TY - JOUR

T1 - Particle-antiparticle mixing, εK and the unitarity triangle in the littlest Higgs model

AU - Buras, Andrzej J.

AU - Poschenrieder, Anton

AU - Uhlig, Selma

N1 - Funding Information:
We would like to thank Thorsten Ewerth, Wolfgang Hollik, Heather Logan and Felix Schwab for useful discussions. Special thanks go to an unknown referee of the first version of our paper who asked us to explain the non-decoupling of T at . This led us to reconsider our calculation of the function S and to include the box diagrams with two T exchanges. In this context we thank also Andreas Weiler for useful discussions. The work presented here was supported in part by the German Bundesministerium für Bildung und Forschung under the contract 05HT4WOA/3 and by the German–Israeli Foundation under the contract G-698-22.7/2002.

PY - 2005/6/6

Y1 - 2005/6/6

N2 - We calculate the K 0 - K0, Bd,s0 - Bd,s0 mixing mass differences ΔMK, ΔMd,s and the CP-violating parameter xL in the littlest Higgs (LH) model. For f/v as low as 5 and the Yukawa < 0.8, the enhancement of ΔMd amounts to at most 20%. Similar comments apply to ΔMs and εK. The correction to ΔMK is negligible. The dominant new contribution in this parameter range, calculated here for the first time, comes from the box diagrams with (WL±, WH±) exchanges and ordinary quarks that are only suppressed by the mass of WH± but do not involve explicit O(v2/f2) factors. This contribution is strictly positive. The explicit O(v2 f2) corrections to the SM diagrams with ordinary quarks and two WL± exchanges have to be combined with the box diagrams with a single heavy T quark exchange for the GIM mechanism to work. These O(v2/f2) corrections are found to be of the same order of magnitude as the (WL± WH±) contribution but only for xL; approaching 0.8 they can compete with it. We point out that for xK 0.85 box diagrams with two T exchanges have to be included. Although formally O (v4 f4), this contribution is dominant for xL ≈ 1 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 O (v2/f2) 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 WL± and WH±.

AB - We calculate the K 0 - K0, Bd,s0 - Bd,s0 mixing mass differences ΔMK, ΔMd,s and the CP-violating parameter xL in the littlest Higgs (LH) model. For f/v as low as 5 and the Yukawa < 0.8, the enhancement of ΔMd amounts to at most 20%. Similar comments apply to ΔMs and εK. The correction to ΔMK is negligible. The dominant new contribution in this parameter range, calculated here for the first time, comes from the box diagrams with (WL±, WH±) exchanges and ordinary quarks that are only suppressed by the mass of WH± but do not involve explicit O(v2/f2) factors. This contribution is strictly positive. The explicit O(v2 f2) corrections to the SM diagrams with ordinary quarks and two WL± exchanges have to be combined with the box diagrams with a single heavy T quark exchange for the GIM mechanism to work. These O(v2/f2) corrections are found to be of the same order of magnitude as the (WL± WH±) contribution but only for xL; approaching 0.8 they can compete with it. We point out that for xK 0.85 box diagrams with two T exchanges have to be included. Although formally O (v4 f4), this contribution is dominant for xL ≈ 1 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 O (v2/f2) 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 WL± and WH±.

UR - http://www.scopus.com/inward/record.url?scp=18444375893&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2005.03.022

DO - 10.1016/j.nuclphysb.2005.03.022

M3 - Article

AN - SCOPUS:18444375893

SN - 0550-3213

VL - 716

SP - 173

EP - 198

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1-2

ER -