HEAVY QUARK CONTRIBUTION TO THE PROTON S MAGNETIC MOMENT

HEAVY QUARK CONTRIBUTION TO THE PROTON S MAGNETIC MOMENT Dominique Toublan University of Maryland with Xiangdong Ji JLab User s Group Annual Meeting, June 2006

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? Proton s magnetic moment: Strange quark contribution? Exciting experimental results Theory: Difficult because m s Λ QCD Learn from light and heavy quark limits Heavy sea-quark contribution?

OUTLINE Experimental results vs theory Sea-quark contribution to the proton s magnetic moment Light and heavy quark limits Warm-up: Muon contribution to the electron s magnetic moment Heavy sea-quark contribution to the proton s magnetic moment Implications for the physical strange quark

WORLD DATA vs THEORY Experiments G s M =0.28±0.20 G s E = 0.006 ±0.016 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 Preliminary K. Paschke, TJNAF 06 (Q 2 0.1GeV 2 ) Contradiction between theory and experiment?

MAGNETIC MOMENT Proton polarized in z-direction µ p = p 1 2 d 3 r ( r j em ) Light sea-quark, meson-cloud model: Heavy sea-quark at lowest order z p / p p δµ sea p <0 Musolf and Burkardt, Leinweber et al. j em µ = Qγ µ Q Heavy sea-quark contribution to proton magnetic moment?

HEAVY STRANGE QUARK Heavy quark limit î effective operator m Q Λ QCD j em µ =C(m Q) α T µα + C(m Q )=κg 3 (m Q )/m 4 Q T µα =14G µσ {G στ,g τα } 5G στ {G στ,g αµ } jµ em Use effective in def. of µ p Kaplan and Manohar

CONTRIBUTION TO µ p Heavy quark limit: δµ Q p =C(m Q) p T yx p + C(m Q )=κg 3 (m Q )/m 4 Q T yx = d [7( E abc a B b )E cz 2( E a E b B a ] B b )B cz Light-by-light scattering at LO in QED Need to calculate p T yx p Euler and Kockel Similar problem: muon contribution to µ e

MUON CONTRIBUTION TO µ e Heavy muon limit m µ m e δµ µ e =(C e/m 4 µ ) e Tγ yx e + Exact calculation: δµ µ e /µ e=k e α 3 em m2 e /m2 µ Therefore: e T γ yx e m2 µ m e +... >0 Laporta and Remiddi

MUON CONTRIBUTION TO µ e How can we understand this? k 3 Power counting: divergence Two scales: Mom. flow ( ), Factorization, dim. 3: m µ m e e T γ yx e =am3 µ +bm2 µ m e+cm µ m 2 e +dm3 e

MUON CONTRIBUTION TO µ e How can we understand this? k 3 Power counting: divergence Two scales: Mom. flow ( ), Factorization, dim. 3: m µ m e e T γ yx e =am3 µ +bm2 µ m e+cm µ m 2 e +dm3 e Lorentz invariance

MUON CONTRIBUTION TO µ e How can we understand this? k 3 Power counting: divergence Two scales: Mom. flow ( ), Factorization, dim. 3: m µ m e e T γ yx e =am3 µ +bm2 µ m e+cm µ m 2 e +dm3 e Symmetry T γ µν =m2 µ ( ) κm e ψσ µν ψ Lorentz invariance + δµ µ e =(C e/m 4 µ )(κm2 µ m e e ψσ yx ψ e )>0 Same result as exact calculation at LO

CONTRIBUTION TO µ p Heavy quark limit: δµ Q p =C(m Q) p T yx p C(m Q )=κg 3 (m Q )/m 4 Q p T yx p =am 3 Q +bm2 Q Λ QCD +cm Q Λ 2 QCD +dλ3 QCD Contributions from 1, 2, and 3 quarks in proton: k 3 k 1 k 0

CONTRIBUTION TO µ p Heavy quark limit: δµ Q p =C(m Q) p T yx p C(m Q )=κg 3 (m Q )/m 4 Q p T yx p =am 3 Q +bm2 Q Λ QCD +cm Q Λ 2 QCD +dλ3 QCD Contributions from 1, 2, and 3 quarks in proton: k 3 L O k 1 N L O k 0 Similar to muon contribution to µ e p T yx p singlequark m 2 Q Λ QCD+

CONTRIBUTION TO µ p Heavy quark limit: p T yx p =Km 2 Q δµ Q p =C(m Q) p T yx p f m f p ψ f σ yx ψ f p

CONTRIBUTION TO µ p Heavy quark limit: p T yx p =Km 2 Q δµ Q p =C(m Q) p T yx p f m f p ψ f σ yx ψ f p Proton tens. charge m u δ u +m d δ d >0 δµ Q p =A(m uδ u +m d δ d )/m 2 Q >0

Heavy quark limit: CONTRIBUTION TO p T yx p =Km 2 Q µ p δµ Q p =C(m Q) p T yx p f m f p ψ f σ yx ψ f p Proton tens. charge m u δ u +m d δ d >0 δµ Q p =A(m uδ u +m d δ d )/m 2 Q >0 Therefore: Non-trivial dependence Light sea: Heavy sea: δµ sea p <0 δµ sea p >0

QUARK MODELS OF THE PROTON Quark models: gluon fields generated by quarks Solve color Maxwell s equation in linear approx. D µ G µν =j ν 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

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 δµ Q p /Cµ p 2.2fm 4 Extrapolation NRQ 1.3fm 4 Bag Strange quark: G s M 0.1

CONCLUSIONS AND OUTLOOK Quark sea and the proton s macroscop. prop.? Strange quark and proton s magnetic moment Exciting experimental results Contradiction with theory? Sea quark contribution to µ p Changes sign for light and heavy sea quark

CONCLUSIONS AND OUTLOOK Quark sea and the proton s macroscop. prop.? Strange quark and proton s magnetic moment Exciting experimental results Contradiction with theory? Sea quark contribution to µ p Changes sign for light and heavy sea quark? Strange quark contribut.: Negative or positive?

CONCLUSIONS AND OUTLOOK Quark sea and the proton s macroscop. prop.? Strange quark and proton s magnetic moment Exciting experimental results Contradiction with theory? Sea quark contribution to µ p Changes sign for light and heavy sea quark Leinweber et al. 10 20MeV Strange quark contribut.: Negative or positive?