Constraining unparticle physics with cosmology and astrophysics

It has recently been suggested that a scale-invariant "unparticle" sector with a nontrivial infrared fixed point may couple to the standard model (SM) via higher-dimensional operators. The weakness of such interactions hides the unparticle phenomena at low energies. We demonstrate how cosmology and astrophysics can place significant bounds on the strength of unparticle-SM interactions. We also discuss the possibility of a having a non-negligible unparticle relic density today.     

Effects of unparticles on running of gauge couplings

Unparticles charged under a gauge group can contribute to the running of the gauge coupling. We show that a scalar unparticle of scaling dimension d contributes to the β function a term that is (2-d) times that from a scalar particle in the same representation. This result has important implications for asymptotic freedom. An unparticle with d>2, in contrast to its matter counterpart, can speed up the approach to asymptotic freedom for a non-Abelian gauge theory and has the tendency to make an Abelian theory also asymptotically free. For not spoiling the excellent agreement of the standard model (SM) with precision tests, the infrared cut-off, m, of such an unparticle would be high but might still be reachable at colliders such as LHC and ILC. Furthermore, if the unparticle scale Λ_U is high enough, unparticles could significantly modify the unification pattern of the SM gauge couplings. For instance, with three scalar unparticles of d∼2.5 in the adjoint representation of the strong gauge group but neutral under the electroweak one, the three gauge couplings would unify at a scale of ∼ 8×10¹² GeV, which is several orders of magnitude below the supersymmetric unification scale. PACS  12.90.+b; 14.80.-j; 11.10.Hi; 12.10.Dm     

Notes on dark energy interacting with dark matter and unparticle in loop quantum cosmology

We investigate the behavior of dark energy interacting with dark matter and unparticle in the framework of loop quantum cosmology. In four toy models, we study the interaction between the cosmic components by choosing different coupling functions representing the interaction. We found that there are only two attractor solutions namely dark energy dominated and dark matter dominated Universe. The other two models are unstable, as they predict either a dark energy filled Universe or one completely devoid of it.     

Finite nuclei in the reggeon “toy model”

Hadron–nucleus amplitudes at high energies are studied in the “toy” Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and loses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprising result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.     

Decay of Z boson into photon and unparticle

We study the decay of the standard model Z boson into unparticle plus a single photon through a one-loop process. As in the anomaly type decay, only the axial-vector part of the Z coupling matching with the vector unparticle and/or the vector part of the Z coupling matching with the axial-vector unparticle can give a nonzero contribution to the decay. We show that the photon spectrum terminates at the end point in accord with Yang's theorem. Existing data on single photon production at LEP I is used to constrain the unparticle sector.     

Towards an asymptotic-safety scenario for chiral Yukawa systems

We search for asymptotic safety in a Yukawa system with a chiral U(N _L)_L? ??U(1)_R symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Gaußian fixed points for 1≤N _L≤57 which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.     

Scalar modifications to gravity from unparticle effects may be testable

Interest has focused recently on low energy implications of a nontrivial scale invariant sector of an effective field theory with an IR fixed point, manifest in terms of "unparticles" with peculiar properties. If unparticle stuff exists it could couple to the stress tensor and mediate a new "fifth" force ("ungravity"). Under the assumption of strict conformal invariance in the hidden sector down to low energies, we compute the lowest order ungravity correction to the Newtonian gravitational potential and find scale invariant power law corrections of type (R_(G)/r)(2d)_(U)(-1), where d_(U) is an anomalous unparticle dimension and R_(G) is a characteristic length scale where the ungravity interactions become significant. It is shown that a discrimination between extra dimension models and ungravity is possible in future improved submillimeter tests of gravity.     

New Phase Transitions of the Ising Model on Cayley Trees

We show that the nearest neighbor Ising model on the Cayley tree exhibits new temperature–driven phase transitions. These transitions occur at various inverse temperatures different from the critical one. They are characterised by a change in the number of Gibbs states as well as by a drastic change of the behavior of free energies at these new transition points. We also consider the model in the presence of an external field and compute the free energies of translation invariant and some alternating boundary conditions.     

Unparticles in gauge theory

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by B _μ(x) ∼ ∂_μ S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the “ungluon” exchange pattern — the “ungluon” propagator.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

B→0+(1+)+ missing energy in unparticle physics

We examine the effects of an unparticle U as a possible source of missing energy in the p-wave decays of a B meson. The dependence of the differential branching ratio on the K0* (K1) - meson's energy is discussed in the presence of scalar and vector unparticle operators and significant deviation from the standard model value is found after addition of these operators. Finally, we have shown the dependence of the branching ratio for the above-mentioned decays on the parameters of unparticle stuff like effective couplings, cutoff scale Au and the scale dimensions du.     

以啄木鸟玩具为例的LCP问题求解

啄木鸟玩具的运动是一个典型的工程力学线性互补问题．本文基于线性互补模型,结合开源Siconos软件,从实验、理论和模拟仿真上详细分析了啄木鸟玩具的运动过程．模拟仿真与实验结果均表明,啄木鸟玩具运动周期可细分为多个过程,初始激振条件的变化不会改变啄木鸟玩具稳定后的运动行为,而套筒与杆摩擦系数的改变会极大地影响啄木鸟的运动．本研究工作对工程力学中的线性互补问题具有很好的借鉴作用．     

Low-energy supersymmetry

We discuss the problem of constructing a model in which supersymmetry is unbroken down to low energies. It is suggested that the scalar partners of quarks and leptons may get their masses through radiative corrections and that the breaking of the weak interactions also occurs through radiative corrections. A toy model is constructed which illustrates these ideas.     

Collider signals of unparticle physics

Phenomenology of the notion of an unparticle U, recently perceived by Georgi, to describe a scale invariant sector with a nontrivial infrared fixed point at a higher energy scale is explored in details. Behaving like a collection of d(U) (the scale dimension of the unparticle operator O(U)) invisible massless particles, this unparticle can be unveiled by measurements of various energy distributions for the processes Z-->f f U and e- e+-->gammaU at e- e+ colliders, as well as monojet production at hadron colliders. We also study the propagator effects of the unparticle through the Drell-Yan tree-level process and the one-loop muon anomaly.     

Global study of electron–quark unparticle interactions

We perform a global fit on parity-conserving electron–quark interactions via spin-1 unparticle exchange. Besides the peculiar features of unparticle exchange due to non-integral values for the scaling dimension \(d_{\mathcal {U}}\) and a non-trivial phase factor \(\exp (-id_{\mathcal {U}}\pi)\) associated with a time-like unparticle propagator, the energy dependence of the unparticle contributions in the scattering amplitudes are also taken into account. The high energy data sets taken into consideration in our analysis are from (1) deep inelastic scattering at high Q ² from ZEUS and H1, (2) Drell–Yan production at Run II of CDF and DØ, and (3) e ⁺ e ^?→ hadrons at LEPII. The hadronic data at LEPII by itself indicated a 3–4 sigma preference of new physics over the Standard Model. However, when all data sets are combined, no preference for unparticle effects can be given. We thus deduce an improved 95% confidence level limit on the unparticle energy scale \(\varLambda_{\mathcal {U}}\).     

Ground state and glass transition of the RNA secondary structure

RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix propagation. The free energy cost for separating a chain into two equal halves offers a quantitative measure of sequence specific pairing. In the low temperature glass phase, this quantity grows quadratically with the logarithm of the chain length, but it switches to a linear behavior of entropic origin in the high temperature molten phase. Transition between the two phases is continuous, with characteristics that resemble those of a disordered elastic manifold in two dimensions. For designed sequences, however, a power-law distribution of pairing energies on a coarse-grained level may be more appropriate. Extreme value statistics arguments then predict a power-law growth of the free energy cost to break a chain, in agreement with numerical simulations. Interestingly, the distribution of pairing distances in the ground state secondary structure follows a remarkable power-law with an exponent -4/3, independent of the specific assumptions for the base pairing energies.     

A quantal toy model for heavy-ion collisions

A one-dimensional toy model of two moving finite boxes is analysed with respect to quantal phenomena associated with heavy-ion dynamics at low and intermediate energies. Special attention is payed to the relation between energy and momentum of the nucleons inside and outside the time-dependent mean field. A Wigner transformation of the one-body density matrix in space and time allows for a unique comparison with classical phase-space dynamics. It is found that high momentum components of the nuclear groundstate wave function approximately become on-shell during the heavy-ion reaction. This leads to the emission of energetic nucleons which do not appear classically. It is furthermore shown, that the low lying eigenstates of the dinuclear system for fixed time are only partly occupied throughout the reaction at intermediate energies. This opens up final phase space for nucleons after producing e.g. a pion or energetic photon. Though the present model does not allow for a reliable calculation of double differential nucleon spectra, pion or photon cross sections, it transparently shows the peculiar features of quantum dynamics in heavy-ion collisions.     

A theory of the origin of silicon carbide polytypes

A new theory of the origin of SiC polytypes is presented in which the observed polytypes are stabilised as equilibrium phases at the high temperatures of growth, the structures becoming frozen in on cooling. Results of first principles pseudopotential total energy calculations show that the SiC polytypes containing only bands of width 2 and 3 are nearly degenerate in energy while all other polytypes have higher energies. We develop an inter-layer interaction model to describe the energies of the polytypes. Calculations of the phonon free energies of several SiC polytypes using the valence overlap shell model are described. These calculations show that the phonon free energy gives rise to effectively long ranged interactions between the SiC layers which can stabilise a large number of ordered polytypes as equilibrium phases.     

Breathing motion of a kink-bag system in (1 + 1) dimensions: Inertia of the vacuum confined in a bag

We examine the breathing motion of a (1 + 1)-dimensional hybrid bag where the confined quarks are coupled with a solitonic chiral field at the bag boundary. The hybrid bag is a toy model for the (1 + 3)-dimensional skyrmion-bag system and its breathing motion has close connection with the excited states of a nucleon such as the Roper resonance. The collective lagrangian for the motion is derived microscopically by focusing on the polarized Dirac sea inside the bag. The mass parameter of the motion is decreased compared with the MIT-bag one owing to the negative contribution from the inertia of the confined vacuum. As a result, the spectra of the motion do not have too low excitation energies despite that the potential energy surface is softened by the vacuum effect.     

High-energy behavior and second class constraints in quantum gravity

It is proposed that sensible high-energy behavior in a quantum theory of gravity may be achieved in a class of theories in which the connection and metric are independent and unconstrained and where the action is chosen so that no derivatives of the metric appear. This is because in these theories all ten of the metric field equations are realized as second class constraints. These can in principle be solved, expressing the operators g_μν as functions of the operators for the components of the connection and their canonical momenta. Thus, the metric has no independent quantum fluctuations, and the instabilities resulting from the usual curvature squared terms are eliminated. Furthermore, there is no need to assume metric compatibility, as it is automatically restored in the low-energy limit by the dominance of dimension-two terms.In order to explore these ideas a toy model with two degrees of freedom, corresponding to a metric and a connection variable, is quantized and shown to have a sensible high energy limit, while a related model, in which a constraint analogous to metric compatibility is imposed, is found to be unstable at high energies.