5-quark component of nucleon: a bridge between `hard’ and `soft’ physics

1. Muenchen Nov 9, 2009 5-quark component of nucleon:a bridge between `hard’ and `soft’ physics Dmitri Diakonov Petersburg Nuclear Physics Institute Ruhr-Uni Bochum

2. Theoretical approaches to hadron physics Limitations: Perturbative QCD:only processes with large momentum transfer Chiral perturbation theory: only small momenta Lattice: chiral physics so far inaccessible, processes in Minkowski space inaccessible

3. Chiral physics is critical to understand hadrons, as seen from the uncertainty principle: When one attempts to measure a quark position to an accuracy better than the pion Compton wave length of 1.4 fm, one produces a pion, i.e. a pair. Hence, viewing baryons as “made of three quarks” contradicts the uncertainty principle [Landau and Peierls (1931)] The statement “nucleons are made of three quarks” is kindergarten physics, and we are immediately punished if we attempt to take it seriously. For example, 1) “spin crisis”: only of the nucleon spin is carried by three valence quarks 2) “mass crisis”: only ¼ of the nucleon sterm is carried by three valence quarks: Both paradoxes are explained by the presence of additional pairs in baryons.

4. [models with massive quarks and (confining) gluon interactions contradict chiral symmetry, as they violate invariance under chiral rotation

5. In general, quarks at low momenta are governed by a Dirac Hamiltonian, with all 5 Fermi terms: The scalar (s), pseudoscalar (p), vector (V), axial (A), and tensor (T) fields have, generally, non-local couplings to quarks, and are fluctuating quantum fields. However, in the limit they can be replaced by the non-fluctuating mean field. equal-time Green function its minimum determines the mean field.

6. valence quarks’ wave function equal-time Green function a theoretical Q.: if what is smaller, the answer: splitting inside SU(3) multiplets is , numerically ~140 MeV splitting between the centers of multiplets is , numerically ~ 230 MeV. Hence, meaning that one can first put , obtain the degenerate SU(3) multiplets, and only at the final stage account for nonzero , leading to splitting inside multiplets and mixing of SU(3) multiplets.

7. Two variants of the mean field : Variant I : the mean field is SU(3)-flavor- and SO(3)-rotation-symmetric, as in the old constituent quark model (Feynman, Isgur, Karl,…) In principle, nothing wrong about it, except that it contradicts the experiment, predicting too many excited states !! Variant II : the mean field for the ground state breaks spontaneouslySU(3) x SO(3) symmetry down to SU(2) symmetry of simultaneous space and isospin rotations, like in the hedgehog Ansatz breaks SU(3) and SO(3) separately but supports SU(2) symmetry of simultaneous spin and isospin rotations ! There is no general rule but we know that most of the heavy nuclei (large A) are not spherically-symmetric. Having a dynamical theory one has to show which symmetry leads to lower ground-state energy. Since SU(3) symmetry is broken, the mean fields for u,d quarks, and for s quark are completely different – like in large-A nuclei the mean field for Z protons is different from the mean field for A-Z neutrons. Full symmetry is restored when one SU(3)xSO(3) rotates the ground and one-particle excited states there will be “rotational bands” of SU(3) multiplets with various spin and parity.

8. Ground-state baryon and lowest resonances We assume confinement (e.g. ) meaning that the u,d and s spectra are discrete. Some of the components of the mean field (e.g. ) are C,T-odd, meaning that the two spectra are not symmetric with respect to One has to fill in all negative-energy levels for u,d and separately for s quarks, and the lowest positive-energy level for u,d. This is how the ground-state baryonN(940,1/2+) looks like. SU(3) and SO(3) rotational excitations of this filling scheme form the lowest baryon multiplets: 1155(8, 1/2+) and 1382(10, 3/2+)

9. QQQ, QQQQQbar, QQQQQQbar Qbar, … wave functions in full glory, of any baryon from the lowest octet and decuplet are encoded in two lines:

11. antiquark distribution at low virtuality (DD, Petrov, Polyakov, Pobylitsa and Weiss, 1996) [solid] vs. phenomenological GRV distribution. If we scan nucleons with a resolution q ~ 600 MeV, only ~65% of nucleons are made of 3 quarks, ~25% are made of 5 quarks, and ~10% of more than 5 quarks. Nevertheless, the fraction of momentum carried by antiquarks is very small:

12. The lowest resonances beyond the rotational excitations[DD (2008)] are (1405, ½-),N(1440, ½+) and N(1535, ½-).They are one-particle excitations: (1405, ½-) and N(1535, ½-) are two different ways to excite an s quark level. N(1535, ½-) is in fact a pentaquark which may explain large hNdecay [B.-S. Zou (2008)] N(1440, ½+) (uud) and (½+) ( ) are two different excitations of the same level of u,dquarks. is an analog of the Gamov-Teller excitation in nuclei! [when a proton is excited to the neutron’s level or vice versa.]

13. Charmed baryons from the large-Nc perspective If one of the Nc u,d quarks is replaced by c or b quark, the mean field is still the same, and all the levels are the same! Therefore, charmed baryons can be predicted from ordinary ones! standard charmed baryons exotic 5-quark charmed baryons Exotic 5-quark charmed baryons are light (~2450 MeV) and can decay only weakly: clear signature, especially in a vertex detector

14. Conclusions 1. “Baryons are made of three quarks” contradicts the uncertainty principle. In fact, already at low resolution ~65% of nucleons are made of 3 quarks, ~25% of 5 quarks, and ~10% of more than 5. 2. The 5-quark component of baryons is rather well understood, and should be measured directly 3. Pentaquarks (whose lowest Fock component has 5 quarks) are not too “exotic” – just Gamov-Teller excitations. In addition to the narrow there is a new prediction of charmed pentaquarks which probably decay only weakly.