# Electroweak stars, nonconservation of baryon and lepton number

1. Apr 3, 2010

### bcrowell

Staff Emeritus
"Electroweak stars: how nature may capitalize on the standard model's ultimate fuel," De-Chang Dai, Arthur Lue, Glenn Starkman, Dejan Stojkovic, http://arxiv.org/abs/0912.0520

Pretty far out, and I'm not sure I believe it. One thing that surprises me is that they claim the standard model has a loophole allowing nonconservation of baryon number and lepton number. Some info: http://en.wikipedia.org/wiki/Chiral_anomaly How well accepted is this, and if it's correct, why can't it be detected in laboratory experiments?

Quark stars and strange stars are already pretty hard to make definite predictions about, and have not been clearly confirmed empirically. Seems like going one step beyond that means building on an already-shaky foundation.

2. Apr 4, 2010

### Haelfix

"One thing that surprises me is that they claim the standard model has a loophole allowing nonconservation of baryon number and lepton number."

T' Hooft showed a long time ago that there are processes that violate B and L with just the simple standard model matter content, however these phenomena are nonperturbative and by consequence highly suppressed. One of the game's in things like Baryogenesis and Leptogenesis model building is to somehow unsuppress them

3. Apr 4, 2010

### bcrowell

Staff Emeritus

What makes it impossible to detect this in the laboratory using current technology?

4. Apr 4, 2010

### Haelfix

Naive nonperturbative calculations on these instanton like effects (arising from the U(1) electroweak anomaly) implies that it is unlikely that a single baryon has ever decayed via these electroweak processes in vacuum and violated B number in the entire observable universe, so small is the effect.

It was later understood that related high temperature physics could catalyze some of these instanton transitions (which we now call sphaleron induced decay at high T) and make them more likely.

Anyway, current experiment has never found a single source of B or L violation in the lab, so this remains theoretical in nature and bounds exist on the magnitude.

Still we know that by the observed asymmetry between matter and antimatter, something has to produce sufficient B number violation, most likely in the early high temperature phase of the early universe, and well we have a ready made mechanism staring at us in the face, ergo many models incorporate this feature.

5. Apr 4, 2010

### bcrowell

Staff Emeritus

Hmm...isn't it also just possible that the universe has always had the baryon number it currently has? I don't see any reason to assume that it had to have B=0 before some specific time.

6. Apr 4, 2010

### Haelfix

It is a theorem by Sakharov (independantly rediscovered by Susskind) that in order to generate matter-antimatter asymmetry (which is an observed effect), you have to have at least some physics at some scale that violates baryon number.

Now no one knows exactly what physics that corresponds to, but you can make educated guesses.

For instance, many GUT theories violate B directly (instead conserving say B-L or B+L) and they are often invoked as plausible mechanisms.

7. Apr 4, 2010

### blechman

of course it's possible, but not very satisfying. in "big bang/inflationary cosmology" all matter and antimatter were created with equal amounts. FRW evolution of the universe would then imply that most of this matter and antimatter annihilates, leaving nothing behind. To assume otherwise would require some pretty crazy tuning, and since "big bang/inflationary cosmology" does a good job explaining things like WMAP, nucleosynthesis and (to some extent) structure formation, you have a hard time of justifying this complication!

those theorems assume "big bang/inflation cosmo" -- you can drop those assumptions if you wish, and all bets are off.

of course, you might be labeled a "crackpot" if you're not careful...

8. Apr 4, 2010

### Orion1

Conservation of baryon number...

The paper cites a proton decay lifetime of $$\tau = 10^{141} \; \text{years}$$.
All current data to date indicates that baryon number is absolutely conserved and that the proton is absolutely stable.

To date, all attempts to observe proton decay events have failed. Recent experiments at the Super-Kamiokande water Cherenkov_radiation detector in Japan give a lower limit of the proton decay_half-life of $$T_{1/2} = 6.6 \cdot 10^{33} \; \text{years}$$ and lifetime $$\tau = 9.5 \cdot 10^{33} \; \text{years}$$.

The paper cites the core temperate of the model greater than or equal to the electroweak symmetry restoration temperature:
$$T_c \geq 100 \; \text{Gev} \; \; \; (1.161 \cdot 10^{15} \; \text{K})$$.

Red giant core temperature:
$$T_c = 1.25 \; \text{to} \; 8.61 \; \text{kev} \; \; \; (1.45 \cdot 10^7 \; \text{to} \; 1 \cdot 10^{8} \; \text{K})$$

An electroweak star at $$1.3 M_{\odot}$$ with a neutrino mass-energy luminosity releasing $$1 M_{\odot}$$ per second would only have a lifetime of 1.3 seconds.

Without a matter + anti-matter burning core, the current universe is simply not energetic enough for a star to enter such a high energy and exotic phase in its stellar evolution and no current scientific data to date can substantiate its existence at all.

The baryon number is nearly conserved in all the interactions of the Standard Model. 'Conserved' means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. An exception is the chiral anomaly. However, sphalerons are not all that common. Electroweak sphalerons can only change the baryon number by 3.

The still hypothetical idea of grand unified theory allows for the changing of a baryon into several leptons (see B − L), thus violating the conservation of baryon and lepton number. Proton decay would be an example of such a process taking place.

GUT theories place matter + anti-matter asymmetry at $$T = 10^{14} \; \text{GeV}$$, which is far too energetic for a matter + anti-matter burning star or stellar evolution, or a supernova explosion.

Has any chiral anomaly ever been detected in any scientific experiment?

Reference:
http://en.wikipedia.org/wiki/Red_giant#Stellar_Evolution"
http://en.wikipedia.org/wiki/Baryon_number" [Broken]
http://en.wikipedia.org/wiki/Chiral_anomaly" [Broken]
http://en.wikipedia.org/wiki/Proton_decay" [Broken]
http://en.wikipedia.org/wiki/Grand_unified_theory" [Broken]
http://arxiv.org/abs/0912.0520" [Broken]

Last edited by a moderator: May 4, 2017
9. Apr 4, 2010

### blechman

Re: Conservation of baryon number...

$\pi^0\rightarrow\gamma\gamma$ is the canonical experimental verification of the chiral anomaly, but no EW instanton transition has been seen to my knowledge.

10. Apr 4, 2010

### bcrowell

Staff Emeritus
I'm not following you here. What are the assumptions of the theorem? By "generate," do you mean to get a nonzero B starting from a zero B at some earlier time? That would make the theorem trivial...?

Does something bad happen to inflation if the total baryon number of the universe is simply nonzero and constant for all time? If you just do standard FRW cosmology without inflation, I don't think anything bad happens if you simply have a nonzero and constant baryon number. In the inflationary epoch, isn't the universe radiation-dominated anyway, so that baryons are more or less irrelevant?

11. Apr 4, 2010

### Haelfix

I'm not quite sure how to put this without getting too technical, b/c the exact story is quite complicated.

The problem is if the laws of physics in the early universe don't have some sort of way to generate an asymmetry between matter and antimatter, you are going to run into the mother of all finetuning problems.

Let us postulate 10^9 more electrons than positrons as an initial condition (I believe that is close to what the current ratio is) as well as to assume exact standard model physics and nothing else (exact baryon number conservation etc).

Now, several effects are happening. One, the electrons and the positrons are going to annihilate, releasing energy into the vacuum. Two, high energy photons (CMB photons) are going to be spitting out positron-electron pairs, but recall, in a ratio that is exactly 1-1 by hypothesis.
Those two effects combined are going to preferentially change the initial conditions and number count into something closer to a 1-1 ratio. If you wait long enough, indeed that will happen.

But then its not that simple. The universe will be expanding, and not necessarily in thermal equilibrium everywhere. So you can imagine that some regions freeze out their particle production, before they can generate 1-1 ratios, leaving the observed relic density. But notice how unstable the situation is, especially if you include a bout of inflation and reheating in the mix. You essentially have to go all the way back to the preinflationary epoch, and tune your initial conditions exquisitively so that you generate the results as measured today. Tiny little changes in those initial conditions (think decimal places) can lead to situations where there is either no antimatter or altogether too much, life couldn't exist and so forth.

Thats not satisfying theoretically, ergo the need for a physics way to create an asymmetry and the discussion above follows.

(Fyi: i've dumbed this down a lot, in order to not talk about CP violation, phase changes of the universe, mass scales and decay pathways etc, why you need departures from thermal equilibrium and so forth, but the general gist survives)

Last edited: Apr 4, 2010
12. Apr 4, 2010

### blechman

Sakharov proposed three conditions that are required to GENERATE a baryon-antibaryon asymmetry after inflation when the universe was thought to be matter-antimatter symmetric (see Haefix's post). These conditions were (in no particular order):

1. CP violating interactions in the early universe.
2. Baryon number violating interactions in the early universe.
3. Nonequilibrium ("first order phase transition") in the early universe.

Now: (1) happens in the SM in the form of the CKM phase, but the phase is too small to describe the asymmetry we see today. (2) happens in the form of these anomalies, but this too is probably too small, although there is hope depending on how much tuning you are willing to tolerate. (3) also happens - the breaking of EW symmetry to electromagetism is a first order transition, but it turns out that it's not "first-order enough!" Roughly speaking, there is not enough "latent heat" in the phase transition to generate the asymmetry we see today.

Moral: baryogenesis is still a very open question, and likely involves "new physics" we don't know about yet! [MY research!!]

I couldn't have said it better than Haelfix's last post!

13. Apr 4, 2010

### blechman

Re: Conservation of baryon number...

what "event"?! the paper is MATH - the LHC will not see sphalerons!

14. Apr 5, 2010

### Orion1

Re: Conservation of baryon number...

As with any exotic particle with a brief lifetime, the LHC will not detect sphalerons directly, however they can be inferred from their decay products.

By 'event' I mean chiral anomalies from pion decay:
$$\pi^0 \to \gamma \gamma$$
$$\pi^0 \to e^+e^- \gamma$$

From which chiral anomaly instanton and sphaleron occurrences or 'events' can be inferred.

The existence of an electroweak star is very improbable in the known universe, however it is more probable for the existence of stars composed entirely of leptonic matter and antimatter.

An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang-Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in nonabelian gauge theory. An instanton can be used to calculate the transition probability for a quantum mechanical particle tunneling through a potential barrier.

A sphaleron is a static (time independent) solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton number. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative. Geometrically, a sphaleron is simply a saddle point of the electroweak potential_energy (in the infinite dimensional field space), much like the saddle point of the surface $z = x^2 - y^2$ in three dimensional analytic geometry.

In the standard model, baryon number violating processes convert three baryons to three antileptons, and related processes. This violates conservation of baryon number and lepton number, but the difference B−L is conserved. A sphaleron is similar to the midpoint (τ = 0) of the instanton, so it is non-perturbative. This means that under normal conditions sphalerons are unobservably rare. However, they would have been more common at the higher temperatures of the early universe. In some theories of baryogenesis an imbalance of the number of leptons and antileptons is formed first by leptogenesis and sphaleron transitions then convert this to an imbalance in the numbers of baryons and antibaryons.

If the difference B−L is conserved at GUT temperature scales with the inclusion of matter + antimatter asymmetry, and the observable baryonic universe is primarily baryonic matter mass predominated, then the observable universe should also have a resultant leptonic antimatter mass dominant influence to compensate for the missing baryonic anti-matter and asymmetric inclusion?

Reference:
http://en.wikipedia.org/wiki/Instanton" [Broken]
http://en.wikipedia.org/wiki/Sphaleron" [Broken]

Last edited by a moderator: May 4, 2017
15. Apr 5, 2010

### humanino

Re: Conservation of baryon number...

I have observed millions of the first one (and world data may be billions, possibly thousands of billions) and thousands of the second one. Those are pretty well established. Maybe I misunderstand.

They involve neither instanton nor sphaleron.

Also, it is pretty well accepted that instantons do occur in QCD, including the cold QCD involve in our body structure. There are many instanton based models which are used everyday and do quite a decent job.

16. Apr 5, 2010

### Orion1

Chiral anomalies from pion decay:
$$\pi^0 \to \gamma \gamma$$
$$\pi^0 \to e^+ e^- \gamma$$

A chiral anomaly is the anomalous nonconservation of a chiral current. In some theories of fermions with a chiral symmetry, the_quantization may lead to the breaking of this (global) chiral symmetry. In that case, the charge associated with the chiral symmetry is not conserved.

The non-conservation happens in a tunneling process from one vacuum to another. Such a process is called instanton. In the case of a symmetry related to the conservation of a fermionic particle number, one may understand the creation of such particles as follows. The definition of a particle is different in the two vacuum states between which the tunneling occurs; therefore a state of no particles in one vacuum corresponds to a state with some particles in the other vacuum.

In particular, there is a Dirac sea of fermions and when such a tunneling happens, it causes the energy levels of the sea fermions to gradually shift upwards for the particles and downwards for the anti-particles, or vice versa. This means particles which once belonged to the Dirac sea become real (positive energy) particles and particle creation happens.

A chiral phenomenon is one that is not identical to its mirror image. The spin of a particle may be used to define a handedness (aka chirality) for that particle. A symmetry transformation between the two is called parity. The action of parity acting on a Dirac fermion is called chiral symmetry.

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. A chiral object and its mirror image are said to be enantiomorphs.

Reference:
http://en.wikipedia.org/wiki/Chirality_%28mathematics%29" [Broken]
http://en.wikipedia.org/wiki/Chirality_%28physics%29" [Broken]
http://en.wikipedia.org/wiki/Chiral_anomaly" [Broken]
http://en.wikipedia.org/wiki/Enantiomorph" [Broken]

#### Attached Files:

File size:
1.9 KB
Views:
145
• ###### CA02.JPG
File size:
1.9 KB
Views:
131
Last edited by a moderator: May 4, 2017
17. Apr 5, 2010

### humanino

I fail to see how this lecturing is relevant to answer my question. To me, the dynamical breaking of chiral symmetry in QCD is not the same as the one relevant to this discussion (physically not the same, although mathematically similar). The matter-antimatter asymmetry is not explained by neutral pion decay. This was already in blechman post

18. Apr 5, 2010

### Frame Dragger

Why has no one asked him why he feels the need to post in blue, and why has no one correlated that choice with a certain lack of... humility, and a "lecture mode". I find that print in bold-face, colours, etc... tends to be aiming for emphasis and importance that cannot be found in the CONTENT.

Or to put it another way, this is the pretty binders you used to use for little projects at school... hoping to get a "+" after that letter grade. :tongue:

Finally... he is paraphrasing wikipedia, which could imply that he has little knowledge of his own, or that he is overreaching.

I would take all of this into consideration when dealing with anomolies of all kinds, physical and personal.

@Orion1: Thanks for the lectures Dr. Feynman, now would you care to to answer the question asked?