Who breaks Electroweak symmetry?

It sounds like a simple question and the Standard Model of Particle Physics, the prevailing theory for the last half century, has a simple answer - it’s the Higgs. The Standard Model theory predicts that the Higgs boson and field acts as a sole player in the game of Electroweak symmetry breaking. It is a strong prediction that has yet to be verified experimentally. Answering this question is one of the pressing goals for the ATLAS experiment during Run 3 and Run 4 at the LHC.

In recent years, the question of who breaks electroweak symmetry arose more and more in unexpected places. One of the major shortcomings of our understanding of particle physics is the matter over anti-matter asymmetry in the universe. While the Standard Model does predict a matter vs. anti-matter asymmetry, it is much too small compared to what we observe. Moreover, the thermal history of electroweak symmetry breaking is important for particle physics and cosmology. If in the early universe, there was a first order electroweak phase transition (think boiling water), this could explain the matter vs. anti-matter asymmetry as well as sources for potentially observable gravitational radiation [1]. The Standard Model’s prediction is again clear – no first-order transition. Therefore if such a transition took place, the Higgs doesn’t act alone and some new physics is present.

The precise predictions of the Standard Model of Particle Physics is both a blessing and a curse. Because the Standard Model has been so successful over the last half century, any model predicting new physics beyond it is massively limited; any new model can’t break 50 years of successful experimental results. However, the redundancy of the Standard Model is a great experimental advantage; the parameters of the Standard Model are over-constrained, meaning that by measuring one set of parameters, such as the mass of the W boson [2], we gain information about something else, such as the stability of the Higgs vacuum. In essence, the Standard Model is a tightly woven tapestry, where pulling on a single thread can effect the entire picture. As an example, in measurements of the width of the Z boson, which are considered one of the pinnacle measurements of the electron-positron collider, LEP, one of the largest uncertainties is that on the strong force coupling, αs – even in an almost pure electroweak environment, the strong force can not be ignored [3]. The Electroweak sector can, therefore, be probed via precision measurements of the Higgs boson and its couplings, through measurements of multi-boson production, scattering and polarisation and through searches for new particles, in particular for an extended Higgs sector.

As the LHC enters its third phase of data-taking, Run 3, the experiments at the LHC are in a unique position to probe the Electoweak sector and the critical questions that surround it. Furthermore, experiments like ATLAS and CMS are the only ones in a position to do so. While other open questions like the nature of Dark Matter are being searched for using a fleet of different experiments, including ATLAS - the Electroweak sector with an energy scale around a few TeV is uniquely suited to the accelerator energies of the LHC. The Run 3 data will allow us to dig into these questions and get first potential hints at the answers, whereas Run 4, at the HL-LHC, will allow us to fully reveal the nature of the electroweak sector.

Revolutionizing Higgs Physics: Unleashing the Power of Run 3

The upcoming Run 3 of the LHC is anticipated to yield an overwhelming amount of data, about 200-250 fb⁻¹, playing a pivotal role in studying the properties of the Higgs boson and providing unprecedented access to remarkably rare Higgs physics processes. These investigations hold the key to unveiling potential indications of new physics. Within the Higgs sector of the Standard Model (SM), various aspects can reveal the presence of new phenomena: the contributions of new Beyond the Standard Model (BSM) particles in Higgs production and decay loops would result in different rates compared to SM predictions.

In approximately one out of a million recorded collisions, referred to as ”events,” the decay of a Higgs boson produces a distinct signature that stands out amidst the thousands of other particles generated simultaneously. The process of creating and subsequently decaying a Higgs boson exhibits a wide range of possibilities, as it can emerge from any combination of massive particles and can decay into various pairs of massive particles. At the LHC, numerous configurations of Higgs production and decay chains can be observed, and each configuration provides specific information about how the Higgs boson interacts with the particles from which it originates and the particles into which it decays.

To study the Higgs properties,comprehensive fits are conducted, encompassing all Higgs channels, to derive the coupling scale factors of the Higgs boson. These fits utilize different assumptions on the total width of the Higgs boson: In fact, the width of the Higgs resonance line shape corresponds directly to the decay rate of the Higgs boson into all its possible decay channels, even if those decays cannot be directly observed. Hence, an unusual width of the Higgs resonance serves as a highly sensitive experimental indicator for the presence of certain novel particle forms, such as Dark Matter, as well as deviations from the expected Higgs interactions with known particles. The width of the line shape can be determined by comparing the observed decay rates at the resonant mass (on-shell) and away from it (off-shell). However, measuring the width faces challenges due to the low event rate and significant background in the off- shell regime. The Higgs boson width has been measured in this way in the ZZ final state but some theoretical assumptions are necessary. Currently, the precision of this measurement has reached the point that gives experimental evidence of off-shell Higgs boson production, yielding a measured total width of the Higgs boson of 4.5^+3.3_−2.5 MeV [4]. Further improvements are anticipated during Run 3 for this measurement. It is interesting to exploit measurements in the γγ final state as the distinct scaling between the interference induced by the strong phase and the Breit-Wigner of the on-shell Higgs rate in this channel may constrain the Higgs total width without the need of further theoretical assumptions. This benchmark, along with measurements in the WW final state, presents interesting avenues for investigation during Run 3.

Figure 1: Observed and predicted Higgs boson production cross-sections and branching fractions. Left: Cross sections for different Higgs boson production processes are measured assuming SM values for the decay branching fractions. Right: Branching fractions for different Higgs boson decay modes are measured assuming SM values for the production cross sections. The lower panels show the ratios of the measured values to their SM predictions. The vertical bar on each point denotes the 68% confidence interval [5].

Figure Fig. 1 shows the ATLAS Run 2 observed and predicted Higgs boson production cross-sections and branching fractions. In Run 2, the precision on the couplings of γγ, WW, ZZ, ττ, and bb to the Higgs boson ranged between 5-10% [5]. By the end of Run 3, the precision of these measurements is expected to surpass the present accuracy by as much as 20-30%. Similar improvements are anticipated for the main Higgs production modes (ggF, VBF, VH, ttH), which were independently observed in Run 2 with cross-section measurements at the 10-20% level. Notably, the increase in the center-of-mass energy to 13.6 TeV during Run 3 is expected to lead to a significant enhancement of Higgs production cross sections, bringing about 10% additional production cross-section to the main production processes.

Consequently, the limiting factors will shift towards the theoretical precision of calculations and systematic uncertainties arising from measurements. Both the theoretical and experimental communities are actively working to address these limitations through various means, such as faster computing for improved theoretical calculations and advancements in simulation and reconstruction techniques. Cutting-edge machine learning methods are also being employed to enhance the accuracy of analyses. These improvements are crucial to meet the precision requirements and computing demands of the HL-LHC, making their development during Run 3 imperative.

Particle masses exhibit a clear pattern, without an apparent guiding principle, and span almost six orders of magnitude, ranging from the 0.5 MeV/c² for electrons in the first generation to 173,000 MeV/c² for the top quark in the third generation. These masses correspond to a range in Higgs interaction strengths from 0.000003 to 1, assuming that a single Higgs field generates the mass in all particle generations. That assumption is so far experimentally untested as only the interactions with 3rd generation particles have been established. With the increased data volume of LHC Run 2+3, constraints on the Higgs interactions with the 2nd generation particles come into reach, allowing a first ever test of the universality of the mass generation mechanism. Anticipated during Run 3 is a major breakthrough in Higgs physics: the observation of Higgs Boson decays to muons. The primary obstacle in detecting the decay of Higgs bosons into muon pairs, lies in their exceptionally low occurrence compared to the overwhelming background. To tackle this small signal-to-background ratio, we will need to implement groundbreaking approaches for estimating the backgrounds. Currently, ATLAS observes a 2.0σ excess over the background only hypothesis [6]. Limited by statistical constraints, we fall slightly short of the required observation significance under Run 3 conditions. However, by combining the ATLAS and CMS efforts, we could achieve an unequivocal discovery of this decay mode. Enhancing and optimizing our analyses to achieve independent observation sensitivity is anyhow one of our main goals for Run 3.

Furthermore, Run 3 will serve as a fundamental benchmark for studying the coupling to second-generation quarks, specifically the charm quark. Decays of the Higgs boson into a pair of c (”charm”) quarks are relatively common; however, the challenge lies in accurately identifying them based on their detector signature. When high-energy quarks transform into collimated jets of bound states known as hadrons, those originating from b or c quarks travel a finite distance before decaying. Techniques based on distance measurements have proven effective in identifying the long-lived and heavy b quarks of the third generation. To address the more challenging scenario of the shorter-lived and lighter charm quarks, innovative analysis techniques and the utilization of boosted Higgs decays have brought the charm quark within reach for the High-Luminosity phase of the LHC. Run 3 will be instrumental in testing and establishing new analysis strategies to pave the way forward.

Figure 2: The observed and expected upper limits on the Higgs Branching ratio to invisible particles at 95% CL for the Run 2 analyses targeting final states mentioned in the x-axis and their combination, the Run 1 combination and the full Run 1+2 result; the 1σ and 2σ contours of the expected limit distribution are also shown [7].

More rare decays, such as the decay to Zγ, have started to emerge. Recently, the combined results from the ATLAS and CMS experiments yielded the first evidence of this process [8]. Run 3 is expected to confirm this discovery with individual experimental evidence. Even more thrilling is the potential for single experiment discovery in the loop-induced rare γγ^∗ process, where evidence has already been achieved during Run 2 while a 3.2σ significance [9] can be obtained in Run 3, so that it is also at the verge of an observation through combining ATLAS and CMS data.

Additionally, it is important to measure the Higgs width due to its potential decay into undetectable particles that do not interact (referred to as invisible width). The ATLAS Collaboration has already excluded branching ratios of Higgs to invisible larger than 11% at 95% CL (see Fig.2), and further improvements are expected during Run 3.

Furthermore, exploring the spin, charge,  and  parity  symmetry  (CP)  properties of the Higgs can provide hints about deviations from the Standard Model, potentially explaining the origin of the matter-antimatter asymmetry in the universe, an enduring open question unresolved within the context of the Standard Model. While the decay kinematics in the final state offer information about these properties, the rates can be used to extract more stringent constraints. Until now, investigations into Higgs interactions have primarily concentrated on quantifying and interpreting interaction rates, neglecting a valuable source of knowledge: the diverse array of shapes exhibited by observable quantities in Higgs interactions.The shape of the kinematic distributions in the final states provides more model-independent information, albeit limited by available statistics. Therefore, substantial improvements are expected through the analyses conducted during Run 3.

In summary, Run 3 of the LHC will play a crucial role for the future of particle physics: The level of precision achievable for Higgs couplings at the High-Luminosity LHC (HL-LHC) will be at the percent level for κ_µ, κ_t, κ_Zγ. It should be noted that in a model-independent manner, Higgs factories are unable to probe κ_t and can only achieve an accuracy of approximately O(10%) on κ_µ, κ_t, κ_Zγ, through loop effects in other decay processes, assuming no competing contributions from new physics. To attain an even higher level of precision, approaching O(1%) for all these observables, advancements in experimental techniques and theoretical calculations will be necessary [10].

Another important aspect to understand the Electroweak Symmetry breaking is the study of the “Higgs potential” and of its self interactions. The Higgs theory presents a fascinating concept suggesting that the vacuum of the universe is not empty, but rather filled with a pervasive ”Higgs field” that possesses significant energy. The arrangement of this Higgs field in the vacuum is deter- mined by the ”Higgs potential,” which not only influences the self-interactions of Higgs bosons but also affects their detectability at particle accelerators. These self-interactions can manifest as Higgs bosons splitting into two separate Higgs bosons, which can either be both detected individually or recombine and contribute to the observed distribution and rate of singly produced Higgs bosons in a modified manner.

Detecting two Higgs bosons presents an experimental challenge due to their extremely low occurrence rate. The detection of double Higgs production stands as a crucial objective for the High-Luminosity Large Hadron Collider (HL-LHC). By utilizing the data from Run 3, the combined sensitivity of the ATLAS and CMS experiments to di-Higgs production would amount to approximately 1.7σ, assuming production in line with the Standard Model (SM). Through ongoing innovations and enhancements, it is projected that a 2σ sensitivity could be achieved [11]. Such an accomplishment would carry significant implications for the future of the HL-LHC program, particularly if any deviations from the predictions of the SM emerge. The full Run 2 results for di-Higgs analyses have achieved unprecedented precisions.

In addition to analysing the di-Higgs final states, the interpretation of modified distributions in single Higgs production, in terms of Higgs self-coupling loops can additionally be used to further constrain the Higgs potential. For example by combining the HH → bbττ and the bbγγ and bbbb channels with single-Higgs boson analyses, stronger constraints on the self-coupling of the Higgs boson can be established as done by the ATLAS Collaboration with the full Run2 dataset.

Through the combination of the double-Higgs analyses, an upper limit at 2.4 at 95% CL is placed on the production cross-section of double-Higgs events normalized to their Standard Model prediction. By integrating the single-Higgs and double-Higgs analyses and assuming that new physics solely influences the Higgs boson self-coupling (Λ_HHH), values outside the range of −0.4 < κ_Λ < 6.3, where κΛ = Λ_HHH/Λ_SMHHH are excluded with a 95% confidence level. The combined single-Higgs and double-Higgs analyses yield results with fewer assumptions by incorporating additional coupling modifiers into the fitting process to account for the Higgs boson’s interactions with other particles in the Standard Model. These are the strongest bounds on the di-Higgs cross-section and Higgs self-coupling strength [12].

These results underscore the emergence of novel concepts during Run2 of the LHC and highlight the remarkable achievements enabled by experimental advancements in result precision. Notably, the individual analyses of HH → bbττ [13] and HH → bbγγ [14] exhibit an astounding sensitivity improvement of fourfold and fivefold, respectively, compared to previous publications. Approximately half of this enhancement can be attributed to advancements in analysis methodologies. Exciting prospects lie ahead as we anticipate further enhancements through the utilization of state-of-the-art machine learning techniques, enhanced b-jet taggers and light jet rejection, and boosted object handling, the inclusion of more channels in the combination. In the upcoming Run 3 of the LHC, di-Higgs analyses will have a central role.

Multi-boson production, scattering, polarization

The electroweak sector can also be probed via measurements of multi-bosons production, the scattering of bosons and measurements of their polarization. Some of the most constraining data in models of new physics and models of cosmology originate from precision multi-boson and Higgs measurements at LEP and the LHC. During Run 1 and Run 2, the ATLAS experiment for the first time mapped out a fleet of multi-boson measurements including detailed differential results. These included measurements of WW, WZ and ZZ production as well as any first observations of tri-boson states like Wyy, WZy and WWW. Many of these final states probe vertices where three or four bosons interact. As the Standard Model has precise predictions of the production cross section of these interactions, these measurements provide tight constraints to any allowed deviations from the predicted electroweak sector. Additional non-Standard Model interactions modify the kinematic distributions of multi-boson production, especially at high momenta of the final state particles. Here, in particular with the additional data from Run 3, these measurements will provide continued insight.

Another important probe of the electroweak sector are measurements of the scattering of vector bosons, where two vector bosons scatter off each other. In vector boson scattering, the presence of the Higgs boson is needed to exactly cancel out the otherwise diverging scattering amplitudes at high energies and prevent unitarity violation at the TeV scale. Any significant deviation from the predicted high-energy behaviour of vector boson scattering would point to new phenomena. Using Run 2 data, the ATLAS experiment made exciting headway by observing vector boson scattering in same-sign WW [15], WZ [16], ZZ [17] and Zy [18]. Run 3 will provide deeper insights into these measurements as more data will allow for extensive differential measurements and great sensitivity to anomalous behavior.

One of the most exciting possibilities of the Run 3 data is the chance to probe longitudinally polarised weak boson scattering. The existence of the longitudinally polarised state of weak bosons is a consequence of the non-vanishing mass of the bosons generated by the electroweak symmetry breaking mechanism. Therefore, these measurements are tightly intertwined to the gauge structure of the Standard Model itself and the particular way this symmetry is spontaneously broken. New interactions would lead to different polarisation behaviour which we can test for via any anomalies in the electroweak sector by measuring angular observables of the final state particles. The cross-section for longitudinal weak boson scattering is small. However, with the help of excellent detector performance and innovative machine learning methods, ATLAS observed for the first time the production of di-boson polarisation in the W^±Z final state [19]. The most sensitive channel to probe for anomalies is, however, the scattering of two longitudinally W bosons. While the cross section of same-sign WW production was observed for the first time using Run 2 data, it is one of the goals of the Run 3 program to measure the polarization. The Run 3 data may not be sufficient but with continued improved detector performance and machine learning we start to break new ground.

Effective field Theories

The question arises as to how to interpret all this information concurrently and whether it is possible to combine other non-Higgs SM measurements to identify possible deviations from SM expectations. In order to address this inquiry, it is necessary to establish a fresh framework that goes beyond the traditional interpretation of Higgs production rates and incorporates shape information, Higgs self-interaction rates and other SM processes including Electroweak precision data and also analyses of processes including top quarks production.

The absence of definitive signals indicating physics beyond the SM at the LHC suggests the possibility of a scale separation between the SM and any potential new physics at higher energies. This motivates the utilization of the Standard Model Effective Field Theory (SMEFT) [20] as a valuable tool for indirectly searching for new physics in LHC data [read also a previous EP news article]. The SMEFT offers the advantages of (near) model-independence, systematic improvement capabilities, and the ability to simultaneously leverage multiple datasets.

Effective Filed theories introduce new-physics states at a high mass scale Λ, significantly larger than the electroweak scale. By expanding in terms of E/Λ, where E represents the typical energy exchanged in a process, the theory provides predictions for experimental observables. This expansion is achieved through a series of operators, which are constructed as gauge-invariant combinations of SM fields with energy dimensions greater than four.

By measuring observables that are sensitive to the effects of SMEFT operators, it becomes possible to constrain the values of c(d)/Λ⁴_d, where c(d)) represents the Wilson coefficients associated with the dimension-d operators O(d). The leading effects of new physics are expected to be captured by dimension-six operators, as higher-dimensional operators are suppressed by greater powers of Λ⁻¹. The extensive measurements conducted by ATLAS, focusing on electroweak interactions, the Higgs boson, and top quarks, exhibit sensitivity to a wide range of operators that impact various aspects of particle interactions. These operators influence Higgs boson couplings, self-interactions of weak bosons, couplings between weak bosons and fermions, as well as four-fermion couplings. To achieve the best possible sensitivity and disentangle the effects of these operators, it is necessary to combine a diverse set of measurements. A first measurement has been performed by the ATLAS Collaboration with the Run2 data [21]. Also CP violating effects can be included.

Conducting a global analysis of constraints on the Wilson coefficients of the SMEFT is of utmost importance when allowing more than a few Wilson coefficients to be non-zero. This is due to the fact that numerous SMEFT operators contribute to multiple observables, emphasizing the need to avoid analyzing different measurement classes in isolation. This feature becomes increasingly important as the statistics of the ATLAS data increases. During the analysis of Run 3, a significant emphasis will be placed on utilizing Effective Field Theories (EFTs). This endeavor holds particular significance as it aims to uncover potential deviations from the Standard Model (SM) that could be amplified through the comprehensive interpretation of diverse measurements. Furthermore, the outcomes of these investigations will play a crucial role in guiding our future research endeavors at the HL-LHC.

Direct searches

In addition to EFT interpretations, New physics beyond the Standard Model can also be searched for directly. Using the Run 3 data at the LHC, a new era into direct searches will be opened. Improvements will be gained from more data and a higher center of mass energy and also from new triggers, improved event reconstruction and improved physics-analysis methods. These new detector improvements and analysis approaches will allow us to target models at lower energies in addition to high energy searches. Using Run 1 and 2 data, the LHC has vastly limited the parameter space for new physics model, from Supersymmetry to dark matter candidates to exotics Higgs particles [22].

Figure 3: Constraints on Wilson coefficients from the combined LHC Higgs and multi-boson results and precision Electroweak analyses, presented in four blocks with different x-axis ranges. The right-hand side panel shows the contribution of each input measurement group to the eigenvector constraint in the Gaussian approximation. [21].

For probing the Electroweak sector, continued searches of extended Higgs sectors are of particular interested. An extended Higgs sector is, for example, needed to lead to a first-order phase transition in the early universe. Using Run 2 data, the searches for an extended Electroweak sector have been vast, covering searches for new diboson resonances, exotic Higgs decays and direct and indirect searches for additional Higgs bosons. The plot below shows an example of the breadth of coverage in the search for additional Higgs bosons, interpreted in the hMSSM model. While this plot shows the wide range and complementary of the different final states and search modes, it also reveals the large, yet to be explored gaps. The added data of Run 3 will benefit us greatly in closing these gaps.

Figure 4: Regions of the [mA, tanβ] plane excluded in the hMSSM via direct searches for heavy Higgs bosons and fits to the measured rates of observed Higgs boson production and decays. Limits are quoted at 95% CL and are indicated for the data (solid lines) and the expectation for the SM Higgs sector (dashed lines). The light shaded or hatched regions indicate the observed exclusions. [23].

As the ATLAS detector enters Run 3, it will usher in new precision for Higgs measurements and couplings, mulit-boson production and searches for new physics. These results together will provide powerful tests to answer the question of ’Who breaks Electroweak symmetry?’

References 

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