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WHERE IS PARTICLE PHYSICS GOING?

JOHN ELLIS Theoretical Particle Physics and Cosmology Group, Physics Department,
King s College London, London WC2R 2LS, UK;
Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland
John.Ellis@cern.ch

(Day Month Year; Day Month Year)

Abstract

The answer to the question in the title is: in search of new physics beyond the Standard Model, for which there are many motivations, including the likely instability of the electroweak vacuum, dark matter, the origin of matter, the masses of neutrinos, the naturalness of the hierarchy of mass scales, cosmological inflation and the search for quantum gravity. So far, however, there are no clear indications about the theoretical solutions to these problems, nor the experimental strategies to resolve them. It makes sense now to prepare various projects for possible future accelerators, so as to be ready for decisions when the physics outlook becomes clearer. Paraphrasing George Harrison, “ If you don’t yet know where you’re going, any road may take you there.”

Contribution to the 2017 Hong Kong UST IAS Programme and Conference on High-Energy Physics.

KCL-PH-TH-2017-18, CERN-TH-2017-080

keywords:

Higgs boson; supersymmetry; dark matter; LHC; future colliders.

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PACS numbers: 12.15.-y, 12.60.Jv, 14.80.Bn, 14.80.Ly

1 Introduction

The bedrock upon which our search for new physics beyond the Standard Model (SM) is founded is our ability to make precise predictions within the Standard Model, notably for the LHC experiments. The predictions of many hard higher-order perturbative QCD calculations have been confirmed, as seen in Fig. 1, providing confidence in predictions for the production of the Higgs boson [1], and for the backgrounds to many searches for new physics.

Refer to caption — Figure 1: Many SM processes have been measured at the LHC, and have cross sections that are generally in excellent agreement with QCD calculations [2].

2 The Flavour Sector

Many measurements in the flavour sector are also consistent with the predictions of the Cabibbo-Kobayashi-Maskawa (CKM) model [3, 4], e.g., there are many consistent measurements of the unitarity triangle, as seen in the left panel of Fig. 2. Historically, the angle $\gamma$ has been the least constrained experimentally, but the LHCb Collaboration has recently published a combined measurement [5] that dominates the world average and is consistent with the other unitarity triangle measurements.

That said, there are several anomalies in the flavour sector of varying significance. For example, there are strengthening indications of violations of $e/\mu$ lepton universality in $B\to Ke^{+}e^{-}$ and $B\to K\mu^{+}\mu^{-}$ decays, [6] and of $\tau/(\ell=e$ or $\mu)$ universality in $B\to D^{(*)}\tau\nu$ decays [7] - to which my attitude is ‘wait and see’, as lepton non-universality has held up very well so far. Much attention has been attracted to the $P_{5}^{\prime}$ angular distribution in $B\to K^{*}\mu^{+}\mu^{-}$ decay [8], which may be accompanied by an anomaly in the $q^{2}$ distribution in $B\to\phi\mu^{+}\mu^{-}$ decay, leading to the constraints on possible new physics contributions to operator coefficients shown in the right panel of Fig. 2 [9]. These both appear at $q^{2}\lesssim 5$ GeV², and I do not know how seriously to take them, in view of my lack of understanding of the non-perturbative QCD corrections in this region. My ignorance also makes it difficult for me to judge the significance of the apparent discrepancy between theory [10, 11] and experiment for $\epsilon^{\prime}/\epsilon$ . Finally, a new kid on the flavour block has been the interesting search for $H\to\mu\tau$ decay [12] discussed below, though this may be reverting towards the SM with the latest Run 2 results [13].

3 Higgs Physics

3.1 The Higgs Mass

The most fundamental Higgs measurement is that of its mass. The combined LHC Run 1 results of ATLAS and CMS based on $H$ decays into $\gamma\gamma$ and $ZZ^{*}\to 2\ell^{+}2\ell^{-}$ yielded [14]

m_{H}\;=\;125.09\pm 0.21({\rm stat.})\pm 0.11({\rm syst.})\,,

(1)

and the preliminary CMS result from Run 2 is consistent with this, with slightly smaller errors [15]:

m_{H}\;=\;125.26\pm 0.20({\rm stat.})\pm 0.08({\rm syst.})\,,

(2)

It is noteworthy that statistical uncertainties dominate, and we can look forward to substantial reductions in the future, determining $m_{H}$ at the per mille. Accurate knowledge of the Higgs mass is important for precision tests of Standard Model (and other) predictions and, as discussed later, is crucial for understanding the (in/meta)stability of the electroweak vacuum.

3.2 Higgs Couplings

The couplings of the Higgs boson to Standard Model particles are completely specified and, consequently, there are definite predictions for its production processes and decay branching ratios [16]. Concretely, one expects gluon-gluon fusion to dominate over vector-boson fusion, production in association with a vector boson and in association with a $t{\bar{t}}$ pair. The dominant $H$ decay mode is predicted to be into $b{\bar{b}}$ , with much smaller branching ratios for $\gamma\gamma$ and $ZZ^{*}\to 2\ell^{+}2\ell^{-}$ .

Much progress was made in Run 1 probing these predictions [17], but much remains to be done. Higgs decays to $\gamma\gamma,ZZ^{*},WW^{*}$ and $\tau^{+}\tau^{-}$ have been measured in gluon-gluon fusion, and there is solid evidence for vector-boson fusion, but the associated production mechanisms have yet to be confirmed. Moreover, there is no confirmation yet of the expected dominant $H\to b{\bar{b}}$ decay mode: LHC evidence is at the level of 2.6 $\sigma$ [18], and the Tevatron experiments have reported evidence at the 2.8- $\sigma$ level. There is indirect evidence for the expected $Ht{\bar{t}}$ vertex via the measurements of gluon-gluon fusion and $H\to\gamma\gamma$ decay, but no significant evidence via associated $Ht{\bar{t}}$ or single $Ht({\bar{t}})$ production. Also on the agenda is the search for $H\to\mu^{+}\mu^{-}$ , which is predicted in the SM to appear at a level close to the current experimental sensitivity.

Fig. 3 is one way of displaying the available information on Higgs couplings [19, 17]. It is a characteristic prediction of the SM that the couplings to other particles should be related to their masses, $\propto m_{f}$ for fermions and $\propto m_{V}^{2}$ for massive vector bosons. The black solid line is a fit where $m\to m^{(1+\epsilon)}$ in the couplings: we see that the combined ATLAS and CMS data are highly consistent with the SM expectation that $\epsilon=0$ , shown as the blue dashed line.

The couplings in Fig. 3 are all flavour-diagonal. The SM predicts that flavour-violating Higgs couplings should be very small, but measurements of flavour-violating processes at low energies would allow either $H\to\mu\tau$ or $H\to e\mu$ with branching ratio $\lesssim 10$ %, whereas the branching ratio for $H\to e\mu$ must be $\lesssim 10^{-5}$ [20]. The was some excitement after Run 1 when the combined CMS and ATLAS data indicated a possible 2- $\sigma$ excess [12]. This has not reappeared in early Run 2 data [13], but remains an open question.

4 Elementary Higgs Boson, or Composite?

There has been a long-running theoretical debate whether the Higgs boson could be as elementary as the other particles in the SM, or whether it might be composite. The elementary option encounters quadratically-divergent loop corrections to the mass of the Higgs boson, which are frequently (usually?) postulated to be cancelled by supersymmetric particles [21] appearing at the TeV scale [22] - which have not yet been seen.

On the other hand, the composite option has been favoured by many with memories of the (composite) Cooper pairs underlying superconductivity, and the (composite) pions associated with quark-antiquark condensation in QCD [23]. A composite Higgs would require a novel set of strong interactions, and early models tended to have a scalar particle much heavier than the Higgs that has been discovered, and to be in tension with the precision electroweak data. These difficulties can be circumvented by postulating that the Higgs is a pion-like pseudo-Nambu-Goldstone boson of a partially-broken larger symmetry that is restored at some higher energy scale [24].

A phenomenological framework that is convenient for characterizing the experimental constraints on such as possibility is provided by the following form of effective Lagrangian that preserves a custodial SU(2)_V symmetry that guarantees $\rho\equiv m_{W}/m_{Z}\cos\theta_{W}=1$ up to quantum corrections [25]:

	$\displaystyle{\cal L}$	$\displaystyle=$	$\displaystyle\frac{v^{2}}{4}{\rm Tr}D_{\mu}\Sigma D^{\mu}\Sigma\left(1+2\kappa_{V}\frac{H}{v}+b\frac{H^{2}}{v^{2}}+\dots\right)-m_{i}\bar{\psi}^{i}_{L}\Sigma\left(\kappa_{F}\frac{H}{v}+\dots\right)+{\rm h.c.}$		(3)
			$\displaystyle+\frac{1}{2}\partial_{\mu}H\partial^{\mu}H+\frac{1}{2}H^{2}+d_{3}\frac{1}{6}\left(\frac{3m_{H}^{2}}{v}\right)H^{3}+d_{4}\frac{1}{24}\left(\frac{3m_{H}^{2}}{v}\right)H^{4}+...\,,$		(3)

where $H$ is the field of the physical Higgs boson and the massive vector bosons are parametrized by the $2\times 2$ matrix $\Sigma=\exp(i\frac{\sigma_{a}\pi_{a}}{v})$ . The terms in (3) are normalized so that the coefficients $\kappa_{V},b,\kappa_{F},d_{i}=1$ in the SM. The question for experiment is whether any of these coefficients exhibit a deviation that might be a signature of some composite Higgs model.

As seen in the left panel of Fig. 4, measurements of Higgs properties (yellow and orange ellipses) and precision electroweak data (blue ellipses) play complementary roles in constraining the $H$ couplings to vector bosons $\kappa_{V}$ and fermions $\kappa_{F}$ in (3) [26]. These constraints can be translated into lower limits on the possible compositeness scale in various models, as seen in the right panel of Fig. 4 [27].

5 Stability of the Electroweak Vacuum

If the Higgs is indeed elementary, the measurements (1, 2) of $m_{H}$ , combined with those of $m_{t}$ , raise important questions about the stability and history of the electroweak vacuum, suggesting the necessity of new physics beyond the SM [28]. The issue is that the Higgs quartic self-coupling $\lambda$ is renormalized not only by itself, which tends to increase it as the energy/mass scale increases, but also by the Higgs coupling to the top quark, which tends to drive it to smaller (even negative) values at higher scales $Q$ , as seen in the left panel of Fig. 5GeV [29]. At leading order:

\lambda(Q)\;\simeq\;\lambda(v)-\frac{3m_{t}^{4}}{2\pi v^{4}}\log\left(\frac{Q}{v}\right)\,,

(4)

The right panel of Fig. 5 displays the results of one calculation of the regions of the $(m_{H},m_{t})$ plane where the electroweak vacuum is stable, metastable or unstable, and yields the following estimate of the ‘tipping point’ $\Lambda_{I}$ where $\lambda$ goes negative [30]:

	$\displaystyle\log_{10}\left(\frac{\Lambda_{I}}{\rm GeV}\right)$	$\displaystyle=$	$\displaystyle 9.4+0.7\left(\frac{m_{H}}{\rm GeV}-125.15\right)$		(5)
		$\displaystyle-$	$\displaystyle 1.0\left(\frac{m_{t}}{\rm GeV}-173.34\right)+0.3\left(\frac{\alpha_{s}(m_{Z})-0.1184}{0.0007}\right)\,.$		(5)

The dominant uncertainty in the calculation of $\Lambda_{I}$ is due to that in $m_{t}$ , followed by that in $\alpha_{s}(m_{Z})$ (which enters in higher order in the calculation), the uncertainty due to the measurement of $m_{H}$ being relatively small. The final result is an estimate

\log_{10}\left(\frac{\Lambda_{I}}{\rm GeV}\right)\;=9.4\pm 1.1\,,

(6)

indicating that we are (probably) doomed, unless some new physics intervenes.

Some people discount this ‘problem’ on the grounds that the prospective lifetime of the vacuum is much longer than its age. However, there is another issue, namely that fluctuations in the Higgs field in the very early Universe would have been much larger than now, and would probably have driven almost everywhere in the Universe into an anti-De Sitter phase from which there would have been no escape [31]. One could postulate that our piece of the Universe happened to be extraordinarily lucky and avoid this fate, but it seems more plausible that some new physics intervenes before the instability scale $\Lambda_{I}$ . Possible such remedies include higher-dimensional operators in the SM effective field theory (see the next Section), a non-minimal Higgs coupling to gravity, or a threshold for new physics such as supersymmetry [32] (see later).

6 The SM Effective Field Theory

An alternative way of analyzing the Higgs and other data is to assume that all the known particles (including the Higgs boson) are SM-like, and look for the effects of physics beyond the SM via an effective field theory (the SMEFT) containing higher-dimensional SU(2) $\times$ U(1)-invariant operators constructed out of SM fields, e.g., of dimension 6 [33]:

{\cal L}_{eff}\;=\;\sum_{n}\frac{c_{n}}{\Lambda^{2}}{\cal O}_{n}\,,

(7)

where the characteristic scale of new physics is described by $\Lambda$ , with the $c_{n}$ being unknown dimensionless coefficients. Data on Higgs properties, precision electroweak data, triple-gauge couplings (TGCs), etc., can all be combined to constrain the SMEFT operator coefficients in a unified and consistent way. Table 6 shows which observables currently provide the greatest sensitivities to some of these operators [34].