Is the Standard Model about to crater?

There are now quite a few discrepancies, or “tensions”, between laboratory experiments and the predictions of the Standard Model (SM) of particle physics. All of them are of the 2–3σ variety, exactly the kind that physicists learn not to take seriously early on. But many have shown up in a series of related measurements, and this is what has attracted physicists’ attention.

In this article, I will concentrate on two sets of discrepancies, both associated with data taken at √s = 7 and 8 TeV in LHC’s Run 1:

1. Using 3 fb^–1 of data, LHCb has reported discrepancies with more or less precise SM predictions, all relating to the rare semileptonic transitions b → sl⁺l⁻, particularly with l = μ. If real, they would imply the presence of new lepton non-universal (LNU) interactions at an energy scale Λ_LNU  ≳ 1 TeV, well above the scale of electroweak symmetry breaking. Especially enticing, such effects would suggest lepton flavour violation (LFV) at rates much larger than expected in the Standard Model.

2. Using 20 fb^–1 of data, ATLAS and CMS have reported 2–3σ excesses near 2 TeV in the invariant mass of dibosons VV = WW, WZ, ZZ and VH = WH, ZH, where H is the 125 GeV Higgs boson discovered in Run 1. To complicate matters, there is also a ~3σ excess near 2 TeV in a CMS search for a right-handed-coupling W_R decaying to l⁺l⁻jet jet (for l = e, but not μ), and a 2.3σ excess near M_jj = 1.9 TeV in dijet production. (Stop! I hear you say, and I can’t blame you!)

If either set of discrepancies were to be confirmed in Run 2, the Standard Model would crack wide open, with new particles and their new interactions providing high-energy experimentalists and theorists with many years of exciting exploration and discovery. If both should be confirmed, Katy bar the door!

But first, I want to tip my hat to one of the longest-standing of all such SM discrepancies: the 2004 measurement of g−2 for the muon is 2.2–2.7σ higher than calculated. For a long time, this has been down-played by many, including me. After all, who pays attention to 2.5σ? (Answer: more than 1000 citations!) But now other things are showing up and, for LHCb, muons seem to be implicated. Maybe there’s something there. We should know in a few years. The new muon g-2 experiment, E989 at Fermilab, is expected to have first results in 2017–2018.

b → sµ⁺µ^– at LHCb

Features of LHCb’s measurements of B-meson decays involving b → sl⁺l⁻ transitions hint consistently at a departure from the SM:

1. The measured ratio, R_K, of branching ratios of B⁺ → K⁺μ⁺μ⁻ to B⁺ → K⁺e⁺e⁻ is 25% lower than the SM prediction, a 2.6σ departure.

2. In an independent measurement, the branching ratio of B⁺ → K⁺μ⁺μ⁻ is 30% lower than the SM prediction, a 2σ deficit. This suggests that the discrepancy is in muons, rather than electrons. LHCb’s muon measurement is more robust than for electrons. However, all indications on the electron mode, including earlier results from Belle and BaBar, are that B → K^(*)e⁺e⁻ is consistent with the SM.

3. The quantity P’₅ in B⁰ → K^*0μ⁺μ⁻ angular distributions exhibits a 2.9σ discrepancy in each of two bins. The size of the theoretical error is being questioned, however.

4. CMS and LHCb jointly measured the branching ratio of B_s → μ⁺μ⁻. The result is consistent with the SM prediction but, interestingly, its central value is also 25% lower (at 1σ).

The R_K and other measurements suggest lepton non-universality in b → sl⁺l⁻ transitions, and with a strength not very different from that of these rare SM processes. This prospect has inspired an avalanche of theoretical proposals of new LNU physics above the electroweak scale, all involving the exchange of multi-TeV particles such as leptoquarks or Z’ bosons.

As a very exciting consequence, LNU interactions at high energy are, in general, accompanied by lepton flavour-violating interactions, unless the leptons involved are chosen to be mass eigenstates. But, as we know from the mismatch between the gauge and mass eigenstates of quarks in the charged weak-interaction currents, there is no reason to make such a choice. Further, that choice makes no sense at Λ_LNU, far above the electroweak scale where those masses are generated. Therefore, if the LHCb anomalies were to be confirmed in Run 2, LFV decays such as B → K^(*)μe/μτ and B_s → μe/μτ should occur at rates much larger than expected in the SM. (Note that LNU and LFV processes do occur in the SM but, being due to neutrino-mass differences, they are tiny.)

LHCb is searching for b → sμe and sμτ in Run 1 data, and will continue in Run 2 with much more data. The μe modes are easier targets experimentally than μτ. However, the simplest hypothesis for LNU is that it occurs in the third-generation gauge eigenstates, e.g., a b’b’τ’τ’ interaction. Then, through the usual mass-matrix diagonalisation, the lighter generations get involved, with LFV processes suppressed by mixing matrix elements that are analogous to the familiar CKM elements. In this case, b → sμτ likely will be the largest source of LFV in B-meson decays.

A final note: there are slight hints of the LFV decay H → μτ. CMS and ATLAS have reported small branching ratios that amount to 2.4σ and 1.2σ, respectively. These are tantalizing, and certainly will be clarified in Run 2.

Diboson excesses at ATLAS and CMS

I will limit this discussion to diboson, VV and VH, excesses near 2 TeV, even though the W_R → l⁺l⁻jet jet and dijet excesses are of similar size and should not be forgotten. ATLAS and CMS measured high-invariant-mass VV (V = W, Z) in non-leptonic events in which both highly boosted V decay into qq’ (also called “fat” V-jets) and semi-leptonic events in which one V decays into l^±ν or l⁺l⁻. In the ATLAS non-leptonic data, a highly boosted V-jet is called a W (Z) if its mass M_V is within 13 GeV of 82.4 (92.8) GeV. In its semi-leptonic data, V = W or Z if 65 < MV < 105 GeV. In the non-leptonic events, ATLAS observed excesses in all three invariant-mass “pots”, M_WW, M_WZ and M_ZZ, although there may be as much as 30% overlap between neighbouring pots. Each of the three excesses amount to 5–10 events. The largest excess is in M_WZ. It is centred at 2 TeV, with a 3.4σ local, 2.5σ global significance. ATLAS’s WZ data and exclusion plot are in figure 1. The WZ excess has been estimated to correspond to a cross-section times branching ratio of about 10 fb. ATLAS observed no excesses near 2 TeV in its semileptonic data. Given the low statistics of the non-leptonic excesses, this is not yet an inconsistency.

In its non-leptonic data, CMS defined a V-jet to be a W or Z candidate if its mass is between 70 and 100 GeV. The exclusion plot for this data shows a ~1.5σ excess over the expected limit near M_VV = 1.9 TeV. In the semi-leptonic data, the V-jet is called a W if 65 < M_V < 105 GeV or a Z if 70 < M_V < 110 GeV – a quite substantial overlap. There is a 2σ excess over the expected background near 1.8 TeV in the l⁺l⁻ V-jet but less than 1σ in the l^±ν V-jet. When the semi-leptonic and non-leptonic data are combined, there is still a 1.5–2σ excess near 1.8 TeV. The CMS exclusion plots are in figure 2.

ATLAS and CMS also searched for resonant structure in VH production. ATLAS looked in the channels lν/l⁺l⁻/νν + bb with one and two b-tags. Exclusion plots up to 1.9 TeV show no deviation greater that 1σ from the expected background. CMS looked in non-leptonic and semi-leptonic channels. The observed non-leptonic exclusion curves look like a sine wave of amplitude 1σ on the expected falling background with, as luck would have it, a maximum at 1.7 TeV and a minimum at 2 TeV. On the other hand, a search for WH → lνbb has a 2σ excess centred at 1.9 TeV in the electron, but not the muon, data.

Many will look at these 2–3σ effects and say they are to be expected when there is so much data and so many analyses; indeed, something would be wrong if there were not. Others, including many theorists, will point to the number, proximity and variety of these fluctuations in both experiments at about the same mass, and say something is going on here. After all, physics beyond the SM and its Higgs boson has been expected for a long time and for good theoretical reasons.

It is no surprise, then, that a deluge of more than 60 papers has appeared since June, vying to explain the 2 TeV bumps. The two most popular explanations are (1) a new weakly coupled W’, Z’ triplet that mixes slightly with the familiar W, Z, and (2) a triplet of ρ-like vector bosons heralding new strong interactions associated with H being a composite Higgs boson. A typical motivation for the W’ scenario is the restoration of right–left symmetry in the weak interactions. The composite Higgs is a favourite of “naturalness theorists” trying to understand why H is so light. The new interactions of both scenarios have an “isospin” SU(2) symmetry. The new isotriplets X are produced at the femtobarn level, mainly in the Drell–Yan process of qq annihilation. Their main decay modes are X^± → W^± _L Z_L and X⁰ → W⁺_L W^–_L, where V_L is a longitudinally polarised weak boson. Generally, the W’, Z’ and the ρ (or its parity partner, an a₁-like triplet) can also decay to W_L, Z_L plus H itself. It follows that the diboson excess attributed to ZZ would really have to be WZ and, possibly, WW. The W, Z-polarisation and the absence of real ZZ are important early tests of these models. (A possibility not considered in the composite Higgs papers, is the production of an f₀-like I = 0 scalar, also at 2 TeV, which decays to W⁺_LW^–_L and Z_LZ_L.)

Although the most likely explanation of the 2 TeV bumps may well be statistics, we should have confirmation soon. The resonant cross-sections are five or more times larger at 13 TeV than at 8 TeV. Thus, the expected LHC running this year and next will produce as much or more diboson data as all of Run 1.

What if both lepton flavour violation and the VV and VH bumps were to be discovered in Run 2? Both would suggest new interactions at or above a few TeV. Surely they would have to be related, but how? New weak interactions could be flavour non-universal (but, then, not right–left symmetric). New strong interactions of Higgs compositeness could easily be flavour non-universal. The possibilities seem endless. So do the prospects for discovery. Stay tuned!

• For the B-meson anomalies, the experimental papers are arxiv.org/abs/1406.6482, arxiv.org/abs/1403.8044, arxiv.org/abs/1505.04160and arxiv.org/abs/1411.4413. For the diboson excesses near 2 TeV, the details of the V-jet construction are in arxiv.org/abs/1506.00962, arxiv.org/abs/1503.04677and arxiv.org/abs/1409.6190for ATLAS, and arxiv.org/abs/1405.1994and arxiv.org/abs/1405.3447 for CMS.

• Among the “tensions” not discussed in this article is also the B → D* τν decay, illustrated on the cover of this issue.