# Tag Info

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To be a little pedantic, nobody has yet done precision spectroscopy of antihydrogen, though the recent success in trapping it at CERN (all over the news this week, paper here) is an early step toward that. It's possible that there are small differences in the spectrum of antihydrogen and hydrogen, though these differences can't be all that large, or they ...

14

Dear Chad, you misinterpret the statement that "the known sources of CP-violation are not enough to explain the matter-antimatter asymmetry in the Universe." You seem to think that the statement means that the known CP-violating parameter (namely the CP-violating phase in the CKM matrix) and the processes based on it are qualitatively insufficient to ...

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Good question! Regarding (2) baryon number is certainly violated at Planckian energies. If you can make a black hole, you can eat up baryons. Luboš Motl's argument that you linked to is correct in this regard. Whether you can make a believable scenario of quantum gravity driven baryogenesis at the Planck time is up in the air as far as I know. It's the old ...

5

It is a non-perturbative effect because it is 1-loop exact. The triangle diagram is actually the least insightful method to think about this, in my opinion. The core of the matter is the anomaly of the chiral symmetry, which you can also, for example, calculate by the Fujikawa method examining the change of the path integral measure under the chiral ...

5

We calculate the free energy (density) for the Higgs field $\phi$ at finite temperature. In the Standard Model, this looks like $\mathcal{F}_{SM}(\phi,T) = -\frac{\pi^2}{90}g_* T^4+V_{SM}(\phi, T) \ ,$ where $g_*$ is the number of degrees of freedom in the SM ($g_*=106.75$). The potential has the form $V_{SM}(\phi,T) = D(T^2-T_0^2)\phi^2 - ... 5 Matter and anti-matter behave in the same way with respect to electromagnetic interactions, so we could not distinguish the two by electromagnetic observations. It was mentioned in the other reply that annihilation from the contact of matter with antimatter would produce a signature gamma radiation that would be easily observable. That is true, but things ... 5 The LHC depends in large measure on it's huge luminosity for its usefulness. Making anti-proton beams is hard, and making them at high luminosity is harder still. While there are advantages to$p\bar{p}$, they are not overwhelming and the luminosity issue drives all. 4 The sphaleron is kind of the opposite of the instanton, and kind of the same. Let's make that statement precise: An instanton is a local minimum of the action that mediates vacuum tunneling (link to an answer of mine how and why instantons do that). The sphaleron sits in-between the vacua, in a certain sense, it is the instanton "in the middle of ... 4 In principle, the number density of photons include all photons, both of cosmic origin (e.g. the CMB) and of astrophysical origin (starlight, gamma-rays from GRBs, radio waves from QSOs, etc.). However, most of these photons are CMB photons, as seen from this figure (from Lacasa 2014): The second largest contribution to the photon density are the cosmic ... 4 Every Speck of matter in the world has its anti form basically that we have antimatter whenever we have matter. This is not exact; in theory any form of matter can have its corresponding form of antimatter, but the universe we live in is predominantly made up of matter. This is an experimental observation because when matter meets antimatter there is a ... 4 Yes, you can observe elastic proton-anti-proton scattering. Indeed, the cross section is not all that different from that of elastic proton-proton scattering. The main difference is that$pp$is predominantly elastic at low energy, and dominantly inelastic at high energy, whereas$p\bar{p}$is dominantly inelastic at all energies. Also note that inelastic ... 4 To achieve a nonzero baryon asymmetry, one needs to satisfy the so-called Sakharov conditions: Baryon$B$violation C-symmetry violation and CP-symmetry violation Interactions out of thermal equilibrium If at least one of these "asymmetries" or "imbalances" is missing, the total$B$of the Universe will remain zero. The Standard Model preserves$B$... 3 Leaving out numerical factors, we have that $$\mathrm{d}j_A = \mathrm{Tr}(F \wedge F)$$ This already shows that we are dealing with a topological quantity, since the RHS is the second Chern character of the gauge field (or rather, the principal bundle associated to it). Now, there is also the (3D) Chern-Simons form $$\omega = \mathrm{Tr}(F \wedge A - ... 3 The interconversion of matter and energy is described by quantum field theory. If you're interested the question What keeps mass from turning into energy? is on this subject. The particular quantum field theory that describes our universe is called the Standard Model, and there are three important symmetries that apply to the standard model - charge ... 3 I'd like to point out that there is a small probability that the assumption on which the question is based: "As I hope is obvious to everyone reading this, the universe contains more matter than antimatter," may not be true, depending on the result of the Aegis experiment at CERN. That's because, as Professor Orzel stated in his answer to this ... 3 Recreating the conditions of the early universe is a popular explanation, not an exact statement of what is happening at the LHC. It was never the primary goal of the LHC to produce anything similar to conditions in the early universe. To whatever extent it does so, that's just a side benefit of the searches for the Higgs boson and supersymmetry. Besides, ... 2 The only source of asymmetry in the Standard Model is from CP violation, and although there is CP violation in the Standard Model it is not large enough to account for the observed asymmetry. It's expected that the asymmetry will be explained by some extension to the standard model, but at the moment we don't know which, if any, of the suggested extensions ... 2 In reply to the second partenthetical question, I wrote that matter created from energy in particle physics experiments is "generally" in the form of particle-antiparticle pairs . This is too restrictive. Quantum numbers have to be conserved, and they are conserved in pair production, but there can also be associated production of mesons etc: For example ... 2 The most common explanation for the "matter-antimatter asymmetry of the Universe" is \rm CP violation in interactions involving leptons. This scenario is usually called leptogenesis because it generates a net excess of leptons compared to anti-leptons. This \rm CP violation is currently unconfirmed by experiment (though there is also not yet any evidence ... 2 I always consider that condition as kinda "orthogonal" to the first two. Thermal equilibrium means Boltzmann distribution. And we also have CPT requiring m_a=m_\bar{a}. And the two straightforwardly lead you back to the a v.s. \bar{a} symmetry. That consideration even leads you to the conclusion that you could even start from B-asymmetric ... 2 The common hypothesis supposes that there is a slight asymetry in a transformation (i.e., slightly more likely in one direction than the other), which is called the "violating CP symmetry" (occuring in the weak interaction). See wikipedia "baryon asymmetry" and "CP violation". 2 1) Nobody knows. It's one of the major unsolved problems in physics today. Our best guess is that it is not true that antimatter is "just the opposite"--probably there is some slight asymmetry between them. But we haven't really found what it is yet, or at least haven't found anything that explains the discrepancy. Despite the huge difference in the modern ... 2 In the Standard Model, the baryon and lepton number are accidental global symmetries. However, they are conserved only at the classical level: quantum corrections do not respect them, i.e., they are anomalous. The interesting thing is that they are violated by exactly the same amount. In terms of currents we write:$$\partial_\mu J_B^\mu=\partial_\mu ... 1$C$stands for charge. Charge symmetry implies that if the charge of all particles were to be inverted - particles become anti-particles and viceversa - the universe would look exactly the same. A universe made of matter would be indistinguishable from one made of antimatter. So if a given process allows for two matter particles (say, a proton and a ... 1 Within the standard model: It cannot! Even though there is CP violation in the SM (as you state), the amount is not enough to give the ratio of$ \frac{n_B}{n_\gamma} \sim 10^{-10} \ .$Furthermore, the electroweak phase transition (EWPT) in the SM is not even a second order transition, but merely a crossover. In order to render the transition ... 1 It would help if you would cite the corresponding sentence, argument or explanation of the book. Nevertheless, I will try to answer your question. I think this paper by Y. Burnier, M. Laine and M. Shaposhnikov might be of interest to you. The change in baryon number at time$t$is proportional to the net baryon number at$t$:$\dot{B}(t)\sim -B(t)+ ...

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When right handed neutrinos are introduced, they imply $L$ violation through their Majorana nature. Their decay into lepton and Higgs doublets $$N\,\longrightarrow l\,\Phi^\dagger$$ violates the lepton number (since $N$ has zero lepton number being Majorana). These decays take place out of thermal equilibrium, therefore a net lepton asymmetry is produced. ...

1

I will try to give an answer, that contradicts a little my comment. I did not do any calculations, but I don't think that sphaleron processes have any influence here, since this should not only hold at very high temperatures. (BTW: this is the partial answer to one of your questions on how leptogenesis can lead to baryogenesis) Through the seesaw mechanism, ...

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Let's define $T_{EW}$ the temperature where the coefficient $m^2_H(T)$ of the operator $H^2$ in the SM lagrangian vanishes: $$m_H^2(T=T_{EW})=0\,.$$ For $T>T_{EW}$ the Higgs vev is vanishing, the EW symmetry in unbroken, and the elementary particles are massless. For $T<T_{EW}$ the the vev is non-vanishing, $v_T\propto -m_H^2/\lambda\neq 0$, the EW ...

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