Particle–antiparticle mixing, image and the unitarity triangle in the littlest Higgs model Original Research Article

We calculate the image–image, image–image mixing mass differences image, image and the CP-violating parameter image in the littlest Higgs (LH) model. For image as low as 5 and the Yukawa parameter image, the enhancement of image amounts to at most 20%. Similar comments apply to image and image. The correction to image is negligible. The dominant new contribution in this parameter range, calculated here for the first time, comes from the box diagrams with (image) exchanges and ordinary quarks that are only suppressed by the mass of image but do not involve explicit image factors. This contribution is strictly positive. The explicit image corrections to the SM diagrams with ordinary quarks and two image exchanges have to be combined with the box diagrams with a single heavy T quark exchange for the GIM mechanism to work. These image corrections are found to be of the same order of magnitude as the (image) contribution but only for image approaching 0.8 they can compete with it. We point out that for image box diagrams with two T exchanges have to be included. Although formally image, this contribution is dominant for image due to non-decoupling of T that becomes fully effective only at this order. We emphasize, that the concept of the unitarity triangle is still useful in the LH model, in spite of the image corrections to the CKM unitarity involving only ordinary quarks. We demonstrate the cancellation of the divergences in box diagrams that appear when one uses the unitary gauge for image and image.