# bootstrap.effectivemass: Computes effective masses with bootstrapping errors In hadron: Analysis Framework for Monte Carlo Simulation Data in Physics

 bootstrap.effectivemass R Documentation

## Computes effective masses with bootstrapping errors

### Description

Generates bootstrap samples for effective mass values computed from an object of class `cf` (a correlation function)

### Usage

```bootstrap.effectivemass(cf, type = "solve")
```

### Arguments

 `cf` a correlation function as an object of type `cf`, preferably after a call to `bootstrap.cf`. If the latter has not been called yet, it will be called in this function. `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 "shifted" 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.

### 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.

"acosh": the effective mass is computed from
m=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=\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).

"shifted": 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 "shifted", 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.

### Value

An object of class `effectivemass` is invisibly returned. It has objects: `effMass`:
The computed effective mass values as a vector of length `Time/2`. For `type="acosh"` also the first value is `NA`, because this definition requires three time slices.

`deffMass`:
The computed bootstrap errors for the effective masses of the same length as `effMass`.

`effMass.tsboot`:
The boostrap samples of the effective masses as an array of dimension RxN, where `R=boot.R` is the number of bootstrap samples and `N=(Time/2+1)`.

and `boot.R`, `boot.l`, `Time`

### Author(s)

Carsten Urbach, curbach@gmx.de

### References

arXiv:1203.6041

`fit.effectivemass`, `bootstrap.cf`, `removeTemporal.cf`

### Examples

```
data(samplecf)
samplecf <- bootstrap.cf(cf=samplecf, boot.R=99, boot.l=2, seed=1442556)
effmass <- bootstrap.effectivemass(cf=samplecf)
summary(effmass)
plot(effmass, ylim=c(0.14,0.15))

```

hadron documentation built on Sept. 9, 2022, 5:06 p.m.