$$U(1)_{B_3-L_2}$$ explanation of the neutral current $$B-$$anomalies
B. C. Allanach
Abstract
Abstract We investigate a speculative short-distance force, proposed to explain discrepancies observed between measurements of certain neutral current decays of B hadrons and their Standard Model predictions. The force derives from a spontaneously broken, gauged $$U(1)_{B_3-L_2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> extension to the Standard Model, where the extra quantum numbers of Standard Model fields are given by third family baryon number minus second family lepton number. The only fields beyond those of the Standard Model are three right-handed neutrinos, a gauge field associated with $$U(1)_{B_3-L_2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and a Standard Model singlet complex scalar which breaks $$U(1)_{B_3-L_2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , a ‘flavon’. This simple model, via interactions involving a TeV scale force-carrying $$Z^\prime $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> vector boson, can successfully explain the neutral current $$B-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> anomalies whilst accommodating other empirical constraints. In an ansatz for fermion mixing, a combination of up-to-date $$B-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> anomaly fits, LHC direct $$Z^\prime $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> search limits and other bounds rule out the domain 0.15 $$\hbox {TeV}< M_{Z^\prime }<$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>TeV</mml:mtext> <mml:mo><</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> <mml:mo><</mml:mo> </mml:mrow> </mml:math> 1.9 TeV at the $$95\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>95</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> confidence level. For more massive $$Z^\prime $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> s, the model possesses a flavonstrahlung signal, where pp collisions produce a $$Z^\prime $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> and a flavon, which subsequently decays into two Higgs bosons.