Tensor Currents May Explain Persistent B-Meson Anomalies

A new global analysis of rare B-meson decays has delivered one of the sharpest constraints yet on a class of hypothetical interactions that could point beyond the Standard Model of particle physics. The study, published in The European Physical Journal C, finds that tensor interactions—long discussed as possible fingerprints of new particles—are too small to explain the persistent discrepancies known as the B anomalies on their own. Instead, the analysis reinforces the case for a different type of new-physics contribution, encoded in the parameter known as the Wilson coefficient (C_9). In one representative fit, the researchers find a shift of approximately (Delta C_9=-1.00), while the tensor coefficients remain close to zero. The result does not eliminate leptoquarks or other exotic theories, but it significantly narrows the room in which tensor-based explanations can operate.

The B anomalies arise in flavour-changing decays in which a bottom quark transforms into a strange quark while producing a charged-lepton pair. These processes, written schematically as (brightarrow sell^+ell^-), are extremely rare in the Standard Model because they occur only through higher-order quantum effects. That rarity makes them unusually sensitive to heavy particles that cannot be produced directly. Several measurements, particularly from the LHCb experiment, have suggested that the observed decay rates and angular distributions do not align perfectly with Standard Model calculations. A deviation in (C_9), which multiplies a semileptonic vector operator, has repeatedly emerged from global fits as a promising way to describe the pattern. Yet uncertainties in hadronic form factors and long-distance strong-interaction effects mean that the interpretation remains a demanding theoretical problem rather than a confirmed discovery.

Qiaoyi Wen of Jinan University and Shaoguan University and Fanrong Xu of Jinan University approached that problem using the effective Hamiltonian formalism. In this framework, the complicated effects of unknown high-energy particles are compressed into Wilson coefficients, while operators describe how quarks and leptons interact at the lower energies of B-meson decay. The Standard Model includes dominant electromagnetic dipole, vector and axial-vector operators, conventionally labelled (O_7), (O9) and (O{10}). Tensor operators, by contrast, involve antisymmetric combinations of gamma matrices, represented by (sigma^{munu}), in both the quark and lepton currents. Their strengths are described by (CT) and (C{T5}), with the latter containing an additional (gamma_5) and therefore a different chiral structure. The Standard Model predicts negligible contributions from these tensor terms, making them clean targets for searches for new physics.

Tensor currents are particularly interesting because they can be generated by scalar leptoquarks—hypothetical particles that couple quarks to leptons. Such particles occur naturally in several grand unified theories and have been proposed as explanations for anomalies in B decays. The authors therefore tested whether adding (CT) and (C{T5}) could relieve the disagreement between theory and experiment. They examined six increasingly broad possibilities: a tensor-only fit; fits combining tensors with (C_9), with (C9) and (C{10}), and with their chirality-flipped counterparts; a scalar-tensor fit; and a full fit in which as many as 14 Wilson-coefficient shifts were allowed to vary. The coefficients were assumed to be real and lepton-flavour universal, meaning that the new interaction was taken to affect electrons and muons in the same way, consistent with the experimental situation used in the study.

A major advance of the work is its use of measurements across the complete dilepton invariant-mass range, denoted by (q^2), rather than focusing only on the low-(q^2) region. The researchers incorporated roughly 440 experimental observables, including exclusive decays such as (Brightarrow Kell^+ell^-) and (Brightarrow K^*ell^+ell^-), the baryonic decay (Lambda_brightarrowLambdaell^+ell^-), the inclusive channel (Brightarrow X_sell^+ell^-), and the rare processes (B_s) and (B_drightarrowmu^+mu^-). New CMS results were included alongside earlier LHCb and other measurements. The analysis used Bayesian inference, comparing theoretical predictions with experimental values through a correlated chi-squared function. Both experimental correlations and theoretical uncertainties, especially those associated with form factors, were included in the covariance matrices. This matters because treating each measurement as independent can make a discrepancy appear more significant than it really is.

To calculate the decay distributions, the authors extended the theoretical expressions to include tensor contributions in both low- and high-(q^2) regimes. In decays to a vector meson such as the (K^*), tensor operators generate additional transversity amplitudes—quantities that track distinct polarization states of the final particles. These amplitudes modify the angular coefficients governing how the decay products are distributed in space. At high (q^2), where the hadrons recoil slowly, improved Isgur–Wise relations and an operator-product expansion reduce the number of independent form factors and help control long-distance effects. At low (q^2), the analysis retained a larger set of form factors to preserve continuity across the full kinematic range. The form factors were parameterized using a simplified series expansion combining light-cone sum-rule and lattice-QCD information. This updated treatment is important because differences in form-factor inputs can shift the preferred values of the Wilson coefficients, especially the right-handed coefficient (C_9′).

The results show a striking division of labour among the possible interactions. In the tensor-only scenario, the fit has a relatively poor reduced chi-squared of about 2.70, indicating that (CT) and (C{T5}) cannot by themselves account for the full pattern of data. Once (Delta C_9) is allowed to vary, the reduced chi-squared falls sharply to about 1.54, and the fitted value of (C9) lies close to (-1). Adding (C{10}) produces a representative solution of ([Delta C9,Delta C{10},CT,C{T5}]simeq[-1.00,0.22,0.01,0.01]), with a reduced chi-squared of (658.5/437=1.51). The significance of the negative (C_9) shift remains essentially unchanged when tensor operators are included. In the broadest fit, most coefficients remain compatible with their Standard Model values at the 95 per cent confidence level, with the main exceptions involving left-handed vector and axial-vector interactions and a possible right-handed vector contribution.

The tensor coefficients themselves remain tightly restricted. Across the lepton-flavour-universal scenarios, their typical allowed size is of order a few hundredths in the global fits, although the authors also describe confidence regions reaching roughly the 0.1 level in broader comparisons. Their 95 per cent confidence boundary can be represented by an elliptical relation. In the tensor-only case, defining (x=Delta CT) and (y=Delta C{T5}), the boundary is (x^2+0.071xy+0.942y^2+0.091x+0.044yleq0). The exact curve is not a fundamental law, but a compact description of the fitted confidence region that can be used when testing models that generate tensor currents. The researchers find that high-(q^2) data provide especially strong constraints in the tensor-only setting, whereas low-(q^2) measurements become more influential when vector or axial-vector interactions are fitted simultaneously. Quantum chromodynamics also changes the coefficients as they evolve between energy scales, while electromagnetic mixing adds a smaller effect; the study estimates that QED contributions do not exceed about 7 per cent of the dominant QCD running effect.

The findings do not close the case on the B anomalies, because the interpretation depends on both future measurements and improved control of hadronic physics. The shift in (C_9) remains a persistent feature of the data-driven analysis, but a Wilson coefficient is not itself a particle: it is an indirect summary of whatever high-energy dynamics may be influencing the decay. A leptoquark model, for example, would need to reproduce the preferred vector interaction while respecting the strong tensor limits and constraints from other flavour processes. The authors also emphasize that the possible negative (C_9′) contribution should be studied alongside further improvements to the form factors, since theoretical inputs can influence its fitted value. As LHCb, CMS and other experiments accumulate larger samples of rare B decays, angular observables and high-(q^2) measurements may distinguish a genuine short-distance effect from underestimated strong-interaction contributions. For now, the message is unusually clear: tensor currents may still exist, but they are unlikely to be the main engine behind the anomalies.