 19
Tests & Improvements: Nuclei 20
Leptoproduction: Had & Nuc Response Free nucleons Nuclei � Elastic Hadronic Elastic Resonances Regge/ Quasi- Deep Inelastic Hadronic Elastic Resonances Regge/ Deep Inelastic Discrete GDR Levels � Pion Production Quasielastic response Part of δ NS : “ C B Nucl ” 21
Impact on δ NS ∆ δ NS = α ⇣ ⌘ C QE − q (0) = − (4 . 6 ± 0 . 9) × 10 � 4 S q A C B π Optimistic: • Correlations Neglects A- • 2-body currents Ave over 20 dep variations • Rel corrections transitions 22
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QE Contribution: Refinements Quantum Monte Carlo • GFMC: 10 B • Auxiliary Field MC: higher A LO β -Decay 24
GFMC & AFMC Pastore 25
Other Nuclear Corrections Free nucleons Nuclei � Elastic Hadronic Elastic Resonances Regge/ Quasi- Deep Inelastic Hadronic Elastic Resonances Regge/ Deep Inelastic Discrete GDR Levels � Pion Production Part of δ NS Low-lying transitions 26
0 + ! 0 + Decay: δ NS One-body Two-body: GS ! GS Towner 1992; T&H compilations Needed: state of art calc’s & tests Full nuclear Greens fn: w/ A n excited intermediate states 27 J. Engel
Dispersion Corrections Two-boson exchange in semileptonic processes: important for elastic PV eN & eA scattering ( 12 C) & nuclear β -decay; beam normal asymmetry, Olympus… provide tests V V γ V γ V = Z 0 , W, γ Abrahamyan et al, PRL 109 (2012) 192501 V = γ Beam normal asymmetry • J Lab Hall A • Future: Mainz, J Lab 28
0 + ! 0 + Dispersion Corrections: δ NS b F : scalar currents Input for V ud & CKM unitarity test • e + vs e - ? Towner & Hardy, PRC 91 (2015) 2, 025501 • Muons ? • Re-compute with state-of-the-art many-body methods • Test w/ A n predictions & expt for 10 B, 14 N, 26 Mg, 34 S, 38 Ar, 42 Ca, 46 Ti, 50 Cr, 54 Fe • Investigate strategy for obtaining reduced error bars 29
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