Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

Little Higgs Models and Precision Electroweak Data

We study the low energy limit of Little Higgs models. The method consists in eliminating the heavy fields using their classical equations of motion in the infinite mass limit. After the elimination of the heavy degrees of freedom we can directly read off deviations from the precision electroweak data. We also examine the effects on the low energy precision experiments.Comment: Misprint in eps3 for the custodial model corrected and additional discussion of the triplet higg

Potts model on recursive lattices: some new exact results

We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths $L_y=2,3,4,5$. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width $L_y=3$ and $L_y=m+2$, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.Comment: 17 pages, 19 figures. v2 typos corrected, title changed and references, acknowledgements and two further original examples added. v3 one further example added. v4 final versio

Singlet Fermionic Dark Matter explains DAMA signal

It has been suggested that, considering channeling effect, the order of a few GeV dark matters which are elastically scattered from detector nuclei might be plausible candidates reconciling the DAMA annual modulation signal with the results of other null experiments. We show that Singlet Fermionic Dark Matter can be such a dark matter candidate, simultaneously providing the correct thermal relic density which is consistent with the WMAP data.Comment: 9 pages, 3 figure

Constraint of B_{d,s}-bar{B}_{d,s} mixing on warped extra-dimension model

Recent CDF measurement of the Bs-Bs oscillation frequency, at the Tevatron imposes significant constraint on various models for new physics. A warped extra-dimension model with custodial isospin symmetry accommodates the Bd-Bd mixing at tree level mainly through the Kaluza-Klein gluons. This is due to the misalignment between the bulk gauge eigenstates and the localized Yukawa eigenstates of the bulk fermions. We adopt the universal 5D Yukawa coupling model where all Yukawa couplings are of order one. The SM fermion mass spectra and mixings are controlled by the bulk Dirac mass parameters. With two versions of the hadronic parameter values, we investigate the implication of the observed BB mixings on this model. The CP-violating effects on the Bd system is shown to provide very strong constraint: The first Kaluza-Klein mass of a gluon has its lower bound about 3.7 TeV with 1 sigma uncertainty.Comment: published version in JHEP, CP-violating effects include

Mass matrix Ansatz and lepton flavor violation in the THDM-III

Predictive Higgs-fermion couplings can be obtained when a specific texture for the fermion mass matrices is included in the general two-Higgs doublet model. We derive the form of these couplings in the charged lepton sector using a Hermitian mass matrix Ansatz with four-texture zeros. The presence of unconstrained phases in the vertices phi-li-lj modifies the pattern of flavor-violating Higgs interactions. Bounds on the model parameters are obtained from present limits on rare lepton flavor violating processes, which could be extended further by the search for the decay tau -> mu mu mu and mu-e conversion at future experiments. The signal from Higgs boson decays phi -> tau mu could be searched at the large hadron collider (LHC), while e-mu transitions could produce a detectable signal at a future e mu-collider, through the reaction e mu -> h0 -> tau tau.Comment: 17 pages, 9 figure

Little Hierarchy, Little Higgses, and a Little Symmetry

Little Higgs theories are an attempt to address the little hierarchy problem, i.e., the tension between the naturalness of the electroweak scale and the precision measurements showing no evidence for new physics up to 5-10 TeV. In little Higgs theories, the Higgs mass-squareds are protected to the one-loop order from the quadratic divergence. This allows the cutoff to be raised up to \~10 TeV, beyond the scales probed by the precision data. However, strong constraints can still arise from the contributions of the new TeV scale particles and hence re-introduces the fine-tuning problem. In this paper we show that a new symmetry, denoted as T-parity, under which all heavy gauge bosons and scalar triplets are odd, can remove all the tree-level contributions to the electroweak observables and therefore makes the little Higgs theories completely natural. The T-parity can be manifestly implemented in a majority of little Higgs models by following the most general construction of the low energy effective theory a la Callan, Coleman, Wess and Zumino. In particular, we discuss in detail how to implement the T-parity in the littlest Higgs model based on SU(5)/SO(5). The symmetry breaking scale f can be even lower than 500 GeV if the contributions from the unknown UV physics at the cutoff are somewhat small. The existence of $T$-parity has drastic impacts on the phenomenology of the little Higgs theories. The T-odd particles need to be pair-produced and will cascade down to the lightest T-odd particle (LTP) which is stable. A neutral LTP gives rise to missing energy signals at the colliders which can mimic supersymmetry. It can also serve as a good dark matter candidate.Comment: 20 pages, 2 figures, RevTeX; v2: Yukawa sector in the SU(5)/SO(5) model slightly modified. Also added comments on the Dirac mass term for the fermionic doublet partner; v3: clarifying comments on the modified Yukawa sector. version to appear on JHE

A "Littlest Higgs" Model with Custodial SU(2) Symmetry

In this note, a ``littlest higgs'' model is presented which has an approximate custodial SU(2) symmetry. The model is based on the coset space $SO(9)/(SO(5)\times SO(4))$. The light pseudo-goldstone bosons of the theory include a {\it single} higgs doublet below a TeV and a set of three $SU(2)_W$ triplets and an electroweak singlet in the TeV range. All of these scalars obtain approximately custodial SU(2) preserving vacuum expectation values. This model addresses a defect in the earlier $SO(5)\times SU(2)\times U(1)$ moose model, with the only extra complication being an extended top sector. Some of the precision electroweak observables are computed and do not deviate appreciably from Standard Model predictions. In an S-T oblique analysis, the dominant non-Standard Model contributions are the extended top sector and higgs doublet contributions. In conclusion, a wide range of higgs masses is allowed in a large region of parameter space consistent with naturalness, where large higgs masses requires some mild custodial SU(2) violation from the extended top sector.Comment: 22 pages + 8 figures; JHEP style, added references and extra discussion on size of T contributions, as well as some other minor clarifications. Version to appear in JHE

t→bWt \to b W in NonCommutative Standard Model

We study the top quark decay to b quark and W boson in the NonCommutative Standard Model (NCSM). The lowest contribution to the decay comes from the terms quadratic in the matrix describing the noncommutative (NC) effects while the linear term is seen to identically vanish because of symmetry. The NC effects are found to be significant only for low values of the NC characteristic scale.Comment: 11 page Latex file containing 2 eps figures (redrawn). More discussion included. To appear in PR

A Composite Little Higgs Model

We describe a natural UV complete theory with a composite little Higgs. Below a TeV we have the minimal Standard Model with a light Higgs, and an extra neutral scalar. At the TeV scale there are additional scalars, gauge bosons, and vector-like charge 2/3 quarks, whose couplings to the Higgs greatly reduce the UV sensitivity of the Higgs potential. Stabilization of the Higgs mass squared parameter, without finetuning, occurs due to a softly broken shift symmetry--the Higgs is a pseudo Nambu-Goldstone boson. Above the 10 TeV scale the theory has new strongly coupled interactions. A perturbatively renormalizable UV completion, with softly broken supersymmetry at 10 TeV is explicitly worked out. Our theory contains new particles which are odd under an exact "dark matter parity", (-1)^{(2S+3B+L)}. We argue that such a parity is likely to be a feature of many theories of new TeV scale physics. The lightest parity odd particle, or "LPOP", is most likely a neutral fermion, and may make a good dark matter candidate, with similar experimental signatures to the neutralino of the MSSM. We give a general effective field theory analysis of the calculation of corrections to precision electroweak observables.Comment: 28 page