331 model predictions for rare B and K decays, and ∆F = 2 processes: an update
Andrzej J. Buras, Fulvia De Fazio
Abstract
A bstract Motivated by the improved results from the HPQCD lattice collaboration on the hadronic matrix elements entering ∆ M s , d in $$ {B}_{s,d}^0-{\overline{B}}_{s,d}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> </mml:math> mixings and the increase of the experimental branching ratio for B s → μ + μ − , we update our 2016 analysis of various flavour observables in four 331 models, M1, M3, M13 and M16 based on the gauge group SU(3) C × SU(3) L × U(1) X . These four models, which are distinguished by the quantum numbers, are selected among 24 331 models through their consistency with the electroweak precision tests and simultaneously by the relation $$ {C}_9^{\textrm{NP}}=-{bC}_{10}^{\textrm{NP}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mn>9</mml:mn> <mml:mi>NP</mml:mi> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mi>bC</mml:mi> <mml:mn>10</mml:mn> <mml:mi>NP</mml:mi> </mml:msubsup> </mml:math> with 2 ≤ b ≤ 5, which after new result on B s → μ + μ − from CMS is favoured over the popular relation $$ {C}_9^{\textrm{NP}}=-{C}_{10}^{\textrm{NP}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mn>9</mml:mn> <mml:mi>NP</mml:mi> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mn>10</mml:mn> <mml:mi>NP</mml:mi> </mml:msubsup> </mml:math> predicted by several leptoquark models. In this context we investigate in particular the dependence of various observables on | V cb |, varying it in the broad range [0 . 0386, 0 . 043], that encompasses both its inclusive and exclusive determinations. Imposing the experimental constraints from ε K , ∆ M s , ∆ M d and the mixing induced CP asymmetries $$ {S}_{\psi {K}_S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>ψ</mml:mi> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> and $$ {S}_{\psi {K}_S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>ψ</mml:mi> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> , we investigate for which values of | V cb | the four models can be made compatible with these data and what is the impact on B and K branching ratios. In particular we analyse NP contributions to the Wilson coefficients C 9 and C 10 and the decays B s , d → μ + μ − , $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mi>ν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mi>ν</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . This allows us to illustrate how the value of | V cb | determined together with other parameters of these models is infected by NP contributions and compare it with the one obtained recently under the assumption of the absence of NP in ε K , ∆ M s , ∆ M d and $$ {S}_{\psi {K}_S} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>ψ</mml:mi> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> .