THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda Universitat Autònoma de Barcelona hadron2011, 13th-17th Juny 2011
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Hyperfine splitting (hydrogen atom): E exp HF = E ( n = 1 , s = 1 ) − E ( n = 1 , s = 0 ) ( s = total spin ) Nature (1972) ν HF = E HF = 1420 . 4057517667 ( 9 ) MHz ( 13 digits ) h THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Hyperfine splitting (hydrogen atom): E exp HF = E ( n = 1 , s = 1 ) − E ( n = 1 , s = 0 ) ( s = total spin ) Nature (1972) ν HF = E HF = 1420 . 4057517667 ( 9 ) MHz ( 13 digits ) h THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Hyperfine splitting (hydrogen atom): E exp HF = E ( n = 1 , s = 1 ) − E ( n = 1 , s = 0 ) ( s = total spin ) Nature (1972) ν HF = E HF = 1420 . 4057517667 ( 9 ) MHz ( 13 digits ) h THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Lamb shift (muonic hydrogen) E ≡ E ( 2 P 3 / 2 ( F = 2 )) − E ( 2 S 1 / 2 ( F = 1 )) PSI: R. Pohl et al., Nature vol. 466, p. 213 (2010) E exp = 206 . 2949 ( 32 ) meV E th = 209 . 9779 ( 49 ) − 5 . 2262 r 2 fm 2 + 0 . 0347 r 3 p p fm 3 meV = 205 . 984 meV using CODATA value r p = 0 . 8768 ( 69 ) fm. E exp − E th = 0 . 311 meV New proposed value: r p = 0 . 84184 ( 67 ) fm. 5 standard deviations!! E LO = 205 . 0074 = O ( m r α 3 ) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Lamb shift (muonic hydrogen) E ≡ E ( 2 P 3 / 2 ( F = 2 )) − E ( 2 S 1 / 2 ( F = 1 )) PSI: R. Pohl et al., Nature vol. 466, p. 213 (2010) E exp = 206 . 2949 ( 32 ) meV E th = 209 . 9779 ( 49 ) − 5 . 2262 r 2 fm 2 + 0 . 0347 r 3 p p fm 3 meV = 205 . 984 meV using CODATA value r p = 0 . 8768 ( 69 ) fm. E exp − E th = 0 . 311 meV New proposed value: r p = 0 . 84184 ( 67 ) fm. 5 standard deviations!! E LO = 205 . 0074 = O ( m r α 3 ) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Lamb shift (muonic hydrogen) E ≡ E ( 2 P 3 / 2 ( F = 2 )) − E ( 2 S 1 / 2 ( F = 1 )) PSI: R. Pohl et al., Nature vol. 466, p. 213 (2010) E exp = 206 . 2949 ( 32 ) meV E th = 209 . 9779 ( 49 ) − 5 . 2262 r 2 fm 2 + 0 . 0347 r 3 p p fm 3 meV = 205 . 984 meV using CODATA value r p = 0 . 8768 ( 69 ) fm. E exp − E th = 0 . 311 meV New proposed value: r p = 0 . 84184 ( 67 ) fm. 5 standard deviations!! E LO = 205 . 0074 = O ( m r α 3 ) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Lamb shift (muonic hydrogen) E ≡ E ( 2 P 3 / 2 ( F = 2 )) − E ( 2 S 1 / 2 ( F = 1 )) PSI: R. Pohl et al., Nature vol. 466, p. 213 (2010) E exp = 206 . 2949 ( 32 ) meV E th = 209 . 9779 ( 49 ) − 5 . 2262 r 2 fm 2 + 0 . 0347 r 3 p p fm 3 meV = 205 . 984 meV using CODATA value r p = 0 . 8768 ( 69 ) fm. E exp − E th = 0 . 311 meV New proposed value: r p = 0 . 84184 ( 67 ) fm. 5 standard deviations!! E LO = 205 . 0074 = O ( m r α 3 ) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Lamb shift (muonic hydrogen) E ≡ E ( 2 P 3 / 2 ( F = 2 )) − E ( 2 S 1 / 2 ( F = 1 )) PSI: R. Pohl et al., Nature vol. 466, p. 213 (2010) E exp = 206 . 2949 ( 32 ) meV E th = 209 . 9779 ( 49 ) − 5 . 2262 r 2 fm 2 + 0 . 0347 r 3 p p fm 3 meV = 205 . 984 meV using CODATA value r p = 0 . 8768 ( 69 ) fm. E exp − E th = 0 . 311 meV New proposed value: r p = 0 . 84184 ( 67 ) fm. 5 standard deviations!! E LO = 205 . 0074 = O ( m r α 3 ) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Precise measurements in atomic physics → Learning about hadron structure Lamb shift (muonic hydrogen) E ≡ E ( 2 P 3 / 2 ( F = 2 )) − E ( 2 S 1 / 2 ( F = 1 )) PSI: R. Pohl et al., Nature vol. 466, p. 213 (2010) E exp = 206 . 2949 ( 32 ) meV E th = 209 . 9779 ( 49 ) − 5 . 2262 r 2 fm 2 + 0 . 0347 r 3 p p fm 3 meV = 205 . 984 meV using CODATA value r p = 0 . 8768 ( 69 ) fm. E exp − E th = 0 . 311 meV New proposed value: r p = 0 . 84184 ( 67 ) fm. 5 standard deviations!! E LO = 205 . 0074 = O ( m r α 3 ) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Theoretical setup We use an effective field theory, Potential Non-Relativistic QED, which describes the muonic hydrogen dynamics and profits from the hierarchy m µ ≫ m µ α ≫ m µ α 2 i ∂ 0 − p 2 � � 2 m r + α ψ ( r ) = 0 r E ∼ mv 2 + corrections to the potential potential NRQED + interaction with ultrasoft photons Scales: m p ∼ Λ χ m µ m p m µ ∼ m π ∼ m r = m p + m µ m r α ∼ m e Expansion parameters, ratios between scales, mainly: m π m p ∼ m µ m p ∼ 1 9 m r α ∼ m r α 2 1 m r α ∼ α ∼ m r 137 Needed precision m r α 5 (heavy quarkonium precision) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Theoretical setup We use an effective field theory, Potential Non-Relativistic QED, which describes the muonic hydrogen dynamics and profits from the hierarchy m µ ≫ m µ α ≫ m µ α 2 i ∂ 0 − p 2 � � 2 m r + α ψ ( r ) = 0 r E ∼ mv 2 + corrections to the potential potential NRQED + interaction with ultrasoft photons Scales: m p ∼ Λ χ m µ m p m µ ∼ m π ∼ m r = m p + m µ m r α ∼ m e Expansion parameters, ratios between scales, mainly: m π m p ∼ m µ m p ∼ 1 9 m r α ∼ m r α 2 1 m r α ∼ α ∼ m r 137 Needed precision m r α 5 (heavy quarkonium precision) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Theoretical setup We use an effective field theory, Potential Non-Relativistic QED, which describes the muonic hydrogen dynamics and profits from the hierarchy m µ ≫ m µ α ≫ m µ α 2 i ∂ 0 − p 2 � � 2 m r + α ψ ( r ) = 0 r E ∼ mv 2 + corrections to the potential potential NRQED + interaction with ultrasoft photons Scales: m p ∼ Λ χ m µ m p m µ ∼ m π ∼ m r = m p + m µ m r α ∼ m e Expansion parameters, ratios between scales, mainly: m π m p ∼ m µ m p ∼ 1 9 m r α ∼ m r α 2 1 m r α ∼ α ∼ m r 137 Needed precision m r α 5 (heavy quarkonium precision) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Theoretical setup We use an effective field theory, Potential Non-Relativistic QED, which describes the muonic hydrogen dynamics and profits from the hierarchy m µ ≫ m µ α ≫ m µ α 2 i ∂ 0 − p 2 � � 2 m r + α ψ ( r ) = 0 r E ∼ mv 2 + corrections to the potential potential NRQED + interaction with ultrasoft photons Scales: m p ∼ Λ χ m µ m p m µ ∼ m π ∼ m r = m p + m µ m r α ∼ m e Expansion parameters, ratios between scales, mainly: m π m p ∼ m µ m p ∼ 1 9 m r α ∼ m r α 2 1 m r α ∼ α ∼ m r 137 Needed precision m r α 5 (heavy quarkonium precision) THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
INTRODUCTION/EXPERIMENT QED HADRONIC CONTRIBUTIONS CONCLUSIONS Theoretical setup � i ∂ 0 − p 2 � L pNRQED = d 3 r d 3 R dtS † ( r , R , t ) 2 m r � � d 3 r 1 4 F µν F µν , − V ( r , p , σ 1 , σ 2 ) + e r · E ( R , t ) S ( r , R , t ) − V ( r , p , σ 1 , σ 2 ) = V ( 0 ) ( r ) + V ( 1 ) ( r ) + V ( 2 ) ( r ) + . . . m µ m 2 µ V ( 0 ) ≡ − 4 π Z µ Z p α V ( k ) 1 ˜ k 2 , 1 α eff ( k ) = α 1 + Π( − k 2 ) , where Π( k 2 ) = α Π ( 1 ) ( k 2 ) + α 2 Π ( 2 ) ( k 2 ) + α 3 Π ( 3 ) ( k 2 ) + ... Z n µ Z m p α ( n , m ) α V ( k ) = α eff ( k )+ ( k ) = α eff ( k )+ δα ( k ) , δα ( k ) = O ( α 4 ) . � eff n , m = 0 n + m = even > 0 THE MUONIC HYDROGEN LAMB SHIFT AND THE DEFINITION OF THE PROTON RADIUS Antonio Pineda
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