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![Page 1: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/1.jpg)
Chung-Wen KaoChung-Yuan Christian University
Taiwan
Review of TBE Physics: Odyssey in the Box
15th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011
Odysseus and the Sirens, Greek Red-Figure Stamnos Vase, c. 480-460 BCE, British Museum
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or get me out of the box!
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Collaboration and Reference
In Collaboration with Hai-Qing Zhou (SouthEast U, China), Keitaro Nagata(CYCU, Taiwan), Yu-Chun Chen(AS, Taiwan), M. Vanderhaeghen(Mainz, Germany), Shin-Nan Yang (NTU,Taiwan)
This talk is based on the following works:(1) H-Q Zhou, CWK, S-N. Yang: Phys.Rev.Lett.99:262001,2007(2) K.Nagata, H-Q Zhou, CWK, S-NYang: Phys.Rev.C79:062501,2009.(3) H-Q Zhou, CWK,S-N Yang, K. Nagata: Phys.Rev.C81:035208,2010(4) Y.C. Chen, CWK, M. Vanderhaeghen: arXiv: 0903.1098
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Prologue: All about the proton
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Proton: our playground
Nucleon is the basic building block of atomic nuclei.
Its internal structure, arising from the underlying quark and gluon constituents, determines its mass, spin, and interactions.
These, in turn, determine the fundamental properties of the nuclei.
Furthermore, proton, as the only stable hadron, provides us the unique opportunity to explore its static properties up to very high precision.
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Using photon as probe
Since the quark carries the electric charge and photon does not participate the strong interaction, the photon is a very good probe.
Experiments with highly energetic electromagnetic probe acting as a micro-scope
virtuality 22 )'( kkQ
electron
k
k '
p Q
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Q
e
p p p hadr
oniz
atio
n
( )Q
e
xp
p
)(Q
e
xp
2
X
Qx 2, mp p
xp
q q
PD
One-Photon Physics: From Low to High
Low Q2, elastic, exclusive High Q2, deeply inelastic, inclusive
Form factors, resonanceParton distribution
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Oedipus explains the riddle of the Sphinx,
"What walks on four feet in the morning, two in the afternoon and three at night?".
Oedipus answered: "Man”.
"What looks like a single particle in low Q2, a bond state of heavy constituents in the middle and a bag of sands at high Q2?".
Oedipus: &^%&$$%???
To completely understand the properties of the proton from QCD is our Holy Grail …..
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Devil is near….
With the recent development of the polarization technology, many experiments can reach record-breaking precision.
However when experimentalists march, a devil is approaching in silence…
We think we know many things about the proton precisely, but do we?
Not really, HiHiHi…..
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ACT 1: In the beginning…. Form factors and TPE effects
10
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Form factor in quantum mechanics
2)(e)( rrdqF rqi
Atomic form factor:
( ) ~ ( ) q F q2
is the Fourier transform of the charge density.
The cross section:
E.g., the hydrogen atom in the ground state:
2
2
2201)(
qaqF
30
2/
8
e)(
0
ar
ar
2)()( rr
charge density
m105.04 10
20
ecma
with Bohr radius
ei k r
rki 'e
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Nucleon E.M form factors
Hofstadter determined the precise size of the proton by measuring their form factor in late 1950s.
"for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons.(1961)
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Rosenbluth Separation Method
Within one-photon-exchange framework:
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Polarization Transfer Method
Polarization transfer cannot determine the values of GE and GM but can determine their ratio R.
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Inconsistency between two methods
SLAC, JLab Rosenbluth data
JLab/HallA Polarization data
Jones et al. (2000)Gayou et al (2002)
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J.Arrington, P.G.Blunden, W.Melnitchuk, arXiv1105.0951
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Go beyond One-Photon exchange
New Structure
P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).
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Two-Photon-Exchange Effects on two techniques
large
small
P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).
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One way or another……. There are two ways to estimate the TPE effect:
Use models to calculate Two-Photon-Exchange diagrams:Like parton model, hadronic model and so on…..
Direct analyze the cross section and polarization data by including the TPE effects:
One-Photon-exchange Two-photon-exchange
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Why Box diagram is not trivial ?
One needs evaluate the Compton tensor.In general, it owns 18 structures! Furthermore, There is no single framework to computer this quantity with arbitrary k2 and (q-k)2.
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Results of hadronic model
Insert the on-shell form factors
P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 91 (2003) 142304
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Inclusion of resonances
Insert the on-shell form factors
S.Kondratyuk, P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 95 (2005) 172503
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Partonic Model Calculation
GPDs
A. V. Afanasev, S. J. Brodsky, C. E. Carlson, Y.-C. Chen, and M. Vanderhaeghen, Phys. Rev. D 72, 013008 (2005).
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5/6
GPDs
x x
t
DVCSDeeply Virtual Compton
Scattering Longitudinal response only
GPDs can be accessed via exclusive reactions in the Bjorken kinematic regime.
The DVCS process is identified via double (eg) or triple (egN) coincidences, allowing for small scale detectors and large luminosities.
Factorisation applies only to longitudinally polarized virtual photons whose contribution to the electroproduction cross section must be isolated..
GPDs
xx
DA
L
DVMPDeeply Virtual
Meson Production),(
),(
t
Hard gluon
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QCD factorization approach
1γ
1γ+2 γ(BLW)
1γ+2 γ(COZ)
N.Kivel and M.Vanderhaeghen, Phys. Rev. Lett.103 (2009) 092004
The leading perturbative QCD (pQCD) contribution to the 2 γ exchange correction to the elastic ep amplitude is given by a convolution integral of the proton distribution amplitudes (DAs) with the hard coefficient function
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Comparison with data
arXiv:1012.0339 JLab Hall C
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Model-independent analysis
Determined from polarization transfer data
TPE effects
From crossing symmetry and charge conjugation:Inputs
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Our Choice of F(Q2, ε)
Fit (A)
Fit (B)
ε→ 1, y→0, F→0 ε→0, y→1, F≠0
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Result of fitsDashed Line: Rosenbluth
Solid line: Fit (A)
Dotted line: Fit (B)
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Result of fitsDashed Line: Rosenbluth
Solid line: Fit (A)
Dotted line: Fit (B)
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Puzzle about nonlinearity
V.Tvaskis et al, PRC 73, 2005
Purely due to TPE
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Fit (A) :
Fit (B):
TPE vs OPE
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Dashed Line : Fit (B) Solid line: Fit (A)
TPE contribution to slope
SLOPE(TPE)/SLOPE(OPE)=C1/(GE/τ)
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Fit (A)
Fit (B)
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Empirical extraction of TPE
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Upcoming TPE experiments
J.Guttmann, N. Kivel, M. Meziane,and M. Vanderhaeghen, arXiv1012.0564
Olympus@DESY experimentare underway. Over the measured range of this experiment, the 2TPE corrections to the e+p/e−p elastic cross section ratio are predicted to vary in the 1 - 6 % range.
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Jlab Hall B E-07-005
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More TPE….. TPE and pion form factors: Y.-B.Dong, S.D.Wang,
Phys.Lett. B684, 123-126 (2010). P.G.Blunden, W.Melnitchouk, J.A.Tjon, Phys. Rev. C81, 018202 (2010).
TPE and deuteron form factors: Y.B.Dong, D.Y.Chen,'Phys. Lett. B675, 426-432 (2009). A.P.Kobushkin, Y.D.Krivenko-Emetov, S.Dubnicka, Phys. Rev. C81, 054001 (2010). A.P.Kobushkin, Y.D.Krivenko-Emetov, [arXiv:1101.1867 [nucl-th]]. Y.~B.~Dong, Phys. Rev. C82, 068202 (2010).
TPE and time-like proton form factors: H.Q.Zhou, D.Y.Chen, Y.B.Dong, Phys.Lett. B675, 305-307 (2009). J.Guttmann, N.Kivel, M.Vanderhaeghen, [arXiv:1101.5967 [hep-ph]].
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Act 2: How strange is strange?TPE effect in parity-violating ep elastic scattering
40
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Strangeness in the nucleon
Goal: Determine the contributions of the strange quark sea ( ) to the charge and current/spin distributions in the nucleon :
“strange form factors” GsE and Gs
M
ss
Puuduu dd ss g +.....•
« sea »
• s quark: cleanest candidate to study the sea quarks
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Parity Violating ep Elastic Scattering
EMEM JQ
M lQ
24
NCV
NCA
FNCPV JgJg
GM 5
5
22
Interference with EM amplitude makes Neutral Current (NC) amplitude accessible
22
~~Z
EM
NCPV
LR
LRPV
M
Q
M
MA
Tiny (~10-6) cross section asymmetry isolates weak interaction
Interference: ~ |MEM |2 + |MNC |2 + 2Re(MEM*)MNC
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OPE vs OZE
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Isolating the neutral weak form factors: vary the kinematics or the targets
p
AMEF AAAQGA
24
2
~ few parts per million
For a proton:
Forward angle Backward angle
eA
pMWA
ZM
pMM
ZE
pEE GGAGGAGGA '2sin41 , ,
![Page 45: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/45.jpg)
sME
dME
uMEME GGGG //// 3
1
3
1
3
2
sMEW
dMEW
uMEW
ZME GGGG /
2/
2/
2/ sin
3
41sin
3
41sin
3
81
NC probes same hadronic flavour structure, with different couplings:
GZ
E/M provide an important new benchmark for testing non-perturbative QCD structure of the nucleon
NF
M
qiFNNuuNJ
Nqq
EM
21 2
Q
Flavour decomposition
![Page 46: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/46.jpg)
Apply Charge Symmetry
snME
spME
unME
dpME
dnME
upME GGGGGG ,
/,/
,/
,/
,/
,/ ,,
GpE,M
GsE,M
GuE,M
GdE,MGn
E,MCharge
symmetry
GpE,M
<N| sγμ s |N>Gn
E,M
GpE,M
GsE,M
Shuffle
Well Measured
As
MEn
MEp
MEFZ
LR
LRPV GGGG
QG
M
MMA ,,,F
2///
2
2
sME
dME
uME
pME GGGG ///
,/ 3
1
3
1
3
2
sME
uME
dME
nME GGGG ///
,/ 3
1
3
1
3
2
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Tree Level is not enough!
The strange form factors are found to be very small, just few percents.
To make sure the extracted values are accurate, it is necessary to take the radiative correction into consideration!
So one has to draw many diagrams as follows…..
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Electroweak radiative corrections
Squeeze eq→eq amplitudes into 4-Fermion contact interactions
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Extraction of strange form factors with radiative corrections
ρ and κ are from electroweak radiative corrections
Strange form factors
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Be aware of the Box!
Box diagram is intricate because it is related with nucleon intermediate states.
Box diagram is special because of its complicated Q2 and ε
dependence
So Can one squeeze the box diagrams into a point?
![Page 53: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/53.jpg)
Zero Transfer Momentum Approximations for Box diagrams
p
q
Q2=t=(p-q)2 =0
Approximation made in previous analysis:
p=q=k
Marciano, Sirlin (1983)
Pe=Pe’=0Pe
Pe’
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High and Low Momentum Integration
N
Low Loop momentum Integration:Only include N intermediate state.Insert the on-shell form factors
High Loop momentum Integration:Lepton and a single quark exchange bosons.Convoluation with PDF
N
=
l l
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But this is nothing but a Procrustean bed!
Gee..it hurts!
Get you!
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MS approximation Initially it is for atomic parity violation. Two exchanged boson carry the same 4-
momentum and lepton momenta are set to be zero. In other words MS approximation is three-fold approximation:
Q2=0. Elab=0 Coulomb force is taken away
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Indeed MS is not good enough !
![Page 58: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/58.jpg)
HQ. Zhou, CWK and SN Yang, PRL, 99, 262001 (2007)
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Adding resonances….
Δ(1232) plays an important role in the low energy regime due to its light mass and its strong coupling to πN systeam.
PRC79:062501 2009; PRC81 035208 2010
Keitaro Nagata, Hai Qing Zhou, CWK and SN Yang
![Page 60: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/60.jpg)
Nagata et al, arXiv:0811.3539 PRC79:062501 2009
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Old
New
Impact of our results
Avoid double counting
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Here we only subtract the soft parts of ρ and κ
HQ Zhou, CWK, SN Yang, K Nagata PRC 81, 035208,2010
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G0 data
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Preliminary
GMs = 0.28 +/- 0.20
GEs = -0.006 +/- 0.016
~3% +/- 2.3% of proton magnetic moment
~20% +/- 15% of isoscalar magnetic moment
~0.2 +/- 0.5% of Electric distribution
One needs to be more sophisticated to extract the strangeness including box diagrams…..
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Partonic calculation of Box diagrams
=
Yu-Chun Chen, C-W K, M. Vanderhaeghen, arXiv 0903.1098
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Partonic calculation of Box diagrams
In MS limit c1=0 so that t1q is associated with ge
V and t2
q is associated with ge
A.
removed because it is Soft contribution
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Partonic calculation of Box diagrams
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Result of Partonic calculation
![Page 69: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/69.jpg)
Comparison with Marciano and Sirlin’s approximation
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Act 3. Heading for the New world, but isn’t it India? TBE and QWEAK
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Qweak experiment
δQw / Qw = 4% δsin2θW / sin2θW = 0.3%
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Cut the Box into two piecesZee axial coupling gA
e
Zee vector coupling gVe
δ γzA
δ γzV
In dispersion calculation the N intermediate state is excluded.
δ γzA (ν=0)=0
δ γzV (ν=0) ≠0
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Dispersion relation approach
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Dispersion relation approach
M.Gorchtein and C.J.Horowitz, Phys.Rev.Lett. 102 (2009) 091806
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Dispersion calculation
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The result of hadronic model is quite different
δN=0.6%δΔ=-0.1%
H.Q. Zhou, CWK and S. N.Yang, in progress.
![Page 77: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/77.jpg)
Recent progress on dispersion relation calculation
A. Sibirtsev, P. G. Blunden, W. Melnitchouk, A. W. Thomas, Phys. Rev. D82 (2010), 013011.
B. C. Rislow, C. E. Carlson, [arXiv:1011.2397]. P. G. Blunden, W. Melnitchouk and A. W.
Thomas, arXiv:1102.5334 Mikhail Gorchtein, C. J. Horowitz, and Michael J.
Ramsey-Musolf, arXiv.1102.3910
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Result of Gorchtein, Horowitz, and Ramsey-Musolf
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Act 4: The puzzle on the size of the proton
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Lamb shift of hydrogen (1947)
According to the hydrogen Dirac equation solution, the energy levels of 2p1/2 state is same with the energy level of 2s1/2 . However, in 1947, Willis Lamb discovered that this was not so - that the 2p1/2 state is slightly lower than the 2s1/2 state resulting in a slight shift of the corresponding spectral line.
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The size of proton and Lamb shift
The Lamb shift is the splitting of an energy level caused by vacuum polarization and other higher order radiative corrections.
The excellent agreement between experimental data and the QED calculation has been seen as the greatest triumph of QED.
However as the experimental technique develops the effect of finite size of the proton becomes non-negligible
such that the measurement of Lamb shift provides information of the charge radius of the proton.
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The size of the proton?
From measurement of hydrogen Lamb shift:
From low Q2 ep elastic scattering data
Charge Radius
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Muonic hydrogen
The muon is about 200 times heavier than the electron Therefore, the atomic Bohr radius of muonic hydrogen is smaller than in ordinary hydrogen.
The μp Lamb shift, ΔE(2P-2S) ≈ 0.2 eV, is dominated by vacuum polarization which shifts the 2S binding energy towards more negative values . The relative contribution of the proton size to ΔE(2P-2S) is as much as 1.8%, two orders of magnitude more than for normal hydrogen atoms.
Thus, the measurement of the Lamb shift of muonic hydrogen is expected to provide the more accurate value.
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Muonic hydrogen Spectrum
![Page 86: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/86.jpg)
How to calculate it?
To calculate the theoretical shift corresponding to the measured transition, some have used perturbation theory with non-relativistic wave-functions to predict the size of the contributing effects, including relativistic effects.
Alternatively one can use the Dirac equation for the muon with the appropriate potential as an effective approximation to the two-particle Bethe-Saltpeter equation to calculate the perturbed wave-functions
![Page 87: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/87.jpg)
Hard work for 40 years This kind of measurement has been considered for over 40
years, but only recent developements in laser technology and muon beams made it feasible to carry it out
The experiment is located at a new beam‐line for low‐energy (5keV) muons of the proton accelerator at the Paul Scherrer Institute (PSI) in Switzerlan
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Surprisingly new result The transition frequency between 2P3/2 and 1S1/2 is
obtained to be Δν = 49881.88(77) GHz , corresponding to an energy difference of ΔE = 206.2949(32) meV
Theory predicts a value of ΔE = 209.9779(49) ‐ 5.2262 rp² + 0.0347 rp³ meV
[rp in fm] This results in a proton radius of rp = 0.84184(36) fm
4% smaller than the previous best estimate, which has been the average of many different measurements made over the years.
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90
To match the 2010 value with the CODATA value, an additional term of0.31meV would be required in the QED equation. This corresponds to 64 times its claimed uncertainty!
Surprisingly new result
R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben, et al., Nature 466, 213–216 (2010).
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Third Zeemach moment
If GE is dipole form
![Page 91: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/91.jpg)
Four possibilities
The experimental results are not right. The relevant QED calculations are incorrect. There is, at extremely low energies and at
the level of accuracy of the `p-atom experiments, physics beyond the standard model“.
A single-dipole form factor is not adequate to the analysis of precise low-energy data.
![Page 92: Chung-Wen Kao Chung-Yuan Christian University Taiwan Review of TBE Physics: Odyssey in the Box 15 th Taiwan Nuclear Physics Summer School Iop AS, 06/27/2011.](https://reader035.fdocuments.us/reader035/viewer/2022062517/56649ef45503460f94c07125/html5/thumbnails/92.jpg)
Controversy about Third Zeemach moment
De Rújula pointed out that if the proton’s third Zemach moment is very large the discrepancy between the two results can be removed. He used some “toy model” and obtained the result:
His number is 13 times larger than the experimental extraction of Friar and Sick, who use electron-proton scattering data to determine:
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Controversy about Third Zeemach moment
Clöt and Miller show that published parametrizations, which take into account a wide variety of electron scattering data, cannot account for the value of the third Zemach moment found . They concluded that enhancing the Zemach moment significantly above the dipole result is extremely unlikely.
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Controversy about Third Zeemach moment
However De Rújula still argued that there is possible to make third Zeemach large and not ruled out by the ep data.His argument based on the fact thatThere is no data corresponds to the
A result based on those data has to be an extrapolation of data with a large spread and a poor χ2 per degree of freedom.
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Higher order QED calculation
one-loop electron self-energy and vacuum polarization
two-loops three-loops pure recoil correction radiative recoil correction finite nuclear size
corrections
By Pachucki
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TPE and Lamb shift
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Dispersion calculation
The imaginary part of TPE is related to the structure functions measured in DIS
Dispersion relations:
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Three kinds of contributions
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Reevaluation of TPE
C. Carlson and M. Vanderhaeghen,arXiv:1101.5965
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New Physics?
V. Barger Cheng-Wei Chiang, Wai-Yee Keung, and Danny Marfatia5 explore the possibility that new scalar, pseudoscalar, vector, axial-vector, and tensor flavor-conserving nonuniversal interactions may be responsible for the discrepancy. They consider exotic particles that among leptons, couple preferentially to muons and find that the many constraints from low energy data disfavor new spin-0, spin-1 and spin-2 particles as an explanation.
Phys.Rev.Lett.106:153001,2011
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Conclusion and Outlook
TBE are crucial for the extraction of the EM form factors and strangeness inside the nucleon!
More delicate estimate of the TBE effect is needed badly! (including more resonances, consider quark-level contributions…….)
Upcoming positron-proton scattering will provide us the precious information of TPE effects.
Uncertainty of TBE may jeopardize the interpretation of QWEAK data and requests an answer.
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Epilogue: Current status of TBE physics
Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning.
Winston ChurchillAfter the second battle of El Alamein, Nov 10,1942
we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, June 4, 1940
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Two bosons are too many,But two cups of ice cream are just perfect!
Thank you for listening….