Light-quark contributions to the magnetic form factor of the Λ(1405)

Abstract

In a recent study of the Λ(1405), the suppression of the strange-quark contribution to the magnetic form factor was interpreted as the discovery of a dominant antikaon-nucleon composition for this low-lying state. We confirm this result by calculating the light u-and d-quark contributions to the Λ(1405) magnetic form factor in lattice QCD in order to determine the extent to which their contributions support this exotic molecular description. Drawing on the recent graded-symmetry approach for the flavor-singlet components of the Λ(1405), the separation of connected and disconnected contributions is performed in both the flavor-octet and singlet representations. The relationship between light-quark contributions to the Λ(1405) magnetic form factor and the connected contributions of the nucleon magnetic form factors is established and compared with lattice calculations of the same quantities, confirming the KN molecular structure of the Λ(1405) in lattice QCD.Resolving and understanding the internal structure of hadronic excited states is an important contemporary problem in the field of nonperturbative QCD. While lattice QCD simulation methods are increasingly able to probe the chiral regime of ground state observables with unprecedented accuracy [1][2][3][4], the resolution of excited-baryon form factors is still at a very early stage [5][6][7][8][9][10].Interest in the Λ(1405) resonance has continued unabated for more than 50 years [10-44] because of its unusually low mass -lower even than the corresponding mass of the negative parity nucleon, despite containing a heavier strange quark. The unexpected position of the Λ(1405) in the spectrum has been explored in several studies, which typically indicate a significant contribution from a KN bound state . The πΣ channel also plays a nontrivial role. It is now widely agreed that there is a two-pole structure in this resonance region [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] stemming from attractive interactions in both the πΣ and KN channels. In making contact with results from lattice QCD [10,40,41], a description of the Λ(1405) over a range of quark masses has been developed [10,32,45], bridging constituent-quark ideas at heavy quark masses and the molecular KN dominance of the Λ(1405) at light quark masses.A recent lattice QCD study of the Λ(1405) reported evidence of a molecular KN structure [10]. There, the role of the strange quark was paramount in signaling the presence of a dominant KN structure. At heavier quark masses approaching the strange quark mass, the three quark flavors (u, d, s) are found to make approximately equal contributions to the magnetic form factor when their charges are set to unity. The underlying flavor symmetry is manifest. However, as the u and d quarks become light, flavor symmetry in the quark contributions to the magnetic form factor is found to be badly broken, and the strange-quark contribution drops by an order of magnitude from its maximum to a nearly vanishing value at the smallest quark mass. This feature h...

Structure of the Roper resonance from lattice QCD constraints

“…These simulations have been supported by analysis involving an effective Hamiltonian [25], which allows a natural connection to be made between the results calculated on a finite lattice volume and the infinite volume of the real world [26,27]. As a result of these studies, it is now clear that the Λ(1405) is essentially an anti-kaon nucleon bound state with very little content corresponding to the sort of threequark state anticipated in a typical quark model [24].…”

“…To make matters worse, the first negative-parity excitation of a strangeness -1 baryon, the famous Λ(1405), is lower in mass than both of these non-strange excited states of the nucleon [22]. Fortunately, in this case there have recently been advances in our understanding, via lattice QCD simulations of not only the mass of this state but the individual valence quark contributions to its electromagnetic form factors [23,24]. These simulations have been supported by analysis involving an effective Hamiltonian [25], which allows a natural connection to be made between the results calculated on a finite lattice volume and the infinite volume of the real world [26,27].…”

Elastic Form Factors of Nucleon Excitations

“…This is evident in both a significant shift in the magnetic moments of the excited proton and neutron, and significant curvature in the pion-mass dependence of the electric form factor. A description of this state as a molecular bound state of KΣ dressed by KΛ, ηN and πN is an intriguing possibility, analogous to the description of the odd-parity Λ(1405) excitation as a molecular bound state of KN dressed by πΣ [11,31]. The proximity of the non-interacting KΣ to the effective energy of the observed lattice state is suggestive.…”

“…For example, Fig. 14 shows dipole fits to the two quark flavours at m π = 411 MeV, with a RMS charge radius of 0.679(38) fm for the doubly represented quark flavour and 0.715 (31) fm for the singly represented quark flavour. These results are very similar to the first negative-parity excitation.…”

Elastic form factors of nucleon excitations in lattice QCD

“…At the lightest two pion masses, the form factor data were insufficient to properly constrain a dipole fit so we do not report magnetic radii at these masses. πN is an intriguing possibility, analogous to the description of the odd-parity Λð1405Þ excitation as a molecular bound state ofKN dressed by πΣ [8,57]. The proximity of the noninteracting KΣ to the effective energy of the observed lattice state is suggestive.…”