by **Robert Kowalewski** from *Nature Physics* 11, 705–706 (2015) doi:10.1038/nphys3464

**A new measurement from the LHCb experiment at CERN’s Large Hadron Collider impinges on a puzzle that has been troubling physicists for decades namely the breaking of the symmetry between matter and antimatter.**

We learn early that the matter in and around us is made up of three particles: electrons, and the up and down quarks found in nuclei. Add in the electron neutrino and we also account for nuclear fission and fusion and the stellar furnace that fuels life on Earth. But nature is not that simple. It replicates this four-particle structure in ‘generations’ of heavier, but otherwise similar, particles. The first evidence for this was the discovery of the muon in 1936. Other second-generation particles were subsequently discovered, as was another unexpected phenomenon: the violation of matter-antimatter (CP) symmetry in neutral kaons^{(1)}. Now, writing in *Nature Physics*, the LHCb collaboration^{(2)} provides fresh evidence to fuel the ongoing discussion surrounding CP violation.

In 1973, Makoto Kobayashi and Toshihide Maskawa proposed a mechanism whereby mixing between the mass and weak eigenstates of quarks would, if there were three generations, result in an irreducible complex phase that could be responsible for CP violation^{(3)}.

The discovery of the first third-generation particle, the tau lepton^{(4)}, came a year later, followed in 1977 by the discovery of the third-generation *‘b’* quark^{(5)}. With the advent of high-intensity electron-positron colliders at the start of the twenty-first century, studies of CP violation in the decays of *B* mesons (which contain a *b* quark) at the BaBar and Belle experiments validated Kobayashi and Maskawas proposal, for which they shared in the 2008 Nobel Prize in Physics.

The CKM matrix – introduced by Kobayashi and Maskawa, following the formative work of Nicola Cabibbo – describes the mixing of quark mass and weak eigenstates in the standard model of particle physics. It is unitary and can be fully specified with four parameters: three real angles and one imaginary phase. This unitarity condition is the basis for a set of testable constraints in the form of products of complex numbers that sum to zero – for example, V^{*}_{ud} V_{ub} + V^{*}_{cd} V_{cb} + V^{*}_{td} V_{tb} = 0 where V_{ub} describes the transition of a *b* quark to a *u* quark. The triangle in Fig. 1 provides a convenient graphical representation of this equation. The unitarity condition connects a large set of measurable quantities in the standard model, including CP-violating asymmetries, which depend on the imaginary phase, and mixing strengths, which are magnitudes such as |V_{ub}| and |V_{cb}|. In the standard model, all the bands corresponding to the different measurements in Fig. 1 should overlap at a unique point, which they do at the current level of precision. The presence of new particles or interactions would contribute to these measurable quantities in different ways, resulting in bands that fail to converge at a point. The ratio of matrix elements |V_{ub}|/|V_{cb}| corresponds to the length of the side of the ‘unitarity triangle’ opposite the angle labelled *β*, which is well determined from measured CP-violating asymmetries. The precise determination of this ratio is a crucial ingredient in providing sensitivity to new particles and interactions.

Experiments at electron-positron colliders have measured |V_{ub}| and |V_{cb}| for many years using two complementary methods based on the decays of a *B* meson to an electron or muon, its associated neutrino and one or more strongly interacting particles. The first method measures exclusive final states whose decay rates are proportional to |V_{qb}|^{2} (where *q = u, c*), and uses lattice quantum chromodynamic (QCD) calculations of form factors to determine |V_{qb}|. The second inclusive method requires only the presence of an electron or muon and sums over many exclusive final states. These summed rates are also proportional to |V_{qb}|^{2}, the determination of |V_{qb}| in this case relies on perturbative QCD calculations and auxiliary measurements. Although these two methods have improved significantly in precision over the years, the values determined for both |V_{ub}| and |V_{cb}| from the inclusive method persistently exceed those from the exclusive method by two to three standard deviations. This has prompted speculation that the familiar left-handed charged weak interaction has a right-handed counterpart that contributes

to this difference.

With this backdrop, the new measurement of the ratio |V_{ub}|/|V_{cb}| from the LHCb experiment at CERN’s Large Hadron Collider (LHC) is a welcome addition to the literature^{(2)}. It is based on a different exclusive decay mode than can

be measured at the electron-positron collider experiments, namely that of a baryon containing *b*, *u* and *d* quarks (a heavier version of the neutruon) that decays into a proton, a muon and a neutrino. Particle physicists have been surprised that these decays, where the missing neutrino prevents reliance on kinematic constraints, can be distinguished from the huge background inherent in proton-proton collisions at the LHC This new result, which makes use of very precise spatial measurements of the decay vertices of short-lived particles and uses innovative analysis techniques, is a noteworthy achievement.

What have we learned? The new experimental information, instead of resolving the inclusive-exclusive puzzle, deepens it. The measurement and corresponding lattice QCD calculation lead to a value for |V_{ub}|/|V_{cb}| that is lower than both the pre-existing exclusive and inclusive determinations. The consistency of the three determinations with a single value is only 1.8%, indicating that particle physicists have more work to do in this area. On a more positive note, the LHCb measurement, when combined with previous measurements, strongly disfavours the hypothesis of a right-handed weak interaction.

(1) Christenson, J. H., Cronin, J. W. Fitch, V L. & Turlay, R. Phys. Rev. Lett. 13, 138-140 (1964).

(2) The LHCb collaboration Nature Phys. 11,743-747 (2015).

(3) Kobayashi, M. & Maskawa, T. Prog. Theor Pinys. 49, 652-657 (1973).

(4) Perl, M. L. et al Phys. Rev. Lett 35,1489-1492 (1975).

(5) Herb, S. W. et al Phys. Rev Lett. 39, 252-255 (1977).