hadron (version 3.1.2)

effectivemass.cf: Computes effective mass values for a correlation function

Description

Computes effective mass values for a correlation function using different type of definitions for the effective mass. This function is mainly indented for internal usage by bootstrap.effectivemass.

Usage

effectivemass.cf(cf, Thalf, type = "solve", nrObs = 1,
  replace.inf = TRUE, interval = c(1e-06, 2), weight.factor = NULL,
  deltat = 1, tmax = Thalf - 1)

Arguments

cf

The correlation function either as a vector of length nrObs*(Thalf+1) or as an array of dimension NxnrObs*(Thalf+1), where N is the number of observations. N will be averaged over.

Thalf

Half of the time extent of the lattice

type

The function to be used to compute the effective mass values. Possibilities are "acosh", "solve", "log", "temporal", "shifted" and "weighted". While the first three assume normal cosh behaviour of the correlation function, "temporal" is desigend to remove an additional constant stemming from temporal states in two particle correlation functions. The same for "subtracted" and "weighted", the latter for the case of two particle energies with the two particle having different energies. In the latter case only the leading polution is removed by removeTemporal.cf and taken into account here.

nrObs

The number of "observables" included in the correlator

replace.inf

If set to TRUE, all Inf values will be replaced by NA. This is needed for instance for bootstrap.effectivemass.

interval

initial interval for the uniroot function when numerically solving for the effective mass.

weight.factor

relative weight for type "weighted" only, see details

deltat

time shift for shifted correlation functions

tmax

t-value up to which the effectivemass is to be computed

Value

Returns a vector of length Thalf with the effective mass values for t-values running from 0 to Thalf-1

Details

A number of types is implemented to compute effective mass values from the correlation function:

"solve": the ratio \(C(t+1) / C(t) = \cosh(-m*(t+1)) / \cosh(-m*t)\) is numerically solved for \(m(t)\).

"acosh": the effective mass is computed from \(m(t)=acosh((C(t-1)+C(t+1)) / (2C(t)))\) Note that this definition is less tolerant against noise.

"log": the effective mass is defined via \(m(t)=\log(C(t) / C(t+1))\) which has artifacts of the periodicity at large t-values.

"temporal": the ratio \([C(t)-C(t+1)] / [C(t-1)-C(t)] = [\cosh(-m*(t))-\cosh(-m*(t+1))] / [\cosh(-m*(t-1))-\cosh(-m(t))]\) is numerically solved for \(m(t)\).

"subtracted": like "temporal", but the differences \(C(t)-C(t+1)\) are assumed to be taken already at the correlator matrix level using removeTemporal.cf and hence the ratio \([C(t+1)] / [C(t)] = [\cosh(-m*(t))-\cosh(-m*(t+1))] / [\cosh(-m*(t-1))-\cosh(-m(t))]\) is numerically solved for \(m(t)\).

"weighted": like "subtracted", but now there is an additional weight factor \(w\) from removeTemporal.cf to be taken into account, such that the ratio \([C(t+1)] / [C(t)] = [\cosh(-m*(t))-w*\cosh(-m*(t+1))] / [\cosh(-m*(t-1))-w*\cosh(-m(t))]\) is numerically solved for \(m(t)\) with \(w\) as input.

References

arXiv:1203.6041

See Also

bootstrap.effectivemass

Examples

# NOT RUN {
data(correlatormatrix)
cfnew <- extractSingleCor.cf(correlatormatrix, id=1)
cfnew <- bootstrap.cf(cfnew, boot.R=99, boot.l=1)
X <- effectivemass.cf(cfnew$cf, Thalf=25, tmax=24)
# }