nuclear structure corrections in light muonic atoms€¦ · q2 from 10-4 gev2 to 10-2 gev2 crema...
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Sonia Bacca
Johannes Gutenberg University, Mainz
+
Nuclear structure corrections in light muonic atoms
Sonia Bacca
What are muonic atoms?
Exotic atoms
2
Sonia Bacca
What are muonic atoms?
Exotic atoms
2
Electron replaced with a muon
Sonia Bacca
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
Sonia Bacca
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
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
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
Sonia Bacca 7
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
Sonia Bacca 7
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
Sonia Bacca 7
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
Sonia Bacca 7
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
Sonia Bacca 7
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
Sonia Bacca 7
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
Sonia Bacca
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
Sonia Bacca 23
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
Sonia Bacca 24
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
Sonia Bacca 25
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
Sonia Bacca 26
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
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