Motivated by a recent investigation into the notion of a quantum space underlying ordinary quantum mechanics, we reformulate here the WWGM formalism with canonical coherent states and wavefunctions as expansion coefficients in terms of this basis as the starting point. It turns out that this provides us with a transparent and coherent story of simple quantum dynamics where both states (pure and mixed, making use of the Tomita representation), as wavefunctions in Hilbert spaces, and observables arise from a single space/algebra. Altogether, putting the emphasis on building our theory out of the underlying relativity symmetry -the centrally extended Galilean symmetry in the case at hand -allows one to naturally derive both a kinematical and a dynamical description of a (free) quantum particle, which moreover recovers the corresponding classical picture (understood in terms of the Koopman-von Neumann formalism) in the appropriate (relativity symmetry contraction) limit. Our formulation here is the most natural framework directly connecting all of the relevant mathematical notions and we hope it may help a general physicist better visualize and appreciate the noncommutative-geometric perspective behind quantum physics.

We present a parametrization of the supersymmetric standard model without R-parity that permits efficient phenomenological analyses of the full model without a priori assumptions. Under the parametrization, which is characterized by a single vacuum expectation value for the scalar components of the Y = −1/2 superfields, the expressions for tree-level mass matrices are quite simple. They do not involve the trilinear R-parity violating couplings; however, the bilinear µ i terms do enter and cannot be set to zero without additional assumptions. We set up a framework for doing phenomenology and show some illustrative results for fermion mass matrices and related bounds on parameters. We find in particular that large values of tanβ can suppress R-parity violating effects, substantially weakening experimental constraints.

Requiring the two-Higgs-doublet model II to accommodate the 3 deviation in the muon anomalous magnetic moment imposes specific constraints on the Higgs spectrum. We analyze the combination of all the relevant available constraints on the model parameter space. The use of constraints from b→s␥, the precision electroweak measurements of R b , and the parameter, together with exclusions from direct searches at CERN LEP, gives extremely severe restrictions on the model parameters. That is ''almost enough'' to destroy the model altogether. The exclusion would be even stronger if the direct searches could be optimized to complement the other constraints, as will be discussed in detail in this work. 1 This 3 deviation was derived using the e ϩ e Ϫ data. If the decay data were used, the deviation would be reduced to about 0.9 ͓2͔, which, however, has model dependence and is thus less reliable. PHYSICAL REVIEW D 68, 053003 ͑2003͒

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We present the full result for the down squark mass-squared matrix in the complete theory of supersymmetry without R parity where all kinds of R-parity violating terms are admitted without bias using an optimal parametrization. The major result is a new contribution to LR squark mixing, involving both bilinear and trilinear R-parity violating couplings. Among other things, the latter leads to neutron electric dipole moment at one-loop level. Similar mechanisms lead to electron electric dipole moment at the same level. We present here a short report on major features of neutron electric dipole moment from supersymmetry without R parity and give the interesting constraints obtained.

Starting from the new sources of LL-and LR-scalar (slepton) mixings due to the R-parity violation, we discuss the structure of lepton-flavor violation focusing on the radiative decay of a muon into an electron. Using an optimal parametrization, we give the general formulas for the one-loop contributions, from which we discuss all combinations of R-parity violating parameters that possibly have a substantial contribution to the µ → e γ decay width. An exact numerical study is performed to obtain explicit bounds on the parameters under the present experimental limit. The most interesting one involves a combination of bilinear and trilinear couplings.

The recent measurement of the muon anomalous magnetic moment a µ shows a 2.6σ deviation from the standard model value. We show that it puts strong constraints on the parameter space of the two-Higgs doublet model (2HDM) II. The dominant contribution of the Higgs bosons comes at the two-loop level, and in order to explain the data it favors a pseudoscalar A with a light mass range and a large tanβ. At 95% C.L., the upper limit for m A is 29 (55) (85) GeV for tanβ = 30 (45) (60), and tanβ is bounded below at 17. This is in sharp contrast to the conclusion one draws from considering one-loop Higgs contributions alone. Finally, we also discuss the role of the Higgs contributions in the minimal supersymmetric standard model. * E-mail: cheung@phys.cts.nthu.edu.tw † E-mail: chouch@phys.sinica.edu. which may suggest the presence of contributions from physics beyond the SM. Taking the above numbers at face value, the range of ∆a µ at 95% C.L. (±1.96σ) is given by 10.3 × 10 −10 < ∆a µ < 74.9 × 10 −10 .Most of the extensions of the SM start with an extended Higgs sector, the simplest of which is the two-Higgs-doublet model (2HDM). In particular, the more interesting model II [3] shares the same Higgs structure as the minimal supersymmetric standard model (MSSM). Hence, going beyond the SM to look for extra contributions to a µ , the 2HDM should be among the first to be examined seriously.In this Rapid Communication, we investigate the contributions from the 2HDM II. Stringent constraints are thus obtained on the parameter space of the model. The results are summarized as follows. In the 2HDM II, the dominant contribution actually comes at the two-loop level, and in order to explain the data ∆a µ is preferred to come from the Higgs pseudoscalar A, the mass of which is required to be less than 29 (55) (85) GeV for tanβ = 30 (45) (60) by the 95% C.L. range of Eq.(2). Moreover, tanβ has to be larger than 17. Recently, there has been some work on the same subject [4]; however, the paper only considered the one-loop contributions from the Higgs bosons, which become smaller than their corresponding two-loop contributions when the Higgs bosons are heavier than a few GeV and substantially smaller for heavier Higgs bosons. It is important to note that the two-loop contributions considered here dramatically change the story of the Higgs sector contributions to a µ and invalidate most of the results of the one-loop studies. Although we focus on the 2HDM II here, a similar conclusion holds for most models with possible large contributions from the Higgs sector. In models with flavor-changing Higgs couplings, in particular, there are potentially 1-loop contributions substantially larger than the flavorconserving ones [5]. However, the Barr-Zee type 2-loop contributions would still have an important role to play and should be taken into consideration. This fact has often been overlooked in the literature.In the MSSM, the dominant contribution comes from the chargino-sneutrino-loop diagrams and it has been shown [6] that to sat...

We investigate the dynamical mass generation resulted from interaction terms with four chiral superfields. The kind of interactions maybe considered a supersymmetric generalization of the four-fermion interactions of the classic Nambu-Jona-Lasinio model. A four-superfield interaction that contains a four-fermion interaction as one of its component terms has been the standard supersymmetrization of the NJL model for decades. Recently, we introduced a holomorphic variant with a dimension five interaction term instead. The latter is a main target of the present analysis. With the introduction of a new perspective on the superfield gap equation, we derive it for each one of the four-superfield interactions, using the supergraph technique. Through analyzing solutions to the gap equations, we illustrate the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part.A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible. The explicit illustration of dynamical symmetry breaking from the holomorphic dimension five interaction is reported for the first time. It has rich and novel features, which would be easily missed without the superfield approach developed here. We also discuss the nature of the bi-superfield condensate and its role of the effective Higgs superfield picture for both cases, illustrating their difference.Note that such a holomorphic quark superfield interaction term can successful account for the electroweak symmetry breaking with Higgs superfields as composites.