In pursuit of right-handed photons

On 17 January 1957, a few months after Chien-Shiung Wu’s discovery of parity violation, Wolfgang Pauli wrote to Victor Weisskopf: “Ich glaube aber nicht, daß der Herrgott ein schwacher Linkshänder ist” (I cannot believe that God is a weak left-hander). But maximal parity violation is now well established within the Standard Model (SM). The weak interaction only couples to left-handed particles, as dramatically seen in the continuing absence of experimental evidence for right-handed neutrinos. In the same way, the polarisation of photons originating from transitions that involve the weak interaction is expected to be completely left-handed.

The LHCb collaboration recently tested the handedness of photons emitted in rare flavour-changing transitions from a b-quark to an s-quark. These are mediated by the bosons of the weak interaction according to the SM – but what if new virtual particles contribute too? Their presence could be clearly signalled by a right-handed contribution to the photon polarisation.

New virtual particles could be clearly signalled by a right-handed contribution to the photon polarisation

The b → sγ transition is rare. Fewer than one in a thousand b-quarks transform into an s-quark and a photon. This process has been studied for almost 30 years at particle colliders around the world. By precise measurements of its properties, physicists hope to detect hints of new heavy particles that current colliders are not powerful enough to produce.

The probability of this b-quark decay has been measured in previous experiments with a precision of about 5%, and found to agree with the SM prediction, which bears a similar theoretical uncertainty. A promising way to go further is to study the polarisation of the emitted photon. Measuring the b → sγ polarisation is not easy though. The emitted photons are too energetic to be analysed by a polarimeter and physicists must find innovative ways to probe them indirectly. For example, a right-handed polarisation contribution could induce a charge-parity asymmetry in the B⁰ → K_Sπ⁰γ or B_s⁰ → φγ decays. It could also contribute to the total rate of radiative b → sγ decays, containing any strange meson, B → X_sγ.

The LHCb collaboration has pioneered a new method to perform this measurement using virtual photons and the largest sample of the very rare B⁰ → K^*0e⁺e^– decay ever collected. First, the sub-sample of decays that come from B⁰ → K^*0γ with a virtual photon that mat­erialises in an electron–positron pair is isolated. The angular distributions of the B⁰ → K^*0e⁺e^– decay products are then used as a polarimeter to measure the handedness of the photon. The number of decays with a virtual photon is small compared to the decays with a real photon, but these latter decays cannot be used as the information on the polarisation is lost.

The size of the right-handed contribution to b → sγ is encoded in the magnitude of the complex parameter C′₇/C₇. This is a ratio of the right- and left-handed Wilson coefficients that are used in the effective description of b → s transitions. The new B⁰ → K^*0e⁺e^– analysis by the LHCb collaboration constrains the value of C′₇/C₇, and thus the photon polarisation, with unprecedented precision (figure 1). The measurement is compatible with the SM prediction.

This result showcases the exceptional capability of the LHCb experiment to study b → sγ transitions. The uncertainty is currently dominated by the data sample size, and thus more accurate studies are foreseen with the large data sample expected in Run 3 of the LHC. More precise measurements may yet unravel a small right-handed polarisation.