3
$\begingroup$

I've noticed the symbol $⊕$ used in a context I'm unfamiliar with. In several papers about the the calculation of the uncertainty of quantities measured with hadron colliders.

For example the uncertainty in transverse momentum given by:

$$ \frac{ \sigma_{P_{T}} }{ P_{T} } = 0.038\% P_{T}\,({\rm in\,GeV}) ⊕ 1.5\% $$

What exactly does $⊕$ mean in this context?

$\endgroup$
  • 3
    $\begingroup$ It's possibly supposed to be +/-; that is, a typographical error. Or a font substitution error if this is from online. $\endgroup$ – Peter Diehr Apr 9 '16 at 19:07
  • 4
    $\begingroup$ Which several papers? Which pages? $\endgroup$ – Qmechanic Apr 9 '16 at 19:37
  • $\begingroup$ It is used once here arxiv.org/abs/1406.0076 and i have seen it used more often in presentations like becher.itp.unibe.ch/LHC/CalorimeterAndJets.pdf So i don't think it's a typo $\endgroup$ – a.orwell Apr 11 '16 at 9:27
  • 1
    $\begingroup$ So your only serious reference is a 100-page paper where it's used once, and you can't even provide the page number, even when asked directly? $\endgroup$ – Emilio Pisanty May 2 '16 at 17:53
  • $\begingroup$ Presumably the example you quote is from this paper? $\endgroup$ – Emilio Pisanty May 2 '16 at 18:09
2
$\begingroup$

This seems to be addition in quadrature of multiple independent uncertainties in a measurement. In particular, if you have a measurement which depends on two quantities $a$ and $b$ whose uncertainties $\delta a$ and $\delta b$ are completely independent and uncorrelated, then their uncertainties will often be combined as

$$\delta(a+b)=\sqrt{\delta a^2+\delta b^2}=:\delta a\oplus\delta b,$$

where the symbol $\oplus$ is sometimes used to indicate this method of uncertainty combination.

For more on this procedure see e.g. this tutorial or simply google for 'addition in quadrature'; for an explicit example of the $\oplus$ notation used in this sense, see this CMS page.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.