We consider top-quark mass effects in the Higgs-interference contribution to $Z$-boson pair production in gluon fusion. While this production mechanism is formally of next-to-next-to leading order, its contribution is numerically important above the top threshold $M_{ZZ}^2=4m_t^2$. This region is essential to constrain the width of the Higgs boson and good control over the top-quark mass dependence is crucial. We determine the form factors that are relevant for the interference contribution at two-loop order using a method based on a conformal mapping and Padé approximants constructed from the expansions of the amplitude for large top mass and around the top threshold.
In these proceedings we discuss $t\bar{t}H$ production at the Large Hadron Collider in the Higgs characterisation model. We demonstrate the importance of off-shell effects and higher-order QCD corrections for this process and highlight the importance of single-resonant contributions for the production of a $\mathcal{CP}$-odd Higgs boson.
We show that the dominant channel proposed for the determination of the Higgs boson trilinear coupling, $pp\to HH+X$ via gluon fusion, exhibits an interference structure that is independent of the collider energy for collider energies in the range $8\,{\rm TeV}\leq \sqrt{s}\leq 100\,{\rm TeV}$ and is almost maximally destructive. This insensitivity to the collider energy remains approximately true for a variety of other two Higgs production mechanisms although the magnitude of the interference varies widely.
The amplitude for scalar Higgs boson production in a fusion of two off-shell gluons is calculated including finite (not infinite) masses of quarks in the triangle loop. In comparison to the effective Lagrangian approach, we have found a new term in the amplitude. The matrix element found can be used in the kt-factorization approach to the Higgs boson production. The results are compared with the calculations for on-shell gluons. Small deviations from the cos(phi)^2-dependence are predicted. The off-shell effects found are practically negligible.
The differences between the on-shell mass and width of the Higgs boson and their pole counterparts are evaluated in leading order. For a heavy Higgs boson, they are found to be sensitive functions of the gauge parameter and become numerically large over a class of gauges that includes the unitary gauge. For a light Higgs boson, the differences remain small in all gauges. The pinch-technique mass and width are found to be close to their pole counterparts over a large range of Higgs boson masses.
We discuss off-shell contributions in Higgs decays to heavy gauge bosons $H\rightarrow VV^{(*)}$ with $V\in\lbrace Z,W\rbrace$ for a standard model (SM) Higgs boson for both dominant production processes $e^+e^-\rightarrow ZH\rightarrow ZVV^{(*)}$ and $e^+e^-\rightarrow ν\barνH\rightarrow ν\barνVV^{(*)}$ at a (linear) $e^+e^-$ collider. Dependent on the centre-of-mass energy off-shell effects are sizable and important for the understanding of the electroweak symmetry breaking mechanism. Moreover we shortly investigate the effects of the signal-background interference in $H\rightarrow γγ$ decay…
Systematic on-shell renormalization programme is carried out for the Higgs and gauge boson sectors of the Minimal Supersymmetric Standard Model. Complete 1-loop results for the 2- and 3-point Green's functions are explicitly given. The Higgs boson masses and the cross sections for the neutral scalar production in the $e^+e^-$ colliders are calculated.
Interference effects play an important role in Electroweak Physics. They are responsible for the restoration of unitarity al large energies. When, as is often the case, higher order corrections are only available for some particular subamplitude, interferences need to be carefully computed in order to obtain the best theoretical prediction. In the new proposal to estimate the total Higgs width from the off shell cross section, the interference between the Higgs signal and the background is essential. It has been recently pointed out in gluon fusion that whenever more than one neutral, CP even,…
We propose a new type of search for a pseudoscalar particle $η$ pair produced via an off-shell Higgs, $pp\to h^*\to ηη$. The search is motivated by a composite Higgs model in which the $η$ is extremely narrow and decays almost exclusively into $Zγ$ in the mass range $65$ GeV$\lesssim m_η\lesssim 160$ GeV. We devise an analysis strategy to observe the novel $ZγZγ$ channel and estimate potential bounds on the Higgs-$η$ coupling. The experimental sensitivity to the signatures depends on the power to identify fake photons and on the ability to predict large photon multiplicities. This search allow…
The measurements of the properties of the Higgs boson still leave room for a non minimal scalar sector. Extensions of the Standard Model typically involve multiple neutral Higgs fields which can interfere among themselves. We show that these interference effects can be substantial taking as example the one Higgs Singlet Model, the simplest renormalizable addition to the SM.
After the discovery of a scalar resonance, resembling the Higgs boson, its couplings have been extensively studied via the measurement of various production and decay channels on the invariant mass peak. Recently, it has been suggested the possibility to use off-shell measurements: in particular, CMS has published results based on the high- invariant mass cross section of the process $gg \to ZZ$, which contains the contribution of the Higgs. While this measurement has been interpreted as a constraint on the Higgs width after very specific assumptions are taken on the Higgs couplings, in this l…
An Aoki-Denner form of the renormalization scheme is suggested for the physical amplitudes in MSSM. The Higgs sector is reparameterized with the mass of the CP odd scalar, and the mass of the heavy CP even one instead of $tanβ$ in our scheme. The counterterms of $tanβ$ is fixed perturbatively on mass shell just within Higgs sector. The counterterms of gauge-scalar mixings are defined with Ward-Takahashi identit ies from scalar-scalar mixings. The effect of the reparameterization is also probed on the radiative correction of the mass of the lightest Higgs.
In the upcoming LHC run we will be able to probe the structure ofthe loop--induced Higgs--gluon coupling through kinematics. First, we establish state-of-the-art simulations with up to two jets to next-to-leading order including top mass effects. They allow us to search for deviations from the low-energy limits in boosted Higgs production. In addition, the size of the top mass effects suggests that they should generally be included in Higgs studies at the LHC. Next, we show how off-shell Higgs production with a decay to four leptons is sensitive to the same top mass effects. We compare the pot…
We discuss the production of a heavy neutral Higgs boson of a CP-conserving Two-Higgs-Doublet Model in gluon fusion and its decay into a four-fermion final state, $gg (\rightarrow VV) \rightarrow e^+e^-μ^+μ^-/e^+e^-ν_l\barν_l$. We investigate the interference contributions to invariant mass distributions of the four-fermion final state and other relevant kinematical observables. The relative importance of the different contributions is quantified for the process in the on-shell approximation, $gg\rightarrow ZZ$. We show that interferences of the heavy Higgs with the light Higgs boson and backg…
One-loop on-shell and off-shell decays $H\rightarrow VV$ with $VV=γγ, Zγ, ZZ$ are presented in this paper. The effects of one-loop on-shell and off-shell Higgs decays in Higgs productions at $e^-e^-$ collisions are also then examined. We find that the impacts of one-loop Higgs decays are significant and they are must be taken into account at $e^-e^-$ collision.
We analyze the Higgs-boson masses and mixing matrices in the NMSSM based on an on-shell (OS) renormalization of the gauge-boson and Higgs-boson masses and the parameters of the top/scalar top sector. We compare the implementation of the OS calculations in the codes NMSSMCALC and NMSSM-FeynHiggs up to $\mathcal{(α_tα_s)}$. We identify the sources of discrepancies at the one- and at the two-loop level. Finally we compare the OS and $\overline{\text{DR}}$ evaluation as implemented in NMSSMCALC. The results are important ingredients for an estimate of the theoretical precision of Higgs-boson mass …
We explicitly calculate the contribution to Higgs production at the LHC from the interference between gluon-gluon and Weak Vector Boson fusion, and compare it to the pure QCD and pure Electro-weak result. While the effect is small at tree level, we speculate it will be significantly enhanced by loop effects.
We show that the narrow-width approximation is insufficient for describing production of supersymmetric particles at the ILC. Especially when cuts are taken into account to extract signals using the narrow-width approximation can be wrong by an order of magnitude.
The Next-to-Minimal Supersymmetric Standard model (NMSSM) appears as an interesting candidate for the interpretation of the Higgs-measurement at the LHC and as a rich framework embedding physics beyond the Standard Model. We consider the renormalization of the Higgs sector of this model in its $\mathcal{CP}$-violating version, and propose a renormalization scheme for the calculation of on-shell Higgs masses. Moreover, the connection between the physical states and the tree-level ones is no longer trivial at the radiative level: a proper description of the corresponding transition thus proves n…
A high luminosity Circular Electron Positron Collider (CEPC) as a Higgs Factory will be helpful to the precision measurement of the Higgs mass. The signal-background interference effect is carefully studied for the Higgs diphoton decay mode in the associated Z boson production at the future $e^+e^-$ colliders at energy $246 {\rm GeV}$. The mass shifts go up from about $20 {\rm MeV}$ to $50 {\rm MeV}$ for the experimental mass resolution ranging from $0.8 {\rm GeV}$ to $2 {\rm GeV}$.
We study the effect of interference between the Standard Model Higgs boson resonance and the continuum background in the process gamma gamma -> H -> b b-bar at a photon collider. Taking into account virtual gluon exchange between the final-state quarks, we calculate the leading corrections to the height of the resonance for the case of a light (m_H < 160 GeV) Higgs boson. We find that the interference is destructive and around 0.1--0.2% of the peak height, depending on the mass of the Higgs and the scattering angle. This suppression is smaller by an order of magnitude than the anticipated expe…
We study interference effects between resonant and nonresonant amplitudes for the $γγ\rightarrow W^+ W^-$ process at a backscattered photon-photon collider. We show that a Higgs boson with $M_H$ > 200 GeV is manifest as a resonant dip in the $W^+W^-$ invariant mass spectrum and we investigate its statistical significance.
A substantial off-shell Higgs boson signal in the gluon fusion and vector boson fusion H --> ZZ and H --> WW channels at the Large Hadron Collider (LHC) facilitates a novel, complementary approach to constraining the total Higgs width Gamma_H. With LHC Run 1 data, experimental analyses by CMS and ATLAS find Gamma_H < 5.4 Gamma_H,SM and Gamma_H < [4.5,7.5] Gamma_H,SM at 95% confidence level, respectively, where Gamma_H,SM is the expected value in the Standard Model at the measured Higgs boson mass. I review the theoretical basis of the new approach and discuss its significance in comparison to …
The importance of off-shell contributions is discussed for $H\to VV^{(*)}$ with $V\in\{Z,W\}$ for large invariant masses $m_{VV}$ involving a standard model (SM)-like Higgs boson with $m_H=125$GeV at a linear collider (LC). Both dominant production processes $e^+e^-\to ZH\to ZVV^{(*)}$ and $e^+e^-\toν\barνH\toν\barνVV^{(*)}$ are taken into account, and the signal processes are compared with background yielding the same final state. The relative size of the off-shell contributions is strongly dependent on the centre-of-mass energy. These contributions can have an important impact on the determi…
We study interference effects in the production channel ZZ + jet, in particular focusing on the role of the Higgs boson. This production channel receives contributions both from Higgs boson-mediated diagrams via the decay $H \to ZZ$ (signal diagrams), as well as from diagrams where the Z-bosons couple directly to a quark loop (background diagrams). We consider the partonic processes $gggZZ$ and $gq \bar{q} ZZ$ in which interference between signal and background diagrams first occurs. Since interference is primarily an off-resonant effect for the Higgs boson, we treat the Z-bosons as on-shell. …
Off-shell Higgs at the high mass tail may shed light on the underlying mechanism of the electroweak symmetry breaking. Due to the large cancellation in the standard model (SM) between the box and Higgs-mediated triangle diagrams, the $gg\to WW(ZZ)$ process in the SM is dominated by the $V_T V_T$ transverse-mode at the high mass tail. The cancellation does not necessarily hold, when there is a sufficiently large new physics contribution resulting in $V_LV_L$ longitudinal mode, which is commonly the case when the Higgs sector is modified. Thus the $V_LV_L$ final states in the high mass tail can …
Mixing effects in the MSSM Higgs sector can give rise to a sizeable interference between the neutral Higgs bosons. On the other hand, factorising a more complicated process into production and decay parts by means of the narrow-width approximation (NWA) simplifies the calculation. The standard NWA, however, does not account for interference terms. Therefore, we introduce a generalisation of the NWA (gNWA) which allows for a consistent treatment of interference effects between nearly mass-degenerate particles. Furthermore, we apply the gNWA at the tree and 1-loop level to an example process whe…
We study the interference of resonant Higgs boson exchange in neutralino production in μ^+ μ^- annihilation with longitudinally polarized beams. We use the energy distribution of the decay lepton in the process \neutralino_j \to \ell^\pm \slepton^\mp to determine the polarization of the neutralinos. In the CP conserving Minimal Supersymmetric Standard Model a non-vanishing asymmetry in the lepton energy spectrum is caused by the interference of Higgs boson exchange channels with different CP eigenvalues. The contribution of this interference is large if the heavy neutral bosons H and A are nea…
We present the full ${\cal O}(\as^2)$ computation of the interference effects between the Higgs diphoton signal and the continuum background at the LHC. While the main contribution to the interference originates on the $gg$ partonic subprocess, we find that the corrections from the $qg$ and $q\bar{q}$ channels amount up to 35% of it. We discuss the effect of these new subprocesses in the shift of the diphoton invariant mass peak recently reported by S. Martin in Ref.\cite{Martin:2012xc}.
We compute next-to-leading order QCD corrections to the top-bottom interference contribution to H+j production at the LHC. To achieve this, we combine the recent computation of the two-loop amplitudes for gg -> Hg and qg -> Hq, performed in the approximation of a small b-quark mass, and the numerical calculation of the squared one-loop amplitudes for gg -> Hgg and qg -> Hqg performed within OpenLoops. We find that QCD corrections to the interference are large and similar to the QCD corrections to the top-mediated Higgs production cross section. We also observe a significant reduction in the ma…
The resonance-continuum interference is usually neglected when the width of a resonance is small compared to the resonance mass. We re-examine this standard by studying the interference effects in high-resolution decay channels, $γγ$ and $ZZ$, of the heavy Higgs boson $H^0$ in nearly aligned two-Higgs-doublet models. For the $H^0$ with a sub-percent width-to-mass ratio, we find that, in the parameter space where the LHC 14 TeV $ZZ$ resonance search can be sensitive, the interference effects can modify the $ZZ$ signal rate by ${\cal O}(10)\%$ and the exclusion reach by ${\cal O}(10)$ GeV. In ot…
New physics frameworks like the Next-to-Minimal Supersymmetric Standard Model and the Next-to-2-Higgs-doublet Model contain three neutral CP-even Higgs bosons. It is possible for the heavier two of these states to have masses identical to each other, which can result in a sizeable quantum interference between their propagators in processes they mediate. For both these models, we study the impact of such interference on the pair-production of the lightest of the three scalars, which we identify with the observed 125 GeV Higgs boson, in the gluon-fusion channel at the Large Hadron Collider (LHC)…
Higgs boson production in association with a charm-quark jet proceeds through two different mechanisms - one that involves the charm Yukawa coupling and the other that involves direct Higgs coupling to gluons. The interference of the two contributions requires a helicity flip and, therefore, cannot be computed with massless charm quarks. In this paper, we consider QCD corrections to the interference contribution starting from charm-gluon collisions with massive charm quarks and taking the massless limit, $m_c \to 0$. The behavior of QCD cross sections in that limit differs from expectations ba…
We discuss effects related to the fact that the final state particles of a reaction e+ e- -> t \bar{t} H are actually produced and they decay off mass shell. For the intermediate mass Higgs boson, which decays preferably into a b\bar{b}-quark pair, the reaction will be observed through reactions with 8 fermions in the final state. Such reactions, already in the lowest order of the standard model, receive contributions typically from a few dozen thousands of the Feynman diagrams, the vast majority of which constitute background to the signal of associated production of the top quark pair and Hi…
An updated version is presented of the Fortran code FeynHiggs for the evaluation of the neutral CP-even Higgs sector masses and mixing angles. It differs from the previous version by a modification of the renormalization scheme concerning the treatment of subleading terms at the one-loop level; the two-loop corrections, for which the leading contributions of O(alpha_t alphas) and O(alpha_t^2) are implemented, are not affected by the modified renormalization prescription. Besides stabilizing the Higgs mass calculations and avoiding unphysically large threshold effects, the mass of the lightest …
We calculate the order O(alpha^2 alpha_s^3) interference effect between the gluon fusion and weak boson fusion processes allowed at the one-loop level in Higgs boson plus 2 jet production at the LHC. The corresponding one-loop amplitudes, which have not been considered in the literature so far, are evaluated analytically using dimensional regularisation and the necessary master integrals with massive propagators are reported. It is discussed in detail how various mechanisms conspire to make this contribution numerically negligible for experimental studies at the LHC.
We discuss the off-shell renormalization properties of the abelian Higgs model in the unitary gauge. The model is not renormalizable according to the usual power counting rules. In this paper, however, we show that with a proper choice of interpolating fields for the massive photon and the Higgs particle, their off-shell Green functions can be renormalized. An analysis of the nature of the extra singularities in the unitary gauge is given, and a recipe for the off-shell renormalization is provided.
Higgs precision program at future lepton collider aims at (sub) percent level precision measurement of the Higgs properties, shedding light to new physics through the Higgs lamppost. Amongst many exclusive Higgs channels that can be measured precisely, the $WW$-fusion to Higgs with subsequent decays into $b\bar b$ final state are of particular importance. This channel provide leading constrains on Higgs total width in the $κ$-framework and greatly improves the constraints in the EFT framework as a distinct production mode other than the Higgsstrahlung process. We argue in this paper that, ther…
The correlation of on- and off-shell Higgs boson production at the LHC in $gg \to h^* \to ZZ$ to bound the Higgs width, under specific model-dependent assumptions, has recently received a lot of attention. As off-shell cross section measurements in this channel suffer from a small signal yield, large backgrounds, and theoretical uncertainties, we propose an alternative complementary constraint which is only possible through the combination of LEP and LHC measurements. Previous precision electroweak measurements at LEP allow for the determination of indirect constraints on Higgs couplings to ve…
The interesting but difficult phenomenology of supersymmetric models at the LHC and ILC demands a corresponding complexity and maturity from simulation tools. This includes multi-particle final states, reducible and irreducible backgrounds, spin correlations, real emission of photons and gluons, virtual corrections etc. Most of these topics are included in the multi-particle Monte Carlo (MC) Event generators Madgraph, WHIZARD and Sherpa. A comparison of these codes is shown, with a special focus on the new release of WHIZARD. I show examples for the necessity of considering full matrix element…
We present an analysis of Higgs-boson production in association with a top-quark pair at the LHC investigating in particular the final state consisting of four b jets, two jets, one identified charged lepton and missing energy. We consider the Standard Model prediction in three scenarios, the resonant Higgs-boson plus top-quark-pair production, the resonant production of a top-quark pair in association with a b-jet pair and the full process including all non-resonant and interference contributions. By comparing these scenarios we examine the irreducible background for the production rate and s…
Measurements of the off-shell Higgs boson production cross section in gg (--> h*) --> ZZ have recently been used by the CMS and ATLAS collaborations to indirectly constrain the total width of the Higgs boson. I point out that the interpretation of these measurements as a Higgs width constraint can be invalidated if additional neutral Higgs boson(s) are present with masses below about 350 GeV.
A computation of inclusive cross sections for neutral Higgs boson production through gluon fusion and bottom-quark annihilation is presented in the MSSM with complex parameters. The predictions for the gluon-fusion process are based on an explicit calculation of the leading-order cross section for arbitrary complex parameters which is supplemented by higher-order corrections: massive top- and bottom-quark contributions at NLO QCD, in the heavy top-quark effective theory the top-quark contribution up to N$^3$LO QCD including a soft expansion for the $\mathcal{CP}$-even component of the light Hi…
We take the first steps towards an entirely on-shell description of the bosonic electroweak sector of the Standard Model. We write down on-shell three particle amplitudes consistent with Poincare' invariance and little group covariance. Tree-level, four particle amplitudes are determined by demanding consistent factorization on all poles and correct UV behaviour. We present expressions for these $2\rightarrow 2$ scattering amplitudes using massive spinor helicity variables. We show that on-shell consistency conditions suffice to derive relations between the masses of the $W^\pm, Z$, the Weinbe…
For the Standard Model extended with a real scalar singlet field, the modification of the heavy Higgs signal due to interference with the continuum background and the off-shell light Higgs contribution is studied for gg --> ZZ, WW --> 4 lepton processes at the Large Hadron Collider. Interference effects can range from O(10%) to O(1) effects for integrated cross sections. Despite a strong cancellation between the heavy Higgs-continuum and the heavy Higgs-light Higgs interference, the full interference is clearly non-negligible and modifies the heavy Higgs line shape. A |M_VV - M_h2| < Gamma_h2 …
Higher loop calculations in the Higgs sector of the standard model at the Higgs mass scale have shown that perturbation theory diverges very badly at about 1 TeV in the on-shell renormalization scheme. The prediction of the position of the Higgs pole in the complex s-plane becomes unreliable. We show that in the pole renormalization scheme this appears to have much better convergence properties, while showing good agreement with the on-shell scheme over the validity range of the latter. This suggests that the pole scheme should be preferable for phenomenological studies of heavy Higgs bosons. …
The gauge dependence of the Higgs-boson mass and width in the on-shell scheme of renormalization is studied in the heavy-Higgs-boson approximation. The corresponding expansions in the pole scheme are analyzed adopting three frequently employed parametrizations. The convergence properties and other theoretical features of the on-shell and pole expansions, as well as their relative merits, are discussed.
This note is to record an unsucessful idea. I tried hard to persuade myself to write this note as I have spent a significant fraction of time during this summer. For Higgs resonant production and decaying in the $s$ channel, $i \to H \to f$, the cross section is proportional to $y_i^2y_f^2/Γ_H$. Thus there is a multi-solution ambiguity on the couplings due to uncertain knowledge on Higgs width. In this work, we study the process $g+q \to g+q+l^++l^-$ with the $t$-channel Higgs boson contribution included. As Higgs boson is not on-shell, this process can be used to measure the Higgs couplings w…
We study chargino production at a muon collider with longitudinally polarized beams and center of mass energies around the heavy neutral Higgs boson resonances. We show that the interference of the CP even and CP odd Higgs bosons can be analyzed using the energy distributions of the lepton or W boson from the chargino two-body decays \tildeχ^\pm_j\to\ell^\mp\tildeν_\ell or \tildeχ^\pm_j \to W^\pm \neutralino_1, respectively. The energy distributions depend on the longitudinal polarization of the decaying chargino, which are correlated to the muon beam polarizations. We define asymmetries in th…
Proposals of measuring the off-shell Higgs contributions and first measurements at the LHC have electrified the Higgs phenomenology community for two reasons: Firstly, probing interactions at high invariant masses and momentum transfers is intrinsically sensitive to new physics beyond the Standard Model, irrespective of a resonant or non-resonant character of a particular BSM scenario. Secondly, under specific assumptions a class of models exists for which the off-shell coupling measurement together with a measurement of the on-shell signal strength can be re-interpreted in terms of a bound on…
We compute the hadronic production of top-antitop pairs in association with a Higgs boson at next-to-leading-order QCD, including the decay of the top and antitop quark into bottom quarks and leptons. Our computation is based on full leading and next-to-leading-order matrix elements for $e^+ ν_e μ^-\barν_μb \bar{b} H(j)$ and includes all non-resonant contributions, off-shell effects and interferences. Numerical results for the integrated cross section and several differential distributions are given for the LHC operating at 13 TeV using a fixed and a dynamical factorization and renormalization…
We derive the width of the Higgs boson into vector bosons. General formulas are derived both for the on-shell decay H -> VV as well for the off-shell decays, H -> V^* V and H -> V^* V^*, where V=γ,W,Z. For the off-shell decays the width of the decaying vector boson is properly included. The formulas are valid both for the Standard Model as well as for arbitrary extensions. As an example we study in detail the gauge-invariant effective Lagrangian models where we can have sizable enhancements over the Standard Model that could be observed at LEP.
A detailed study of Higgs interference effects at the one-loop level in the 1-Higgs-Singlet extension of the Standard Model (1HSM) is presented for the WW and tt decay modes with fully leptonic WW decay. We explore interference effects for benchmark points with a heavy Higgs mass that significantly exceeds 2*m_t. In the WW channel, the Higgs signal and the interfering continuum background are loop induced. In the tt channel, which features a tree-level background, we also calculate the interference with the one-loop background, which, due to the appearance of the absorptive part, is found to d…
