We describe details of the renormalization of two-loop integrals relevant to the calculation of the nucleon mass in the framework of manifestly Lorentz-invariant chiral perturbation theory using infrared renormalization. It is shown that the renormalization can be performed while preserving all relevant symmetries, in particular chiral symmetry, and that renormalized diagrams respect the standard power counting rules. As an application we calculate the chiral expansion of the nucleon mass to order O(q^6).
N=1 SQCD with SU(N_c) colors and N_F flavors of light quarks is considered within the dynamical scenario which assumes that quarks can be in two different phases only. These are: a) either the HQ (heavy quark) phase where they are confined, b) or they are higgsed, at the appropriate values of parameters of the Lagrangian. The mass spectra of this (direct) theory and its Seibergs dual are obtained and compared, for quarks of equal or unequal masses. It is shown that in all cases when there is the additional small parameter at hand (it is 0<(3N_c-N_F)/N_F << 1 for the direct theory, or its analog 0<(2N_F-3N_c)/N_F << 1 for the dual one), the mass spectra of the direct and dual theories are parametrically different. A number of other regimes are also considered.
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the translational symmetry. We then introduce a Minimal Subtraction (MS) and a Modified Minimal Subtraction (MS-Bar) scheme to renormalize the result. Finally, we consider dimensional transmutation as encountered in the case of compact extra-dimensions.
Neutrinoless double beta decay is one of the most sensitive approaches in non-accelerator particle physics to take us into a regime of physics beyond the standard model. This article is a brief review of the experiments in search of neutrinoless doub
le beta decay from 76Ge. Following a brief introduction of the process of double beta decay from 76Ge, the results of the very first experiments IGEX and Heidelberg-Moscow which give indications of the existence of possible neutrinoless double beta decay mode has been reviewed. Then ongoing efforts to substantiate the early findings are presented and the Majorana experiment as a future experimental approach which will allow a very detailed study of the neutrinoless decay mode is discussed.
The quadratic pion scalar radius, la r^2ra^pi_s, plays an important role for present precise determinations of pipi scattering. Recently, Yndurain, using an Omn`es representation of the null isospin(I) non-strange pion scalar form factor, obtains la
r^2ra^pi_s=0.75pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omn`es equations, la r^2ra^pi_s=0.61pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Yndurains method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input pipi phase shifts, a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is la r^2ra_s^pi=0.65pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0 pipi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.
We discuss the fundamemtal constants in the Standard Model of particle physics, in particular possible changes of these constants on the cosmological time scale. The Grand Unification of the observed strong, electromagnetic and weak interactions implies relations between time variation of the finestructure constant alpha and the QCD scale $Lambda_c$. The astrophysical observation of a variation implies a time variation of $10^{-15} / year$. Several experiments in Quantum Optics, which were designed to look for a time variation of $Lambda_c$, are discussed.
Since there are dark matter particles (neutrino) with mass about 10^(-1)eV in the universe, the superstructures with a scale of 10^(19) solar mass [large number A is about 10^(19)] appeared around the era of the hydrogen recombination. The redshift z distributions of quasars support the existence of superstructures. Since there are superstructures in the universe, it is not necessary for the hypothesis of dark energy. While neutrino is related to electro-weak field, the fourth stable elementary particles (delta particle) with mass about 10^(0)eV to 10^(1)eV is related to gravitation-strong field, which suggests p + anti(p)--> n/anti(n) + anti(delta particle)/(delta particle) and that some new meta-stable baryons appeared near the TeV region. Therefore, a twofold standard model diagram is proposed, and related to many experiment phenomena: The new meta-stable baryons decays produce delta particles, which are helpful to explain the Dijet asymmetry phenomena at LHC of CERN, the different results for the Fermilabs data peak, etc; However, according to the (B-L) invariance, the sterile neutrino from the event excess in MiniBooNe can not be the fourth neutrino but rather the delta particle; We think that the delta particles are related to the phenomenon about neutrinos FTL, and that anti-neutrinos are faster than neutrinos. FTL is also related to the cosmic inflation, singular point disappearance, and abnormal red shift of SN Ia. Some experiments and observations are suggested. In the Extension section, we clarify mass tree, our finite universe, cosmic dual expansions, dual SM etc. And the LHC can look for new particles with decay products graviton/delta particle and new interaction indeed.
In this work, we first use Thompsons renormalization group method to treat QCD-vacuum behavior close to the regime of asymptotic freedom. QCD-vacuum behaves effectively like a paramagnetic system of a classical theory in the sense that virtual color charges (gluons) emerge in it as spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Making a classical analogy with the paramagnetism of Landaus theory,we are able to introduce a kind of Landau effective action without temperature and phase transition for simply representing QCD-vacuum behavior at higher energies as magnetization of a paramagnetic material in the presence of a magnetic field H. This reasoning allows us to use Thompsons heuristic approach in order to extract an effective susceptibility ($chi>0$) of QCD-vacuum. It depends on logarithmic of energy scale u to investigate hadronic matter. Consequently,we are able to get an effective magnetic permeability ($mu>1$) of such a paramagnetic vacuum. As QCD-vacuum must obey Lorentz invariance,the attainment of $mu>1$ must simply require that the effective electrical permissivity is $epsilon<1$,in such a way that $muepsilon=1$ (c^2=1).This leads to the antiscreening effect, where the asymptotic freedom takes place. On the other hand, quarks cofinement, a subject which is not treatable by perturbative calculations, is worked by the present approach. We apply the method to study this subject in order to obtain the string constant, which is in agreement with the experiments.
This work tabulates measured and derived values of coefficients for Lorentz and CPT violation in the Standard-Model Extension. Summary tables are extracted listing maximal attained sensitivities in the matter, photon, neutrino, and gravity sectors. Tables presenting definitions and properties are also compiled.
The spectrum of the glueball with $J^{PC}=0^{--}$ is computed using different bottom-up holographic models of QCD. The results indicate a lowest-lying state lighter than in the determination by other methods, with mass $m simeq 2.8$ GeV. The in-medium properties of this gluonium are investigated, and stability against thermal and density effects is compared to other hadronic systems. Production and decay modes are identified, useful for searching the $J^{PC}=0^{--}$ glueball.
