What prevent reaction changing leptons to hadrons?

[ndung200790]

Please teach me this:
What prevent the reaction changing leptons to hadrons and vice versa?.Because both leptons and hadrons are ruled by electro-weak interaction,so why the reaction can not happen?
Thank you very much in advance.

 

[Vanadium 50]

Try and write down a reaction that does this.

 

[humanino]

\pi^\pm\rightarrow\mu^\pm\nu_\mu

 

[Polyrhythmic]

Where did you read that it wasn't possible?

 

[Bill_K]

The Wikipedia page on "Proton decay". It's never been observed, and current experimental limits give a lifetime greater than 10³³ years.

 

[ndung200790]

So,considering electro-weak interaction,the lepton and baryon number conservation is violated?

 

[ndung200790]

And I do not understand why proton can not decay under electro-weak interaction?

 

[Polyrhythmic]

The Wikipedia page on "Proton decay". It's never been observed, and current experimental limits give a lifetime greater than 10³³ years.

True, you can find the experimental data at:
http://pdg.lbl.gov/2011/tables/contents_tables.html .

 

[ndung200790]

I hear that the Standard Model can deduce the lepton and baryon number conservation laws.Is that correct?

 

[ndung200790]

Sorry,now I realize in pion decay process both lepton and baryon number are conservable.

 

[humanino]

The Wikipedia page on "Proton decay". It's never been observed, and current experimental limits give a lifetime greater than 10³³ years.

Then the question should have read "baryon", not "hadron".

 

[humanino]

So,considering electro-weak interaction,the lepton and baryon number conservation is violated?

Mesons have zero hadron number (quark-anti quark pair). The lepton number on the left hand side of the reaction above is also zero (lepton-antilepton).

 

[humanino]

And I do not understand why proton can not decay under electro-weak interaction?

It can, but within the standard model it is a non-perturbative anomaly with exponentially suppressed probability, at least at the current temperature of the universe. Did you read the wikipage
http://en.wikipedia.org/wiki/Proton_decay
?

 

[ndung200790]

Please teach me(sketch) how to demontration the lepton and baryon number conservation laws with Standard Model?

 

[arivero]

Guys, instead of addressing the original poster, what about addressing the original post? I mean, the question is interesting by itself, to write down where Barion and Lepton numbers do appear in the standard model, and how the ungauged quantity upgrades to a gauged one in SU(5), in SO(10) and, differently perhaps, in Pati-Salam.

 

[ndung200790]

So,at Standard Model level of knownledge,the lepton and baryon number conservation laws are based on experiment but not theoretical theory?

 

[arivero]

So,at Standard Model level of knownledge,the lepton and baryon number conservation laws are based on experiment but not theoretical theory?

Well, the SM preserves B and L obviously, in fact Weinberg discuss L explicitly in his fundational paper. When you go up to unified theories you find couplings violation B and L, but amazingly B+L (or B-L) is still preserved. So B violation (aka proton decay) become a warhorse against GUT theories: experiment does not allow for a gauge boson corresponding to B, L related charges.

More intriguingly, Salam and others proved that the putative SU(3)xSU(2)xU(1) symmetry of some 7 differential manifolds do not allow for charges as the standard model, but then Bailin and others hinted that using still an extra dimension solved the problem. And you get GUT groups then. But you are not supposed to have more than 7 extra dimensions, so this addition should not produce a gauge boson.

In any case, if you play some days (or weeks) with the hypercharges of the standard model, eventually you will find that a right isospin plus a B+L number do a better, more aesthetic, play that the SM hypercharge. Try.

 

[kloptok]

So,at Standard Model level of knownledge,the lepton and baryon number conservation laws are based on experiment but not theoretical theory?

As far as I know, yes - conservation of baryon and lepton number is primarily an experimental fact. (Although I would say that basically B and L are introduced just because they are a conserved quantity.)

More precisely, B and/or L conservation is not a gauged symmetry of the Standard Model, and therefore not as profound as for example conservation of electric charge. Therefore future unified theories could allow for B/L violation, as mentioned in previous posts.

 

[ndung200790]

Thank very much all of you.Now I think that by combination color and flavor we can deduce the lepton and baryon number conservation laws, because the weak gauge bosons(that are (1,3) and (1,1)) can not change quark(that are (3,2) and (3,1)) into lepton(that are (1,2) and (1,1)).But in SU(5) theory,the conservation laws are violated,because in this theory there are superheavy gauge bosons(that are (3,2) and (bar3,2)) that permit quark change to lepton.For example (u,d)--->e+(X,Y)(that is (3,2)--->(1,1)x(3,2)).Is that correct?

 

[ndung200790]

I mean in Standard Model,by combination of color and flavor we can deduce the lepton and baryon number conservation laws.

 

[arivero]

I mean in Standard Model,by combination of color and flavor we can deduce the lepton and baryon number conservation laws.

Yep, you can say that no transition in the SM violates lepton nor baryion number. In this sense the SM preserves B, L, but only as global transformations. You mas consider that old practicioners of gauge theory had a kind of lemma "if you find a global symmetry, you must look also for the loal version", and then for them it was very natural to look for locally gauged B+L.

Definitely there is something. Consider the Left-Right model, then you can forget hypercharges and buld the electric charge as a combination of barion number, lepton number, left isospin and right isospin.