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Excited baryons from Bayesian priors and overlap fermions

Using the constrained-fitting method based on Bayesian priors, we extract the masses of the two lowest states of octet and decuplet baryons with both parities. The calculation is done on quenched 16^3x28 lattices of a=0.2 fm using an improved gauge action and overlap fermions, with the pion mass as low as 180 MeV. The Roper state N(1440)1/2+ is clearly observed for the first time as the 1st-excited state of the nucleon from the standard interpolating field. Together with other baryons, our preliminary results indicate that the level-ordering of the low-lying baryon states on the lattice is largely consistent with experiment. The realization is helped by cross-overs between the excited 1/2+ and 1/2- states in the region of pion mass from 300 to 400 MeV.

Using the constrained-fitting method based on Bayesian priors, we extract the masses of the two lowest states of octet and decuplet baryons with both parities. The calculation is done on quenched 16 3 × 28 lattices of a = 0.2 fm using an improved gauge action and overlap fermions, with the pion mass as low as 180 MeV. The Roper state N (1440) 1 2 + is clearly observed for the first time as the 1st-excited state of the nucleon from the standard interpolating field. Together with other baryons, our preliminary results indicate that the level-ordering of the low-lying baryon states on the lattice is largely consistent with experiment. The realization is helped by cross-overs between the excited 1 2 + and 1 2 − states in the region of mπ ∼ 300 to 400 MeV.
The rich structure of the excited baryon spectrum, as documented by the particle data group [1], provides a fertile ground for exploring the nature of quark-quark interactions. One outstanding example is the ordering of the lowestlying states which has the order of positive and negative-parity excitations inverted between N , ∆ and Λ channels. Conventional quark models have difficulty explaining the ordering in a consistent manner. There are two contrasting views. One is from the constituent quark model [2,3] which has the interaction dominated by onegluon-change type, i.e., color-spin λ c 1 · λ c 2 σ 1 · σ 2 . The other is based on Goldstone-bosonexchange [4] which has flavor-color λ f 1 ·λ f 2 σ 1 · σ 2 as the dominant part. Even though evidence from valence QCD [5] supports the flavor-color picture, the challenge of reproducing the ordering still faces lattice QCD.
There exist a number of lattice studies of the excited baryon spectrum using a variety of actions [6][7][8][9][10]. The nucleon channel is the most- * presented by F.X. Lee  studied, focusing on two independent local fields: (2) χ 1 is the standard nucleon operator, while χ 2 , which has a vanishing non-relativistic limit, is sometimes referred to as the 'bad' nucleon operator. Note that baryon interpolating fields couple to both positive and negative-parity states, which can be separated by well-established parityprojection techniques. The consensus so far appears to be that, first, the negative-parity splitting of N ( 1 2 − ) is largely established and consistent with experiment. Secondly, the Roper state N ′ ( 1 2 + ) as the 1st-excited state of the nucleon is still elusive. Since χ 2 couples little to the nucleon ground state, there was initial speculation that it couples to the Roper state. But that identification has been mostly abandoned since the mass extracted from χ 2 is consistently too high. What χ 2 couples to remains an open question.
The lattice size we use is 16 3 × 28 with the scale of a = 0.202(1) fm set from f π , which is our preferred choice for scale [11]. We consider a wide range of quark masses: 26 masses with the lowest m π = 180 MeV (or m π /m ρ =0.248), very     close to the physical limit, and with 18 masses below the strange quark mass. We analyzed 80 configurations. Details of the simulation can be found in [12].
We adapted the constrained curve-fitting method advocated in [13,14], adhering to the following guidelines: a) fit as many time slices in the correlation function G data (t) and as many terms in G theory (t) as possible; b) use prior knowledge, such as A > 0 and E n − E n−1 > 0; c) seek guide for priors from a subset of data (empirical Bayes method); d) un-constrain the term of interest in G theory (t) to have conservative error bars. The details of the implementation are discussed in [15]. Further study is under way to check the stability of the fitting algorithm, especially in the small mass region where the signal worsens, and to automate the fitting process. To make sure that the results are not due to finite-volume effects [16] (our lowest Lm π ≈ 3), we are repeating the entire calculation on a smaller lattice of 12 3 × 28 with all other parameters fixed. The lowest m π on this lattice is about 250 MeV, small enough to probe the crossover region.