Tensions between experiment and the Standard Model prediction regarding lepton universality violations (i.e. that all charged leptons behave identically except for differences flowing from their different masses) is the most important hint of beyond the Standard Model physics at the Large Hadron Collider (LHC). As the paper explains in the introduction, reviewing work before this presentation:
But a new analysis reported in a recent conference paper argues that the differences between tau leptons and muons is not statistically significant even in these decays. It finds a predicted R(D*) on a purely theoretical Standard Model basis to be: 0.275 ± 0.008 (about 1.3 sigma).
At this point, a natural question arises: why is the SM HFLAV theoretical average in Eq. (4) so different from the DM estimate in Eq. (19)? The answer has to be found in the shape of the FFs [ed. Form Factors].
Form factors are one of the most technical parts of quantum chromodynamics. (QCD), right on the frontier of what we understand, so its a natural place for a discrepancy to arise.
If so, the likelihood that the LHC will see no beyond the Standard Model physics surges.
This tends to favor my hypothesis that the source of the discrepancy is a separate additional source of electrons in B meson decays which isn't being screened out as expected, or isn't properly considered in the analysis, for some reason. The conclusion of the conference paper states:
We have reviewed the main properties of the Dispersion Matrix approach, which is an attractive tool to implement unitarity and LQCD calculations in the analysis of exclusive semileptonic decays of mesons and baryons. It has several interesting properties. In particular, it does not rely on any assumption about the momentum dependence of the hadronic form factors and it can be based entirely on first principles (i.e. unitarity and analiticity) and on non-perturbative inputs.
We have discussed the application of the DM method to the b → c and the b → u quark transitions and the resulting theoretical determinations of the LFU observables. In this sense, our main result is that the anomalies in semileptonic charged-current B decays have been strongly lightened. In fact, we have consistency between theory and experiment at the 1.3σ level for both R(D) and R(D∗ ), separately.
To achieve this goal, it is fundamental to avoid the mixing among theoretical calculations and experimental data to describe the shape of the FFs of interest.
The caution about mixing theoretical calculations and experimental data is also at the heart of the discrepancy between the two leading calculations of the Standard Model prediction for muon g-2, which the calculation that mixes the two strongly discrepant and in tension with experiment, and the one which is purely theoretical in much less tension with the experimental result, just as in this LFU violation comparison.
One of the strongest reasons to think that the LFU violation hints are misleading us is that many other processes with the same W boson mediated mechanism as the one believed to be at work in B meson decays and which governs these decays in the Standard Model show no sign of LFU violation to great precision.
The new conference paper and its abstract are as follows:
We present the results of the application of the unitarity-based Dispersion Matrix approach to semileptonic charged-current B decays. This method allows to achieve a non-perturbative and completely model-independent determination of the hadronic form factors. Starting from lattice results available at large values of the momentum transfer, the behaviour of the form factors in their whole kinematical range is obtained without introducing any explicit parameterization of their momentum dependence.
We will focus on the analysis of Lepton Flavour Universality by computing the τ/μ ratios of the branching fractions of the B→D(∗)ℓν and B→πℓν decays. The most important result is that, for the first time, the discrepancies between the SM expectation values and the measurements of the Lepton Flavour Universality ratios for the B→D(∗)ℓν decays are reduced at the 1.3σ level for each of the two channels, separately.
Guido Martinelli, et al., "LFU ratios in B decays using Lattice QCD and Unitarity" arXiv:2205.13952 (May 27, 2022) (Contribution to "La Thuile 2022, XXXV Rencontres de Physique de la Vallée d'Aoste").
Footnote Regarding The CKM Matrix
The paper also notes another B meson decay anomaly.
On the one hand, we have the so-called |Vcb| puzzle, i.e. the discrepancy between the inclusive and the exclusive determinations of the CKM matrix element |Vcb|. According to the FLAG Review 2021 [1], there is a ∼ 2.8σ tension between the exclusive estimate (that depends on the form factors parametrization) and the inclusive one, namelyA new more precise estimate of the inclusive value has also recently appeared [2], namely |Vcb|incl = 42.16(50), which is compatible with the inclusive FLAG value in Eq. (1).
But, this discrepancy is less notable, despite having a similar statistical significance, because it is very common for inclusive and exclusive measurements to have discrepancies in the direction observed (something that is also the case, for example, for the mean lifetime of free neutrons), and because global tests of the CKM matrix can point us to the value which is closer to the truth.
A global fit of the CKM matrix via the Particle Data Group, as of 2021, favors a value of Vcb of 40.53 +0.83/-0.61 x 10^3, i.e. a two sigma spread of 39.31 x 10^3 to 42.19 x 10^3, which is between and consistent with both the global average inclusive and global average exclusive measured values of this CKM matrix element. The uncertainty in Vcb constrained by the necessity of a global fit is about ± 2%.
. . .
Highlights from previous posts on related topics
Over the last eight years disparate experimental results and disparate calculations of the Standard Model expectations related to lepton flavor universality tests have produced mixed results. Some have disfavored lepton flavor universality violations (LFUV), either generally, or in particular kinds of decays, while others have shown continued evidence for LFUV in semi-leptonic decays of certain kinds of B mesons to certain kinds of D mesons.
Twenty-one posts at this blog, in addition to this post over those eight years (excluding overall reviews of the state of high energy physics or unsolved problems in physics), have tracked those developments, almost back to the point when experimental hints of LFUV were first reported.
The main conclusions of the twenty-one other posts regarding the existence of LFUV (some of which discuss more than one paper or experimental results, and others of which analyze multiple previously blogged results when taken together) are recapped below. I have largely omitted the discussions of experimental models that could explain what is observed if the observations of LFUV discrepancies with Standard Model expectations persist given new experimental data, improved analysis of both the data, and improved calculations of the Standard Model expectations for selected LFUV sensitive obserbables.
* A New Experimental Challenge To Lepton Universality Overstates Significance (November 30, 2021) ("Rather than being a five sigma discovery class evidence in a new decay channel for LFU violation, this result is actually consistent with LFU at the two sigma level, and actually, as a result, if anything, it tends to disfavor the conclusion that LFU violation is present in any context outside of semi-leptonic B meson decays. But given the great uncertainty in the ratio of the two values, this new experiment, honestly, doesn't really tell us anything one way or the other.")
* Another Search For Lepton Universality Violation Comes Up Empty (October 18, 2021) (finding no LFU violation in semi-leptonic decays of neutral and charged B mesons to kaons of like charge).
* Lepton Universality Violation Considered Again (April 13, 2021) (suggesting cherry picking issues since lepton universality violations are not found in tau lepton decays or pion decays, and are not found in anti-B meson and D* meson decays or in Z boson decays. There is no evidence of LFV in Higgs boson decays either; that many new physics models that explain the intriguing anomalies in the b-quark flavour sector are severely constrained by Bs-mixing; and discussing the coincidence that the ratio could be explained by additional pion path decays if the data collection cutoffs which should exclude decays in this path failed to do so).
* Lepton Universality Not Violated In Top Quark Decays (February 26, 2021) (the title says it all and is notable since these decays should almost all have intermediate b quark paths).
* Belle Experiment At LHCb Finds No Evidence Of Lepton Flavor Universality Violations (January 12, 2021) (finding no LFU violation in semi-leptonic decays of neutral and charged B mesons to kaons of like charge).
* Apparent Lepton Universality Violations Are Probably Measurement And Statistical Errors (December 22, 2020) (in a semileptonic decay of a b quark, the leptons arise from one or two subsequent leptonic W boson decays. So, if W boson decays don't display violations of lepton universality, then either the leptons observed in semileptonic b quark decays are produced by some means other than an intermediate W boson decay, exclusive to b meson decays, which decays preferentially to lighter leptons, or there is some error in the observation. The latter result is infinitely more likely.)
* How Big Are The Lepton Universality Violation Tensions With The Standard Model? (September 16, 2020) (The flavor anomalies reported in RK, RK∗, P′5 and (Bs→ϕμ+μ−) indicate lepton flavor universality violation in b→sl+l− quark level transition decays. The deviation from the SM prediction reported in the underlying flavor observables currently stand at the level of 2.5σ, 2.4σ, 3.3σ and 3.7σ, respectively).
* ATLAS Finds No Evidence Of Lepton Universality Violations In W-Boson Decays (July 29, 2020) (the ratio of the rate of decay of W bosons to τ-leptons and muons, R(τ/μ)=B(W→τντ)/B(W→μνμ) . . . is found to be 0.992±0.013[±0.007(stat)±0.011(syst)] and is in agreement with the hypothesis of universal lepton couplings as postulated in the Standard Model. This is the most precise measurement of this ratio, and the only such measurement from the Large Hadron Collider, to date).
* B Meson Decay Anomalies Getting Smaller With More Data (September 9, 2019) (Belle collaboration announced their new measurements on RD and RD∗ which are in agreement with their Standard Model (SM) predictions within 1.2σ. After inclusion of these measurements, the discrepancy between the world averages and the SM predictions of RD-RD∗ comes down from 4.1σ to 3.1σ)).).. . . . . . The higher values of RD and RD∗ are assumed to occur due to new physics (NP) contribution to the b → c τ ν¯ decay. New physics in b → c {e/µ} ν¯ is ruled out by other data.)
* How Not To Write An Abstract (June 24, 2019) (In summary, BESIII has . . . [a] LFU test at a very high precision (1.5% for Cabbibo favoured decays and 4% for Cabbibo suppressed decays) has been performed while no evidence of violation is found. Search for charm semileptonic decays to scalar mesons were performed at BESIII and the current results are in favor of the SU(3) nonet tetraquark description of a0(980), f0(500) and f0(980). Moreover, our sensitivity to rare charm leptonic and semileptonic decays has been improved by several magnitudes with the huge statistics at LHCb, and strong constraints have been set for various new physics models with recent measurements.)
* Lepton Flavor Violations In B Meson Decays Still Seen In Experimental Evidence (updated March 27, 2019) (Following the updated measurement of the lepton flavour universality (LFU) ratio R_K in B -> Kll decays by LHCb, as well as a number of further measurements, e.g. R_K* by Belle and B_s -> mu mu by ATLAS, we analyse the global status of new physics in b -> s transitions in the weak effective theory at the b-quark scale, in the Standard Model effective theory at the electroweak scale, and in simplified models of new physics. We find that the data continues to strongly prefer a solution with new physics in semi-leptonic Wilson coefficients . . . After the completion of this work, new preliminary results on RD and RD∗ using semileptonic tags were presented by Belle [109]. The new results, that are slightly closer to the SM predictions compared to an average of previous Belle results, are not yet included in our analysis).
* A Review Of Lepton Universality In B Meson Decays (September 18, 2018) (A possible violation of LU is hinted at in two different classes of semileptonic b-quark decays. The measurements are obtained from experiments at the B-factories (BaBar, Belle and soon Belle-II) as well as at the LHC (LHCb). For these processes the SM predictions can be computed using an effective Hamiltonian approach that separates short and long-distance contributions, and require non-perturbative inputs (e.g. form factors) obtained through diverse theoretical methods. Tensions at the level of 4–5 σ are observed in b→ clν [charm quark, negative charged lepton, corresponding anti-neutrino] decays, which are mediated at tree level through a W± boson in the SM, when the branching ratios of decays with l = τ and l = e, µ are compared. Deviations at the level of 3–4 σ are also present in b→ sll [strange quark, lepton and anti-lepton] decays, which are mediated through a loop in the SM, when comparing the branching ratios for l = e and l = µ.)
* B Quark Decays Still Anomalous (June 25, 2018) (it seems that the probability of getting a muon pair from particular interactions is about three-quarters of the probability of what the Standard Model says it should be.)
* Maybe b quark decays aren't weird after all (January 18, 2018) (Many new physics models that explain the intriguing anomalies in the b-quark flavour sector are severely constrained by Bs-mixing, for which the Standard Model prediction and experiment agreed well until recently. New non-perturbative calculations point, however, in the direction of a small discrepancy in this observable. Using up-to-date inputs to determine ΔMSMs, we find a severe reduction of the allowed parameter space of Z′ and leptoquark models explaining the B-anomalies. Remarkably, in the former case the upper bound on the Z′ mass approaches dangerously close to the energy scales already probed by the LHC.; B decays proceeding via b→cℓν transitions with ℓ=e or μ are tree-level processes in the Standard Model. They are used to measure the CKM element Vcb, as such forming an important ingredient in the determination of e.g. the unitarity triangle; hence the question to which extend they can be affected by new physics contributions is important, specifically given the long-standing tension between Vcb determinations from inclusive and exclusive decays and the significant hints for lepton flavour universality violation in b→cτν and b→sℓℓ decays. We perform a comprehensive model-independent analysis of new physics in b→cℓν, considering vector, scalar, and tensor interactions, including for the first time differential distributions of B→D∗ℓν angular observables. We show that these are valuable in constraining non-standard interactions. Specifically, the zero-recoil endpoint of the B→Dℓν spectrum is extremely sensitive to scalar currents, while the maximum-recoil endpoint of the B→D∗ℓν spectrum with transversely polarized D∗ is extremely sensitive to tensor currents. We also quantify the room for e-μ universality violation in b→cℓν transitions, predicted by some models suggested to solve the b→cτν anomalies.)
* Some B Meson Decay Anomalies Disappear In Run-2 Data (May 10, 2017) (After Run 1 of the LHC, global fits to b→sℓℓ observables show a deviation from the Standard Model (SM) with a significance of ∼ 4 standard devations. An example of a b→sℓℓ process is the decay of a B0s meson into two muons (B0s→μ+μ−). The latest analysis of B0(s)→μ+μ− decays by LHCb with Run 1 and Run 2 data is presented. The B0s→μ+μ− decay is observed for the first time by a single experiment. In addition, the first measurement of the B0s→μ+μ−effective lifetime is performed. No significant excess of B0→μ+μ− decays is observed. All results are consistent with the SM and constrain New Physics in b→sℓℓ processes.)
* Experimental Confirmation Of Koide's Rule And Lepton Universality In Tau Leptons (September 28, 2017) (The experiment confirmed this prediction of the Standard Model comparing a ratio of two experimental results that should be 1.0 if lepton universality is correct. The measured value of that ratio is: 1.0016 ± 0.0042. Thus, the experimental outcome was again less than half of a standard deviation due to experimental uncertainty from the predicted value and lepton universality is confirmed.)
* Mixed Results In A Test Of Lepton Universality (December 17, 2016) (in semilepton B meson decays to kaons a new experimental result finds a local 2.6 sigma deviation from the Standard Model expectation of charged lepton universality in particular kinds of B meson decays. But, after considering look elsewhere effects, it is consistent with the Standard Model.)
* Another Experimental Confirmation of Lepton Universality (December 5, 2016) (semileptonic B decays to τ leptons (semitauonic decays) . . . for the decay process B¯ → D(∗) τ −ν¯τ. The decays B¯ → D(∗) τ −ν¯τ have been studied by the Belle, BaBar and LHCb experiments. Most of these studies have measured ratios of branching fractions, defined as R(D(∗) ) = B(B¯ → D(∗) τ −ν¯τ )/B(B¯ → D(∗) l−ν¯l−). The denominator is the average of l− = e−, µ− for Belle and BaBar, and l− = µ− for LHCb. The ratio cancels numerous uncertainties common to the numerator and the denominator. The current averages of the three experiments are R(D) = 0.397 ± 0.040 ± 0.028 and R(D∗ ) = 0.316 ± 0.016 ± 0.010, which are 1.9 and 3.3 standard deviations (σ) away from the SM predictions of R(D) = 0.299 ± 0.011 or 0.300 ± 0.008 and R(D∗ ) = 0.252±0.003, respectively. The overall discrepancy with the SM is about 4σ. . . .Our study includes an R(D∗) measurement independent of the previous studies, in which leptonic τ decays have been used.)
* Tau Decays Still Match Standard Model Expectations (September 8, 2015) (While other experiments have shown what could be noise, or could be weak evidence of violations of lepton universality or lepton flavor violations, a new LHCb experiment paper finds no violations of lepton universality, no lepton flavor violations, no lepton number violations and no baryon number violations in tau lepton decays. All of the tau lepton decays observed are in accord with the Standard Model expectation and the bounds on lepton or baryon number violations derived are very strict. . . . A study of pion decays released this past June likewise confirms lepton universality to high precision. There has been weak evidence of lepton universality violations and lepton flavor non-conservation in B meson decays and Higgs boson decays, but those could just be statistical flukes or due to systemic error. It is not easy to imagine why lepton universality might be violated with B meson decays, but not pion or tau lepton decays.)
* New Experiment Tends To Confirm Electron-Muon Universality (June 22, 2015) (a new experimental results, looking at the decays of positively charged pions to electrons and muons respectively, confirms Standard Model prediction of muon-electron universality to within 0.1%.)
* Interesting LHCP 2013 (Barcelona) Higgs Conference Abstracts (June 9, 2014) (Present measurements of b->c tau nu and b->u tau nu transitions differ from the standard model predictions of lepton flavor universality by almost 4 sigma. . . . Some of the strongest evidence for beyond the Standard Model behavior involves Lepton flavor violations where decays to electrons are about 25% more common than decays to muons, contrary to a Standard Model expectation of equal frequencies. This is a promising place to look for new physics. Motl discusses the results in a post here.)
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