In a model with dynamical gluon mass, we investigate the bound states of two and three gluons via a Schrödinger equation. The short distance potential is approximated by onegluon-exchange while the long distance part is assumed to be of a breakable string. We estimate the masses and in particular the sizes of low-lying bound states with no orbital angular momentum. By considering quantum-mechanical smearing of the gluon fields and normalizing to lattice results on M 0 ++ and M 2 ++ , we find that the 0 ++ glueball is rather small in size compared with the others. The fitted gluon mass is of order 600 to 700 MeV, which is reasonable. The 0 −+ , 1 −− and 3 −− three gluon glueball states are nearly degenerate, and their mass ratio with 2 ++ is largely independent of all parameters and consistent with lattice calculations. We estimate the mass of the 1 −− glueball to be around 3.1−3.7 GeV, which is close to the mass of J/ψ and ψ ′ .

We construct a Z g model for leptons where all Yukawa couplings are of order unity, but known lepton masses are generated radiatively, order by order. The seed is provided by fourth generation leptons E and A'. and two additional Higgs doublets are introduced to give nearest-neighbor Yukawa couplings. Loop masses are generated when Z 8 is softly broken down to Z 2 , while m, and n1, generation require Higgs bosons to be weak scale. The Z 2 symmetry forbids p-.e y. The most stringent bound comes from ~-.~p + e ' . The model has implications for r -+ e y , pe-.be conversion, p -e v , F , . and FCNC decays of E and N (such as E-. r e ' p S ) .PACS number(s): 12.15.Ff, 12.60.Fr, 14.60.Hi A major mystery regarding fermion flavor is the very wide range of its mass spectrum. Neutrinos appear to be massless, while known masses range from the electron's 0.511 MeV, to over 120 GeV [ I ] for the top quark. In the standard S U ( 2 ) L X U ( 1 ) electroweak model, a single Higgs doublet is responsible for generating all masses. The natural scale is v = ( \ J Z~~) -"~= 2 4 6 GeV, where G F is the Fermi coupling. The puzzle is then twofold. On one hand, the dimensionless Yukawa couplings f are scattered over a wide range, and there is an empirical family hierarchy, e.g., f,+ f , e f , , for each type of fermion. On the other hand, we have f 6 1 for all known fermions, except for the top quark where f,-1. This is in contrast with the gauge couplings (at W scale) g , = 0.36, g2= 0.65, and g 3 = 1.2 for strong SU(3).It was suggested a long time ago [2] that the observed fermion mass hierarchy may be due to radiative mechanisms. It is desirable to have Yukawa couplings f-1, just like gauge couplings. Given that f i m , l v~0 . 0 1 is itself rather small, we would naturally need new leptons to provide the "seed" for mass generation in the lepton sector. Neutrino counting N , = 2.992 0.04 and direct search limits m~ , mN>Mz/2 [3] imply that new sequential leptons E and N are at scale v , deviating sharply from earlier patterns [4]. In this Rapid ~o m m u n i c a t i o~,~w e construct a simple model where E and N receive mass at the tree level, but all lower generation lepton masses are generated by loop processes.We start with the lepton sector of minimal "3 + 1" generations [4], where there is only one right-handed neutral lepton N R . Consider a discrete Z8 symmetry ( w s = 1 ) . We assign both i l L = ( f i l L ,2,L) and e l R to transform as w" ww', w ' , w4 for i=1-4, respectively, while N R transforms as w 4 . The scalar sector consists of three doublets Q 3 , and Q 5 , transforming as 1 , w', and w S , respectively. Thus, aside from E = e 4 and N, only nearest-neighbor Yukawa couplings are allowed, where &= i a 2 @ * = ( @ ( I * , -4 -) as usual. We assume C P invariance for simplicity.If only ( 4 ; ) = v / \i?. E and N become massive and are naturally at v scale if f44, f44-1. The lower generation leptons remain massless at this stage, protected by the Z8 symmetry. To allow for radiative mass generation, the Z , symmetry is s...

The spectrum of two-gluon glueballs below 3 GeV is investigated in a potential model with dynamical gluon mass using variational method. The short distance potential is approximated by one-gluon exchange, while the long distance part is taken as a breakable string. The mass and size of the radial as well as orbital excitations up to principle quantum number n = 3 are evaluated. The predicted mass ratios are compared with experimental and lattice results.PACS numbers: 12.39.MK Quantum Chromodynamics (QCD) is widely accepted as the theory of strong interactions. It is generally believed that the gluon self-coupling in QCD implies the existence of bound states of confined gluons known as glueballs. The experimental discovery of these glueballs would be very important and would give further support to the theory of QCD. However, numerous technical difficulties have so far hampered our unequivocal identification of glueballs by experiment, largely because glueball states can mix strongly with nearby qq resonances. Nevertheless, the estimation of mass and size of pure gluon glueball states should still be pursued. This could guide experimental searches, as well as provide calibration for models of glueballs.Over the past 20 years there has been an on-going effort to obtain a nonperturbative form for the gluon propagator. Perhaps one of the most interesting result is that the gluon may have a dynamically generated mass [1]. The existence of a mass scale, or the absence of a pole at k 2 = 0, is natural if one assumes that gluons do not propagate to infinity, i.e., these propagators describe confined gluons. The concept of massive gluon has been widely used in independent field theoretic studies, and examples about the consequences of massive gluons can be found in the literature [2][3][4][5][6][7].In this paper, we focus on the calculation of two-gluon glueball systems and extend our previous work [8] on the estimation of the mass and size of low lying glueball states, using the variational method in the potential model of Cornwall and Soni [9,10]. The main feature of the present work is the consideration of radial as well as orbital excitations, up to principle quantum number n = 3.To exhibit both asymptotic freedom and the nonAbelian nature of QCD, gluon dynamics can be described as massive spin-one fields interacting through one-gluon exchange and a breakable string. At short distance the effective coupling constant of the gluon-gluon interaction becomes small and the interaction can be treated perturbatively. The short distance potential is approximated by one-gluon exchange and can be extracted from the tree-level Feynman amplitude of Fig. 1,where q is the momentum transfer of the system. At long distance, the non-Abelian nature of QCD implies gluon confinement via nonperturbative effects. These nonperturbative effects are implemented by introducing a string potential V str which is assumed to be spin independent,where β is related to the adjoint string tension K A viaIn the potential V str , the color screening of...

With no New Physics seen at the LHC, a second Higgs doublet remains attractive and plausible. The ratio R µ/τ B = B(B → µν)/B(B → τν) is predicted at 0.0045 in both the Standard Model and the two Higgs doublet model type II, but it can differ if extra Yukawa couplings exist in Nature.Considering recent Belle update on B → µν, the ratio could be up by a factor of two in the general two Higgs doublet model, which can be probed by the Belle II experiment with just a few ab −1 .