Nuclear Polarizability Corrections to the LambShift of µD

O. Javier Hernandez

Chen Ji, Sonia Bacca, N. Nevo Dinur, N. Barnea

TRIUMF / The University of Manitoba

O.J. Hernandez, et al. Phys. Lett. B 766, 344 (2014).

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 1 / 8

The Proton Radius Puzzle

New measurements of protoncharge radius in µH disagree withCoData determination.

36 Scientiic American, February 2014

0.84 0.85 0.86 0.87 0.88 0.89

Hydrogen spectroscopy experiment

Initial 2010 results

Updated 2013 results

Scattering experiment at the Mainz Microtron accelerator

All scattering measurements prior to the Mainz Microtron experiment

Error bar

femtometer

Proton radius using muonic hydrogen Proton radius using other experiments

Average of all measurements

SOU

RC

E: R

AN

DO

LF P

OH

L

The Incompatible MeasurementsThe size of the proton should stay the same no matter how one measures it. Laboratories have deduced the proton radius from

scattering experiments [see box on opposite page] and by measuring the energy levels of hydrogen atoms in spectroscopy experiments.

These results were all consistent to within the experimental error. But in 2010 a measurement of the energy levels of so-called muonic

hydrogen [see box on page 38] found a signiicantl: lower proton radius. Attempts to e9plain the anomal: have so far failed.

R E S U L T S

© 2014 Scientific American

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 2 / 8

The Proton Radius Puzzle

New measurements of protoncharge radius in µH disagree withCoData determination.

36 Scientiic American, February 2014

0.84 0.85 0.86 0.87 0.88 0.89

Hydrogen spectroscopy experiment

Initial 2010 results

Updated 2013 results

Scattering experiment at the Mainz Microtron accelerator

All scattering measurements prior to the Mainz Microtron experiment

Error bar

femtometer

Proton radius using muonic hydrogen Proton radius using other experiments

Average of all measurements

SOU

RC

E: R

AN

DO

LF P

OH

L

The Incompatible MeasurementsThe size of the proton should stay the same no matter how one measures it. Laboratories have deduced the proton radius from

scattering experiments [see box on opposite page] and by measuring the energy levels of hydrogen atoms in spectroscopy experiments.

These results were all consistent to within the experimental error. But in 2010 a measurement of the energy levels of so-called muonic

hydrogen [see box on page 38] found a signiicantl: lower proton radius. Attempts to e9plain the anomal: have so far failed.

R E S U L T S

© 2014 Scientific American

7σ Discrepancy!

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 2 / 8

Extraction of 〈r 2ch〉 from the Lamb Shift

Expansion up to α5

∆E (2S − 2P) = δQED + δPol + δZem +m3

rα4

12〈r2ch〉

δQED corrections arise from vacuum polarizationand muon self-interaction

δPol arises from 2γ exchange process

CREMA collaboration has measured the Lamb shift in µD

Previous estimates of δPol by Pachucki used only AV18 potential

Use chiral EFT at different orders and vary cuttoff at each order to betterestimate error

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 3 / 8

Nuclear Polarizability

The δZem term is given by:

δZem = −π(Zα)2

3|φ(0)|2

∫d3r

∫d3r ′r3ρ(r ′)ρ(|r − r ′|)

The δPol term is expanded as:

δPol ∼∑i

δOi⇒ δO ∝

∫g(ω)SO(ω)dω

The Nuclear Response Function

SO(ω) =1

2J0 + 1

∑f 6=i

|〈i |O|f 〉|2δ(ω − Ef + Ei )

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 4 / 8

Comparison to Other Work and Experimental Data

E0 [MeV] 〈r 2str 〉1/2d [fm] Qd [fm2] αE [fm3]

AV18 Our 2.2246 1.967 0.270 0.633Wiringa et al. 2.2246 1.967 0.270

N3LO-EM Our 2.2246 1.974 0.2750 0.633Our+RC+MEC 1.978 0.285Entem\Machleidt 2.2246 1.978 0.285

Experiment 2.224575(9) 1.97507(78) 0.285783(30) 0.70(5)0.61(4)

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 5 / 8

Nuclear Polarizability Corrections: AV18

Pachucki ’11 Our work ’14 Pachucki ’15

δ(0) δ(0)D1 -1.910 -1.907 -1.910

δ(0)L 0.035 0.029 0.026

δ(0)T − -0.012 −δ(0)C 0.261 0.262 0.261

δ(0)M 0.016 0.008 0.008

δ(1) δ(1)Z3 − 0.357 −

δ(2) δ(2)R2 0.045 0.042 0.042

δ(2)Q 0.066 0.061 0.061

δ(2)D1D3 -0.151 -0.139 -0.139

δNS δ(1)Z1 − 0.064 −δ(1)np − 0.017 −δ(2)NS − -0.015 -0.020

δApol − -1.235 −δZem − -0.421 −δApol + δZem -1.638 -1.656 -1.671

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 6 / 8

Nuclear Polarizability Corrections: Chiral EFT

1.69

1.68

1.67

1.66

1.65

δA pol

+δ Zem

[m

eV

]

N3 LO EM

AV18(a)

1.94

1.93

1.92

1.91

1.90

δ(0

)D

1 [

meV

]

N3 LO EM

AV18(b)

N LO N2 LO N3 LO0.0066

0.0070

0.0074

0.0078

δ(0

)M

[m

eV

]

N3 LO EM

AV18(c)

Error Budget

Pot. Dep. 0.5%Chiral Conv. 0.3%Atomic Phys. 1%

Total 1.16%

⇒ Well within the exp.requirement!

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 7 / 8

Thank You For Listening!

O. Javier Hernandez (TRIUMF/UofM) Nucl. Polarizability Corrections: µD 8 / 8