Sreerup Raychaudhuri TIFR

Transcription

1 The Boson in the Model Sreerup Raychaudhuri TIFR

2 What everyone knows

3 What everyone knows Electroweak interactions are very accurately described by a local SU(2) U(1) gauge theory The gauge symmetry does not permit the gauge bosons to have masses, which would make the weak interaction long-range Parity violation does not permit the fermions to have masses Masses for gauge bosons and fermions are generated by spontaneous symmetry-breaking in a scalar sector with tachyonic masses In the unitary gauge, the massless scalars are absorbed as the longitudinal modes of the gauge bosons; there remains one massive scalar, called the Higgs boson

4 What we now know from experiment New particle which decays to and ZZ boson (spin 0,2)

5 It has a mass around GeV This is not inconsistent with a SM Higgs boson

6 Signal strength measurements μ = N ex (H XX ) N SM (H XX ) = L σ ex (pp H) B ex (H XX ) L σ SM (pp H) B SM (H XX )

7 Signal strength measurements μ = N ex (H XX ) N SM (H XX ) = L σ ex (pp H) B ex (H XX ) L σ SM (pp H) B SM (H XX )

8 Landau-Yang theorem

9 Yukawa couplings should be proportional to the fermion mass Giardino et al, arxiv: This is consistent with these masses arising from SSB

10 "If it looks like a duck, walks like a duck, and quacks like a duck, then it probably is a duck." Senator Joseph McCarthy (1952)

11 "If it looks like a duck, walks like a duck, and quacks like a duck, then it probably is a duck." Senator Joseph McCarthy (1952) "But, what kind of duck is it? What are the ideological underpinnings of the duck? What are the operational imperatives of the duck? Is the duck a cat in disguise? Does the duck/cat have allies? What are the rules of engagement for duck/cats? Do duck feathers change? Dean Rose

12 What theorists think of this discovery It is not unreasonable to assume that this particle is the Higgs boson of the Standard Model, especially since we have no empirical evidence to the contrary...

13 If it is a Higgs boson, we will automatically have perturbative unitarity in WW scattering at high energies Cheung, Kingman et al. Phys. Rev. D78 (2008) Higgsless models are no longer required......though there is still space for heavy vector resonances

14 The scalar potential is now known exactly

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16 Nature seems to like interactions (other than gravity) to be weak at high energies...

17 Some people like to speculate even further...

18 Some people like to speculate even further...

19 The Curious Case of the Scalar Potential

20 The whole edifice of symmetry-breaking has been built on the assumption that the scalar potential has multiple degenerate stable vacua... The origin of these vacua lie in the assumption of a tachyonic mass scale, which is responsible for creating all the masses

21 Coleman and Weinberg (1973) V(Φ) = μ 2 Φ Φ + λ Φ Φ 2 μ is the only mass scale in the entire SM If we drop the μ term, the SM has scale invariance conformal invariance But then, all the particles will remain massless...

22 Coleman and Weinberg (1973) V(Φ) = μ 2 Φ Φ + λ Φ Φ 2 μ is the only mass scale in the entire SM If we drop the μ term, the SM has scale invariance conformal invariance But then, all the particles will remain massless... So what? In QCD, the quarks and gluons could well be massless But the bulk of the observable mass in the Universe comes from hadron masses, i.e. from the QCD scale, a Landau pole generated by quantum corrections to the QCD Lagrangian Could the masses in the electroweak sector also arise from quantum corrections to the scalar potential?

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25 Coleman-Weinberg effective potential V(φ 2 0 ) = λ 4 φ Bφ 4 0 log φ 0 2 M 2 Extremise: V 2 φ = φ 0 2 λ B + 2B log φ 2 0 M 2 = 0 Maximum at φ 0 2 = 0 Minimum at φ 2 0 = M 2 e 1 λ 1 2 2B 2 = m CW This is the typical symmetry-breaking (Ginzburg-Landau) form with degenerate vacua for φ 0 = M CW

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28 Abandon scale invariance: let μ exist as a fundamental scale

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30 Nature seems to prefer triviality to conformal invariance

31 If λ = 0, the potential has no minimum This would be catastrophic!

32 Why would it be catastrophic? Suppose we get λ = 0 at a scale of (say) GeV Even though the Universe is now at a temperature of around GeV, there exists a tiny probability that it could develop a bubble of GeV somewhere, perhaps in some years... Such a bubble would mean super-intense radiation and hence its neighbourhood would also get heated above GeV, i.e. the bubble would expand at the speed of light fiery death of the Universe

33 Why would it be catastrophic? Suppose we get λ = 0 at a scale of (say) GeV Even though the Universe is now at a temperature of around GeV, there exists a tiny probability that it could develop a bubble of GeV somewhere, perhaps in some years... Such a bubble would mean super-intense radiation and hence its neighbourhood would also get heated above GeV, i.e. the bubble would expand at the speed of light fiery death of the Universe Far away galaxy? UHE cosmic rays Early Universe

34 It may not be a catastrophe for the Universe, but it is certainly a catastrophe for the Higgs boson...

35 Rescue options: Planck scale Metastability New physics Perhaps the value of λ goes negative only above the Planck scale... Perhaps radiative corrections to the potential create a deeper minimum (the true vacuum)... Perhaps the running of λ is different once we go beyond the electroweak scale

36 Perhaps the value of λ < 0 only above the Planck scale...

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39 Perhaps the best way to get a reliable measurement of the top quark mass is from the cross-section measurement, since this is well defined in perturbation theory However, the cross-section has large errors at LHC, principally due to PDF errors... This would be the best we can get even by 2030 Thus, we may have to wait for the ILC to resolve this issue Long wait!

40 Perhaps radiative corrections to the potential create a deeper minimum (the true vacuum)... V(φ 2 0 ) = μ2 2 φ λ 4 φ Bφ 4 0 log φ 0 2 M 2

41 We would require the lifetime for tunnelling between the false vacuum and the true vacuum to be greater than the age of the Universe (13.8 bn years)

42 Perhaps the running of λ is different once we go beyond the electroweak scale There is some new physics at a scale Λ, well below the triviality point where the running of the self-coupling λ changes such that it ceases to fall monotonically... This scale Λ then acts as a cutoff for the SM But then we would have a hierarchy problem... Which requires to be cured by more new physics

43 Hierarchy problem

44 Hierarchy problem Solutions: reduce Λ to a TeV cancel the Λ 2 terms

45 Curiouser and curiouser : the problem of dark energy

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49 Summary The Higgs mechanism in the Standard Model solves many problems at one go We have found a new particle whose properties nicely match the Higgs boson of the Standard Model A light Higgs boson (perhaps) creates a problem with stability of the vacuum, to say nothing of dark energy This may or may not require new physics; if so, we might have to solve a hierarchy problem. This would then require us to have more new physics The present data does not tell us anything for sure

50 "Raffiniert ist der Herrgott, aber boshaft ist er nicht"