Archive for parity

Some B-Mode Background

Posted in Astrohype, Science Politics, The Universe and Stuff with tags , , , , , , , , , , , on March 15, 2014 by telescoper

Well, in case you hadn’t noticed, the cosmology rumour mill has gone into overdrive this weekend primarily concerning the possibility that an experiment known as BICEP (an acronym formed from Background Imaging of Cosmic Extragalactic Polarization). These rumours have been circulating since it was announced last week that the Harvard-Smithsonian Center for Astrophysics (CfA) will host a press conference  on Monday, March 17th, to announce “a major discovery”. The grapevine is full of possibilities, but it seems fairly clear that the “major discovery” is related to one of the most exciting challenges facing the current generation of cosmologists, namely to locate in the pattern of fluctuations in the cosmic microwave background evidence for the primordial gravitational waves predicted by models of the Universe that involve inflation.

Anyway, I thought I’d add a bit of background on here to help those interested make sense of whatever is announced on Monday evening.

Looking only at the temperature variation across the sky, it is not possible to distinguish between tensor  (gravitational wave) and scalar (density wave) contributions  (both of which are predicted to be excited during the inflationary epoch).  However, scattering of photons off electrons is expected to leave the radiation slightly polarized (at the level of a few percent). This gives us additional information in the form of the  polarization angle at each point on the sky and this extra clue should, in principle, enable us to disentangle the tensor and scalar components.

The polarization signal can be decomposed into two basic types depending on whether the pattern has  odd or even parity, as shown in the nice diagram (from a paper by James Bartlett)

The top row shows the E-mode (which look the same when reflected in a mirror and can be produced by either scalar or tensor modes) and the bottom shows the B-mode (which have a definite handedness that changes when mirror-reflected and which can’t be generated by scalar modes because they can’t have odd parity).

The B-mode is therefore (at least in principle)  a clean diagnostic of the presence of gravitational waves in the early Universe. Unfortunately, however, the B-mode is predicted to be very small, about 100 times smaller than the E-mode, and foreground contamination is likely to be a very serious issue for any experiment trying to detect it. To be convinced that what is being measured is cosmological rather than some sort of contaminant one would have to see the signal repeated across a range of different wavelengths.

Moreover, primordial gravitational waves are not the only way that a cosmological B-mode signal could be generated. Less than a year ago, a paper appeared on the arXiv by Hanson et al. from SPTpol, an experiment which aims to measure the polarization of the cosmic microwave background using the South Pole Telescope. The principal result of this paper was to demonstrate a convincing detection of the so-called “B-mode” of polarization from gravitational lensing of the microwave background photons as they pass through the gravitational field generated by the matter distributed through the Universe. Gravitational lensing can produce the same kind of shearing effect that gravitational waves generate, so it’s important to separate this “line-of-sight” effect from truly primordial signals.

So we wait with bated breath to see exactly what is announced on Monday. In particular, it will be extremely interesting to see whether the new results from BICEP are consistent with the recently published conclusions from Planck. Although Planck has not yet released the analysis of its own polarization data, analysis of the temperature fluctuations yields a (somewhat model-dependent) conclusion that the ratio of tensor to scalar contributions to the CMB pattern is no more than about 11 per cent, usually phrased in the terms, i.e. R<0.11. A quick (and possibly inaccurate) back-of-the-envelope calculation using the published expected sensitivity of BICEP suggests that if they have made a detection it might be above that limit. That would be really interesting because it might indicate that something is going on which is not consistent with the standard framework. The limits on R arising from temperature studies alone assume that both scalar and tensor perturbations are generated by a relatively simple inflationary model belonging to a class in which there is a direct relationship between the relative amplitudes of the two modes (and the shape of the perturbation spectrum). So far everything we have learned from CMB analysis is broadly consistent with this simplifying assumption being correct. Are we about to see evidence that the early Universe was more complex than we thought? We'll just have to wait and see…

Incidentally, once upon a time there was a British experiment called Clover (involving the Universities of  Cardiff, Oxford, Cambridge and Manchester) which was designed to detect the primordial B-mode signal from its vantage point in Chile. I won’t describe it in more detail here, for reasons which will become obvious.

The chance to get involved in a high-profile cosmological experiment was one of the reasons I moved to Cardiff in 2007, and I was looking forward to seeing the data arriving for analysis. Although I’m primarily a theorist, I have some experience in advanced statistical methods that might have been useful in analysing the output.  Unfortunately, however, none of that actually happened. Because of its budget crisis, and despite the fact that it had spent a large amount (£4.5M) on it already,  STFC decided to withdraw the funding needed to complete it (£2.5M)  and cancelled the Clover experiment. Had it gone ahead it would probably have had two years’ data in the bag by now.

It wasn’t clear that Clover would have won the race to detect the B-mode cosmological polarization, but it’s a real shame it was withdrawn as a non-starter. C’est la vie.

Time will say nothing but I told you so…

Posted in The Universe and Stuff with tags , , , , , , , , , , , on November 20, 2012 by telescoper

A blog post at Nature News just convinced me that it’s time to post something about science for a change.

The paper (just published in Physical Review Letters) that inspired the Nature piece is entitled Observation of Time-Reversal Violation in the B0 Meson System and its publication gave me an excuse find the answer to a question that I’d wondered about for a while.

Although I’m not a real particle physicist, I have in the past been called upon to teach courses on particle theory (first at Nottingham and then here in Cardiff). One of the things I’ve emphasized in lectures on this subject is the importance of symmetries in particle physics and, perhaps even more important, the idea that symmetries you might think would hold in theory might actually be violated in the real world.

A good starting point is to think about parity. A parity transformation involves flipping the sign of all the spatial coordinates used to define a system; this operation involves the reflection of a system through the origin of the coordinate system so is connected with the notion of “handedness”. In quantum mechanics, an eigenstate of the parity operator P has two possible eigenvalues: +1 (even) or -1 (odd). One might expect this to be a “good”  quantum number in the sense that it is a quantity that is conserved during particle interactions. This is the case in many situations, but turns out not to be true in weak interactions; parity violation has been known about since the 1950s, in fact.

Another interesting symmetry relates to the operator C which represents charge conjugation. The charge-conjugation operation involves changing particles into anti-particles, e.g. inverting the electrical charge on the electron to make a positron.  Since the electron and positron seem to be identical apart from the different charge one suspects a general symmetry might apply here too. However, weak interactions are also known to violate C-symmetry (for example because under the action of C on a left-handed neutrino would turn into a left-handed anti-neutrino, which doesn’t exist in the standard model).

So if C and P aren’t conserved separately could the combined operation (CP)  represent a symmetry? CP acting on a left-handed neutrino would create a right-handed anti-neutrino, which does exist in the standard model so this seems a promising possibility. But no. CP is also violated in certain weak interactions. It’s always the weak interactions that mess things up, actually. Very irritating of them.

Now we come to the crux. In any model of particle interactions based on quantum field theory, the combination CPT has to be an exact symmetry. In this composite operator T represents time-reversal, so if you change particles into antiparticles, perform a parity flip, and run the clock backwards everything should look exactly the same. A corollary of this, since we know that CP is not an exact symmetry is that T can’t be either (otherwise it couldn’t restore the violation caused by CP). But how to test whether T is violated?

In fact, in lecturing on this topic I’ve always ended there and moved onto something else.  I’ve often wondered how one might test for T-violation but never arrived at an answer.  You can’t know everything.

Anyway, the answer is explained nicely in an explanatory article published with the paper. The B-mesons discussed in the paper are electrically neutral particles, but they can nevertheless exist as distinct particles and antiparticles. In this respect they are similar to their (lighter) cousins the neutral Kaons which played an important role in establishing CP violation back in the 60s.

Mesons comprise  a quark and an anti-quark bound together by the strong force. The neutral Kaon comprises a down quark and an anti-strange quark (or, if you prefer, a strange antiquark) whereas the anti-Kaon is an anti-down and a strange. Although these combinations have the same electrical charge (zero) they carry different overall quark flavour numbers and are therefore discernibly different. The B-mesons involve the bottom anti-quark and a down quark (and vice-versa for the anti-B).

The experiment analysed here, called BaBar and situated at the Stanford Linear Accelerator facility, detected B-mesons initially created as entangled pairs of B and anti-B each of which subsequently decays into either a CP-eigenstate or a pure flavour eigenstate.  To study T reversal, the physicists selected just those events in which  one meson decayed into a flavour state and the other  into a CP eigenstate.  These decays can happen in either order, but if T symmetry were to hold, then the decay rate of the second particle should not depend on whether the first particle decayed into a CP-eigenstate or a pure flavour state.  The experiment showed that there is a difference in these rates and therefore T-symmetry is broken. A time machine is not needed after all; the direction of time is supplied by the particles’ own spontaneous decays.

This isn’t an unexpected result. I reckon most particle physicists were pretty sure proof of T-violation would be found at some point. But it’s certainly a very clever experiment and it goes down as another success for the standard model of particle physics.

Through the Looking Glass

Posted in The Universe and Stuff with tags , , , on November 15, 2010 by telescoper

I’m afraid I’m too busy again for a proper post, so I’ll resort once again to the supply of wonderful Richard Feynman clips on Youtube. Here’s a particularly nice one, about the mysterious matter of mirrors. I might use this later on this year when I talk about parity to my particle physics class!


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Clover and Out

Posted in Science Politics, The Universe and Stuff with tags , , , , , , , , , on March 31, 2009 by telescoper

One of the most exciting challenges facing the current generation of cosmologists is to locate in the pattern of fluctuations in the cosmic microwave background evidence for the primordial gravitational waves predicted by models of the Universe that involve inflation.

Looking only at the temperature variation across the sky, it is not possible to distinguish between tensor  (gravitational wave) and scalar (density wave) contributions  (both of which are predicted to be excited during the inflationary epoch).  However, scattering of photons off electrons is expected to leave the radiation slightly polarized (at the level of a few percent). This gives us additional information in the form of the  polarization angle at each point on the sky and this extra clue should, in principle, enable us to disentangle the tensor and scalar components.

The polarization signal can be decomposed into two basic types depending on whether the pattern has  odd or even parity, as shown in the nice diagram (from a paper by James Bartlett)

The top row shows the E-mode (which look the same when reflected in a mirror and can be produced by either scalar or tensor modes) and the bottom shows the B-mode (which have a definite handedness that changes when mirror-reflected and which can’t be generated by scalar modes because they can’t have odd parity).

The B-mode is therefore (in principle)  a clean diagnostic of the presence of gravitational waves in the early Universe. Unfortunately, however, the B-mode is predicted to be very small, about 100 times smaller than the E-mode, and foreground contamination is likely to be a very serious issue for any experiment trying to detect it.

An experiment called Clover (involving the Universities of  Cardiff, Oxford, Cambridge and Manchester) was designed to detect the primordial B-mode signal from its vantage point in Chile. You can read more about the way it works at the dedicated webpages here at Cardiff and at Oxford. I won’t describe it in more detail here, for reasons which will become obvious.

The chance to get involved in a high-profile cosmological experiment was one of the reasons I moved to Cardiff a couple of years ago, and I was looking forward to seeing the data arriving for analysis. Although I’m primarily a theorist, I have some experience in advanced statistical methods that might have been useful in analysing the output.  It would have been fun blogging about it too.

Unfortunately, however, none of that is ever going to happen. Because of its budget crisis, and despite the fact that it has spent a large amount (£4.5M) on it already,  STFC has just decided to withdraw the funding needed to complete it (£2.5M)  and cancel the Clover experiment.

Clover wasn’t the only B-mode experiment in the game. Its rivals include QUIET and SPIDER, both based in the States. It wasn’t clear that Clover would have won the race, but now that we know  it’s a non-runner  we can be sure it won’t.