Naturalness and Theoretical Constraints on the Higgs Boson Mass

Arbitrary regularization dependent parameters in Quantum Field Theory are usually fixed on symmetry or phenomenology grounds. We verify that the quadratically divergent behavior responsible for the lack of naturalness in the Standard Model (SM) is intrinsically arbitrary and regularization dependent. While quadratic divergences are welcome for instance in effective models of low energy QCD, they pose a problem in the SM treated as an effective theory in the Higgs sector. Being the very existence of quadratic divergences a matter of debate, a plausible scenario is to search for a symmetry requirement that could fix the arbitrary coefficient of the leading quadratic behavior to the Higgs boson mass to zero. We show that this is possible employing consistency of scale symmetry breaking by quantum corrections. Besides eliminating a fine-tuning problem and restoring validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of $\delta m^{2}/m^{2}_{H}$ (where m _H is the renormalized Higgs mass and δm ² is the 1-loop Higgs mass correction). Whereas $\delta m^{2}/m^{2}_{H}<1$ (perturbative regime) in this scenario allows the Higgs boson mass around the current accepted value, the inclusion of the quadratic divergence demands $\delta m^{2}/m^{2}_{H}$ arbitrarily large to reach that experimental value.     

The apparent excess in the Higgs to di-photon rate at the LHC: New Physics or QCD uncertainties?

The Higgs boson with a mass _MH≈126 GeV$M_H\approx 126\text{GeV}$ has been observed by the ATLAS and CMS experiments at the LHC and a total significance of about five standard deviations has been reported by both collaborations when the channels H→γγ$H\to \gamma \gamma$ and H→ZZ→4?$H\to ZZ\to 4?$ are combined. Nevertheless, while the rates in the later search channel appear to be in accord with those predicted in the Standard Model, there seems to be an excess of data in the case of the H→γγ$H\to \gamma \gamma$ discovery channel. Before invoking new physics contributions to explain this excess in the di-photon Higgs rate, one should verify that standard QCD effects cannot account for it. We describe how the theoretical uncertainties in the Higgs boson cross section for the main production process at the LHC, gg→H$gg\to H$, which are known to be large, should be incorporated in practice. We further show that the discrepancy between the theoretical prediction and the measured value of the gg→H→γγ$gg\to H\to \gamma \gamma$ rate, reduces to about one standard deviation when the QCD uncertainties are taken into account.     

Higgs production in gluon fusion beyond NNLO

We construct an approximate expression for the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order (N³LO) in _αs${\alpha }_s$ with finite top mass. We argue that an accurate approximation can be constructed by exploiting the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummation. We support our argument with an explicit comparison of the approximate and the exact expressions up to the highest (NNLO) order at which the latter are available. We find that the approximate N³LO result amounts to a correction of 17%$17\text{\%}$ to the NNLO QCD cross section for production of a 125 GeV Higgs at the LHC (8 TeV), larger than previously estimated, and it significantly reduces the scale dependence of the NNLO result.     

Can supersymmetry breaking lead to electroweak symmetry breaking via formation of scalar bound states?

The recent discovery of the putative 125 GeV Higgs boson has motivated a number of attempts to reconcile its relatively large mass with the predictions of the minimal supersymmetric standard model (MSSM). Some approaches invoked large trilinear supersymmetry breaking terms _At$A_t$ between stops and one of the elementary Higgs fields. We consider the possibility that electroweak symmetry breaking may be triggered by supersymmetry breaking with a large _At$A_t$, large enough to generate a composite field with the same quantum numbers as the Higgs boson and with a non-vanishing vacuum expectation value. In the resulting vacuum, the usual relation between the gauge couplings and the Higgs self-coupling does not apply, and there is no reason to expect the same upper bound on the mass of the lightest Higgs boson. In a simple model where the bound state is assumed to have no mixing with the other fields, we calculate the critical coupling _At$A_t$ necessary for symmetry breaking using the lowest-order Bethe–Salpeter (BS) equation. Study of the BS equation is complicated by the structure of its lowest-order kernel, which is a crossed box graph, but we find an accurate approximation to its solution. In a realistic model, the mixing of the bound state with the fundamental Higgs boson creates a symmetry-breaking seesaw. We outline the steps toward a realistic model.     

Higgs boson search significance deformations due to mixed-in scalars

The existence of exotic scalars that mix with the Standard Model (SM) Higgs boson can affect Higgs boson phenomenology in a multitude of ways. We consider two light Higgs bosons with shared couplings to SM fields and with masses close to each other, in the range where the h→WW→lνlν$h\to WW\to l\nu l\nu$ is an important search channel. In this channel, we do not find the dilution of significance of the ‘SM-like’ Higgs boson that is naively expected because of the mixing. This is because of leakage of events from the other scalar into its signal region. Nevertheless, we show that the broadening of the h→WW→lνlν$h\to WW\to l\nu l\nu$ significance plots of Standard Model Higgs boson searches could indicate the first evidence of the extra scalar state.     

Has a fermiophobic Higgs boson been detected at the LHC?

We show that, in the present inclusive searches for the Higgs boson at the LHC, a fermiophobic Higgs mimics the standard-model-like Higgs if its mass is around 125 GeV. For that mass the order-of-magnitude reduction of fermiophobic Higgs production cross sections is compensated by a corresponding increase in the Higgs branching fraction into γγ  , while the WW^?$W{W}^{?}$, ZZ^?$Z{Z}^{?}$, Zγ signal yields are predicted to be somewhat smaller. The excess seen in the ATLAS and CMS fermiophobic Higgs boson searches in the γγ channel, including the exclusive vector-boson-fusion analysis, could point to a fermiophobic rather than a standard-model Higgs boson. If the Higgs boson will turn out to be fermiophobic, many of our present ideas of new physics should be revised.     

Higgs boson searches via dileptonic bottomonium decays

We explore the pseudoscalar ηb${\eta }_b$ and the scalar χ_b0${\chi }_{b0}$ decays into ?⁺?⁻${?}^{+}{?}^{-}$ to probe whether it is possible to probe the Higgs sectors beyond that of the Standard Model. We, in particular, focus on the Minimal Supersymmetric Standard Model, and determine the effects of its Higgs bosons on the aforementioned bottomonium decays into lepton pairs. We find that the dileptonic branchings of the bottomonia can be sizeable for a relatively light Higgs sector.     

QCD as a topologically ordered system

We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ$\theta$ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1)_A$U{\left(1\right)}_A$ problem where the would be η^′${\eta }^{\prime }$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1)_A$U{\left(1\right)}_A$ problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations.     

A new extensions of MSSM: FMSSM

We propose an extension of the MSSM by adding vector like ‘matter’ fields with masses near the TeV scale. This extension allows us to generate the masses of the bottom quark and tau lepton via radiative corrections such that only up type Higgs doublet couples with quarks and leptons. In addition to providing a natural explanation of the hierarchies between m_b,τ$m_{b,\tau }$ and mt$m_t$, this new extension, which we call FMSSM, allows the heavy sector of the MSSM Higgs bosons to be essentially fermiophobic as well as gaugephobic. Moreover, in this scenario there is no upper bound for the parameter tanβ$\tan \beta$. FMSSM can be distinguished from the MSSM, and has peculiar and unorthodox signals at the LHC, especially for the Higgs sector.     

Another step towards a no-lose theorem for NMSSM Higgs discovery at the LHC

We show how the LHC potential to detect a rather light CP-even Higgs boson of the NMSSM, H₁$H_1$ or H₂$H_2$, decaying into CP-odd Higgs states, A₁A₁$A_1{A}_1$, can be improved if Higgs-strahlung off W bosons and (more marginally) off top–antitop pairs are employed alongside vector boson fusion as production modes. Our results should help extracting at least one Higgs boson signal over the NMSSM parameter space.     

Combining direct & indirect kaon CP violation to constrain the warped KK scale

The Randall–Sundrum (RS) framework has a built in protection against flavour violation, but still generically suffers from little CP problems. The most stringent bound on flavour violation is due to ?K${\mathrm{?}}_K$, which is inversely proportional to the fundamental Yukawa scale. Hence the RS ?K${\mathrm{?}}_K$ problem can be ameliorated by effectively increasing the Yukawa scale with a bulk Higgs, as was recently observed in arXiv:0810.1016. We point out that incorporating the constraint from ?^′/?K${\mathrm{?}}^{\prime }/{\mathrm{?}}_K$, which is proportional to the Yukawa scale, raises the lower bound on the KK scale compared to previous analyses. The bound is conservatively estimated to be 5.5 TeV, choosing the most favorable Higgs profile, and 7.5 TeV for the profile which roughly reproduces the two site case. Relaxing this bound might require some form of RS flavour alignment. As a by-product of our analysis, we also provide the leading order flavour structure of the theory with a bulk Higgs.     

Renormalization group fixed point with a fourth generation: Higgs-induced bound states and condensates

In the Standard Model with four generations, the two-loop renormalization group equations for the Higgs quartic and Yukawa couplings show a quasi fixed point structure which does not appear at the one-loop level. This quasi fixed point behavior indicates a possible restoration of scale symmetry above some physical cut-off scale ΛFP${\Lambda }_{\mathrm{FP}}$. We conjecture that there exists a true fixed point which is reached at a similar energy scale. If the masses of the fourth family are sufficiently large, this cut-off scale, ΛFP${\Lambda }_{\mathrm{FP}}$, is situated in the range of a few TeV to the order of ¹⁰² TeV${10}^2\text{TeV}$, above which the Higgs quartic and Yukawa couplings become practically constant. We found that around ΛFP${\Lambda }_{\mathrm{FP}}$ the strong Yukawa couplings make it possible for the fourth generation to form bound states, including composite extra Higgs doublets. In this scenario the fourth generation condensates are obtained without introducing Technicolor or other unknown interactions.     

Implications of neutrino mass generation from QCD confinement

We consider the possibility that the quark condensate formed by QCD confinement generates Majorana neutrino masses mν$m_{\nu }$ via dimension seven operators. No degrees of freedom beyond the Standard Model are necessary, below the electroweak scale. Obtaining experimentally acceptable neutrino masses requires the new physics scale Λ∼TeV$\Lambda \sim \text{TeV}$, providing a new motivation for weak-scale discoveries at the LHC. We implement this mechanism using a Z₃$Z_3$ symmetry which leads to a massless up quark above the QCD chiral condensate scale. We use non-helicity-suppressed light meson rare decay data to constrain Λ. Experimental constraints place a mild hierarchy on the flavor structure of dimension seven operators and the resulting neutrino mass matrix.     

The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory

Recently we have reported on the existence of finite energy SU(2) Yang–Mills–Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft–Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft–Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z$z$-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z$z$-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ$\lambda$. However the dipole separation and the magnetic dipole moment decrease with λ$\lambda$. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.