Oklo: case study in extracting information on fundamental - PowerPoint PPT Presentation

Oklo: case study in extracting information on fundamental interactions from CN processes Edward Davis edward.davis@ku.edu.kw Kuwait University ACFI Workshop: “Tests of Time-Reversal in Nuclear and Hadronic Processes” (November 6 to 8, 2014)

Outline Introduction What is Oklo? Why is Oklo interesting? Interpretation of Oklo Unified treatment Earlier estimate of sensitivity to quark mass Interpretation of Oklo within many-body chiral EFT model Ingredients of model Sensitivity to quark mass: approximations & results Comparisons with epithermal TRNI studies Analysis in epithermal regime Final result Final thoughts

What is Oklo? ◮ Site (in Gabon) of natural fission reactors ◮ active ∼ 2 × 10 9 years ago ◮ characteristic distribution of isotopes ( � = natural abundances) ◮ SLOW neutron + HEAVY nucleus = SENSITIVE receiver

Why is Oklo interesting? ◮ Bounds on shifts in resonances = ⇒ Most restrictive bound on ∆ α = α then − α now α/α ( yr − 1 ) z ∆ α/α now ˙ Atomic clock (Al + /Hg + ) ( − 1 . 6 ± 2 . 3) × 10 − 17 0 Oklo ( n + 149 Sm ) ( − 1 . 0 �→ 0 . 7) × 10 − 8 ( − 4 �→ 5) × 10 − 18 0.16 ( − 0 . 25 ± 1 . 6) × 10 − 6 Meteorites 0.43 ( − 5 . 7 ± 1 . 1) × 10 − 6 Quasar absorption (MM) 0 . 2 − 4 . 2 10 3 Cosmic µ wave background − 0 . 013 �→ 0 . 015 10 9 < 6 × 10 − 2 Big-bang nucleosynthesis Adapted from ProgTheorPhys.126.993. [Oklo result: ModPhysLettA.27.1250232]

Why is Oklo interesting? ◮ Bounds on shifts in resonances = ⇒ Most restrictive bound on ∆ α = α then − α now α/α ( yr − 1 ) z ∆ α/α now ˙ Atomic clock (Al + /Hg + ) ( − 1 . 6 ± 2 . 3) × 10 − 17 0 Oklo ( n + 149 Sm ) ( − 1 . 0 �→ 0 . 7) × 10 − 8 ( − 4 �→ 5) × 10 − 18 0.16 ( − 0 . 25 ± 1 . 6) × 10 − 6 Meteorites 0.43 ( − 5 . 7 ± 1 . 1) × 10 − 6 Quasar absorption (MM) 0 . 2 − 4 . 2 10 3 Cosmic µ wave background − 0 . 013 �→ 0 . 015 10 9 < 6 × 10 − 2 Big-bang nucleosynthesis Adapted from ProgTheorPhys.126.993. [Oklo result: ModPhysLettA.27.1250232] ◮ Issue: influence of QCD parameters, specifically changes in light quark mass m q ≡ 1 2 ( m u + m d ) ?

Interpretation of Oklo: unified treatment [IntJModPhysE.23.1430007] � � ∆ X q ∆ α m q ◮ ∆ E r ≡ E r ( Oklo ) − E r ( now ) = k q + k α X q = X q α Λ QCD ◮ k q independent of mass number A ! ◮ Conjecture based on study of p-shell nuclei/schematic CN model [PhysRevC.79.034302/PhysRevD.67.063513] ◮ k q susceptible to nuclear matter analysis ◮ Order of magnitude estimate for k q ? Model dependent k q ≃ +10 MeV k q ≃ − 40 MeV (Walecka model) (Chiral model) ( k α ≃ − 1 MeV [NuclPhysB.480.37] )

Interpretation of Oklo: unified treatment [IntJModPhysE.23.1430007] � � ∆ X q ∆ α m q ◮ ∆ E r ≡ E r ( Oklo ) − E r ( now ) = k q + k α X q = X q α Λ QCD ◮ k q independent of mass number A ! ◮ Conjecture based on study of p-shell nuclei/schematic CN model [PhysRevC.79.034302/PhysRevD.67.063513] ◮ k q susceptible to nuclear matter analysis ◮ Order of magnitude estimate for k q ? Model dependent k q ≃ +10 MeV k q ≃ − 40 MeV (Walecka model) (Chiral model) ( k α ≃ − 1 MeV [NuclPhysB.480.37] )

Interpretation of Oklo: Walecka model estimate of k q [PhysRevC.79.034302] CN ◮ Shift δ E r (due to δ X q ) − − − → Depth U 0 of nuclear mean-field model � δ m N � δ E r + 2 δ r 0 + δ U 0 1 ≈ − 3 ) ( R = r 0 A U 0 m N r 0 U 0 � �� � Independent of A ◮ Walecka model estimate of U 0 -term implies (Ignore δ r 0 ) � � δ X q δ E r ≈ 7 . 50 δ m S − 5 . 50 δ m V − δ m N 7 . 50 K q S − 5 . 50 K q V − K q ≡ N U 0 m S m V m N X q ◮ Uncertain microscopic interpretation of scalar S and vector V No first principles calculation of K q S , K q − → bosons V K q S , K q V chosen such that k q ∼ +10 MeV ◮ In PhysRevC.79.34302 ,

Interpretation of Oklo: Walecka model estimate of k q [PhysRevC.79.034302] CN ◮ Shift δ E r (due to δ X q ) − − − → Depth U 0 of nuclear mean-field model � δ m N � δ E r + 2 δ r 0 + δ U 0 1 ≈ − 3 ) ( R = r 0 A U 0 m N r 0 U 0 � �� � Independent of A ◮ Walecka model estimate of U 0 -term implies (Ignore δ r 0 ) � � δ X q δ E r ≈ 7 . 50 δ m S − 5 . 50 δ m V − δ m N 7 . 50 K q S − 5 . 50 K q V − K q ≡ N U 0 m S m V m N X q ◮ Uncertain microscopic interpretation of scalar S and vector V No first principles calculation of K q S , K q − → bosons V K q S , K q V chosen such that k q ∼ +10 MeV ◮ In PhysRevC.79.34302 ,

Interpretation of Oklo: Walecka model estimate of k q [PhysRevC.79.034302] CN ◮ Shift δ E r (due to δ X q ) − − − → Depth U 0 of nuclear mean-field model � δ m N � δ E r + 2 δ r 0 + δ U 0 1 ≈ − 3 ) ( R = r 0 A U 0 m N r 0 U 0 � �� � Independent of A ◮ Walecka model estimate of U 0 -term implies (Ignore δ r 0 ) � � δ X q δ E r ≈ 7 . 50 δ m S − 5 . 50 δ m V − δ m N 7 . 50 K q S − 5 . 50 K q V − K q ≡ N U 0 m S m V m N X q ◮ Uncertain microscopic interpretation of scalar S and vector V No first principles calculation of K q S , K q − → bosons V K q S , K q V chosen such that k q ∼ +10 MeV ◮ In PhysRevC.79.34302 ,

Interpretation of Oklo within many-body chiral EFT model ◮ Plausible paradigm relating U 0 to QCD?

Interpretation of Oklo within many-body chiral EFT model ◮ Plausible paradigm relating U 0 to QCD? “M¨ unchen” model Ingredients Nuclear property Large scalar & vector self-energies Spin-orbit interaction Chiral π N ∆-dynamics + Pauli-blocking Binding & saturation NuclPhysA.750.259 NuclPhysA.770.1

Interpretation of Oklo within many-body chiral EFT model ◮ Plausible paradigm relating U 0 to QCD? “M¨ unchen” model ◮ Calculation of U for symmetric nuclear matter

Interpretation of Oklo within many-body chiral EFT model ◮ Plausible paradigm relating U 0 to QCD? “M¨ unchen” model ◮ Calculation of U for symmetric nuclear matter Long range interactions In-medium χ PT to 3 loops (1 & 2 π exchange, 1 & 2 virtual ∆ excitation)

Interpretation of Oklo within many-body chiral EFT model ◮ Plausible paradigm relating U 0 to QCD? “M¨ unchen” model ◮ Calculation of U for symmetric nuclear matter Long range interactions In-medium χ PT to 3 loops (1 & 2 π exchange, 1 & 2 virtual ∆ excitation) ∆(1232) degree of freedom Appropriate (∆ − N mass ≃ k Fermi ) Ensures model phenomenologically satisfactory NuclPhysA.750.259

Interpretation of Oklo within many-body chiral EFT model ◮ Plausible paradigm relating U 0 to QCD? “M¨ unchen” model ◮ Calculation of U for symmetric nuclear matter Long range interactions In-medium χ PT to 3 loops (1 & 2 π exchange, 1 & 2 virtual ∆ excitation) ∆(1232) degree of freedom Appropriate (∆ − N mass ≃ k Fermi ) Ensures model phenomenologically satisfactory Short range interactions 2 contact-terms Strengths fitted directly to nuclear NuclPhysA.750.259 matter properties

Sensitivity to quark mass: approximations & results Long & intermediate range interaction terms → ˜ U 0 = � U 0 i i � M π g A � 4 � ˜ � U 0 = π (9 + 6 u 2 ) tan − 1 u − 9 u k F + . . . ( u = M π ) m N 4 2 π F π � �� � Twice iterated 1 π -exchange (2 medium insertions) ◮ In terms of hadronic parameters P (i.e. M π , F π , g A , m N & ∆) �� � � P � � m q � δ ˜ δ ˜ U 0 = 1 U 0 U 0 i δ U 0 i δ P δ m q δ m q = U 0 U 0 δ m q U 0 U 0 i δ P P δ m q m q P , i � �� � � �� � = K q = K P U 0 i P ◮ Discard all but P = m π term: K q 2 ≫ other K q M π ≈ 1 P ’s � �� � Berengut et al. (2013) ◮ Result: δ ˜ U 0 = − 0 . 28 δ m q = ⇒ k q ∼ 10 MeV (!) U 0 m q Same as PhysRevC.79.034302 but with controlled approximations

Sensitivity to quark mass: approximations & results Long & intermediate range interaction terms → ˜ U 0 = � U 0 i i � M π g A � 4 � ˜ � U 0 = π (9 + 6 u 2 ) tan − 1 u − 9 u k F + . . . ( u = M π ) m N 4 2 π F π � �� � Twice iterated 1 π -exchange (2 medium insertions) ◮ In terms of hadronic parameters P (i.e. M π , F π , g A , m N & ∆) �� � � P � � m q � δ ˜ δ ˜ U 0 = 1 U 0 U 0 i δ U 0 i δ P δ m q δ m q = U 0 U 0 δ m q U 0 U 0 i δ P P δ m q m q P , i � �� � � �� � = K q = K P U 0 i P ◮ Discard all but P = m π term: K q 2 ≫ other K q M π ≈ 1 P ’s � �� � Berengut et al. (2013) ◮ Result: δ ˜ U 0 = − 0 . 28 δ m q = ⇒ k q ∼ 10 MeV (!) U 0 m q Same as PhysRevC.79.034302 but with controlled approximations