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In the framework of heavy quark effective theory we use QCD sum rules to calculate the masses of thecs (0 + , 1 + ) and (1 + , 2 + ) excited states. The results are consistent with that the states D sJ (2317) and D sJ (2460) observed by BABAR and CLEO are the 0 + and 1 + states in the j l = 1 2 + doublet.

If the fourth generation fermions exist, the new quarks could influence the branching ratios of the decays of B → X s γ and B → X s l + l − . We obtain two solutions of the fourth generation CKM factor V *We use these two solutions to calculate the new contributions of the fourth generation quark to Wilson coefficients of the decay of B → X s l + l − . The branching ratio and the forward-backward asymmetry of the decay of B → X s l + l − in the two cases are calculated. Our results are quite different from that of SM in one case, almost same in another case. If Nature chooses the formmer, the B meson decays could provide a possible test of the forth generation existence.

The rare decays ⌳ b →⌳␥ and ⌳ b →⌳l ϩ l Ϫ (lϭe,) are examined. We use QCD sum rules to calculate the hadronic matrix elements governing the decays. The ⌳ polarization in the decays is analyzed and it is shown that the polarization parameter in ⌳ b →⌳␥ does not depend on the values of hadronic form factors. The energy spectrum of ⌳ in ⌳ b →⌳l ϩ l Ϫ is given. ͓S0556-2821͑99͒02511-4͔

We embed the flipped SU (5) models into the SO(10) models. After the SO(10) gauge symmetry is broken down to the flipped SU (5) × U (1) X gauge symmetry, we can split the five/one-plets and ten-plets in the spinor 16 and 16 Higgs fields via the stable sliding singlet mechanism. As in the flipped SU (5) models, these ten-plet Higgs fields can break the flipped SU (5) gauge symmetry down to the Standard Model gauge symmetry. The doublet-triplet splitting problem can be solved naturally by the missing partner mechanism, and the Higgsino-exchange mediated proton decay can be suppressed elegantly. Moreover, we show that there exists one pair of the light Higgs doublets for the electroweak gauge symmetry breaking. Because there exist two pairs of additional vector-like particles with similar intermediate-scale masses, the SU (5) and U (1) X gauge couplings can be unified at the GUT scale which is reasonably (about one or two orders) higher than the SU (2) L × SU (3) C unification scale. Furthermore, we briefly discuss the simplest SO(10) model with flipped SU (5) embedding, and point out that it can not work without fine-tuning.

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We consider 4-dimensional N = 1 supersymmetric SO(10) models inspired by deconstruction of 5-dimensional N = 1 supersymmetric orbifold SO(10) models and high dimensional nonsupersymmetric SO(10) models with Wilson line gauge symmetry breaking. We discuss the SO(10) × SO(10) models with bi-fundamental link fields where the gauge symmetry can be broken down to the Pati-Salam, SU (5)×U (1), flipped SU (5)×U (1) ′ or the standard model like gauge symmetry. We also propose an SO(10)×SO(6)×SO(4) model with bi-fundamental link fields where the gauge symmetry is broken down to the Pati-Salam gauge symmetry, and an SO(10)×SO(10) model with bi-spinor link fields where the gauge symmetry is broken down to the flipped SU (5) × U (1) ′ gauge symmetry. In these two models, the Pati-Salam and flipped SU (5) × U (1) ′ gauge symmetry can be further broken down to the standard model gauge symmetry, the doublet-triplet splittings can be obtained by the missing partner mechanism, and the proton decay problem can be solved.We also study the gauge coupling unification. We briefly comment on the interesting variation models with gauge groups SO(10) × SO(6) and SO(10) × flipped SU (5) × U (1) ′ in which the proton decay problem can be solved.

The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate their effects for the well known E(6) model. Considering the breaking chains E6 → H = SO(10) × U V ′ (1) → SU (5) × UV (1) × U V ′ (1) → SU (3) × SU (2) × UZ(1) × UV (1) × U V ′ (1) and E6 → H = SO(10) × U V ′ (1) → SU (4) × SUL(2) × SUR(2) × U V ′ (1) → SU (3) × SUL(2) × SUR(2) × US(1) × U V ′ (1), we derive and give all of the Clebsch-Gordan coefficients Φ (r) s,z associated with E6 breaking to the standard model. Physical effects of nonzero vacuum expectations of SM singlets Higgs in E6 grand unified theories are discussed.PACS numbers: 12.10. Dm, 12.10.Kt, Grand unification theories (GUT) are among the most promising models for physics beyond the standard model (SM). Grand unification assumes that the three gauge coupling constants in SM should be unified at a high scale, the unification scale M G , but would be split at low energy due to their different renormalization group evolution from the grand unification scale to low scales. It seems that the assumption is supported by experiments since there is the apparent unification of the measured gauge couplings within the minimal SUSY SM (MSSM) at scale M G ∼ 2 × 10 16GeV [1][2][3][4]. In addition to the GUT scale, one has the Planck scale defined byGeV at which quantum gravity enters [5,6]. It is well-known that the GUT scale M G is smaller than the Planck scale M P l by two orders of magnitude. Therefore, we can investigate unification of particle interactions including effects of gravity in the effective field theory approach. That is, we introduce non-renormalizable higher dimension operators to describe the effects of quantum gravity. They are d ≥ 5 operators which are induced by gravity, enter the Lagrangian scaled by factors Of (M P l ) −(d−4) with order unity coefficients, and are subject only to the constraints of the symmetries (gauge invariance, supersymmetry, etc.) of the low energy theory. The presence of higher-dimensional operators generated at the Planck scale must have impact to GUT and its phenomenology, as has been shown in Refs. [5,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. These operators modify the usual gauge coupling unification condition [7][8][9][10][11][12][13]. They affect analysis of proton decay [5,15,16] and supersymmetric (SUSY) particle spectrum in SUSY GUT and supergravity [17][18][19][20][21][22][23][24]. Therefore, one should consider effects of these higher dimension operators in model building of GUT and SUSY GUT.The effects to the unification of gauge couplings produced by dimension-5 operators which are singlets of the grand unified gauge group G and formed from gauge field strengths G µν and Higgs multiplets H k of Gwhere a,b are group indices and k labels different multiplets, have been examined systematically for G = SU (5), SO(10) in the ref. [25]. In particular, differing from those given before in the literatu...