/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 Given that each particle contain... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 44: Problem 27

Given that each particle contains only combinations of \(\boldsymbol{u}, \boldsymbol{d}, \boldsymbol{s}, \overline{\boldsymbol{u}}, \overline{\boldsymbol{d}},\) and \(\bar{s},\) use the method of Example 44.7 to deduce the quark content of (a) a particle with charge \(+e,\) baryon number \(0,\) and strangeness \(+1 ;\) (b) a particle with charge \(+e,\) baryon number -1 and strangeness \(+1 ;\) (c) a particle with charge \(0,\) baryon number +1 , and strangeness -2 .

Short Answer

Expert verified
The quark content of the three particles are: (a) \(\bar{d}s\), (b) \(\bar{u}\bar{s}\bar{s}\), and (c) \(us\bar{s}\).

Step by step solution

01

Deduce the Quark Content of the First Particle

For the first particle with charge \(+e\), baryon number \(0\), and strangeness \(+1\), we can deduce its quark content. Because the baryon number is zero, this suggests the particle is a meson, composed of a quark-antiquark pair. In addition, the quark pair needs to generate an overall charge of \(+e\), which is equivalent to \(+1\) natural units of charge. This is achieved by a \(\bar{d}\) anti-down quark which has a charge of \(+\frac{1}{3}\) and a \(s\) strange quark with a charge of \(+\frac{2}{3}\), adding up to \(+1\). The strangeness of \(+1\) can be achieved since a \(\bar{d}\) has strangeness \(0\) and a \(s\) quark has strangeness of \(-1\), which due to the antiquark being \(\bar{s}\), it flips the sign to result in \(+1\). So, the quark content is \(\bar{d}s\).
02

Deduce the Quark Content of the Second Particle

For the second particle with charge \(+e\), baryon number \(-1\), and strangeness \(+1\), this will be an antibaryon since the baryon number is negative. Antiparticles are made of antiquarks, so there will be three antiquarks. Given the properties of the up, down and strange antiquarks, the only way to obtain a charge of \(+e\) is to combine one anti-up quark (\(\bar{u}\)) and two anti-strange quarks (\(\bar{s}\)). These three antiquarks have a total charge of \(+1\) and a baryon number of \(-1\), matching the givens. The strangeness also fits, as the two anti-strange quarks will confer a total strangeness of \(+2\). So, the quark content is \(\bar{u}\bar{s}\bar{s}\).
03

Deduce the Quark Content of the Third Particle

For the third particle with charge \(0\), baryon number \(+1\), and strangeness \(-2\), this will be a baryon since the baryon number is positive. Baryons are composed of three quarks. Given the properties of the up, down and strange quarks, the only way to obtain a charge of \(0\) is to combine an \(u\) quark and two \(s\) quarks. These three quarks have a total charge of \(0\) and a baryon number of \(+1\), matching the givens. The strangeness also fits, as the strange quark confers a strangeness of \(-1\), and there are two of them, giving a total strangeness of \(-2\). So, the quark content is \(us\bar{s}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Particle Physics
Particle physics is the branch of science that studies the basic elements of matter and the forces that govern their interactions. It aims to understand the universe at the smallest scale and energy levels by examining particles like quarks and leptons, the building blocks of the visible universe. These particles are organized under various quantum numbers, such as charge, baryon number, and strangeness, which help identify and predict their behavior in different interactions. The study of particle physics is crucial for advancing our understanding of fundamental physics and phenomena such as cosmology and the early universe.
Baryon Number
The baryon number is a quantum number that helps distinguish between baryons and other particles like mesons and leptons. Baryons are particles composed of three quarks, and they include well-known particles like protons and neutrons. The baryon number is a conserved quantity, meaning it remains constant in isolated systems during particle interactions. Baryons are assigned a baryon number of +1, while antibaryons, which are made of three antiquarks, have a baryon number of -1. Mesons, composed of a quark-antiquark pair, carry a baryon number of 0, reflecting their status as non-baryonic particles.
Strangeness
Strangeness is a quantum number used in particle physics to account for the presence of strange quarks in a particle. It was initially introduced to explain the unusually long lifetimes of certain particles produced in high-energy collisions. In terms of quark composition, a strange quark (\( s \)) has a strangeness value of -1. Conversely, an anti-strange quark (\( \bar{s} \)) has a strangeness of +1. Strangeness is conserved in strong and electromagnetic interactions but not in weak interactions. The conservation or change of strangeness provides insight into the types of processes or interactions a particle may undergo.
Meson
Mesons are one of the basic building blocks studied in particle physics, classified as particles with a baryon number of 0. They are composed of one quark and one antiquark, and their combinations lead to various meson types, possessing different properties such as mass and charge. For example, the kaon is a type of meson that includes strange quarks, allowing for decays signifying the violation of symmetries in fundamental physics. Mesons play a vital role in mediating forces between baryons, particularly in the strong interaction, which is key to understanding how atomic nuclei are held together.
Antibaryon
Antibaryons are the antiparticles of baryons and consist of three antiquarks. These particles have a baryon number of -1, opposite to the baryons' +1. Examples of antibaryons include the antiproton and antineutron. Due to their opposite baryon number, when a baryon meets an antibaryon, they can annihilate each other, producing photons or other particle-antiparticle pairs. The study of antibaryons and their properties helps physicists explore the symmetries of the universe and understand concepts such as matter-antimatter asymmetry, which is significant in explaining why more matter than antimatter exists in the universe today.
Quark-Antiquark Pairs
Quark-antiquark pairs are fundamental constituents in the study of particle physics, particularly in the formation of mesons. A quark-antiquark pair consists of one quark and its corresponding antiquark, which can create a particle with distinct properties based on their type and charge. These pairs are crucial in explaining how mesons behave and interact with other particles. The existence and transformation of quark-antiquark pairs underlie many aspects of the strong nuclear force, the fundamental interaction that holds quarks together within hadrons. Understanding these pairs allows scientists to delve further into the energy and forces at play in the subatomic world.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In which of the following decays are the three lepton numbers conserved? In each case, explain your reasoning. (a) \(\mu^{-} \rightarrow \mathrm{e}^{-}+v_{e}+\bar{v}_{\mu}\) (b) \(\tau^{-} \rightarrow \mathrm{e}^{-}+\bar{\nu}_{e}+\nu_{\tau}\) (c) \(\pi^{+} \rightarrow \mathrm{e}^{+}+\gamma_{i}\) (d) \(\mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\bar{\nu}_{e}\)

What is the energy of each photon produced by positronelectron annihilation? (a) \(\frac{1}{2} m_{e} v^{2},\) where \(v\) is the speed of the emitted positron; (b) \(m_{e} v^{2} ;(c) \frac{1}{2} m_{e} c^{2} ;\) (d) \(m_{e} c^{2}\).

Consider a collision in which a stationary particle with mass \(M\) is bombarded by a particle with mass \(m,\) speed \(t_{0}\). and total energy (including rest cnergy) \(E_{m}\). (a) Use the Lorentz transformation to write the velocities \(v_{m}\) and \(v_{M}\) of particles \(m\) and \(M\) in terms of the speed \(v_{\mathrm{cm}}\) of the center of momentum. (b) Use the fact that the total momentum in the center-of-momentum frame is zero to obtain an expression for \(v_{\mathrm{cm}}\) in terms of \(m, M,\) and \(v_{0}\). (c) Combine the results of parts (a) and (b) to obtain Eq. (44.9) for the total energy in the center-of- momentum frame.

The 7 TeV proton bunches that circulate in opposite directions around the \(27 \mathrm{~km}\) ring of the Large Hadron Collider smash together at beam crossings every 25 ns. (a) How many bunches mect every second? (b) Each bunch has 115 billion protons. Of these, typically 20 collide during each crossing. Estimate the fraction of protons that collide per crossing. (c) Estimate how many collisions take place each second. (d) The bunches are \(30 \mathrm{~cm}\) long and are squeezed to a diameter of \(20 \mu \mathrm{m}\). Estimate the density of protons in a bunch, in units of protons/mm \(^{3}\). (c) Estimate the density of hadrons in ordinary matter. (Hint: Divide your mass, which is mostly due to hadrons, by the mass of a proton to get the number of hadrons in your body. Then divide by the estimated volume.)

The strong nuclear force can be crudely modeled as a Hooke's-law spring force, increasing linearly with the quark scparation distance. The energy stored in this "spring" corresponds to the energy content of the gluon field. In this picture, as quarks are further separated, increasing energy is stored between them. At a critical separation distance, the energy converts to matter, and a new quark-antiquark pair is generated, guaranteeing that there can never be a free quark. (a) A proton has a diameter of about \(1.5 \mathrm{fm}\). Fstimate the repulsive Coulomb force between two up quarks separated by \(0.5 \mathrm{fm}\). (b) Model the strong force as \(F_{\mathrm{s}}=k s,\) where \(s\) is the distance between two quarks. If this force balances the electrostatic repulsion between two up quarks when \(s=0.5 \mathrm{fm},\) what is the effective spring constant \(k,\) in \(\mathrm{SI}\) units? (c) Convert \(k\) into units of \(\mathrm{MeV} / \mathrm{fm}^{2}\). (d) How much energy is stored in the gluon field when \(s=0.5 \mathrm{fm} ?\) The mass of an up quark is thought to be about \(2.3 \mathrm{MeV} / \mathrm{c}^{2}\). (e) How much energy is needed to produce an up quark and an antiup quark? (f) How far would two up quarks need to be separated so that the gluon energy \(\frac{1}{2} k s^{2}\) matches the rest energy of an up-antiup quark pair?
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Space Physics

Read Explanation

Scientific Method Physics

Read Explanation

Electrostatics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.