Z Boson Research Articles

Helicity amplitudes without gauge cancellation for electroweak processes

In the 5-component representation of weak bosons, the first four components make a Lorentz four vector, representing the transverse and longitudinal polarizations excluding the scalar component of the weak bosons, whereas its fifth component corresponds to the Goldstone boson. We obtain the 5×5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\ imes 5$$\\end{document} component propagators of off-shell weak bosons, proposed previously and named after the Goldstone boson equivalence theorem, by starting from the unitary-gauge representation of the tree-level scattering amplitudes, and by applying the BRST (Becchi–Rouet–Stora–Tyutin) identities to the two sub-amplitudes connected by each off-shell weak-boson line. By replacing all weak boson vertices with those among the off-shell 5-component wavefunctions, we arrive at the expression of the electroweak scattering amplitudes, where the magnitude of each Feynman amplitude has the correct on-shell limits for all internal propagators, and hence with no artificial gauge cancellation among diagrams. Although our derivation is limited to the tree-level only, it allows us to study the properties of each Feynman amplitude separately, and then learn how they interfere in the full amplitudes. We implement the 5-component weak boson propagators and their vertices in the numerical helicity amplitude calculation code HELAS (Helicity Amplitude Subroutines), so that an automatic amplitude generation program such as MadGraph can generate the scattering amplitudes without gauge cancellation. We present results for several high-energy scattering processes where subtle gauge-theory cancellation among diagrams takes place in all the other known approaches.

Dead cone effect in charm and bottom quark jets

The evolution of a heavy quark initiated jet is mainly ruled by gluon bremsstrahlung. As a consequence of the dead-cone effect, this radiation is suppressed in the forward direction at angles smaller than that proportional to the heavy quark mass MQ, i.e. Θ0=MQ/EQ at energy EQ of the primary quark. In this paper, we unveil this effect in charm and bottom quark jets using DELPHI and OPAL data from Z0 boson decays in e+e− annihilation at center of mass energy 91.2 GeV. The analysis of the reconstructed heavy quark fragmentation function in momentum space shows the strong suppression of hadrons at high momenta in such events compared to light quark fragmentation by a factor ≲1/10. The amount of this suppression is well reproduced by perturbative QCD (pQCD) within the Modified Leading Logarithmic Aproximation and the compact scheme of Local Parton Hadron Duality (MLLA-LPHD). As a new result, we obtain an almost perfect agreement between the light quark fragmentation functions expected at W0∝MQ from DELPHI and OPAL data with Pythia8 and shed light on the reasons for the existence of the ultra-soft gluon excess at small momentum fraction in comparison with pQCD predictions.

Stringent bounds on HWW and HZZ anomalous couplings with quantum tomography at the LHC

Quantum tomography provides the full reconstruction of the density matrix of a state. We use it to study the Higgs boson decay into weak gauge bosons. Anomalous couplings beyond the Standard Model can be constrained by means of observables easily defined in terms of the polarization density matrix. We describe a strategy based on three observables that together provide the most stringent limits. Two of these observables are linked to the entanglement between the polarizations of the two gauge bosons, the other is based on CP-odd combinations of one momentum and two polarizations. We find for the Z channel that this strategy offers, already with the available LHC data, limits competitive with the best available bounds. We argue that the inclusion of these observables in routine experimental analyses can lead to more stringent global fit limits.

Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders

Quantum entanglement of weak interaction gauge bosons produced at colliders can be explored by computing the corresponding polarization density matrix. To this end, we consider the Higgs boson decays Hrightarrow W W^* and Hrightarrow Z Z^*, in which W^* and Z^* are off-shell states, and the WW, WZ and ZZ di-boson production in proton collisions. The polarization density matrix of the di-boson state is determined by the amplitude of the production process and can be experimentally reconstructed from the angular distribution of the momenta of the final states into which the gauge bosons decay. We show that a suitable instance of the Bell inequality is violated in Hrightarrow Z Z^* to a degree that can be tested at the LHC with future data. The same Bell inequality is violated in the production of WW and ZZ boson pairs for invariant masses above 900 GeV and scattering angles close to pi /2 in the center of mass frame. LHC data in this case are not sufficient to establish the violation of the Bell inequality. We also analyze the prospects for detecting Bell inequality violations in di-boson final states at future e^+e^- and muon colliders. A further observable that provides a lower bound on the amount of polarization entanglement in the di-boson system is computed for each of the examined processes. The analytic expressions for the polarization density matrices are presented in full in an Appendix. We also provide the unitary matrices required in the optimization procedure necessary in testing the Bell inequalities.

Inflation and electroweak symmetry breaking

We present a model of Cosmological Electroweak Symmetry Breaking (CEWSB), where a Higgs-like field and a cosmological background of weak boson gauge fields interact with gravity to realize the epoch of cosmic inflation, which is then followed by a Higgs resonance preheating. As a result, the scale of electroweak symmetry breaking is linked with the end of inflation. The theory is equipped with a shift symmetry that can protect the Higgs mass, and it has close semblance to natural inflation and its variants. As the Higgs field's amplitude decays at the end of inflation, its mass emerges. The model has a built in Higgs self-resonance preheating mechanism which leads to the possible emergence of the cosmic microwave background (CMB) due to resonant Higgs, quark and lepton production after inflation. We provide a pathway to implement a similar mechanism with the realistic Higgs-doublet of the standard electroweak theory and discuss phenomenological considerations.

Amplitude-assisted tagging of longitudinally polarised bosons using wide neural networks

Extracting longitudinal modes of weak bosons in LHC processes is essential to understand the electroweak-symmetry-breaking mechanism. To that end, we propose a general method, based on wide neural networks, to properly model longitudinal-boson signals and hence enable the event-by-event tagging of longitudinal bosons. It combines experimentally accessible kinematic information and genuine theoretical inputs provided by amplitudes in perturbation theory. As an application we consider the production of a Z boson in association with a jet at the LHC, both at leading order and in the presence of parton-shower effects. The devised neural networks are able to extract reliably the longitudinal contribution to the unpolarised process. The proposed method is very general and can be systematically extended to other processes and problems.

Test of CP Invariance in Higgs Boson Vector-Boson-Fusion Production Using the H→γγ Channel with the ATLAS Detector.

A test of CP invariance in Higgs boson production via vector-boson fusion has been performed in the H→γγ channel using 139 fb^{-1} of proton-proton collision data at sqrt[s]=13 TeV collected by the ATLAS detector at the LHC. The optimal observable method is used to probe the CP structure of interactions between the Higgs boson and electroweak gauge bosons, as described by an effective field theory. No sign of CP violation is observed in the data. Constraints are set on the parameters describing the strength of the CP-odd component in the coupling between the Higgs boson and the electroweak gauge bosons in two effective field theory bases: d[over ˜] in the HISZ basis and c_{HW[over ˜]} in the Warsaw basis. The results presented are the most stringent constraints on CP violation in the coupling between Higgs and weak bosons. The 95% C.L. constraint on d[over ˜] is derived for the first time and the 95% C.L. constraint on c_{HW[over ˜]} has been improved by a factor of 5 compared to the previous measurement.

Search for high-mass exclusive γγ → WW and γγ → ZZ production in proton-proton collisions at sqrt{s} = 13 TeV

A search is performed for exclusive high-mass γγ → WW and γγ → ZZ production in proton-proton collisions using intact forward protons reconstructed in near-beam detectors, with both weak bosons decaying into boosted and merged jets. The analysis is based on a sample of proton-proton collisions collected by the CMS and TOTEM experiments at sqrt{s} = 13 TeV, corresponding to an integrated luminosity of 100 fb−1. No excess above the standard model background prediction is observed, and upper limits are set on the pp → pWWp and pp → pZZp cross sections in a fiducial region defined by the diboson invariant mass m(VV) > 1 TeV (with V = W, Z) and proton fractional momentum loss 0.04 < ξ < 0.20. The results are interpreted as new limits on dimension-6 and dimension-8 anomalous quartic gauge couplings.

Testing neutrino dipole portal by long-lived particle detectors at the LHC

We discuss the potential of using detectors aimed for searching long-lived particles (LLP) at the high-luminosity LHC run, to probe the neutrino dipole models. This is achieved by taking the heavy neutral leptons (HNL) of the models as candidates of the LLPs. Taking into account the dipole couplings to the weak bosons, d_{W,Z}, which control the production of the HNLs at the LHC, we discuss the reach on the electromagnetic dipole couplings, d_gamma , by searching for a single high-energy photon at LLP detectors. Four typical scenarios are considered in this paper, scenario A, B with d_{W}=0 or d_{Z}=0, and scenario C, D with d_{W,Z}gg d_gamma . We show the sensitivity on d_gamma , can be fairly different depending on the relations between the d_{W,Z} and d_gamma . And the LLP detectors can potentially extend the sensitivity on dipole couplings during the high-luminosity runs of the LHC in certain scenarios.

Non-factorizable virtual corrections to Higgs boson production in weak boson fusion beyond the eikonal approximation

Non-factorizable virtual corrections to Higgs boson production in weak boson fusion at next-to-next-to-leading order in QCD were estimated in the eikonal approximation [1]. This approximation corresponds to the expansion of relevant amplitudes around the forward limit. In this paper we compute the leading power correction to the eikonal limit and show that it is proportional to first power of the Higgs boson transverse momentum or the Higgs boson mass over partonic center-of-mass energy. Moreover, this correction can be significantly enhanced by the rapidity of the Higgs boson. For realistic weak boson fusion cuts, the next-to-eikonal correction reduces the estimate of non-factorizable contributions to fiducial cross section by (20) percent.

Semi-inclusive deeply inelastic electron nucleus scattering in the eN collinear frame

Our understanding of the parton-level structure in the nucleon comes predominantly from the electron deeply inelastic scattering measurements with very high precision. It deserves further study. We therefore calculate the neutral current jet production semi-inclusive deeply inelastic scattering process in this paper. Neutral current implies that interactions can be mediated by the photon, Z0 boson and their interference. The initial electron is assumed to be polarized and then scattered off by a target particle with spin 1. After obtaining the differential cross section, we calculate sets of quantities, including structure functions, azimuthal asymmetries, parity-violating asymmetries and charge asymmetries. They can be measured in the experiments. We find that these quantities are expressed in terms of the parton distribution functions and the electroweak coefficients. These coefficients are different from that in the γ⁎N collinear frame. As a result, our calculation provides a set of new quantities for determining the electroweak couplings as well as the parton distribution functions in the deeply inelastic scattering. It is helpful to test the universality of the parton distribution functions or to understand the hadronic weak interactions and strong interactions simultaneously.

Higgs boson origin from a gauge symmetric theory of massive composite particles and massless W± and Z0 bosons at the TeV scale

The ultraviolet completion is the Standard Model (SM) gauge-symmetric four-fermion couplings at the high-energy cutoff. Composite particles appear in the gauge symmetric phase in contrast with SM particles in the spontaneous symmetry-breaking phase. The critical point between the two phases is a weak first-order transition. It relates to an ultraviolet fixed point for an SM gauge symmetric theory of composite particles in the strong coupling regime. The low-energy SM realizes at an infrared fixed point in the weak coupling regime. Composite bosons dissolve into SM particles at the phase transition, and in the top-quark channel, they become a composite SM Higgs boson and three Goldstone bosons. Extrapolation of SM renormalization-group solutions to high energies implies that the gauge-symmetric theory of composite particles has a characteristic scale of about 5.1 TeV. We discuss the phenomenological implications of composite SM Higgs boson in the gauge symmetry-breaking phase, and massive composite bosons coupling to massless W± and Z0 gauge bosons in the gauge symmetric phase.

Some new observations for the Georgi-Machacek scenario with triplet Higgs scalars

The Georgi-Machacek model, introducing a complex and a real scalar triplet as additional components of the electroweak symmetry breaking sector, enables substantial triplet contributions to the weak gauge boson masses, subject to the equality of the complex and the real triplet vacuum expectation values (vev) via a custodial SU(2) symmetry. We present an updated set of constraints on this scenario, from collider data (including those from 137/139~fb$^{-1}$ of luminosity at the Large Hadron Collider), available data on the 125-GeV scalar, indirect limits and also theoretical restrictions from vacuum stability and unitarity. It is found that some bounds get relaxed, and the phenomenological potential of the scenario is more diverse, if the doubly charged scalar in the spectrum can decay not only into two like-sign $W$'s but also into one or two singly charged scalars. Other interesting features are noticed in a general approach, such as substantial $\gamma\gamma$ and $Z\gamma$ branching ratios of the additional custodial singlet scalar, and appreciable strength of the trilinear interaction of a charged scalar, the $W$ and the $Z$. Finally,, we take into account the possibility of custodial SU(2) breaking, resulting in inequality of the real and the complex scalar vevs which too in principle may allow large triplet contribution to weak boson masses. Illustrative numerical results on the modified limits and predictions are presented, once more taking into account all the constraints mentioned above.

Anomalous Higgs boson couplings in weak boson fusion production at NNLO in QCD

The production of Higgs bosons in weak boson fusion has the second largest cross section among Higgs-production processes at the LHC. As such, this process plays an important role in detailed studies of Higgs interactions with vector bosons. In this paper we extend the available description of Higgs boson production in weak boson fusion by considering anomalous $HVV$ interactions and NNLO QCD radiative corrections at the same time. We find that, while leading order QCD predictions are too uncertain to allow for detailed studies of the anomalous couplings, NLO QCD results are sufficiently precise, most of the time. The NNLO QCD corrections alter the NLO QCD predictions only marginally, but their availability enhances the credibility of conclusions based on NLO QCD computations.

Elementary particle non-perturbative mass generation. A step towards a beyond-the-Standard-Model model

We show that a recently discovered non-perturbative field-theoretical mechanism giving mass to elementary fermions, is also capable of generating a mass for the weak bosons, when the model is extended to encompass weak interactions, and can thus be used as a viable alternative to the Higgs scenario. A detailed analysis of this remarkable feature shows that the non-perturbatively generated fermion and W masses have the parametric form mf∼Cf(α)ΛRGI and MW∼gwcw(α)ΛRGI, respectively, where the coefficients Cf(α) and cw(α) are functions of the gauge couplings, gw is the weak coupling and ΛRGI is the RGI scale of the theory. In view of these expressions, we see that to match the experimental values of the top quark and W masses, we are led to conjecture the existence of a yet unobserved sector of massive fermions (that we denote Tera-fermions) subjected, besides ordinary Standard Model interactions, to a super-strong gauge interactions (Tera-interactions), so that the full theory (SM plus Tera-particles) will have an RGI scale ΛRGI≡ΛT≫ΛQCD in the TeV region. This approach offers a solution of the Higgs mass naturalness problem (there is no fundamental Higgs), an understanding of the fermion mass hierarchy and a physical interpretation of the electro-weak scale as a fraction of ΛT.

Impact of the electromagnetic field on Z0 leptonic invariant mass in ultrarelativistic heavy ion collisions

The extraordinary strong magnetic field generated in ultrarelativistic heavy ion collisions makes it possible to investigate many novel effects in the hot QCD matter, and a direct probe of it thus becomes an urgent task in the field. Here we report a new way to probe it, where the leptonic invariant mass distribution of Z0 boson will be modified in the presence of the magnetic field due to the Lorentz force on the lepton pairs from the decay of Z0 boson. It is found that the magnetic field can decrease the mean value of Z0 leptonic invariant mass and increase its width, and both shifts approximately depend on the integral of the magnetic field over its time duration quadratically.

Daughter Higgs Boson in the Unified Composite Model

In the unified subquark model of all fundamental particles and forces, the mass of the Higgs boson in the standard model of electroweak interactions (mH) is predicted to be about 2√6 mW / 3 (where mW is the mass of the charged weak boson, W ), which agrees well with the experimental values of about 125 GeV found by the ATLAS and CMS Collaborations at the LHC in 2011. It seems to indicate that the Higgs boson is a composite of the iso-doublet spinor subquark-antisubquark pairs well described by the unified subquark model with either one of subquark masses vanishing or being very small compared to the other. In the unified composite model, there may appear a daughter of the Higgs boson whose mass is predicted to be 2 mW /√3, which agrees well with the experimental values of about 95 GeV for the excess events, found by the LEP experiments and recently by the CMS experiment. This agreement seems to strongly indicate not only the compositeness of the Higgs bosons but also the validity of the unified composite model of all fundamental particles and forces.

Electroweak corrections to Higgs boson production via W W fusion at the future LHeC

Precision measurement of quark Yukawa couplings is a crucial aspect of the Higgs property study. Proposed as a future upgrade of the Large Hadron Collider (LHC), the Large Hadron electron Collider (LHeC) provides opportunities to probe quark Yukawa couplings with a high precision because of relatively low QCD background as compared with that of the Higgs processes at the LHC. For this purpose, it is important to have a precision prediction of the Higgs production rate at the LHeC. The leading production channel of the Higgs boson at the LHeC is via weak boson fusion (WBF) which has the unique kinematic feature of forward tagging jets. As QCD corrections are suppressed by the simple color structure of the process, electroweak (EW) radiative corrections become particularly important. In this paper, we focus on the EW radiative corrections at next-to-leading order for the Higgs-boson production via charge current WBF processes at the LHeC. In the two renormalization schemes we use, the EW corrections are respectively at the level of 9% and 18% relative to the leading order result, for a center-of-mass energy at 1.98 TeV, and the next-to-leading order results in both schemes agree up to a truncation error expected from the perturbative method. The size of the EW corrections exceeds that from QCD radiations and is shown to be important for the study of Higgs phenomenology.

Phenomenological implications of the new Littlest Higgs model with T-parity

We investigate the parameter space of the new Littlest Higgs model with T-parity (NLHT) recently introduced to cure some pathologies of the original LHT. The model requires extra fermion content and additional pseudo-Goldstone bosons. While the heavy top quark sector is similar, there are both T-odd and T-even heavy quarks and leptons with masses proportional to just two sets of Yukawa matrices in flavor space, one more than in the LHT. The new scalars are a singlet and real triplet, T-odd, with masses controlled by gauge and Yukawa couplings, independent of the spontaneous symmetry breaking scale f, and hence potentially light. Imposing that no mass exceeds the cutoff scale, applying current lower bounds on vector-like quarks and assuming a simplified model with mass degenerate heavy fermions compatible with the heavy photon as dark matter constituent, we find that f gets constrained within the interval between 2 and 3 TeV, the common Yukawa coupling of heavy leptons gets fixed and the Yukawa coupling of heavy quarks becomes greatly correlated to the top quark Yukawa couplings. The particle spectrum is then bounded from below and above, with the (lightest) heavy photon at about 0.5 TeV, not far from the heavy leptons, the new scalars below 1 TeV, the usual complex scalar triplet close to the heavy weak bosons at about 1.5 to 2.5 TeV, and the heavy quarks and top quark partners between 2 and 5 TeV. The new scalars decay predominantly to a standard and a T-odd lepton and have a width comparable to that of the Higgs.

Quartic Gauge-Higgs couplings: constraints and future directions

Constraints on quartic interactions of the Higgs boson with gauge bosons have been obtained by the experimental LHC collaborations focussing on the so-called κ framework of flat rescalings of SM-like interactions in weak boson fusion (WBF) Higgs pair production. While such approaches are admissible to obtain a qualitative picture of consistency with the SM when the statistical yield is low, once more statistics become available a more theoretically consistent framework of limit setting is desirable. Reviewing the constraints provided at the Large Hadron Collider, we first show that these limits are robust when considered in a leading order context. Turning to radiative corrections, we demonstrate the limitations of this approach in the SM, and by adopting Higgs effective field theory techniques, we clarify the sensitivity from single Higgs measurements to rescalings of quartic Higgs-gauge couplings. We then discuss avenues for sensitivity improvements of WBF analyses employing Graph Neural Networks to combat the large contributing backgrounds.