# Examples of mass predictions using running masses

1. Apr 20, 2015

### arivero

Do we have some?

I mean, the typical argument voiced each time that someone tries to fit mass patterns against whatever formula is "you should be using running masses", or more precisely "you should be using all the masses renormalised at the same scale". And indeed it is a very logical requiriment. What I am wondering is, has such requirement been successful any time? It could be useful to be able to provide some working examples when doing this argument.

2. Apr 21, 2015

### kurros

I'm not quite sure what you refer to. Usually you want to use pole masses to compare to experiment, rather than running masses, right? Unless you have some object for which pole masses are badly defined, like the light quarks, due to confinement.

3. Apr 21, 2015

### arivero

I was thinking for instance on the comments on Koide equation, which even for leptons is critiquised on the ground that it does not work for running masses.

Or, a slightly less exotic think, takes Connes' geometrical production of the Standard Model langrangian from curvature. During the derivation he gets some relationship between the sum of fermion masses and the sum of electroweak bosons. Even thinking that it is not a unification model, people asked the equality to be applied in the GUT point with running masses and then try to get low energy predicitons.

I can understand that there is some good argument supporting this requirement.... but has it ever worked sometime, for some theory?

4. Apr 21, 2015

### kurros

Oh I see. Yeah sure, if you are thinking of GUTs then you'd expect some algebraic relationship between running masses, i.e. Lagrangian parameters, to be happening at the GUT scale, or at some symmetry breaking scale or whatever, since the relationship is coming from the group theory, and have only a complicated indirect relationship to the measured particle masses. Has it ever worked? Well, I'd have to check the details, but doesn't something similar happen in electroweak theory? I.e. there is a simple algebraic relationship between the W and Z masses, in terms of the Weinberg angle, or gauge couplings, which comes from the group theory; but these aren't the W and Z pole masses, they are running masses of some kind, since sin(theta_W) is a running parameter (since the gauge couplings are running parameters).

5. Apr 21, 2015

### RGevo

You would use running masses if you were in a renormalisation scheme computing things with running masses.

It's scheme dependent, so you can always just change scheme.

An example of this is extracting the top mass (msbar mass) from the ttbar cross section. Then one can use the known relation between pole and msbar mass to extract a value for the pole mass (at the order the msbar was extracted from the ttbar theory prediction).

If these koide equations don't work for running masses, do they work for pole masses extracted from the running masses? If not, the statement is then they are inconsistent with the renormalised theory I guess...

6. Apr 21, 2015

### arivero

Just to confirm... Do you say that if a equation for masses does not work for the running ones but it still works for the pole masses, it is still consistent with the renormalised theory?

7. Apr 21, 2015

### arivero

Yep, probably this is the best example, or perhaps the only one, of a successful mass prediction from running masses. Still I am not sure because a lot of textbooks refer to "tree-level" when stating the prediction for the quotient of W and Z; and they are so near that a tree level renormalised relation is not easy to distinguish of a plain relationship for pole masses.

8. Apr 22, 2015

### kurros

Yeah that's what I am not super clear on. The PDG has a bit of stuff related to this (http://pdg.lbl.gov/2012/reviews/rpp2012-rev-standard-model.pdf). I am looking near eq. 10.10, here they say:

"The on-shell scheme [63] promotes the tree-level formula sin2 θW = 1 − M2 W /M2 Z to a definition of the renormalized sin2 θW to all orders in perturbation theory"

so I guess it can be considered more than just a tree-level relation, though it is defined that way so maybe this isn't such a deep statement, I'm not sure. I guess sin2 θW is not really so interesting, it is the relationship to the gauge couplings which is more "fundamental". They do talk about that a little later, and it seems the normal formula can also be preserved there, though they use the MSbar scheme rather than on-shell scheme there. Anyway these still can't be pole masses, so I think we can say that these sort of relationships are not expected to occur between pole masses.

9. Apr 26, 2015

### arivero

Hmm, what about see saw? Is the see saw calculated with running masses at the seesaw scale and then neutrino masses are renormalized, run down the slope to the milli-eV? Or are they pole masses already before seesaw?