Presented By: Oscar Javier Hernandez Nuclear structure corrections in muonic atoms: Quantifying theoretical uncertainties In collaboration with: Andreas Ekström Nir Nevo Dinur Chen Ji Sonia Bacca Nir Barnea Phys. Lett. B 778, 377-383, (2018)
The growing proton radius puzzle 1 [Chen et al, JPG 45, 093002, 2018. ]
The growing proton radius puzzle 1 [Chen et al, JPG 45, 093002, 2018. ]
There is a discrepancy between eD and μD data 2 [Chen et al, JPG 45, 093002, 2018. ]
There is a discrepancy between eD and μD data 5.6 σ 2 [Chen et al, JPG 45, 093002, 2018. ]
There is a discrepancy between eD and μD data 5.6 σ 3.5σ 2 [Chen et al, JPG 45, 093002, 2018. ]
There is a discrepancy between eD and μD data 5.6 σ 3.5σ 2 [Chen et al, JPG 45, 093002, 2018. ]
The Lamb shift 3
The Lamb shift The dominant nuclear structure corrections are given by the two-photon exchange 3
The Lamb shift The dominant nuclear structure corrections are given by the two-photon exchange * C. E. Carlson et al. Phys. Rev. A 89, 022504 (2014). J. J. Krauth, et al. Ann. of Phy. 366, 168 (2016). Nucleonic Nuclear 3
The physics problem 228.7766 (10) meV Theory 1.7096 (200) meV Experiment 1.7638 (68) meV 4
The physics problem 228.7766 (10) meV Theory 1.7096 (200) meV Experiment 1.7638 (68) meV 4
The physics problem 228.7766 (10) meV Theory 1.7096 (200) meV Experiment 1.7638 (68) meV 4
The nuclear polarizability is a sum of many terms μD 5 [JPG 45, 093002, 2018. ]
The nuclear polarizability is a sum of many terms Corrections are ordered according to the power of the expansion parameter η Each correction is an integral over the response μD 5 [JPG 45, 093002, 2018. ]
Improving the uncertainty estimates LO NLO ... N2LO ... 6 Ekström et al., PRL (2013), JPG (2015), Carlsson et al., PRX (2016)
Improving the uncertainty estimates LO NLO Statistical uncertainties: ... N2LO ... 6 Ekström et al., PRL (2013), JPG (2015), Carlsson et al., PRX (2016)
Improving the uncertainty estimates LO NLO Statistical uncertainties: ... Systematic uncertainties: N2LO ... 6 Ekström et al., PRL (2013), JPG (2015), Carlsson et al., PRX (2016)
Improving the uncertainty estimates LO NLO Statistical uncertainties: ... Systematic uncertainties: N2LO ... 6 Ekström et al., PRL (2013), JPG (2015), Carlsson et al., PRX (2016)
Improving the uncertainty estimates LO NLO Statistical uncertainties: ... Systematic uncertainties: N2LO ... Single Nucleon: 6 Ekström et al., PRL (2013), JPG (2015), Carlsson et al., PRX (2016)
Improving the uncertainty estimates LO NLO Statistical uncertainties: ... Systematic uncertainties: N2LO ... Single Nucleon: Higher Order Corrections: 6 Ekström et al., PRL (2013), JPG (2015), Carlsson et al., PRX (2016)
Statistical uncertainties Propagate uncertainty using standard techniques 7
Statistical uncertainties N2LOsim 8
Statistical uncertainties Statistical uncert. Correction % Uncert. Statistical 0.06 N2LOsim 8
Sytematic Tlab uncertainties Systematic Tlab uncert. Correction % Uncert. Statistical 0.06 N2LOsim Tlab Sys. 0.2 9
Chiral truncation uncertainties = ... NLO LO Expand observable in the same Chiral EFT pattern, 10
Chiral truncation uncertainties = ... NLO LO Expand observable in the same Chiral EFT pattern, Truncation uncertainty can then be calculated according to Correction % Uncert. Chiral Trunc. 0.4 10
Additional uncertainties Two body currents + relativistic corr. Correction % Uncert. MEC 0.15 Seagull Pion-in-flight Rel. Corr. 0.05 11
Additional uncertainties * C. E. Carlson et al. Phys. Rev. A 89, 022504 (2014). J. J. Krauth, et al. Ann. of Phy. 366, 168 (2016). Two body currents + relativistic corr. Correction % Uncert. MEC 0.15 Seagull Pion-in-flight Rel. Corr. 0.05 Single Nucleon Physics Nucleon* 0.6 11
Additional uncertainties * C. E. Carlson et al. Phys. Rev. A 89, 022504 (2014). J. J. Krauth, et al. Ann. of Phy. 366, 168 (2016). Two body currents + relativistic corr. Correction % Uncert. MEC 0.15 Seagull Pion-in-flight Rel. Corr. 0.05 Single Nucleon Physics Nucleon* 0.6 Atomic 1.0 Phys. Atomic Physics uncert. 11
Final uncertainty budget +0.008 +0.001 +0.005 +0.0102 +0.172 +0.22 meV 12
Uncertainty comparisons [Krauth et. al. ] [Pohl et. al. Science] 13
Uncertainty in other muonic atoms 14 [Chen et al, JPG 45, 093002, 2018. ]
Uncertainty in other muonic atoms η-expansion uncertainty estimates are quite large in A=3 systems. Can we confirm this estimate using Bayesian methods? 14 [Chen et al, JPG 45, 093002, 2018. ]
Estimating the natural scale parameter Can we identify the scale parameter of our expansion (η) and unknown coefficients ? 15
Estimating the natural scale parameter Can we identify the scale parameter of our expansion (η) and unknown coefficients ? 15
Estimating the natural scale parameter Can we identify the scale parameter of our expansion (η) and unknown coefficients ? Bayesian parameter estimation problem independent 15
MCMC Sampling 3He 3H EMCEE 16
Preliminary estimates Physics based estimates 0.107 0.109 0.109 0.110 17
Outlook Results: Experimental vs theory difference improved by thorough analysis of nuclear TPE uncertainty. Uncertainty in TPE cannot solve the 5.6 σ discrepancy. 18
Outlook Results: Experimental vs theory difference improved by thorough analysis of nuclear TPE uncertainty. Uncertainty in TPE cannot solve the 5.6 σ discrepancy. Uncertainty Analysis: Use bayesian methods to combine statistical and chiral EFT truncation uncertainty Complete Bayesian η-expansion uncertainty analysis Reduce atomic physics uncert. 18
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