New evidence from CERN’s Large ElectronPositron collider (LEP) sheds more light on the way quarks can transform.

The CabibboKobayashiMaskawa (CKM) matrix codifies the probabilities of quark or antiquark transitions in weak interactions. Its individual elements the probabilities that a quark or antiquark will turn into a different kind of quark or antiquark in a weak interaction are not predicted by theory, and measuring them has been a major preoccupation of physicists in recent years. With the step up in energy to the W-boson production threshold at LEP in 1996, the experiments at CERN’s flagship collider have begun to make their contribution to this important area of particle physics. Results from LEP’s first two years of W-boson running were presented at this year’s major particle physics conference, ICHEP’98, in Vancouver in July.

The CKM matrix owes its origins to the phenomenon of CP-violation, a subtle difference between Nature’s treatment of matter and antimatter. CP-violation was discovered by James Cronin and Val Fitch at Brookhaven in 1964. At the time, physicists knew of just three quarks, up, down and strange, whose transitions were described by Nicola Cabibbo. His picture did not allow CP violation since the transition probabilities for quarks and antiquarks were identical, putting matter and antimatter on equal footing.

### Extended matrix

To accommodate Cronin and Fitch’s observation, the Japanese physicists Makoto Kobayashi and Toshihide Maskawa extended Cabibbo’s ideas to six quarks with the resulting 3×3 CKM matrix whose nine elements govern the transition probabilities between these quarks or their antiquarks. Since the CKM formulation does not specify whether these probabilities are the same for quarks and antiquarks, it opens the door to CP-violation.

To a good approximation, the CKM elements on the diagonal, which relate quarks of the same family, up and down, charm and strange, and top and bottom, are expected to be close to one. In other words quarks prefer to keep things in the family, the probability of changing into a quark or antiquark from a different family being small.

Up to now, most CKM measurements have been made by studying the weak decays of quarks, but many have been hampered by the fact that it is generally not a quark which is observed to decay but a hadron. As a consequence, assumptions about the behaviour of the hadron have to be folded in with the experimental measurement in order to extract a result.

The best measured CKM element, V_{ud}, which gives the probability that an up quark will become a down quark, does not suffer from this problem. It is measured to a few parts in a thousand by comparing beta decay with muon decay, processes which do not involve assumptions about hadron structure. The next element on the diagonal however, V_{cs}, does suffer from hadronic uncertainties. It is measured only to an accuracy of around 16% from the decays of c quark-containing D mesons into s quark containing kaons.

The advent of W-boson production at LEP has opened up a new route to measuring V_{cs} without relying on hadron decays. LEP’s four experiments, Aleph, Delphi, L3, and Opal, identify and count particles containing c quarks emerging from W decays. They then divide this number by the total number of W decays producing hadrons. Since there are six known quark combinations a W boson can decay to, three of which involve c quarks, the resulting ratio is expected to be a half. Any deviation could indicate that W-bosons can decay in ways unknown to the Standard Model (the theory which encapsulates our current knowledge of elementary particle interactions). Combining the results from all the experiments, however, yields a ratio of 0.506 with an uncertainty of 12%. Good news for the Standard Model.

The LEP measurement of V_{cs} comes from combining this ratio with previously measured values of the other CKM elements. This yields a value of 0.987 with an uncertainty of under 12%, a marked improvement on the previous 16% measurement. However, the LEP result is still dependent on measurements of other matrix elements. An alternative analysis, which requires more data to become competitive, aims to overcome this hurdle. By simultaneously identifying particles containing c quarks and particles containing s quarks, the aim is to measure V_{cs} directly from W decays into a c and an s. As more data are analysed, the LEP experiments hope to reduce the uncertainty on V_{cs} to a few percent. If this matrix element can be so accurately measured, perhaps it will shed light on hadron models instead of the other way round.