Results of the High Statistics Run (~600 configs)

This page documents the results of the high statistics run.

Reliable results

Please see my results page for a summary of the results.

Unresolved problems

There appears to be an inconsistency in the data that is unsmeared with the data that is smeared. Specifically, data from the local-local correlator only gives a different ground state than data from the 1S-1S correlator only. The difference is quite significant: several sigma. I'll document my procedure here, in hopes that someone can spot a flaw.

Effective mass plots

Note that both seem to plateau at just under 1.2. The fact that the 1S-1S state shows larger oscillations will be seen in the later fit results.

Choice of priors

I select the following priors:
self.energies = [1.15, 1.15, 1.65, 1.65] self.epriors = [[1.15, .3], [1.15, .3], [1.65, .3], [1.65, .3]] self.momentum_scale = .02 This means the ground state energy for both the oscillating and non-oscillating state is set to 1.15 +- 0.3. The energy splittings are set to 0.5 +- 0.3. These priors come from the observation that the effective mass plots plateau at a little under 1.2, and an energy splitting of 0.5 worked well for the charmonium states.

One-correlator fits to D_s p000 state

Fitting to only the local-local correlator gives a chi^2 of 0.672

The states are (left-to-right) ground non-osc, ground osc, excited non-osc, excited osc, etc. Notice that the second excited non-oscillating state has a larger error bar than the first excited non-oscillating state. This is often an indication that the true state is the higher one, and the intermediate state is a ghost. I check this by looking at the effects of varying the priors (red is my default prior, other points are from changing prior width by a factor of 2)

Note that the stable states are E0, E1, E3, and E4. Given that we only really care about E0, the ghost state at E2 is probably not too troubling, however we can test this by repeating the test with different priors. Here are results after changing the priors to
self.energies = [1.15, 1.15, 2.15, 1.65] self.epriors = [[1.15, .3], [1.15, .3], [2.15, .3], [1.65, .3]]

This shows that if the priors are wide enough, it still prefers the "ghost" state. Zooming in on the ground state (which is all we really care about) to see how much of an effect this ghost state has gives:

So the ghost state does have a noticable effect, but it's within errors.

One-correlator fits to D_s p300 state

So far we've only looked at the zero-momentum state. What happens if we go to non-zero momentum? With the original priors, the local-local correlator gives a chi^2 of 1.468

Varying priors and looking at the 6-state fit:

We see we the local-local correlator gives us information on the first four energy levels.

Looking at the states:

momentum	chi^2	E_0 (non-osc)	E_1 (osc)
p000	0.598	1.160411+-0.001574	1.304344+-0.052982
p100	0.611	1.198161+-0.001909	1.309180+-0.027291
p110	0.754	1.235330+-0.001978	1.328822+-0.021794
p111	0.812	1.269191+-0.002392	1.352700+-0.019934
p200	0.816	1.299864+-0.002803	1.370436+-0.019971
p210	0.925	1.329377+-0.003313	1.387991+-0.020310
p211	1.115	1.356833+-0.004013	1.405540+-0.022241
p220	1.206	1.405483+-0.005652	1.419148+-0.028040
p221	1.628	1.426339+-0.006816	1.432008+-0.032399
p300	1.468	1.426712+-0.006655	1.434678+-0.033606

One-correlator fits to D_s^* p000 state

A local-local correlator fit gives a chi^2 of 1.629

Once again, we have a ghost state.

One-correlator fits to D_s^* p300 state

The problem arises when we try to fit to higher-momentum states. For example, at p300, the chi^2 is 2.878

What's especially important here is that the oscillating state is lower than the non-oscillating state! Zooming in makes this easier to see:

Does this mean we still have a bug???

Looking at the full set of momentum states shows there is a continuous transition from having the non-oscillating state being the ground state (as is the case for the p000 data) to the oscillating state be the ground state (p300 data). They appear to cross at p210/p211. The chi^2 grows fairly steadily:

momentum	chi^2	E_0 (non-osc)	E_1 (osc)
p000	1.629	1.230400+-0.004150	1.394627+-0.027678
p100	1.316	1.266324+-0.004469	1.365309+-0.018575
p110	1.257	1.305496+-0.002999	1.367801+-0.015626
p111	1.376	1.335849+-0.003326	1.377412+-0.014039
p200	1.533	1.363374+-0.003689	1.397594+-0.014639
p210	1.960	1.390373+-0.004243	1.408207+-0.014645
p211	2.354	1.416113+-0.004997	1.422612+-0.015410
p220	3.142	1.460429+-0.006723	1.442906+-0.019644
p221	3.341	1.480052+-0.008128	1.455231+-0.022237
p300	2.878	1.485314+-0.008112	1.449153+-0.024104