HEAVY QUARK CONTRIBUTION TO THE PROTONS MAGNETIC MOMENT

HEAVY QUARK CONTRIBUTION TO THE PROTON’S MAGNETIC MOMENT Dominique Toublan University of Maryland with Xiangdong Ji PAVI 06, Milos, May 2006

INTRODUCTION • Proton: ØNaïve: 3 quarks bound by strong interaction ØQCD: Sea of virtual gluons, quark-antiq. pairs ð What are its consequences for the macroscopic properties of the proton? • Proton’s magnetic moment: ØStrange quark contribution? § Exciting experimental results § Theory: Difficult because m s » ¤ Q C D § 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 ØLight 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 s = 0: 28 § 0: 20 GM G Es = ¡ 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: 1 Ge. V 2 ) Contradiction between theory and experiment?

MAGNETIC MOMENT • Proton polarized in z-direction ³ ´ R ¹ 1 = hp j " p 2 d 3 r r £ ~j em ~ z jp "i =hp " jp "i • Light sea-quark, meson-cloud model: ±¹ sea p < 0 Musolf and Burkardt, Leinweber et al. • Heavy sea-quark at lowest order ¹ ¹Q j ¹em = Q° Heavy sea-quark contribution to proton magnetic moment?

HEAVY STRANGE QUARK • Heavy quark limit effective operator m Q À ¤ QCD j ¹em = C ( m Q ) @® T¹ ® + ¢¢¢ 3 4 Ø C ( m Q ) = · g ( m Q ) =m Q ¾¿ ¾¿ Ø T¹ ® = 14 G ¹ ¾f G ; G ¿ ® g¡ 5 G ¾¿ f G ; G ® ¹ g • Use effective j em ¹ in def. of ¹ p Kaplan and Manohar

¹ CONTRIBUTION TO p • Heavy quark limit: ±¹ Q p = C ( m Q ) hp " j T y x jp "i + ¢¢¢ 3 4 Ø C ( m Q ) = · g ( m Q ) =m Q Ø Ty x = P h d a bc 7( E~ a ¢B~ b ) E cz ~ a ¢E ~ b ¡ B~ a ¢B~ b ) B cz ¡ 2( E i ØLight-by-light scattering at LO in QED Euler and Kockel • Need to calculate hp " j Ty x jp "i • Similar problem: muon contribution to ¹ e

¹ MUON CONTRIBUTION TO e • Heavy muon limit m¹ À me Ø ±¹ ¹ e = ( C e =m 4¹ ) hej Ty° x jei + ¢¢¢ • Exact calculation: ¹ 3 2 2 Ø ±¹ e = K e ®em m e =m ¹ + : : : > 0 ° 2 Ø Therefore: hej Ty x jei » m ¹ m e Laporta and Remiddi

¹ MUON CONTRIBUTION TO e • How can we understand this? 3 k ØPower counting: divergence ØTwo scales: Mom. flow (m ¹ ), m e ØFactorization, dim. 3: hej Ty° x jei = a m 3¹ + b m 2¹ m e + c m ¹ m 2 e + d m e 3

¹ MUON CONTRIBUTION TO e • How can we understand this? 3 k ØPower counting: divergence ØTwo scales: Mom. flow (m ¹ ), m e ØFactorization, dim. 3: hej Ty° x jei = a m 3¹ + b m 2¹ m e + c m ¹ m 2 e + d m e 3 ! Lorentz invariance

¹ MUON CONTRIBUTION TO e • How can we understand this? 3 k ØPower counting: divergence ØTwo scales: Mom. flow (m ¹ ), m e ØFactorization, dim. 3: hej Ty° x jei = a m 3¹ + b m 2¹ m e + c m ¹ m 2 e + d m e 3 ! Lorentz invariance ³ ´ • Symmetry ) T¹° º = m 2¹ · m e ù ¾¹ º à + ¢¢¢ ) ±¹ ¹ e = ( C e =m 4¹ ) ( · m 2¹ m e hej ù ¾y x à jei ) > 0 ØSame result as exact calculation at LO

¹ CONTRIBUTION TO p Q = C ( m ) hp " j T ±¹ y x jp "i Q • Heavy quark limit: p 3 ( m ) =m 4 = C m · ( ) g Q Q Ø Q 3 + b m 2 ¤ = T a m " "i hp j jp y x Ø Q Q QCD + c m Q ¤ 2 Q C D + d ¤ 3 Q C D • Contributions from 1, 2, and 3 quarks in proton: » k 3 » k 1 » k 0

¹ CONTRIBUTION TO p Q = C ( m ) hp " j T ±¹ y x jp "i Q • Heavy quark limit: p 3 ( m ) =m 4 = C m · ( ) g Q Q Ø Q 3 + b m 2 ¤ = T a m " "i hp j jp y x Ø Q Q QCD + c m Q ¤ 2 Q C D + d ¤ 3 Q C D • Contributions from 1, 2, and 3 quarks in proton: » k 3 L O » k 1 N L O Similar to muon contribution to ¹ e hp " j Ty x jp "i si n gl e q u ar k » m 2 Q ¤ Q C D + ¢¢¢ » k 0

¹ CONTRIBUTION TO • Heavy quark limit: ±¹ 2 = K m " "i hp j. T jp y x Ø Q p = C ( m Q ) hp " j Ty x jp "i P ¹ f ¾y x à f jp "i m " à hp j f f Q p

¹ CONTRIBUTION TO • Heavy quark limit: ±¹ 2 = K m " "i hp j. T jp y x Ø Q Proton tens. charge ) ±¹ Q p p = C ( m Q ) hp " j Ty x jp "i P ¹ f ¾y x à f jp "i m " à hp j f f Q p m u ±u + m d ±d > 0 = A ( m u ±u + m d ±d ) =m 2 Q > 0

¹ CONTRIBUTION TO • Heavy quark limit: ±¹ 2 = K m " "i hp j. T jp y x Ø Q = C ( m Q ) hp " j Ty x jp "i P ¹ f ¾y x à f jp "i m " à hp j f f Q p Proton tens. charge ) ±¹ Q p p m u ±u + m d ±d > 0 = A ( m u ±u + m d ±d ) =m 2 Q > 0 • Therefore: Non-trivial dependence sea ØLight sea: ±¹ p < 0 sea > 0 ±¹ ØHeavy sea: p

QUARK MODELS OF THE PROTON • Quark models: gluon fields generated by quarks • Solve color Maxwell’s equation in linear approx. D ¹ G¹ º = j º • 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 ØSame as 8 copies of e. m. fields

QUARK MODELS: RESULTS • Spin-dependent color magnetic field: ØNRQ model: constit. quark magnetic dipole ØMIT bag: quasi-massless quark orbit. motion • Contribution from single polarized quark ØGround state = largest contribution ±¹ Q =C ¹ p p ' 2: 2 fm¡ 4 1: 3 fm¡ 4 NRQ Bag Extrapolation s ' G Strange quark: M 0: 1

CONCLUSIONS AND OUTLOOK • Quark sea and the proton’s macroscop. prop. ? • Strange quark and proton’s magnetic moment ØExciting experimental results ØContradiction with theory? • Sea quark contribution to ¹ p ØChanges 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 ØExciting experimental results ØContradiction with theory? • Sea quark contribution to ¹ p ØChanges 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 ØExciting experimental results ØContradiction with theory? • Sea quark contribution to ¹ p ØChanges sign for light and heavy sea quark Leinweber et al. » 10¡ 20 M e. V • Strange quark contribut. : Negative or positive?