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1 vote
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How scale invariance is broken in nature?

By definition a system will exhibit scale invariance at low energies if it has an IR fixed point. I am having some doubts on how to interpret this fact in terms of quantum field theory and to ...
AoZora's user avatar
  • 1,914
6 votes
3 answers
1k views

Dressing vs. renormalization

In the past, my understanding was always that the processes of dressing a bare quantity (such as mass or charge) and renormalizing these same properties are different things. Dressing, as far as I ...
Janosh's user avatar
  • 1,294
1 vote
1 answer
422 views

Leading order DGLAP evolution

Consider the leading-order (LO) DGLAP ((Dokshitzer–Gribov–Lipatov–Altarelli–Parisi) equation $$x \mu^2 \frac{d xg(x,\mu^2)}{d\mu^2}= \alpha_s \int_x^1 dz P_{gg}(z) \frac{x}{z} g(\frac{x}{z}, \mu^2) + \...
CAF's user avatar
  • 3,599
1 vote
0 answers
55 views

Possible intermediate scales of baryogenesis?

The conventional beyond Standard Model explanation of baryogenesis is that, within Grand Unified Theories (GUT), there exist some new heavy scalar bosons of mass $M_{\rm GUT}\sim10^{15}$ GeV, which ...
Thomas's user avatar
  • 1,803
4 votes
2 answers
1k views

Why do we have a TeV scale?

When model building we don't want to introduce any new scales into our theory. We usually try to have new particles at the Higgs (TeV) scale (to solve the hierarchy problem), at the GUT scale, or at ...
JeffDror's user avatar
  • 9,005
10 votes
2 answers
2k views

What is the hierarchy problem?

BACKGROUND So far I understood that the hierarchy problem was the large difference between the gravitational scale, $M_{pl}\sim 10^{18}\; [GeV]$, compared with the electroweak scale, $M_{ew}\sim 10^3\...
Dox's user avatar
  • 1,758
8 votes
4 answers
726 views

How can there be a quantum field theory that predicts all particle masses?

Say I have a theory with only one (energy) scale, e.g. one given by the fundamental constants $$\epsilon=\sqrt{\dfrac{\hbar c^5}{G}}.$$ In this case, where I can't compare to something else, is there ...
Nikolaj-K's user avatar
  • 8,693
1 vote
1 answer
166 views

Classical black holes?

How big should the black hole be so we can consider it to be classical? When they claim that we can not probe shorter distances than the Planck length, can it be true? The argument says that, doing ...
Newman's user avatar
  • 2,596
4 votes
2 answers
418 views

Is the form of the Lagrangian relevant before the renormalization procedure?

In the renormalization procedure, is writing things like $$\varphi=\sqrt{Z_{\varphi}}\ \varphi_R\ ,\ \ m_0^2=Z_m\ m_R^2\ ,\ \ g_0=Z_g \mu^{\epsilon}\ g_R$$ and $$Z_i=1+\sum_{\nu=1}^\infty C_i^{(\...
Nikolaj-K's user avatar
  • 8,693