There are particles called bottom mesons or \({\rm{B}}\)-mesons. One of them is the \({{\rm{B}}^{\rm{ - }}}\)meson, which has a single negative charge; its baryon number is zero, as are its strangeness, charm, and topness. It has a bottomness of \({\rm{ - 1}}\). What is its quark configuration?

Short Answer

Expert verified

The quark configuration of the \({\rm{B - }}\)meson particle is \({B^ - } = \left( {b\bar u} \right)\).

Step by step solution

01

Concept Introduction

Mesons are hadronic subatomic particles made up of an equal number of quarks and antiquarks, generally one of each, and linked together by strong interactions in particle physics.

A quark is a basic ingredient of matter and a sort of elementary particle.

Antiquarks are the antiparticles that correspond to each flavour of quark.

02

Quantum numbers for \({{\rm{B}}^{\rm{ - }}}\)

Find the quark compositions for\({{\rm{B}}^{\rm{ - }}}\)given that all its quantum numbers as follows –

\({\rm{B}}\)

\({\rm{Q}}\)

\({\rm{S}}\)

\({\rm{t}}\)

\({\rm{b}}\)

\({\rm{c}}\)

\({{\rm{B}}^{\rm{ - }}}\)

\({\rm{0}}\)

\({\rm{ - 1}}\)

\({\rm{0}}\)

\({\rm{0}}\)

\({\rm{ - 1}}\)

\({\rm{0}}\)

03

Quark configuration for \({{\rm{B}}^{\rm{ - }}}\)

Now, find its quark configuration –

Since \({{\rm{B}}^{\rm{ - }}}\) is a meson. Thus, it consists of quark and anti-quark.

\({B^ - } = \left( {q\bar q} \right)\)

Since it has a bottomness of \(b = - 1\) Therefore, the quark is the bottom \({\rm{b}}\).

\({B^ - } = \left( {b\bar q} \right)\)

Since its charge is \({\rm{ - 1}}\) and the charge of the bottom quark is \({\rm{ - 1/3}}\). Thus, an anti-quark with charge \({\rm{ - 2/3}}\) is needed. The options available are – \({\rm{\bar u,\bar c,}}\) and \({\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftarrow$}} \over t} }}\).

Since its topness and charm are zero. Therefore,\({\rm{\bar c,}}\)and \({\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftarrow$}} \over t} }}\) cannot be considered.

Hence, the quark configuration for the \({\rm{B}}\)-meson \({{\rm{B}}^{\rm{ - }}}\) is –

\({B^ - } = \left( {b\bar u} \right)\)

Therefore, the quark configuration is obtained as \({B^ - } = \left( {b\bar u} \right)\).

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Most popular questions from this chapter

Plans for an accelerator that produces a secondary beam of \({\rm{K}}\)-mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of \({\rm{500 MeV}}\).

(a) What would the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/{\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) be for these particles?

(b) How long would their average lifetime be in the laboratory?

(c) How far could they travel in this time?

Another component of the strong nuclear force is transmitted by the exchange of virtual \[{\rm{K - }}\]mesons. Taking \[{\rm{K - }}\]-mesons to have an average mass of \[{\rm{495}}\;{\rm{MeV/}}{{\rm{c}}^{\rm{2}}}\], what is the approximate range of this component of the strong force?

How can the lifetime of a particle indicate that its decay is caused by the strong nuclear force? How can a change in strangeness imply which force is responsible for a reaction? What does a change in quark flavor imply about the force that is responsible?

How can quarks, which are fermions, combine to form bosons? Why must an even number combine to form a boson? Give one example by stating the quark substructure of a boson.

(a) Show that the conjectured decay of the proton, \({\rm{p}} \to {\pi ^{\rm{0}}}{\rm{ + }}{{\rm{e}}^{\rm{ + }}}\), violates conservation of baryon number and conservation of lepton number.

(b) What is the analogous decay process for the antiproton?

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