Analysis and interpretation of data

E. Oset, J. Garzon, A. Martinez Torres, A. Ramos, S. Prelovsek, Wei Hong Liang

π N scattering and the N*(1535), N*(1650), N*(1700) resonances Analysis of KD, KD* scattering from lattice QCD energy levels: The D0s

*(2317) and Ds1*(2460) B0 and B0

s J/ψ ππ and the f0(500), f0(980) resonances

One of the popular ways to analysize data lately has been the use of the chiral unitay approach: π N and pseudoscalar-baryon coupled channels are considered in a unitary scheme, via the Bethe Salpeter equation, and the interaction is taken from the chiral Lagrangians. Recently, the need to include vector-baryon channels has become compeling. The local hidden gauge approach allows the extrapolation of the chiral Lagrangians to the vector sector:

π N scattering and the N*(1535), N*(1650), N*(1700)

Hidden gauge formalism for vector mesons, pseudoscalars and photons Bando et al. PRL, 112 (85); Phys. Rep. 164, 217 (88); U. G: Meissner Phys Rep 161 (88)

I=1/2, JP=1/2- (d-wave) (s-wave)

al are fit parameters

γi are fit parameters

For pseudoscalar-baryon -> pseudoscalar-baryon interaction

Best fit with the new channels

Best fit with only pseudoscalar –baryon channels ( Inoue et al 2002)

Im

Re

Results

The N*(1650) appears now, which could not be obtained with the PB channels alone

Subtracion contants in Inoue et al

The unnatural values of ai were interpreted by Hyodo et al. as a signal that relevant components are missing in the wave function. Hyodo, Jido, Hosaka 2012, Hyodo 2014, Sekihara, Jido, Hyodo 2014

Values of this work

JP=3/2- sector We get two resonances

Mohler, Lang, Leskovek, Prolovsek, Woloshyn , PRL 2013, PRD 2014

Reanalysis of the work:

In that work, using KD and KD* interpolators in Nf=2+1 they obtain 3 energy levels

One channel

Poles and couplings

Let us take an energy independent potential

In two channels

Gamermann, Nieves, E.O. , Ruiz-Arriola, PRD 2010

Effect of missing channels. Assume two channels neglecting V22 for simplicity

Define Energy dependent

Probability to have the 1 channel Probability of the channel eliminated

Generalization of Weinberg compositeness condition, (Weinberg PR 65, Baru PLB 2004.) Different derivations and generalization , Jido, Hyodo, Hosaka 2008, Sekihara, Hyodo, Jido 2011, Hyodo, Jido, Hosaka 2012, Hyodo 2013, Sekihara, Hyodo, Jido 2014

For example

T-matrix in a finite box

L

Momentum eigenstates in the box, periodical boundary conditions

Doering, Meissner, E.O., Rusetski, E P J A 2011

One channel case

Eigenenergies of the box

This is Luescher formula in our formalism

Limitation: you only get the phase shifts for the energies which are eigenenergies of the box

For KD For KD*

A best fit is conducted to the lattice energies to determine the parameters of V

A. Martinez-Torres, E. O., S. Prelovsek and A. Ramos, arXiv:1412.1706

With the potential obtained we evaluate the T matrix in the continuum and determine scattering properties and a bound state

Systematic uncertainties, Quoted numbers are for fits with central values of energies:

The message: Systematic uncertainties from this source are about 5 times smaller than the statistical. Uncertainties from extrapolating to mD and mD* physical masses are similar.

W.H. Liang, EO PLB 2014

They study decay of B into J/ψ and π+π-

No trace of f0(500) One normalization is arbritary but the two decays share the same normalization

Exp: Aaij 2011, 2012, 2014 Li (Belle), Aaltonen (CDF), Abasov (D0)

Our result

Exp:

Our result

Exp:

Note: all the ratios and the mass distributions are obtained with no free parameters, the only one has been fitted to scattering data.

Conclusions: - The need to improve description of data has shown the relevance of vector baryon - components in states formely thought as made only from pseudoscalar-baryon. - An easy, even more accurate and technically easier reformulation of Luescher approach is done. Energy spectra in F V Scattering amplitude in continuum, but for all energies, not only for the eigenenergies of the box. - The use of recent QCD lattice simulation results on the KD and KD* interaction allowed us to determine the existence of bound states, associated to the D*s0(2317) and D*s1(2460) states, the scattering length and effective range, and the probability that these states contain KD and KD* respectively, showing the power of QCD lattice simulations to unravel the nature of resonances. - B, and also D weak decays are showing a great potential to improve our knowledge

on the nature of low lying scalar mesons and many other resonances.