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

or get me out of the box!

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

Prologue: All about the proton

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.

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

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

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 …..

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…..

ACT 1: In the beginning…. Form factors and TPE effects

10

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

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)

Rosenbluth Separation Method

Within one-photon-exchange framework:

Polarization Transfer Method

Polarization transfer cannot determine the values of GE and GM but can determine their ratio R.

Inconsistency between two methods

SLAC, JLab Rosenbluth data

JLab/HallA Polarization data

Jones et al. (2000)Gayou et al (2002)

J.Arrington, P.G.Blunden, W.Melnitchuk, arXiv1105.0951

Go beyond One-Photon exchange

New Structure

P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

Two-Photon-Exchange Effects on two techniques

large

small

P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

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

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.

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

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

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).

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

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

Comparison with data

arXiv:1012.0339 JLab Hall C

Model-independent analysis

Determined from polarization transfer data

TPE effects

From crossing symmetry and charge conjugation:Inputs

Our Choice of F(Q2, ε)

Fit (A)

Fit (B)

ε→ 1, y→0, F→0 ε→0, y→1, F≠0

Result of fitsDashed Line: Rosenbluth

Solid line: Fit (A)

Dotted line: Fit (B)

Result of fitsDashed Line: Rosenbluth

Solid line: Fit (A)

Dotted line: Fit (B)

Puzzle about nonlinearity

V.Tvaskis et al, PRC 73, 2005

Purely due to TPE

Fit (A) :

Fit (B):

TPE vs OPE

Dashed Line : Fit (B) Solid line: Fit (A)

TPE contribution to slope

SLOPE(TPE)/SLOPE(OPE)=C1/(GE/τ)

Fit (A)

Fit (B)

Empirical extraction of TPE

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.

Jlab Hall B E-07-005

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]].

Act 2: How strange is strange?TPE effect in parity-violating ep elastic scattering

40

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

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

OPE vs OZE

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 , ,

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

qq

EM

21 2

Q

Flavour decomposition

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

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…..

Electroweak radiative corrections

Squeeze eq→eq amplitudes into 4-Fermion contact interactions

Extraction of strange form factors with radiative corrections

ρ and κ are from electroweak radiative corrections

Strange form factors

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?

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’

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

But this is nothing but a Procrustean bed!

Gee..it hurts!

Get you!

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

Indeed MS is not good enough !

HQ. Zhou, CWK and SN Yang, PRL, 99, 262001 (2007)

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

Nagata et al, arXiv:0811.3539  PRC79:062501 2009

Old

New

Impact of our results

Avoid double counting

Here we only subtract the soft parts of ρ and κ

HQ Zhou, CWK, SN Yang, K Nagata PRC 81, 035208,2010

G0 data

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…..

Partonic calculation of Box diagrams

=

Yu-Chun Chen, C-W K, M. Vanderhaeghen, arXiv 0903.1098

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

Partonic calculation of Box diagrams

Result of Partonic calculation

Comparison with Marciano and Sirlin’s approximation

Act 3. Heading for the New world, but isn’t it India? TBE and QWEAK

Qweak experiment

δQw / Qw = 4% δsin2θW / sin2θW = 0.3%

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

Dispersion relation approach

Dispersion relation approach

M.Gorchtein and C.J.Horowitz, Phys.Rev.Lett. 102 (2009) 091806

Dispersion calculation

The result of hadronic model is quite different

δN=0.6%δΔ=-0.1%

H.Q. Zhou, CWK and S. N.Yang, in progress.

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

Result of Gorchtein, Horowitz, and Ramsey-Musolf

Act 4: The puzzle on the size of the proton

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.

82

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.

83

The size of the proton?

From measurement of hydrogen Lamb shift:

From low Q2 ep elastic scattering data

Charge Radius

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.

85

Muonic hydrogen Spectrum

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

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

88

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.

89

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).

Third Zeemach moment

If GE is dipole form

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.

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:

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.

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.

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

TPE and Lamb shift

Dispersion calculation

The imaginary part of TPE is related to the structure functions measured in DIS

Dispersion relations:

Three kinds of contributions

Reevaluation of TPE

C. Carlson and M. Vanderhaeghen,arXiv:1101.5965

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

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.

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

Two bosons are too many,But two cups of ice cream are just perfect!

Thank you for listening….