In the QCD context, the non-singlet structure functions of u and d -quarks are identical, save the initial quark densities. Electroweak radiative corrections, being flavor-dependent, bring further difference between the non-singlets. This difference is calculated in the double-logarithmic approximation and the impact of the electroweak corrections on the non-singlet intercepts is estimated numerically.
We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be heavy, we integrate it out and perform a matching to the well-established electroweak chiral Lagrangian with one light Higgs.
The successful description of current data provided by the Standard Model includes fundamental fermions that are color-singlets and electroweak-nonsinglets, but no fermions that are electroweak-singlets and color-nonsinglets. In an effort to understand the absence of such fermions, we construct and study {\it gedanken} models that do contain electroweak-singlet chiral quark fields. These models exhibit several distinctive properties, including the absence of any neutral lepton and the fact that both the $(uud)$ and $(ddu)$ nucleons are electrically charged. We also explore how such models coul…
Singlet extensions of the Standard Model (SM) allow for a strongly first order electroweak phase transition, because of trilinear terms in the tree-level potential. We present a systematic procedure to study the parameter space of the Next-to-Minimal Supersymmetric SM (NMSSM). We find that this model is consistent with electroweak baryogenesis for a wide range of parameters, allowing Higgs masses up to at least 115 GeV.
The model of radiative neutrino mass with dark matter proposed by one of us is extended to include a real singlet scalar field. There are then two important new consequences. One is the realistic possibility of having the lightest neutral singlet fermion (instead of the lightest neutral component of the dark scalar doublet) as the dark matter of the Universe. The other is a modification of the effective Higgs potential of the Standard Model, consistent with electroweak baryogenesis.
We extend the so-called singlet doublet dark matter model, where the dark matter is an admixture of a Standard Model singlet and a pair of electroweak doublet fermions, by a singlet scalar field. The new portal coupling of it with the dark sector not only contributes to the dark matter phenomenology (involving relic density and direct detection limits), but also becomes important for generation of dark matter mass through its vacuum expectation value. While the presence of dark sector fermions affects the stability of the electroweak vacuum adversely, we find this additional singlet is capable…
We consider singlet extensions of the standard model, both in the fermion and the scalar sector, to account for the generation of neutrino mass at the TeV scale and the existence of dark matter respectively. For the neutrino sector we consider models with extra singlet fermions which can generate neutrino mass via the so called inverse or linear seesaw mechanism whereas a singlet scalar is introduced as the candidate for dark matter. We show that although these two sectors are disconnected at low energy, the coupling constants of both the sectors get correlated at high energy scale by the cons…
SUSY models with a gauge singlet easily allow for a strongly first order electroweak phase transition (EWPT). We discuss the wall profile, in particular transitional CP violation during the EWPT. We calculate CP violating source terms for the charginos in the WKB approximation and solve the relevant transport equations to obtain the generated baryon asymmetry.
We reconsider the strength of the electroweak phase transition in the singlet Majoron extension of the Standard Model, with a low (~TeV) scale of the singlet VEV. A strongly first order phase transition, of interest for electroweak baryogenesis, is found in sizeable regions of the parameter space, especially when the cross-coupling lambda_{hs}|S|^2|H|^2 between the singlet and the doublet Higgs is significant. Large Majorana Yukawa couplings of the singlet neutrinos, y_i S nu_i^c nu_i, are also important for strengthening the transition. We incorporate the LEP and Tevatron constraints on the H…
We investigate the viability of electroweak baryogenesis in a model with a first order electroweak phase transition induced by the addition of two gauge singlet scalars. A vector-like lepton doublet is introduced in order to provide CP violating interactions with the singlets and Standard Model leptons, and the asymmetry generation dynamics are examined using the vacuum expectation value insertion approximation. We find that such a model is readily capable of generating sufficient baryon asymmetry while satisfying electron electric dipole moment and collider phenomenology constraints.
The neutral component of a real pseudoscalar electroweak (EW) triplet can produce a diphoton excess at 750 GeV, if it is somewhat mixed with an EW singlet pseudoscalar. This triplet-singlet mixing allows for greater freedom in the diboson branching ratios than the singlet-only case, but it is still possible to probe the parameter space extensively with 300 fb$^{-1}$. The charged component of the triplet is pair-produced at the LHC, which results in a striking signal in the form of a pair of $Wγ$ resonances with an irreducible rate of 0.27 fb. Other signatures include multiboson final states fr…
Among various scenarios of baryon asymmetry of the Universe, electroweak baryogenesis is directly connected with physics of the Higgs sector. We discuss spectra of gravitational waves which are originated by the strongly first order phase transition at the electroweak symmetry breaking, which is required for a successful scenario of electroweak baryogenesis. In the $Z_3$ symmetric singlet scalar model, the significant gravitational waves are caused by the multi-step phase transition. We show that the model can be tested by measuring the characteristic spectra of the gravitational waves at futu…
We consider a model with a gauge singlet Dirac fermion as a cold dark matter candidate. The dark matter particle communicates with the Standard Model via a gauge singlet scalar mediator that couples to the Higgs. The scalar mediator also serves to create a tree-level barrier in the scalar potential which leads to a strongly first order electroweak phase transition as required for Electroweak Baryogenesis. We find a large number of models that can account for all the dark matter and provide a strong phase transition while avoiding constraints from dark matter direct detection, electroweak preci…
The framework of the electroweak chiral Lagrangian with a light Higgs is extended by an additional scalar and then generalized to N scalars in the Higgs sector. Divergences from scalar fluctuations are renormalized up to one loop using the background field method. The results are crosschecked against the case of one scalar. A subset of the divergences is demonstrated and crosschecked diagrammatically. Together with the complete one-loop renormalization of the electroweak chiral theory with one light Higgs conducted previously, this constitutes a renormalization framework of any pure scalar ext…
We study a scalar singlet dark matter (DM) having mass in sub-TeV regime by extending the minimal scalar singlet DM setup by additional vector like fermions. While the minimal scalar singlet DM satisfies the relic and direct detection constraints for mass beyond TeV only, presence of its portal coupling with vector like fermions opens up additional co-annihilation channels. These vector like fermions also help in achieving electroweak vacuum stability all the way up to Planck scale. We find that for one generation of vector like quarks consisting of a $SU(2)_L$ doublet and a singlet, scalar si…
We explore the use of the Inverse Amplitude Method for unitarization of scattering amplitudes to derive the existence and properties of possible new heavy states associated with perturbative extensions of the electroweak breaking sector of the Standard Model starting from the low energy effective theory. We use a toy effective theory generated by integrating out a heavy singlet scalar and compare the pole mass and width of the unitarized amplitudes with those of the original model. Our results show that the Inverse Amplitude Method reproduces correctly the singlet mass up to factors of O(1-3),…
We study resonant leptogenesis at the electroweak phase transition in the singlet Majoron model with right-handed neutrinos. We consider a scenario, where the SM gauge group and the lepton number break down spontaneously during a second-order electroweak phase transition. We calculate the flavour- and temperature-dependent leptonic asymmetries, by including the novel contributions from the transverse polarisations of the W+/- and Z bosons. The required resummation of the gauge-dependent off-shell heavy-neutrino self-energies is consistently treated within the gauge-invariant framework of the P…
Electroweak baryogenesis is a simple and attractive candidate mechanism for generating the observed baryon asymmetry in the Universe. Its viability is sometimes investigated in terms of an effective field theory of the Standard Model involving higher dimension operators. We investigate the validity of such an effective field theory approach to the problem of identifying electroweak phase transitions strong enough for electroweak baryogenesis to be successful. We identify and discuss some pitfalls of this approach due to the modest hierarchy between mass scales of heavy degrees or freedom and t…
There has been much recent interest in long-lived massive particles at the LHC, understood as those with lifetimes between tens of micrometers and several meters. In this context we consider the possibility of long-lived electroweak singlet scalars charged under colour $\mathrm{SU}(3)$ with masses near a TeV. The shortest lifetime of interest is already longer than typical hadronisation scales. These exotic new particles would therefore appear as colour singlet bound states of the new scalars with quarks and gluons and it is their colour charge that prevents them from decaying. In particular w…
We study the electroweak phase transition in the minimal extension of the Standard Model: an extra complex singlet with zero vacuum expectation value. The first-order phase transition is strengthened by the cubic term triggered in the one-loop effective potential by the extra boson. Plasma effects are considered to leading order: they shield the cubic terms and weaken the first-order phase transition. We find a region in the parameter space where baryon asymmetry washout is avoided for Higgs masses consistent with present experimental bounds. However in that region the theory becomes non-pertu…
SUSY models with a gauge singlet easily allow for a strong first order electroweak phase transition (EWPT) if the vevs of the singlet and Higgs fields are of comparable size. We discuss the profile of the stationary expanding bubble wall and CP-violation in the effective potential, in particular transitional CP-violation inside the bubble wall during the EWPT. The dispersion relations for charginos contain CP-violating terms in the WKB approximation. These enter as source terms in the Boltzmann equations for the (particle--antiparticle) chemical potentials and fuel the creation of a baryon asy…
The Higgs potential of the standard model with an additional real Higgs singlet is studied in order to examine if it may allow the strongly first order electroweak phase transition. It is found that there are parameter values for which this model at the one-loop level with finite temperature effect may allow the desired phase transition. Those parameter values also predict that the masses of the neutral scalar Higgs bosons of the model are consistent with the present experimental bound, and that their productions in $e^+e^-$ collisions may be searched at the proposed ILC with $\sqrt s$ = 500 G…
We study the phenomenology of gauge singlet extensions of the Standard Model scalar sector and their implications for the electroweak phase transition. We determine the conditions on the scalar potential parameters that lead to a strong first order phase transition as needed to produce the observed baryon asymmetry of the universe. We analyze the constraints on the potential parameters derived from Higgs boson searches at LEP and electroweak precision observables. For models that satisfy these constraints and that produce a strong first order phase transition, we discuss the prospective signat…
We study the prospects for probing a gauge singlet scalar-driven strong first order electroweak phase transition with a future proton-proton collider in the 100 TeV range. Singlet-Higgs mixing enables resonantly-enhanced di-Higgs production, potentially aiding discovery prospects. We perform Monte Carlo scans of the parameter space to identify regions associated with a strong first-order electroweak phase transition, analyze the corresponding di-Higgs signal, and select a set of benchmark points that span the range of di-Higgs signal strengths. For the $b\bar{b}γγ$ and $4τ$ final states, we in…
We study the electroweak phase transition in the framework of scalar singlet-doublet mixed dark matter model, where the particle dark matter candidate is the lightest neutral Higgs that comprised of the CP-even component of inert doublet and a singlet scalar. The dark matter can be dominated by the inert doublet or singlet scalar depending on the mixing. We present several benchmark models to investigate the two situations after imposing several theoretical and experimental constraints. An additional singlet scalar and the inert doublet drive the electroweak phase transition to be strongly fir…
The effective potential at finite temperature is constructed within the minimal standard model when a real Higgs singlet is added on. We find that a region of parameter space exists for which one can find a first order transition strong enough to prevent the erasure due to sphalerons of baryon asymmetry, while keeping the mass of the smallest Higgs boson above the experimental lower bound of about 60 GeV.
We introduce in an arbitrary supersymmetric version of the standard model without elementary scalars a logarithmic operator which is irrelevant in the limit in which all symmetries are respected. However through a dynamical mechanism of the Nambu Jona Lasinio type this operator may produce two fermion vacuum condensates that may account for electroweak and contribute to supersymmetry breaking. Some of the phenomenological consequences of this set-up are discussed.
A simple analytic expression for the non-singlet structure function $f_{NS}$ is given. The expression is derived from the result of Ref. [1] obtained by low $x$ resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD.
We update the phenomenology of gauge singlet extensions of the Standard Model scalar sector and their implications for the electroweak phase transition. Considering the introduction of one real scalar singlet to the scalar potential, we analyze present constraints on the potential parameters from Higgs coupling measurements at the Large Hadron Collider (LHC) and electroweak precision observables for the kinematic regime in which no new scalar decay modes arise. We then show how future precision measurements of Higgs boson signal strengths and Higgs self-coupling could probe the scalar potentia…
We consider virtual electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)xU(1) singlet gauge boson in the asymptotic region $s\gg M_W^2$, where the invariant mass $s$ of the external gauge boson is much higher than the weak-boson mass scale. Using the sector-decomposition method we compute mass singularities, which arise as logarithms of $s/M_W^2$ and $1/ε$ poles in $D=4-2ε$ dimensions, to one- and two-loop next-to-leading logarithmic accuracy. In this approximation we include all contributions of order $α^l ε^{k} log^{j+k}(s/M_W^2)$, with $l=1,2$ and $j…
Direct detection experiments are the only way to obtain indisputable evidence of the existence of dark matter (DM) in the form of a particle. These experiments have been used to probe many extensions of the Standard Model (SM) that provide DM candidates. Experimental results like the latest ones from XENON1T lead to severe constraints in the parameter space of many of the proposed models. In a simple extension of the SM, the addition of a complex singlet to the SM content, one-loop corrections need to be taken into account because the tree-level cross section is proportional to the DM velocity…
Revisiting Singlet Fermion Dark Matter with a Scalar Portal: Connecting Higgs Phenomenology and Strong Electroweak Phase Transition
Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）；Gokhale Memorial Girls’ College（戈卡尔纪念女子学院）；University of Delhi（德里大学）；Central China Normal University（华中师范大学）
We present the next-to-leading-order calculation of the partial decay widths of light CP-even Higgs bosons decaying into four fermions in the Two-Higgs-Doublet Model and a Singlet Extension of the Standard Model. Different renormalization schemes are applied in the calculation, which is implemented into the analysis tool PROPHECY4F. Some sample results on the Higgs->4fermions decay widths illustrate how the corrections reduce the dependence on the renormalization scale and the choice of the scheme.
Taking into account the negative results of direct searches for beyond the Standard Model fields and the consequent mass gap between Standard Model and possible unknown states, the use of electroweak effective theories is justified. Whereas at low energies we consider a non-linear realization of the electroweak symmetry breaking with a singlet Higgs and a strongly-coupled ultraviolet completion, at higher energies the known particles are assumed to be coupled to heavy states: bosonic fields with $J^P=0^\pm$ and $J^P=1^\pm$ (in electroweak triplets or singlets and in QCD octets or singlets) and…
We have studied the effects of the complete logarithmic electroweak O(alpha) corrections on the production of vector-boson pairs WZ, ZZ, and WW at the LHC. These corrections are implemented into a Monte Carlo program for pp -> 4f (+γ) with final states involving four or two leptons using the double-pole approximation. We numerically investigate purely leptonic final states and find that electroweak corrections lower the predictions by 5-30% in the physically interesting region of large di-boson invariant mass and large angle of the produced vector bosons.
We consider two-loop leading and next-to-leading logarithmic virtual corrections to arbitrary processes with external massless fermions in the electroweak Standard Model at energies well above the electroweak scale. Using the sector-decomposition method and alternatively the strategy of regions we calculate the mass singularities that arise as logarithms of Q^2/MW^2, where Q is the energy scale of the considered process, and 1/εpoles in D=4-2εdimensions, to one- and two-loop next-to-leading logarithmic accuracy. The derivations are performed within the complete electroweak theory with spontane…
We revisit the electroweak phase transition in the standard model with a real scalar, utilizing several calculation methods to investigate scheme dependences. We quantify the numerical impacts of Nambu-Goldstone resummation, required in one of the schemes, on the strength of the first-order electroweak phase transition. We also employ a gauge-independent scheme to make a comparison with the standard gauge-dependent results. It is found that the effect of the Nambu-Goldstone resummation is typically $\sim1\%$. Our analysis shows that both gauge-dependent and -independent methods give qualitativ…
In the framework of type-II two-Higgs-doublet model with a singlet scalar dark matter $S$, we study the dark matter observables, the electroweak phase transition, and the gravitational wave signals by such strongly first order phase transition after imposing the constraints of the LHC Higgs data. We take the heavy CP-even Higgs $H$ as the only portal between the dark matter and SM sectors, and find the LHC Higgs data and dark matter observables require $m_S$ and $m_H$ to be larger than 130 GeV and 360 GeV for $m_A=600$ GeV in the case of the 125 GeV Higgs with the SM-like coupling. Next, we ca…
We propose a two component dark matter set-up by extending the Standard Model with a singlet and a hypercharge-less triplet scalars, each of them being odd under different $Z_2$ symmetries. We observe that the inter-conversion between the two dark matter components allow a viable parameter space where masses of both the dark matter candidates can be below TeV, even though their individual contribution to single component dark matter rules out any such sub-TeV dark matter. We find that a lighter mass of the neutral component of the scalar triplet, playing the role of one dark matter component, …
The naturalness of electroweak scale in the models of type-I seesaw mechanism with ${\cal O}(1)$ Yukawa couplings requires TeV scale masses for the fermion singlets. In this case, the tiny neutrino masses have to arise from the cancellations within the seesaw formula which are arranged by fine-tuned correlations between the Yukawa couplings and the masses of fermion singlets. We motivate such correlations through the framework of discrete symmetries. In the case of three Majorana fermion singlets, it is shown that the exact cancellation arranged by the discrete symmetries in seesaw formula nec…
An addition to the Standard Model of a real, gauge-singlet scalar field, coupled via a Higgs portal interaction, can reopen the possibility of a strongly first-order electroweak phase transition (EWPT) and successful electroweak baryogenesis (EWBG). If a discrete symmetry that forbids doublet-singlet mixing is present, this model is notoriously difficult to test at the Large Hadron Collider. As a result, it emerged as a useful benchmark for evaluating the capabilities of proposed future colliders to conclusively test EWPT and EWBG. In this paper, we evaluate the bubble nucleation temperature t…
We calculate the baryon asymmetry of the Universe in the Z3-invariant Next-to-Minimal Supersymmetric Standard Model where the interactions of the singlino provide the necessary source of charge and parity violation. Using the closed time path formalism, we derive and solve transport equations for the cases where the singlet acquires a vacuum expectation value (VEV) before and during the electroweak phase transition. We perform a detailed scan to show how the baryon asymmetry varies throughout the relevant parameter space. Our results show that the case where the singlet acquires a VEV during t…
We consider W-boson scattering at high-energy e+ e- colliders and study one-loop logarithmic electroweak corrections within the Standard Model assuming a light Higgs boson. We present explicit analytical results for W+ W- -> W+ W-. Using the equivalent vector-boson approximation, we have implemented these corrections into a Monte Carlo program for the process e+ e- -> nue anti-nue W+ W-. The quality of the equivalent vector-boson approximation and of the logarithmic high-energy approximation for the electroweak corrections is discussed in detail. The impact of the radiative effects is quantita…
We study the feasibility of strong first-order electroweak phase transition (EWPT) in a degenerate-scalar scenario of a complex singlet extension of the Standard Model, in which a mass of an additional scalar is nearly degenerate with that of the Higgs boson, 125 GeV. This scenario is known to provide an exquisite solution for circumventing constraints from dark matter direct detection experiments due to cancellations between two scattering amplitudes mediated by two scalars. In the analysis of EWPT, we employ two gauge-invariant calculation schemes on the scalar potential and two familiar res…
The small-x behavior of the singlet contributions to the polarized structure function g_2(x,Q^2) is calculated in the double-logarithmic approximation of perturbative QCD. The dominant contribution is due to the gluons which, in contrast to the unpolarized case, mix with the fermions also in the small-x domain. We find a power-like growth in 1/x in the odd-signature parts of the amplitude with the same power as in the singlet function g_1(x,Q^2) at x<< 1.
We consider hadronic production of a Z boson in association with a jet and study one- and two-loop electroweak logarithmic corrections in the region of high Z-boson transverse momentum, p_T >> M_Z, including leading and next-to-leading logarithms. Numerical results for the LHC and Tevatron colliders are presented. At the LHC these corrections amount to tens of per cent and will be important for interpretation of the measurements.
In Next Linear Colliders at TeV scale, electroweak double logarithmic corrections, which come from the infrared behaviors of theory can not be neglected. It is well known that in QED and QCD, double logarithmic corrections are resummed to all orders, and these corrections can be exponentiated, resulting in the Sudakov form factor. However it is never trivial that double logarithmic corrections in electroweak theory can be exponentiated, because of the spontaneous breaking of symmetry and the pattern of that. We discuss the electroweak double logarithmic corrections at two loop level and explai…
It is widely believed that the existence of singlet scalars in some Standard Model extensions can easily make the electroweak phase transition strongly first order, which is needed for the electroweak baryogenesis scenario. In this paper, we will examine the strength of the electroweak phase transition in the simplest extension of the Standard Model with a real singlet using the sphaleron energy at the critical temperature. We find that the phase transition is stronger by adding a singlet; and also that the criterion for a strong phase transition Omega (Tc)/Tc>1, where Omega =(v^2+(x-x0)^2)^(1…
We compute the MSSM one-loop contributions to the asymptotic energy behaviour of fermion-antifermion pair production at future lepton-antilepton colliders. Besides the conventional logarithms of Renormalization Group origin, extra SUSY linear logarithmic terms appear of "Sudakov-type". In the TeV range their overall effect on a variety of observables can be quite relevant and drastically different from that obtained in the SM case.
The scalar singlet model extends the Standard Model with the addition of a new gauge singlet scalar. We re-examine the limits on the new scalar from oblique parameter fits and from a global fit to precision electroweak observables and present analytic expressions for our results. For the case when the new scalar is much heavier than the weak scale, we map the model onto the dimension-six Standard Model effective field theory (SMEFT) and review the allowed parameter space from unitarity considerations and from the requirement that the electroweak minimum be stable. A global fit to precision ele…
We propose a new dynamical relaxation mechanism of the little hierarchy problem, based on a singlet extension of the minimal supersymmetric standard model (MSSM). In this scenario, the small soft mass parameter of an MSSM singlet is responsible for the electroweak symmetry breaking and the non-zero Higgs vacuum expectation value, whereas the effect of the large soft mass parameter of the Higgs boson, -m_{h_u}^2 is dynamically compensated by a flat direction of the MSSM singlets. The small singlet's soft mass and the Z boson mass can be protected, even if the stop mass is heavier than 10 or 20 …
We study several aspects of electroweak vacuum metastability when an extra gauge singlet scalar, a viable candidate for a dark matter particle, is added to the standard model of particle physics, which is assumed to be valid up to the Planck scale. Phase diagrams are drawn for different parameter spaces, and based on that, we graphically demonstrate how the confidence level, at which stability of electroweak vacuum is excluded, depends on such new physics parameters.
We present the minimal model of electroweak baryogenesis induced by fermions. The model consists of an extension of the Standard Model with one electroweak singlet fermion and one pair of vector like doublet fermions with renormalizable couplings to the Higgs. A strong first order phase transition is radiatively induced by the singlet-doublet fermions, while the origin of the baryon asymmetry is due to asymmetric reflection of the same set of fermions on the expanding electroweak bubble wall. The singlet-doublet fermions are stabilized at the electroweak scale by chiral symmetries and the Higg…
We investigate an electroweak interacting dark matter (DM) model in which the DM is the neutral component of the SU$(2)_L$ triplet fermion that couples to the standard model (SM) Higgs sector via an SM singlet Higgs boson. In this setup, the DM can have a CP-violating coupling to the singlet Higgs boson at the renormalizable level. As long as the nonzero Higgs portal coupling (singlet-doublet Higgs boson mixing) exists, we can probe CP violation of the DM via the electric dipole moment of the electron. Assuming the $\mathcal{O}(1)$ CP-violating phase in magnitude, we investigate the relationsh…
We analyse a simple extension of the SM with just an additional scalar singlet coupled to the Higgs boson. We discuss the possible probes for electroweak baryogenesis in this model including collider searches, gravitational wave and direct dark matter detection signals. We show that a large portion of the model parameter space exists where the observation of gravitational waves would allow detection while the indirect collider searches would not.
