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.

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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