Dominique Toublan

1
HEAVY QUARK CONTRIBUTION TO THE PROTONS MAGNETIC
MOMENT

• Dominique Toublan
• University of Maryland
• with Xiangdong Ji

PAVI06, Milos, May 2006
2
INTRODUCTION

• Proton
• Naïve 3 quarks bound by strong interaction
• QCD Sea of virtual gluons, quark-antiq. pairs
• What are its consequences for the macroscopic
  properties of the proton?

• Protons magnetic moment
• Strange quark contribution?
• Exciting experimental results
• Theory Difficult because
• Learn from light and heavy quark limits

• Heavy sea-quark contribution?

3
OUTLINE

• Experimental results vs theory
• Sea-quark contribution to the protons magnetic
  moment
• Light and heavy quark limits
• Warm-up Muon contribution to the electrons
  magnetic moment
• Heavy sea-quark contribution to the protons
  magnetic moment
• Implications for the physical strange quark

4
WORLD DATA vs THEORY
Experiments
Theory 16. Skyrme Model 17. Dispersion Relation
18. Dispersion Relation 19. Chiral Quark
Soliton Model 20. Perturbative Chiral Quark Model
21. Lattice 22. Lattice charge symmetry

• Contradiction between theory and experiment?

Preliminary
K. Paschke, TJNAF 06
5
MAGNETIC MOMENT

• Proton polarized in z-direction

• Light sea-quark, meson-cloud model

Musolf and Burkardt, Leinweber et al.

• Heavy sea-quark at lowest order

• Heavy sea-quark contribution to proton magnetic
  moment?

6
HEAVY STRANGE QUARK

• Heavy quark limit ? effective operator

Kaplan and Manohar

• Use effective in def. of

7
CONTRIBUTION TO

• Heavy quark limit

• Light-by-light scattering at LO in QED

Euler and Kockel

• Need to calculate
• Similar problem muon contribution to

8
MUON CONTRIBUTION TO

• Heavy muon limit

• Exact calculation
• Therefore

Laporta and Remiddi
9
MUON CONTRIBUTION TO

• How can we understand this?
• Power counting divergence
• Two scales Mom. flow ( ),
• Factorization, dim. 3

10
MUON CONTRIBUTION TO

• How can we understand this?
• Power counting divergence
• Two scales Mom. flow ( ),
• Factorization, dim. 3

Lorentz invariance
11
MUON CONTRIBUTION TO

• How can we understand this?
• Power counting divergence
• Two scales Mom. flow ( ),
• Factorization, dim. 3

Lorentz invariance

• Symmetry
• Same result as exact calculation at LO

12
CONTRIBUTION TO

• Heavy quark limit

• Contributions from 1, 2, and 3 quarks in proton

13
CONTRIBUTION TO

• Heavy quark limit

• Contributions from 1, 2, and 3 quarks in proton

N L O
L O
Similar to muon contribution to
14
CONTRIBUTION TO

• Heavy quark limit

15
CONTRIBUTION TO

• Heavy quark limit

Proton tens. charge
16
CONTRIBUTION TO

• Heavy quark limit

Proton tens. charge

• Therefore
• Non-trivial dependence
• Light sea
• Heavy sea

17
QUARK MODELS OF THE PROTON

• Quark models gluon fields generated by quarks
• Solve color Maxwells equation in linear approx.
• Of course, other gluons also hold the proton
  together, generating potential between quarks,
  bag confinement,
• Assumption correlation btwn polarized gluons and
  quarks are generated correctly by models
• Ignore non-linear effects
• Same as 8 copies of e.m. fields

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QUARK MODELS RESULTS

• Spin-dependent color magnetic field
• NRQ model constit. quark magnetic dipole
• MIT bag quasi-massless quark orbit. motion

• Contribution from single polarized quark
• Ground state largest contribution

NRQ
Bag
Extrapolation Strange quark
19
CONCLUSIONS AND OUTLOOK

• Quark sea and the protons macroscop. prop.?
• Strange quark and protons magnetic moment
• Exciting experimental results
• Contradiction with theory?
• Sea quark contribution to
• Changes sign for light and heavy sea quark

20
CONCLUSIONS AND OUTLOOK

• Quark sea and the protons macroscop. prop.?
• Strange quark and protons magnetic moment
• Exciting experimental results
• Contradiction with theory?
• Sea quark contribution to
• Changes sign for light and heavy sea quark
• Strange quark contribut. Negative or positive?

?
21
CONCLUSIONS AND OUTLOOK

• Quark sea and the protons macroscop. prop.?
• Strange quark and protons magnetic moment
• Exciting experimental results
• Contradiction with theory?
• Sea quark contribution to
• Changes sign for light and heavy sea quark
• Strange quark contribut. Negative or positive?

Leinweber et al.
22
CONCLUSIONS AND OUTLOOK

• Quark sea and the protons macroscop. prop.?
• Protons magnetic moment
• Exciting experim. results for strange quark
• Contradiction with theory?
• Sea quark contribution to
• Changes sign for light and heavy sea quark
• Strange quark contribut. Negative or positive?

?
23
World Data at Q2 0.1 GeV2
Note excellent agreement of world data set
GEs -0.12 0.29 GMs 0.62 0.32
Would imply that 7 of nucleon magnetic moment is
Strange
Caution the combined fit is approximate.
Correlated errors and assumptions not taken into
account
K. Paschke, TJNAF 06
24
World Data near Q2 0.1 GeV2
GMs 0.28 /- 0.20 GEs -0.006 /- 0.016 3
/- 2.3 of proton magnetic moment 0.2 /- 0.5
of Electric distribution
HAPPEX-only fit suggests something even
smaller GMs 0.12 /- 0.24 GEs -0.002 /-
0.017
Preliminary
Caution the combined fit is approximate.
Correlated errors and assumptions not taken into
account
25
World Data near Q2 0.1 GeV2
GMs 0.28 /- 0.20 GEs -0.006 /- 0.016 3
/- 2.3 of proton magnetic moment 0.2 /- 0.5
of Electric distribution
HAPPEX-only fit suggests something even
smaller GMs 0.12 /- 0.24 GEs -0.002 /-
0.017
Preliminary
Caution the combined fit is approximate.
Correlated errors and assumptions not taken into
account
26
WORLD DATA vs THEORY
16. Skyrme Model - N.W. Park and H. Weigel,
Nucl.Phys.A 451, 453 (1992) 17. Dispersion
Relation - H.W. Hammer, U.G. Meissner, D.
Drechsel, Phys.Lett. B 367, 323 (1996) 18.
Dispersion Relation - H.-W. Hammer and
Ramsey-Musolf, Phys.Rev.C60, 045204 (1999) 19.
Chiral Quark Soliton Model - A.Sliva et al.,
Phys.Rev.D 65, 014015 (2001) 20. Perturbative
Chiral Quark Model - V. Lyubovitskij et al.,
Phys.Rev.C 66, 055204 (2002) 21. Lattice - R.
Lewis et al., Phys.Rev.D 67, 013003 (2003) 22.
Lattice charge symmetry -Leinweber et al,
Phys.Rev.Lett. 94, 212001 (2005)
hep-lat/0601025
27
LATTICE INDIRECT APPROACH

• D. B. Leinweber et. al. PRL94, 212001 (2005)
• Find two expressions

R is the ratio of strange to down quark sea
contribution.

• They assume 0ltRlt1, and hence
• Gs must be negative!
• From a model, they find
• R 0.139, hence µs -0.046!
• However, R could be a number
• less than 0 or larger than 1.
• if R-0.5, Gs 0.2!

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MUON CONTRIBUTION TO

• Heavy muon limit

• Exact calculation
• Therefore

Laporta and Remiddi
29
SINGLE QUARK

• Contribution from a single polarized quark
• Ground state largest contribution

30
OVERALL CONTRIBUTION

• Sum of contribution from all diagrams
• Ground state largest contribution
• WRONG Color factor!
• Non-trivial spin-color correlation
• Need to introduce excited intermediate quark
  states

?
?
In g.s.
?
31
CONCLUSIONS AND OUTLOOK

• Influence of quark sea on protons macroscopic
  properties?
• Protons magnetic moment
• Exciting experim. results for strange quark
• Contradiction with theory?
• Sea quark contribution to
• Changes sign for light and heavy sea quark
• Strange quark
  contribution
• Negative?
• Positive?

32
CONCLUSIONS AND OUTLOOK

• What is the influence of the quark sea on the
  protons macroscopic properties?
• Protons magnetic moment
• Exciting experim. results for strange quark
• Contradiction with theory?
• Sea quark contribution to protons magnetic
  moment as a function of sea-quark mass
• Changes sign for light and heavy sea quark
• Strange quark contribut.
  very sensitive to QCD dyn.
• Negative or positive?

?