A Telescoping method for Double Summations

We present a method to prove hypergeometric double summation identities. Given a hypergeometric term $F(n,i,j)$, we aim to find a difference operator $L=a_0(n) N^0 + a_1(n) N^1 +...+a_r(n) N^r$ and rational functions $R_1(n,i,j),R_2(n,i,j)$ such that $L F = \Delta_i (R_1 F) + \Delta_j (R_2 F)$. Based on simple divisibility considerations, we show that the denominators of $R_1$ and $R_2$ must possess certain factors which can be computed from $F(n, i,j)$. Using these factors as estimates, we may find the numerators of $R_1$ and $R_2$ by guessing the upper bounds of the degrees and solving systems of linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's identities, the Ap\'ery-Schmidt-Strehl identity, the Graham-Knuth-Patashnik identity, and the Petkov\v{s}ek-Wilf-Zeilberger identity.Comment: 22 pages. to appear in J. Computational and Applied Mathematic

Applicability of the qq-Analogue of Zeilberger's Algorithm

The applicability or terminating condition for the ordinary case of Zeilberger's algorithm was recently obtained by Abramov. For the $q$-analogue, the question of whether a bivariate $q$-hypergeometric term has a $qZ$-pair remains open. Le has found a solution to this problem when the given bivariate $q$-hypergeometric term is a rational function in certain powers of $q$. We solve the problem for the general case by giving a characterization of bivariate $q$-hypergeometric terms for which the $q$-analogue of Zeilberger's algorithm terminates. Moreover, we give an algorithm to determine whether a bivariate $q$-hypergeometric term has a $qZ$-pair.Comment: 15 page

Higgs Triplets, Decoupling, and Precision Measurements

Electroweak precision data has been extensively used to constrain models containing physics beyond that of the Standard Model. When the model contains Higgs scalars in representations other than SU(2) singlets or doublets, and hence rho not equal to one at tree level, a correct renormalization scheme requires more inputs than the three needed for the Standard Model. We discuss the connection between the renormalization of models with Higgs triplets and the decoupling properties of the models as the mass scale for the scalar triplet field becomes much larger than the electroweak scale. The requirements of perturbativity of the couplings and agreement with electroweak data place strong restrictions on models with Higgs triplets. Our results have important implications for Little Higgs type models and other models with rho not equal to one at tree level.Comment: 23 page

TeV Scale Seesaw and a flavorful Z' at the LHC

Small neutrino masses and their large mixing angles can be generated at the TeV scale by augmenting the Standard Model with an additional generation dependent, anomaly-free U(1)_{nu} symmetry, in the presence of three right-handed neutrinos. The Z' gauge boson associated with the breaking of the U(1)_{nu} symmetry can be produced at the LHC. The flavorful nature of the Z' can be established by measuring its non-universal couplings to the charged leptons as determined by the lepton's U(1)_{nu} charges, which also govern the neutrino flavor structure. While the LHC has the potential of discovering the Z' up to M_{Z'} = 4.5 TeV with 100 fb^(-1) data at the center of mass energy sqrt{s} = 14 TeV, to establish the flavorful nature of the Z' requires much higher integrated luminosity. For our bench mark parameters that are consistent with neutrino oscillation data, at sqrt{s} = 14 TeV, a 5 sigma distinction between the dielectron and dimuon channels for M_{Z'} = 3 TeV requires 500 fb^(-1) of data. We find that the forward backward asymmetry distributions can also be useful in distinguishing the dielectron and dimuon channels in the low invariant mass and transverse momentum regions.Comment: 9 pages, 13 figures; v2: version to appear in Phys. Rev.

Antiarrhythmic and proarrhythmic effects of subcutaneous nerve stimulation in ambulatory dogs

Background High output subcutaneous nerve stimulation (ScNS) remodels the stellate ganglia and suppresses cardiac arrhythmia. Objective To test the hypothesis that long duration low output ScNS causes cardiac nerve sprouting, increases plasma norepinephrine concentration and the durations of paroxysmal atrial tachycardia (PAT) in ambulatory dogs. Methods We prospectively randomized 22 dogs (11 males and 11 females) into 5 different output groups for 2 months of ScNS: 0 mA (sham) (N=6), 0.25 mA (N=4), 1.5 mA (N=4), 2.5 mA (N=4) and 3.5 mA (N=4). Results As compared with baseline, the changes of the durations of PAT episodes per 48 hours were significantly different among different groups (sham, -5.0±9.5 s; 0.25 mA 95.5±71.0 s; 1.5 mA, -99.3±39.6 s; 2.5 mA, -155.3±87.8 s and 3.5 mA, -76.3±44.8 s, p<0.001). The 3.5 mA group had greater reduction of sinus heart rate than the sham group (-29.8±15.0 bpm vs -14.5±3.0 bpm, p=0.038). Immunohistochemical studies showed that the 0.25 mA group had a significantly increased while 2.5 mA and 3.5 mA stimulation had a significantly reduced growth-associated protein 43 nerve densities in both atria and ventricles. The plasma Norepinephrine concentrations in 0.25 mA group was 5063.0±4366.0 pg/ml, which was significantly higher than other groups of dogs (739.3±946.3, p=0.009). There were no significant differences in the effects of simulation between males and females. Conclusions In ambulatory dogs, low output ScNS causes cardiac nerve sprouting, increases plasma norepinephrine concentration and the duration of PAT episodes while high output ScNS is antiarrhythmic

Relating Leptogenesis to Low Energy Flavor Violating Observables in Models with Spontaneous CP Violation

In the minimal left-right symmetric model, there are only two intrinsic CP violating phases to account for all CP violation in both the quark and lepton sectors, if CP is broken spontaneously by the complex phases in the VEV's of the scalar fields. In addition, the left- and right-handed Majorana mass terms for the neutrinos are proportional to each other due to the parity in the model. This is thus a very constrained framework, making the existence of correlations among the CP violation in leptogenesis, neutrino oscillation and neutrinoless double beta decay possible. In these models, CP violation in the leptonic sector and CP violation in the quark sector are also related. We find, however, that such connection is rather weak due to the large hierarchy in the bi-doublet VEV required by a realistic quark sector.Comment: RevTeX4, 21 pages; v2: references added, version to appear in Phys. Rev.

Spectroscopy of q3qˉ3\rm{q}^3\bar{\rm{q}}^3-States in Quark Model and Baryon-Antibaryon Enhancements

We study the mass spectrum of the $\rm{q}^3\bar{\rm{q}}^3$ mesons both from the quark model with triquark correlations and from common quark model with colormagnetic interactions and with relative S-waves between quarks. Two cluster configurations $(\rm{q}^3)-(\bar{\rm{q}}^3)$ and $(\rm{q}^2\bar{\rm{q}})-(\rm{q}\bar{\rm{q}}^2)$ are considered. In the spectrum we find rather stable states which have the same quantum number with particle resonances which are corresponding to the $p\bar{p}$ enhancement, $p\bar{\Lambda}$ enhancement and $\Lambda\bar{\Lambda}$ enhancement with spin-$\mathbf{0}$ or $\mathbf{1}$. This imply these enhancements are NOT experimental artifacts. The color-spin-flavor structures of $p\bar{p}$, $p\bar{\Lambda}$, and $\Lambda\bar{\Lambda}$ enhancements are revealed. The existence of spin-$\mathbf{1}$ $\Lambda\bar{\Lambda}, p\bar{\Lambda}, p\bar{p}$ enhancements is predicted.Comment: 45 pages, 5 figure

Dirac Leptogenesis with a Non-anomalous U(1)′U(1)^{\prime} Family Symmetry

We propose a model for Dirac leptogenesis based on a non-anomalous $U(1)^{\prime}$ gauged family symmetry. The anomaly cancellation conditions are satisfied with no new chiral fermions other than the three right-handed neutrinos, giving rise to stringent constraints among the charges. Realistic masses and mixing angles are obtained for all fermions. The model predicts neutrinos of the Dirac type with naturally suppressed masses. Dirac leptogenesis is achieved through the decay of the flavon fields. The cascade decays of the vector-like heavy fermions in the Froggatt-Nielsen mechanism play a crucial role in the separation of the primodial lepton numbers. We find that a large region of parameter space of the model gives rise to a sufficient cosmological baryon number asymmetry through Dirac leptogenesis.Comment: 8 pages, 8 figures, version to appear in JHE