Remove the sqrt(2) normalisation from the scalar longitudinal mode

Following from lalsuite!910 (merged) (cc @max-isi) the sqrt(2) normalisation should be removed from the scalar longitudinal mode's response, to agree with the normalisation of the other modes and make Fb = -Fl.

approved this merge request

I'm looking at the LALInference MR and wondering why @max-isi says it was originally introduced incorrectly? For example, Eq. 1 here also has this factor of sqrt(2).

I'll defer to @max-isi here. I know the link Nishizawa paper does have the sqrt(2) in it, but I've also seen papers that say Fb = -Fl, which you do not get if you include the sqrt(2) factor.

Hi @sylvia.biscoveanu this comes down to the definition of the polarization amplitudes.

We usually write the detector output as

$h = F^A h_A$

, with an implicit sum over polarizations

$A$

and the response defined as

$F_A = e^A_{ab} D^{ab}$

for polarization tensors

$e^A$

and detector tensor

$D^{ab}$

. Furthermore, we usually want the polarization amplitudes

$h_A$

to correspond to the metric components in some standard (synchronous) gauge, $h_{ab} = h_A e^{A}_{ab}

$. In particular for the longitudinal mode ($

\ell$), this means (picking a frame)

$h_{zz} = h_\ell$

and there's no

$\sqrt{2}$

that appears anywhere. (This might become clearer if you look at Sect. IIA in http://arxiv.org/abs/1710.03794)

Now, we are free to redefine the polarization tensors and amplitudes however we want, but everything must be kept consistent in the expression for the detector output

$h$

. For example, like Nishizawa and other theorists, we can use this freedom to enforce that

$e^{\ell}_{ab}$

have the same norm as the other polarization tensors (note, e.g., that

$e^{+}_{ab} e^{+}{}^{ab} = 2$

, while

$e^{\ell}_{ab} e^{\ell}{}^{ab} = 1$

). That is, we can redefine

$e^{\ell}_{ab} \rightarrow \sqrt{2} e^{\ell}_{ab}$

to get

$e^{\ell}_{ab} e^{\ell}{}^{ab} = 2$

. However, this comes at the price of either modifying what you mean by

$h_{\ell} \rightarrow h_\ell / \sqrt{2}$

, or changing the detector output expression to be

$h = \sum_{A\neq \ell}F^A h_A + F^\ell h_\ell / \sqrt{2}$

. So it's annoying.

This is all to say that the

$\sqrt{2}$

I introduced amounted to a redefinition of the longitudinal polarization amplitude that means it's no longer the

$h_{zz}$

metric component as one would expect (like for the other polarizations) but

$h_{zz}/\sqrt{2}$

, and you end up with

$F_b \neq - F_\ell$

artificially.

@matthew-pitkin is this ready to be merged?

changed milestone to %0.5.5

approved this merge request

resolved all threads

merged

mentioned in commit 75bb453d