nuclear structure corrections in light muonic atoms€¦ · q2 from 10-4 gev2 to 10-2 gev2 crema...

Sonia Bacca

Johannes Gutenberg University, Mainz

+

Nuclear structure corrections in light muonic atoms

Sonia Bacca

What are muonic atoms?

Exotic atoms

2

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What are muonic atoms?

Exotic atoms

2

Electron replaced with a muon

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What are muonic atoms?

Exotic atoms

2

Electron replaced with a muon

e-

Ordinary atoms

µ-

Muonic atoms

muon more sensitive to the nucleus

Hydrogen-like systems

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What are muonic atoms?

Exotic atoms

2

Electron replaced with a muon

Can be used as a precision probe for the nucleus

e-

Ordinary atoms

µ-

Muonic atoms

muon more sensitive to the nucleus

Hydrogen-like systems

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Production and measurements

3

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e-The proton charge radius is measured from: electron-proton interactions: 0.8770 ± 0.0045 fm

eH spectroscopy e-p scattering

Pohl et al., Nature (2010)Antognini et al., Science (2013)

µ- muonic -proton interactions: 0.8409 ± 0.0004 fm 𝜇H Lamb-shift

Proton Radius Puzzle

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e-The proton charge radius is measured from: electron-proton interactions: 0.8770 ± 0.0045 fm

eH spectroscopy e-p scattering

Pohl et al., Nature (2010)Antognini et al., Science (2013)

µ- muonic -proton interactions: 0.8409 ± 0.0004 fm 𝜇H Lamb-shift

7 �

Is lepton universality violated?

Proton Radius Puzzle

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e-The proton charge radius is measured from: electron-proton interactions: 0.8770 ± 0.0045 fm

eH spectroscopy e-p scattering

Pohl et al., Nature (2010)Antognini et al., Science (2013)

µ- muonic -proton interactions: 0.8409 ± 0.0004 fm 𝜇H Lamb-shift

7 �

Proton Radius Puzzle

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Experimental efforts

6

Higher precision electron scattering experiments

Q2 from 10-4 GeV2 to 10-2 GeV2

Repeat traditional measurement with windowless gas jet target (2019/20)

ISR measurement, not competitive, Phys.Lett. B 771 (2017) 194-198

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Experimental efforts

6

Higher precision electron scattering experiments

Q2 from 10-4 GeV2 to 10-2 GeV2

MUSE collaboration

Measure both e+/e- and 𝜇+/µ- to reduce uncertainties

Repeat traditional measurement with windowless gas jet target (2019/20)

ISR measurement, not competitive, Phys.Lett. B 771 (2017) 194-198

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Experimental efforts

6

Higher precision electron scattering experiments

Q2 from 10-4 GeV2 to 10-2 GeV2

CREMA collaboration

CREMA collaboration currently measuring Lamb shift in light muonic atoms: Deuterium, Helions, etc.

MUSE collaboration

Measure both e+/e- and 𝜇+/µ- to reduce uncertainties

Repeat traditional measurement with windowless gas jet target (2019/20)

ISR measurement, not competitive, Phys.Lett. B 771 (2017) 194-198

Sonia Bacca

Experimental efforts

6

Higher precision electron scattering experiments

Q2 from 10-4 GeV2 to 10-2 GeV2

CREMA collaboration

CREMA collaboration currently measuring Lamb shift in light muonic atoms: Deuterium, Helions, etc.

MUSE collaboration

Measure both e+/e- and 𝜇+/µ- to reduce uncertainties

Repeat traditional measurement with windowless gas jet target (2019/20)

ISR measurement, not competitive, Phys.Lett. B 771 (2017) 194-198

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µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D (results released) 𝜇4He+ (analyzing data)

𝜇3He+ (analyzing data)

𝜇3H (impossible?) 𝜇6Li2+, 𝜇7Li2+ (future)

Understanding the Proton Radius Puzzle

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µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D (results released) 𝜇4He+ (analyzing data)

𝜇3He+ (analyzing data)

𝜇3H (impossible?) 𝜇6Li2+, 𝜇7Li2+ (future)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

Understanding the Proton Radius Puzzle

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µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D (results released) 𝜇4He+ (analyzing data)

𝜇3He+ (analyzing data)

𝜇3H (impossible?) 𝜇6Li2+, 𝜇7Li2+ (future)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

well known

Understanding the Proton Radius Puzzle

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µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D (results released) 𝜇4He+ (analyzing data)

𝜇3He+ (analyzing data)

𝜇3H (impossible?) 𝜇6Li2+, 𝜇7Li2+ (future)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

well known

Understanding the Proton Radius Puzzle

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µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D (results released) 𝜇4He+ (analyzing data)

𝜇3He+ (analyzing data)

𝜇3H (impossible?) 𝜇6Li2+, 𝜇7Li2+ (future)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

well known 'm4

r(Z↵4)

12

4

Understanding the Proton Radius Puzzle

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µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D (results released) 𝜇4He+ (analyzing data)

𝜇3He+ (analyzing data)

𝜇3H (impossible?) 𝜇6Li2+, 𝜇7Li2+ (future)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

well known 'm4

r(Z↵4)

12

4

unknown NS corrections

Understanding the Proton Radius Puzzle

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µ-

CM

Theoretical derivation of TPE

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Perturbative potential: correction to the bulk Coulomb

µ-

CM

Theoretical derivation of TPE

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Perturbative potential: correction to the bulk Coulomb

µ-

CM

Theoretical derivation of TPE

Using perturbation theory at second order one obtains the expression for TPEup to order

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Theoretical derivation of TPE

9

Take non-relativistic kinetic energy in muon propagator Neglect Coulomb force in the intermediate state Expand the muon matrix elements in powers of η

η=

Non relativistic term

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Theoretical derivation of TPE

9

Take non-relativistic kinetic energy in muon propagator Neglect Coulomb force in the intermediate state Expand the muon matrix elements in powers of η

η=

Non relativistic term

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Theoretical derivation of TPE

9

Take non-relativistic kinetic energy in muon propagator Neglect Coulomb force in the intermediate state Expand the muon matrix elements in powers of η

★ “virtual” distance traveled by the proton between the two-photon exchange

★ Uncertainty principle

★ ⌘ =

η=

Non relativistic term

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★ dominant term, related to the energy-weighted integral of the dipole response function

Theoretical derivation of TPE Non relativistic term

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★ dominant term, related to the energy-weighted integral of the dipole response function

Theoretical derivation of TPE Non relativistic term

★ Related to Zemach moment elastic contribution

�(1)Z3 =⇡

3mr(Z↵)2�2(0)

ZZd3Rd3R0|R�R0|3 ⇢p0(R)⇢p0(R

0)

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★ dominant term, related to the energy-weighted integral of the dipole response function

★ leads to energy-weighted integrals of three different response functions

Theoretical derivation of TPE Non relativistic term

★ Related to Zemach moment elastic contribution

�(1)Z3 =⇡

3mr(Z↵)2�2(0)

ZZd3Rd3R0|R�R0|3 ⇢p0(R)⇢p0(R

0)

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Consider the Coulomb force in the intermediate states Naively , actually logarithmically enhanced

Related to the dipole response function

Friar (1977), Pachucki (2011)

Coulomb term

Theoretical derivation of TPE

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Consider the Coulomb force in the intermediate states Naively , actually logarithmically enhanced

Related to the dipole response function

Friar (1977), Pachucki (2011)

Coulomb term

Take the relativistic kinetic energy in muon propagator Related to the dipole response function

Relativistic terms

Theoretical derivation of TPE

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Consider the Coulomb force in the intermediate states Naively , actually logarithmically enhanced

Related to the dipole response function

Friar (1977), Pachucki (2011)

Coulomb term

Take the relativistic kinetic energy in muon propagator Related to the dipole response function

Relativistic terms

Consider finite nucleon-size by including their charge distributions and obtain terms, e.g.,

Finite nucleon-size corrections

�(1)R1 = �8⇡mr(Z↵)2�2(0)

Z Zd3Rd3R0|R�R0|

2

�2⇢pp0 (R,R0)� �⇢np0 (R,R0)

�

Theoretical derivation of TPE

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Theoretical derivation of TPE

�TPE

= �AZem

+ �NZem

+ �Apol

+ �Npol

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Theoretical derivation of TPE

�TPE

= �AZem

+ �NZem

+ �Apol

+ �Npol

�Apol

= �(0)D1

+ �(1)R3

+ �(1)Z3

+ �(2)R2 + �(2)Q + �(2)D1D3

+ �(0)C

+�(0)L + �(0)T + �(0)M + �(1)R1 + �(1)Z1 + �(2)NS

�AZem = ��(1)Z3 � �(1)Z1

Need to calculate and related uncertainties.�TPE

Friar an Payne (‘97)

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�E2S�2P = �QED +AOPEhr2c i+ �TPE

The uncertainty of the extracted radius depends on the precision of the TPE

Roughly: 95% 4% 1%

TPE needs to be know precisely, in order to exploit the experimental precision.

A matter of precision

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�E2S�2P = �QED +AOPEhr2c i+ �TPE

The uncertainty of the extracted radius depends on the precision of the TPE

Roughly: 95% 4% 1%

TPE needs to be know precisely, in order to exploit the experimental precision.

A matter of precision

Uncertainties comparison

Atom Exp uncertainty on ΔE2S-2PUncertainty on TPE prior to the discovery

of the proton radius puzzle

µ2H 0.003 meV 0.03 meV*

µ3He+ 0.08 meV 1 meV

µ4He+ 0.06 meV 0.6 meV

µ 6,7Li++ 0.7 meV 4 meV

*Leidemann, Rosenfelder ’95 using few-body methods

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Ab Initio Nuclear Theory

H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .

• Solve the Schrödinger equation for few-nucleons

HN

HN CM

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Ab Initio Nuclear Theory

H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .

• Solve the Schrödinger equation for few-nucleons

HN

HN CM

Hyper-spherical harmonics expansions for A=3,4,6,7 Barnea, Leidemann, Orlandini PRC 61 (2000) 054001

For A=2 we use an harmonic oscillator expansion

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Ab Initio Nuclear Theory

H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .

• Solve the Schrödinger equation for few-nucleons

HN

HN CM

Hyper-spherical harmonics expansions for A=3,4,6,7 Barnea, Leidemann, Orlandini PRC 61 (2000) 054001

For A=2 we use an harmonic oscillator expansion

• To compute the response functions, we use the Lorentz integral transform method directly or the Lanczos sum rule method.

Efros, et al., JPG.: Nucl.Part.Phys. 34 (2007) R459

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Ab Initio Nuclear Theory

H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .

• Solve the Schrödinger equation for few-nucleons

HN

HN CM

Hyper-spherical harmonics expansions for A=3,4,6,7 Barnea, Leidemann, Orlandini PRC 61 (2000) 054001

For A=2 we use an harmonic oscillator expansion

• To compute the response functions, we use the Lorentz integral transform method directly or the Lanczos sum rule method.

Efros, et al., JPG.: Nucl.Part.Phys. 34 (2007) R459

• We will use nuclear interactions derived from chiral effective filed theory (at various orders) and traditional potentials (AV18+UIX)

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4He

An example

S.B. and Saori Pastore, Journal of Physics G.: Nucl. Part. Phys. 41, 123002 (2014)

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An example

S.B. and Saori Pastore, Journal of Physics G.: Nucl. Part. Phys. 41, 123002 (2014)

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Muonic Deuterium

AV18 in agreement with Pachucki (2011)+ Pachucki, Wienczek (2015)J. Hernandez et al, Phys. Lett. B 736, 344 (2014)

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Deuteron radius puzzle

18

μe

e

Pohl et al, Science 353, 669 (2016)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

Hernandez et al., PLB 736, 334 (2014) Pachucki (2011)+ Pachucki, Wienczek (2015)

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Deuteron radius puzzle

18

μe

e

5.6�

Pohl et al, Science 353, 669 (2016)

�E2S�2P = �QED +AOPEhr2c i+ �TPE

Hernandez et al., PLB 736, 334 (2014) Pachucki (2011)+ Pachucki, Wienczek (2015)

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Deuteron radius puzzle

19

�E2S�2P = �QED +AOPEhr2c i+ �TPE

μe

e

5.6�

µH+iso: rp from µH and deuterium isotopic shift r2d -r2p: Parthey et al., PRL 104 233001 (2010)

Pohl et al, Science 353, 669 (2016)

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Deuteron radius puzzle

19

�E2S�2P = �QED +AOPEhr2c i+ �TPE

μe

e

5.6�

2.6�

µH+iso: rp from µH and deuterium isotopic shift r2d -r2p: Parthey et al., PRL 104 233001 (2010)

Pohl et al, Science 353, 669 (2016)

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J. Hernandez et al, Phys. Lett. B 778, 377 (2018)

µ2H

Only sightly mitigate the “small” proton radius puzzle (2.6 to 2 𝝈)

Order-by-order chiral expansion

Theory, PLB 2014

Statistical and systematic uncertainty analysis

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Higher order corrections in 𝛼

21

Three-photon exchange

Pachucki et al., Phys. Rev. A 97 062511 (2018)

(Z𝛼)6 correction, negligible

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Higher order corrections in 𝛼

21

Kalinowski, Phys. Rev. A 99 030501 (2019)One the many 𝛼6 corrections, supposedly the largest

Consistent within 1𝜎solves the small deuteron-radius puzzle

�TPE = �1.750+14�16 meV

�TPE = �1.7638(68) meV

Theory

Exp

Large deuteron-radius puzzle still unsolved! New data on electron scattering expected from MAMI and from the future MESA

Three-photon exchange

Pachucki et al., Phys. Rev. A 97 062511 (2018)

(Z𝛼)6 correction, negligible

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Uncertainties quantifications

22

Uncertainties sources • Numerical • Nuclear model • Nucleon-size • Truncation of multiples • η-expansion• expansion in Z𝛼

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Uncertainties quantifications

22

Uncertainties sources • Numerical • Nuclear model • Nucleon-size • Truncation of multiples • η-expansion• expansion in Z𝛼

10−4

10−3

10−2

10−1

100

0 5 10 15 20

Devia

tio

n

Kmax

leading dipole correction

4He

C.Ji et al., JPG: Part. Nucl. 45, 093002 (2018)

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Reduction of Uncertainties

Atom Exp uncertainty on ΔE2S-2P

Uncertainty on TPE prior to the discovery of the puzzle Uncertainty on TPE: ab initio

µ2H 0.003 meV 0.03 meV 0.02 meV

µ3He+ 0.08 meV 1 meV 0.3 meV

µ4He+ 0.06 meV 0.6 meV 0.4 meV

µ 6,7Li++ 0.7 meV 4 meV

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Reduction of Uncertainties

Atom Exp uncertainty on ΔE2S-2P

Uncertainty on TPE prior to the discovery of the puzzle Uncertainty on TPE: ab initio

µ2H 0.003 meV 0.03 meV 0.02 meV

µ3He+ 0.08 meV 1 meV 0.3 meV

µ4He+ 0.06 meV 0.6 meV 0.4 meV

µ 6,7Li++ 0.7 meV 4 meV

1976 2017-6

-5.5

-5

-4.5

-4

δA

po

l [m

eV]

µ3He

+

Rinker Carlson et al.

2016

Nevo Dinur et al.

~ ~~~

time

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Reduction of Uncertainties

Atom Exp uncertainty on ΔE2S-2P

Uncertainty on TPE prior to the discovery of the puzzle Uncertainty on TPE: ab initio

µ2H 0.003 meV 0.03 meV 0.02 meV

µ3He+ 0.08 meV 1 meV 0.3 meV

µ4He+ 0.06 meV 0.6 meV 0.4 meV

µ 6,7Li++ 0.7 meV 4 meV

1974 1976 1977-4

-3

-2

δA

po

l [m

eV]

µ4He

+

Bernabeau, Karlskog Rinker Friar Ji et al.2013

~ ~~~

time

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Reduction of Uncertainties

Atom Exp uncertainty on ΔE2S-2P

Uncertainty on TPE prior to the discovery of the puzzle Uncertainty on TPE: ab initio

µ2H 0.003 meV 0.03 meV 0.02 meV

µ3He+ 0.08 meV 1 meV 0.3 meV

µ4He+ 0.06 meV 0.6 meV 0.4 meV

µ 6,7Li++ 0.7 meV 4 meV

What about µ6,7Li++?

Go to Poster Session, Contribution by Simone Li MuliThu 18:30

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Summary and Outlook

• Ab initio calculations have allowed to substantially reduce uncertainties in TPE

• Independently on the nature of the puzzle, these calculations are needed to support any spectroscopic measurement with muonic atoms

• In the future we will investigate the hyperfine splitting of muonic deuterium and the Lamb shift in muonic lithium atoms

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Summary and Outlook

• Ab initio calculations have allowed to substantially reduce uncertainties in TPE

• Independently on the nature of the puzzle, these calculations are needed to support any spectroscopic measurement with muonic atoms

• In the future we will investigate the hyperfine splitting of muonic deuterium and the Lamb shift in muonic lithium atoms

Thanks to my collaboratorsN.Barnea, O.J. Hernandez, C.Ji, S.Li Muli, N.Nevo Dinur, A. Poggialini

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Summary and Outlook

• Ab initio calculations have allowed to substantially reduce uncertainties in TPE

• Independently on the nature of the puzzle, these calculations are needed to support any spectroscopic measurement with muonic atoms

• In the future we will investigate the hyperfine splitting of muonic deuterium and the Lamb shift in muonic lithium atoms

Thanks to my collaboratorsN.Barnea, O.J. Hernandez, C.Ji, S.Li Muli, N.Nevo Dinur, A. Poggialini

Thank you for your attention!

Sonia Bacca

Backup Slides

27

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Uncertainties quantifications

28

C.Ji et al., JPG: Part. Nucl. 45, 093002 (2018)

Uncertainties sources • Numerical • Nuclear model • Isospin symmetry breaking • Nucleon-size • Truncation of multiples • η-expansion• expansion in Z𝛼