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Acionamento de Máquinas Elétricas
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1.11 The Standard Model (1978 – ?) 57 1.5 The same formula applies to the mesons (with Σ → π, Λ → η, etc.), except that in this case, for reasons that remain something of a mystery, you must use the squares of the masses. Use this to 'predict' the mass of the η. How close do you come? 1.6 The mass formula for decuplets is much simpler — equal spacing between the rows: mΔ − mΣ* = mΣ* − mΞ* = mΞ* − mΩ Use this formula (as Gell-Mann did) to predict the mass of the Ω−. (Use the average of the first two spacings to estimate the third.) How close is your prediction to the observed value? 1.7 (a) Members of the baryon decuplet typically decay after 10−23 seconds into a lighter baryon (from the baryon octet) and a meson (from the pseudo-scalar meson octet). Thus, for example, Δ++ → p+ + π+. List all decay modes of this form for the Δ−, Σ*, and Ξ*−. Remember that these decays must conserve charge and strangeness (they are strong interactions). (b) In any decay, there must be sufficient mass in the original particle to cover the masses of the decay products. (There may be more than enough; the extra will be 'soaked up' in the form of kinetic energy in the final state.) Check each of the decays you proposed in part (a) to see which ones meet this criterion. The others are kinematically forbidden. 1.8 (a) Analyze the possible decay modes of the Ω−, just as you did in Problem 1.7 for the Δ, Σ*, and Ξ*−. See the problem? Gell-Mann predicted that the Ω− would be 'metastable' (i.e., much longer lived than the other members of the decuplet), for precisely this reason. (The Ω− does in fact decay, but by the much slower weak interaction, which does not conserve strangeness.) (b) From the bubble chamber photograph (Figure 1.9), measure the length of the Ω− track, and use this to estimate the lifetime of the Ω−. (Of course, you don't know how fast it was going, but it's a safe bet that the speed was less than the velocity of light; let's say it was going about 0.1c. Also, you don’t know if the reproduction has enlarged or shrunk the scale, but never mind: this is quibbling over factors of 2, or 5, or maybe even 10. The important point is that the lifetime is many orders of magnitude longer than the 10−23 seconds characteristic of all other members of the decuplet). 1.9 Check the Coleman-Glashow relation [Phys. Rev. B134, 671 (1964)]: Σ+ - Σ- = p - n + Ξ0 - Ξ- (the particle names stand for their masses). 1.10 Look up the table of ‘known’ mesons compiled by Roos, M. (1963) Reviews of Modern Physics, 35, 314, and compare the current Particle Physics Booklet to determine which of the 1963 mesons have stood the test of time. (Some of the names have been changed, so you will have to work from other properties, such as mass, charge, strangeness, etc.) 1.11 Of the spurious particles you identified in Problem 1.10, which are ‘exotic’ (i.e., inconsistent with the quark model)? How many of the surviving mesons are exotic? 1.12 How many different meson combinations can you make with 1, 2, 3, 4, 5, or 6 different quark flavors? What’s the general formula for n flavors? 1.13 How many different baryon combinations can you make with 1, 2, 3, 4, 5, or 6 different quark flavors? What’s the general formula for n flavors? 1.14 Using four quarks (u, d, s, and c), construct a table of all the possible baryon species. How many combinations carry a charm of +1? How many carry charm +2, and +3? 1.15 Same as Problem 1.14, but this time for mesons. 1.16 Assuming the top quark is too short-lived to form bound states (‘truthful’ mesons and baryons), list the 15 distinct meson combinations qq̅ (not counting antiparticles) and the 35 distinct baryon combinations qqq. From the Particle Physics Booklet and/or other sources, determine which of these have been found experimentally. Give their name, mass, and year of discovery (just the lightest one, in each case). Thus, for instance, one baryon entry would be sss : Ω-, 1672 MeV/c², 1964. All hadrons are (presumably) various excitations of these 50 quark combinations. 1.17 A. De Rujula, H. Georgi, and S. L. Glashow [Physical Review, D12, 147 (1975)] estimated the so-called constituent quark masses* to be: mu ≈ md = 336 MeV/c², ms = 540 MeV/c², and mc = 1500 MeV/c² (the bottom quark is about 4500 MeV/c²). If they are right, the average binding energy for members of the baryon octet is ≈62 MeV. If they all had exactly this binding energy, what would their masses be? Compare the actual values and give the percent error. (Don’t try this on the other supermultiplets, however. There really is no reason to suppose that the binding energy is the same for all members of the group. The problem of hadron masses is a thorny issue, to which we shall return in Chapter 5.) 1.18 Shupe, M. (1979) [Physics Letters, 8GB, 87] proposed that all quarks and leptons are composed of two even more elementary constituents: ς (with charge –1/3) and η (with charge zero) – and their respective antiparticles, ς̅ and η̅. You’re allowed to combine them in groups of three particles or three antiparticles (ςςη, for example, or η̅η̅η̅). Construct all of the eight quarks and leptons in the first generation in this manner. (The other generations are supposed to be excited states.) Notice that each of the quark states admits three possible permutations (ςςη, ςης, ηςς, for example) – these correspond to the three colors. Mediators can be constructed from three particles plus three antiparticles. W+, Z0, and γ involve three like particles and three like antiparticles (W- = ςςς̅̅̅̅η̅η̅, for example). Construct W+, Z0, and γ in this way. Gluons involve mixed combinations (ςςη̅η̅ζ̅, for instance). How many possibilities are there in all? Can you think of any way to reduce this down to eight? 1.19 Your roommate is a chemistry major. She knows all about protons, neutrons, and electrons, and she sees them in action every day in the laboratory. But she is skeptical when you tell her about positrons, muons, neutrinos, pions, quarks, and intermediate vector bosons. Explain to her why none of these plays any direct role in chemistry. (For instance, in the case of the muon a reasonable answer might be ‘They are unstable, and last only a millionth of a second before disintegrating.’) * For reasons we will come to in due course, the effective mass of a quark bound inside a hadron is not the same as the ‘bare’ mass of the ‘free’ quark.
Envie sua pergunta para a IA e receba a resposta na hora
Texto de pré-visualização
1.11 The Standard Model (1978 – ?) 57 1.5 The same formula applies to the mesons (with Σ → π, Λ → η, etc.), except that in this case, for reasons that remain something of a mystery, you must use the squares of the masses. Use this to 'predict' the mass of the η. How close do you come? 1.6 The mass formula for decuplets is much simpler — equal spacing between the rows: mΔ − mΣ* = mΣ* − mΞ* = mΞ* − mΩ Use this formula (as Gell-Mann did) to predict the mass of the Ω−. (Use the average of the first two spacings to estimate the third.) How close is your prediction to the observed value? 1.7 (a) Members of the baryon decuplet typically decay after 10−23 seconds into a lighter baryon (from the baryon octet) and a meson (from the pseudo-scalar meson octet). Thus, for example, Δ++ → p+ + π+. List all decay modes of this form for the Δ−, Σ*, and Ξ*−. Remember that these decays must conserve charge and strangeness (they are strong interactions). (b) In any decay, there must be sufficient mass in the original particle to cover the masses of the decay products. (There may be more than enough; the extra will be 'soaked up' in the form of kinetic energy in the final state.) Check each of the decays you proposed in part (a) to see which ones meet this criterion. The others are kinematically forbidden. 1.8 (a) Analyze the possible decay modes of the Ω−, just as you did in Problem 1.7 for the Δ, Σ*, and Ξ*−. See the problem? Gell-Mann predicted that the Ω− would be 'metastable' (i.e., much longer lived than the other members of the decuplet), for precisely this reason. (The Ω− does in fact decay, but by the much slower weak interaction, which does not conserve strangeness.) (b) From the bubble chamber photograph (Figure 1.9), measure the length of the Ω− track, and use this to estimate the lifetime of the Ω−. (Of course, you don't know how fast it was going, but it's a safe bet that the speed was less than the velocity of light; let's say it was going about 0.1c. Also, you don’t know if the reproduction has enlarged or shrunk the scale, but never mind: this is quibbling over factors of 2, or 5, or maybe even 10. The important point is that the lifetime is many orders of magnitude longer than the 10−23 seconds characteristic of all other members of the decuplet). 1.9 Check the Coleman-Glashow relation [Phys. Rev. B134, 671 (1964)]: Σ+ - Σ- = p - n + Ξ0 - Ξ- (the particle names stand for their masses). 1.10 Look up the table of ‘known’ mesons compiled by Roos, M. (1963) Reviews of Modern Physics, 35, 314, and compare the current Particle Physics Booklet to determine which of the 1963 mesons have stood the test of time. (Some of the names have been changed, so you will have to work from other properties, such as mass, charge, strangeness, etc.) 1.11 Of the spurious particles you identified in Problem 1.10, which are ‘exotic’ (i.e., inconsistent with the quark model)? How many of the surviving mesons are exotic? 1.12 How many different meson combinations can you make with 1, 2, 3, 4, 5, or 6 different quark flavors? What’s the general formula for n flavors? 1.13 How many different baryon combinations can you make with 1, 2, 3, 4, 5, or 6 different quark flavors? What’s the general formula for n flavors? 1.14 Using four quarks (u, d, s, and c), construct a table of all the possible baryon species. How many combinations carry a charm of +1? How many carry charm +2, and +3? 1.15 Same as Problem 1.14, but this time for mesons. 1.16 Assuming the top quark is too short-lived to form bound states (‘truthful’ mesons and baryons), list the 15 distinct meson combinations qq̅ (not counting antiparticles) and the 35 distinct baryon combinations qqq. From the Particle Physics Booklet and/or other sources, determine which of these have been found experimentally. Give their name, mass, and year of discovery (just the lightest one, in each case). Thus, for instance, one baryon entry would be sss : Ω-, 1672 MeV/c², 1964. All hadrons are (presumably) various excitations of these 50 quark combinations. 1.17 A. De Rujula, H. Georgi, and S. L. Glashow [Physical Review, D12, 147 (1975)] estimated the so-called constituent quark masses* to be: mu ≈ md = 336 MeV/c², ms = 540 MeV/c², and mc = 1500 MeV/c² (the bottom quark is about 4500 MeV/c²). If they are right, the average binding energy for members of the baryon octet is ≈62 MeV. If they all had exactly this binding energy, what would their masses be? Compare the actual values and give the percent error. (Don’t try this on the other supermultiplets, however. There really is no reason to suppose that the binding energy is the same for all members of the group. The problem of hadron masses is a thorny issue, to which we shall return in Chapter 5.) 1.18 Shupe, M. (1979) [Physics Letters, 8GB, 87] proposed that all quarks and leptons are composed of two even more elementary constituents: ς (with charge –1/3) and η (with charge zero) – and their respective antiparticles, ς̅ and η̅. You’re allowed to combine them in groups of three particles or three antiparticles (ςςη, for example, or η̅η̅η̅). Construct all of the eight quarks and leptons in the first generation in this manner. (The other generations are supposed to be excited states.) Notice that each of the quark states admits three possible permutations (ςςη, ςης, ηςς, for example) – these correspond to the three colors. Mediators can be constructed from three particles plus three antiparticles. W+, Z0, and γ involve three like particles and three like antiparticles (W- = ςςς̅̅̅̅η̅η̅, for example). Construct W+, Z0, and γ in this way. Gluons involve mixed combinations (ςςη̅η̅ζ̅, for instance). How many possibilities are there in all? Can you think of any way to reduce this down to eight? 1.19 Your roommate is a chemistry major. She knows all about protons, neutrons, and electrons, and she sees them in action every day in the laboratory. But she is skeptical when you tell her about positrons, muons, neutrinos, pions, quarks, and intermediate vector bosons. Explain to her why none of these plays any direct role in chemistry. (For instance, in the case of the muon a reasonable answer might be ‘They are unstable, and last only a millionth of a second before disintegrating.’) * For reasons we will come to in due course, the effective mass of a quark bound inside a hadron is not the same as the ‘bare’ mass of the ‘free’ quark.