Standard Model without elementary scalars and high energy Lorentz violation

If Lorentz symmetry is violated at high energies, interactions that are usually non-renormalizable can become renormalizable by weighted power counting. Recently, a CPT invariant, Lorentz violating extension of the Standard Model containing two scalar-two fermion interactions (which can explain neutrino masses) and four fermion interactions (which can explain proton decay) was proposed. In this paper we consider a variant of this model, obtained suppressing the elementary scalar fields, and argue that it can reproduce the known low-energy physics. In the Nambu–Jona-Lasinio spirit, we show, using a large N _c expansion, that a dynamical symmetry breaking takes place. The effective potential has a Lorentz invariant minimum and the Lorentz violation does not reverberate down to low energies. The mechanism generates fermion masses, gauge-boson masses and scalar bound states, to be identified with composite Higgs bosons. Our approach is not plagued by the ambiguities of approaches based on non-renormalizable vertices. The low-energy effective action is uniquely determined and predicts relations among parameters of the Standard Model.     

Review of searches for Higgs bosons and beyond the Standard Model Physics at the Tevatron

The energy frontier is currently at the Fermilab Tevatron accelerator, which collides protons and antiprotons at a center-of-mass energy of 1.96 TeV. The luminosity delivered to the CDF and DØ experiments has now surpassed the 4 fb^?1. This paper reviews the most recent direct searches for Higgs bosons and beyond-the-standard-model (BSM) physics at the Tevatron. The results reported correspond to an integrated luminosity of up to 2.5 fb^?1 of Run II data collected by the two Collaborations. Searches covered include the standard model (SM) Higgs boson (including sensitivity projections), the neutral Higgs bosons in the minimal supersymmetric extension of the standard model (MSSM), charged Higgs bosons and extended Higgs models, supersymmetric decays that conserve or violate R-parity, gauge-mediated supersymmetric breaking models, long-lived particles, leptoquarks, compositeness, extra gauge bosons, extra dimensions, and finally signature-based searches. Given the excellent performance of the collider and the continued productivity of the experiments, the Tevatron physics potential looks promising for discovery with the coming larger data sets. In particular, evidence for the SM Higgs boson could be obtained if its mass is light or near 160 GeV. The observed (expected) upper limits are currently a factor of 3.7 (3.3) higher than the expected SM Higgs boson cross section at m _H =115 GeV and 1.1 (1.6) at m _H =160 GeV at 95% C.L.     

Revisiting the global electroweak fit of the Standard Model and beyond with Gfitter

The global fit of the Standard Model to electroweak precision data, routinely performed by the LEP electroweak working group and others, demonstrated impressively the predictive power of electroweak unification and quantum loop corrections. We have revisited this fit in view of (i) the development of the new generic fitting package, Gfitter, allowing for flexible and efficient model testing in high-energy physics, (ii) the insertion of constraints from direct Higgs searches at LEP and the Tevatron, and (iii) a more thorough statistical interpretation of the results. Gfitter is a modular fitting toolkit, which features predictive theoretical models as independent plug-ins, and a statistical analysis of the fit results using toy Monte Carlo techniques. The state-of-the-art electroweak Standard Model is fully implemented, as well as generic extensions to it. Theoretical uncertainties are explicitly included in the fit through scale parameters varying within given error ranges. This paper introduces the Gfitter project, and presents state-of-the-art results for the global electroweak fit in the Standard Model (SM), and for a model with an extended Higgs sector (2HDM). Numerical and graphical results for fits with and without including the constraints from the direct Higgs searches at LEP and Tevatron are given. Perspectives for future colliders are analysed and discussed. In the SM fit including the direct Higgs searches, we find M _H =116.4_−1.3^+18.3 GeV, and the 2σ and 3σ allowed regions [114,145] GeV and [[113,168] and [180,225]] GeV, respectively. For the strong coupling strength at fourth perturbative order we obtain α _S (M _Z ²)=0.1193_−0.0027^+0.0028(exp )±0.0001 (theo). Finally, for the mass of the top quark, excluding the direct measurements, we find m _t =178.2_−4.2^+9.8 GeV. In the 2HDM we exclude a charged-Higgs mass below 240 GeV at 95% confidence level. This limit increases towards larger tan β, e.g., is excluded for tan β=70.     

Non-Differentiable Mechanical Model and Its Implications

Considering that the motions of the particles take place on fractals, a non-differentiable mechanical model is built. Only if the spatial coordinates are fractal functions, the Galilean version of our model is obtained: the geodesics satisfy a Navier-Stokes-type of equation with an imaginary viscosity coefficient for a complex speed field or respectively, a Schrödinger-type of equation or hydrodynamic equations, in the case of irrotational movements. Moreover, in this approach, the analysis of the fractal fluid dynamics generates conductive properties in the case of movements synchronization both on differentiable and fractal scales, and convective properties in the absence of synchronization (e.g. laser ablation plasma is analyzed). On the other hand, if both the spatial and temporal coordinates are fractal functions, it results that, the geodesics satisfy a Klein-Gordon-type of equation on a Minkowskian manifold.     

Standard candle central exclusive processes at the Tevatron and LHC

Central exclusive production (CEP) processes in high-energy proton—(anti)proton collisions offer a very promising framework within which to study both novel aspects of QCD and new physics signals. Among the many interesting processes that can be studied in this way, those involving the production of heavy (c,b) quarkonia and γ γ states have sufficiently well understood theoretical properties and sufficiently large cross sections that they can serve as ‘standard candle’ processes with which we can benchmark predictions for new physics CEP at the CERN Large Hadron Collider. Motivated by the broad agreement with theoretical predictions of recent CEP measurements at the Fermilab Tevatron, we perform a detailed quantitative study of heavy quarkonia (χ and η) and γ γ production at the Tevatron, RHIC and LHC, paying particular attention to the various uncertainties in the calculations. Our results confirm the rich phenomenology that these production processes offer at present and future high-energy colliders.     

■Study of the Standard Model and Majorana neutrino contributions to

Lepton number violation processes can be induced by the Majorana neutrino exchange, which provide evidence for the Majorana nature of neutrinos. In addition to the natural explanation of the small neutrino masses,Type-I seesaw mechanism predicts the existence of Majorana neutrinos. The aim of this work is to study the B meson rare decays B~+→K~((*))+μ~+μ~-in the Standard Model and its extensions, and then to investigate the same-sign decay process B~+→K~((*)-)μ~+μ~+. The corresponding dilepton invariant mass distributions are calculated. It is found that the dilepton angular distributions could shed light on the properties of new interactions induced by Majorana neutrinos.     

Electroweak symmetry breaking and beyond the Standard Model physics — A review

In this talk, I shall first discuss the Standard Model Higgs mechanism and then highlight some of its deficiencies making a case for the need to go beyond the Standard Model (BSM). The BSM tour will be guided by symmetry arguments. I shall pick up four specific BSM scenarios, namely, supersymmetry, little Higgs, gauge-Higgs unification, and the Higgsless approach. The discussion will be confined mainly on their electroweak symmetry breaking aspects.      

Towards a measurement of the two-photon decay width of the Standard Model Higgs boson at a Photon Collider

A study of the measurement of the two photon decay width times the branching ratio of the Standard Model Higgs boson with a mass of 120 GeV in photon–photon collisions is presented, assuming a γ γ integrated luminosity of 80 fb⁻¹ in the high energy part of the spectrum. The analysis is based on the reconstruction of the Higgs events produced in the γ γ→H process, followed by the decay of the Higgs into a pair. A statistical error of the measurement of the two-photon width, Γ(H→γ γ), times the branching ratio of the Higgs boson, BR is found to be 2.1% for one year of data taking.     

Dynamical Aspects of Mean Field Plane Rotators and the Kuramoto Model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N→∞ limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N→∞ limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K _c . We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K _c .     

Classical and Non-relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter.     

The equivalence theorem for the heavy-Higgs Standard Model and the gauged nonlinear σ-model

The equivalence theorem states that the leading part of the amplitude for a process with external longitudinally polarized vector bosons is given by the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons. The validity of this theorem within the standard model with a heavy Higgs boson and within the gauged nonlinear -model (in which the Higgs boson is absent) is shown. Furthermore it is examined to what extent also internal lines other than scalar lines can be neglected. A simple power-counting method is developed which determines the leading diagrams for a given process at an arbitrary loop order. This method is also applied to effective Lagrangians with additional nonstandard interaction terms of higher dimension (chiral Lagrangians).     

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.     

Generalized Eigenvalue-Counting Estimates for the Anderson Model

We generalize Minami’s estimate for the Anderson model and its extensions to n eigenvalues, allowing for n arbitrary intervals and arbitrary single-site probability measures with no atoms. As an application, we derive new results about the multiplicity of eigenvalues and Mott’s formula for the ac-conductivity when the single site probability distribution is Hölder continuous.     

Decoherence and CPT Violation in a Stringy Model of Space-Time Foam

I discuss a model inspired from the string/brane framework, in which our Universe is represented (after perhaps appropriate compactification) as a three brane, propagating in a bulk space time punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the bulk, the D-particles cross it, and from an effective observer on D3 the situation looks like a “space-time foam” with the defects “flashing” on and off (“D-particle foam”). The open strings, with their ends attached on the brane, which represent matter in this scenario, can interact with the D-particles on the D3-brane universe in a topologically non-trivial manner, involving splitting and capture of the strings by the D0-brane defects. Such processes are consistently described by logarithmic conformal field theories on the world-sheet of the strings. Physically, they result in effective decoherence of the string matter on the D3 brane, and as a result, of CPT Violation, but of a type that implies an ill-defined nature of the effective CPT operator. Due to electric charge conservation, only electrically neutral (string) matter can exhibit such interactions with the D-particle foam. This may have unique, experimentally detectable (in principle), consequences for electrically-neutral entangled quantum matter states on the brane world, in particular the modification of the pertinent Einstein-Podolsky-Rosen (EPR) Correlation in neutral mesons in an appropriate meson factory. For the simplest scenarios, the order of magnitude of such effects might lie within the sensitivity of upgraded φ-meson factories.     

Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0

This paper investigates infinite-time spreading and finite-time blow-up for the Keller-Segel system. For 0 < m ≤  2 ? 2 / d, the L ^p space for both dynamic and steady solutions are detected with ${p:=\frac{d(2-m)}{2} }$ p : = d ( 2 - m ) 2 . Firstly, the global existence of the weak solution is proved for small initial data in L ^p . Moreover, when m > 1 ? 2 / d, the weak solution preserves mass and satisfies the hyper-contractive estimates in L ^q for any p < q < ∞. Furthermore, for slow diffusion 1 < m ≤  2 ? 2/d, this weak solution is also a weak entropy solution which blows up at finite time provided by the initial negative free energy. For m > 2 ? 2/d, the hyper-contractive estimates are also obtained. Finally, we focus on the L ^p norm of the steady solutions, it is shown that the energy critical exponent m = 2d/(d + 2) is the critical exponent separating finite L ^p norm and infinite L ^p norm for the steady state solutions.     

What is the minimal supersymmetric Standard Model from F-theory?

We construct gauge theory of SU(3)×SU(2)×U(1)$\mathit{SU}(3)\times \mathit{SU}(2)\times U(1)$ by spectral cover from F-theory and ask how the Standard Model is extended under minimal assumptions on Higgs sector. For the requirement on different numbers between Higgs pairs and matter generations (respectively one and three) distinguished by R-parity, we choose a universal G  -flux obeying SO(10)$\mathit{SO}(10)$ but slightly breaking _E6$E_6$ unification relation. This condition forces distinction between up and down Higgs fields, suppression of proton decay operators up to dimension five, and existence and dynamics of a singlet related to μ-parameter.     

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the q-state Potts model on various families of graphs G in a generalized external magnetic field that favors or disfavors spin values in a subset I _s ={1,…,s} of the total set of possible spin values, Z(G,q,s,v,w), where v and w are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial Ph(G,q,s,w) that counts the number of colorings of the vertices of G subject to the condition that colors of adjacent vertices are different, with a weighting w that favors or disfavors colors in the interval I _s . We derive powerful new upper and lower bounds on Z(G,q,s,v,w) for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for Z(G,q,s,v,w) on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.     

A Stochastic Differential Equation Model with Jumps for Fractional Advection and Dispersion

The path of a tracer particle through a porous medium is typically modeled by a stochastic differential equation (SDE) driven by Brownian noise. This model may not be adequate for highly heterogeneous media. This paper extends the model to a general SDE driven by a Lévy noise. Particle paths follow a Markov process with long jumps. Their transition probability density solves a forward equation derived here via pseudo-differential operator theory and Fourier analysis. In particular, the SDE with stable driving noise has a space-fractional advection-dispersion equation (fADE) with variable coefficients as the forward equation. This result provides a stochastic solution to anomalous diffusion models, and a solid mathematical foundation for particle tracking codes already in use for fractional advection equations.     

Stationary Properties and Stochastic Resonance for a Saturation Laser Model with Cross-correlation Between Quantum Noise Terms

The stationary properties of a saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise are investigated theoretically. Using the Novikov theorem and the Sargent technique, we obtain the analytic expressions of the stationary probability density distribution, the mean, the variance and the skewness of the saturation laser model. The cross-correlation coefficient λ and other parameters can make the stationary probability density distribution P _st (I) generate interesting two-extrema structure, one-extremum structure, or no-extremum structure. It is clearly found that a first- order-like-transition is induced by the coupling strength |λ| of the complex quantum noise terms in the saturation laser model. When the laser system is operated above the threshold, the mean 〈I〉 becomes larger and the output of the laser intensity increases; however the coupling strength |λ| attenuates the output of the laser intensity. When the laser is operated near and below the threshold, the mean 〈I〉 becomes smaller, the output of the laser intensity decreases, and |λ| still attenuates the output of the laser intensity. When a periodic signal is added to a saturation laser model with cross-correlation between quantum noise terms, the interesting stochastic resonance phenomena occur at λ=0. The noise intensity Q decreases the values of the resonance peak, however, the amplitude of the periodic signal B enhances the values of the resonance peak.     

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension . This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to . NSF Grant DMS-0503712.