Seesaw at the LHC Xiao-Gang He CHEP, PUK and CTS, NTU 1. Theoretical models for small neutrino masses 2. Type II seesaw at the LHC 3. Type I and III: Small light and heavy neutrino mixing at the LHC 4. New possibility for Type-I and III seesaw at LHC 5. Model realization for large light and heavy mixing 6. Conclusions

1. Theoretical models for small neutrino masses

Some theoretical models for neutrino masses Loop generated neutrino masses: The Zee Model (Zee, PLB, 1980) Add: h (1,1)(1) scalar (a,b)(c) SU(3)xSU(2)xU(1) numbers Replace one Higgs double by two: phi^{1,2} No tree level neutrino mass term! At one loop:

Simplest Zee model: f_2 = 0 Ruled out by present data. (X. -G Simplest Zee model: f_2 = 0 Ruled out by present data. (X.-G. He, EPJC, 2003) With f_2 non-zero. Can be consistent with data.

2. Type II Seesaw at the LHC P. ~Fileviez Perez et al 2. Type II Seesaw at the LHC P.~Fileviez Perez et al., Type-II [arXiv:0805.3536 [hep-ph]];

Del Aguila and Aguilar-Saavedra

P. Perez et al.

3. Type I and III: Small light and heavy neutrino mixing at the LHC What LHC can do for neutrino physics? A lot. One of them is to probe heavy degree of freedom in models producing neutrino masses and mixing. Production of new particles, the most direct test! T.~Han and B.~Zhang, Heavy neutrino t LHC [arXiv:hep-ph/0604064]; M. Nebot et al., Zee Model arXiv:0711.0483 [hep-ph]]. R.~Franceschini et al.,Type-III [arXiv:0805.1613 [hep-ph]]. F.~del Aguila etal., Type I, II, III [arXiv:0808.2468 [hep-ph]]. A.~Arhrib et al.,Type I+III Seesaw, arXiv:0904.2390 [hep-ph]; W.~Chao et al., Type I +II [arXiv:0804.1265 [hep-ph]]; X.-G. He et al., Type I and III, arXiv: 0908.1607[hep-ph] X.-G. He and Ernest Ma, arXiv:0907.2737[hep-ph] T. Li and X.-G. He., Type III, arXiv:0907.4193[hep-ph].

Some features about Type I and III Seesaw Models

Type-I seesaw at LHC

V_{lN} ~ (m_\nu/m_N)^{1/2} < 10^{-6} for one generation. Too small!

There are exceptions to the “general solution”

Even with small V_{lN} Type-III seesaw can be tested at the LHC Tong Li and Xiao-Gang He, arXiv:0907.4193[hep-ph]

4. New possibility for Type-I and III seesaw at LHC X. -G. He et al 4. New possibility for Type-I and III seesaw at LHC X.-G. He et al., arXiv:0907.1607[hep-ph]

Some sample solutions

For U_{\nu U} of order 0.03, the cross section can be as large as 1 fb for m_N up to 150 GeV. Not hopelessly small!

5. Model realization for large light and heavy mixing X. -G. He and E 5. Model realization for large light and heavy mixing X.-G. He and E. Ma, arXiv:0907.2737[hep-ph]

6. Conclusions One can have theoretical models in which the elements in U_{\nu N} can be as large as a few percent. For the single N (Type-I, III) and E (Type-III) production, the cross section can be as large as 1 fb with masses as heavy as 150 GeV. No displaced vertex in the large mixing case. Decay pattern very different from the small mixing solutions discussed earlier. For Type III seesaw, heavy leptons can be probed up to 1 TeV at the LHC. There are chances that underlying theory for neutrino mass and mixing be tested at the LHC. Plus other new experiments on neutrinos going to operation soon, more information about neutrinos will come.

An exciting LHC era is ahead of us! Other interesting things related to neutrino physics Neutrino properties may also hold the key to many cosmological problems, such as leptogenesis can explain why our universe is matter dominated one. If through seesaw models, the heavy neutrinos can be a slow as TeV scale. More flavor physics: mu -> e gamma, mu -> eee, e - \mu conversion Neutrino oscillations, mass measurement s: Dirac or Majorana, CPV or CPC …… Much can be done with other facilities too. Together with LHC An exciting LHC era is ahead of us!