M. Nemevsek - Neutrino Mass and the LHC

1. Neutrino mass and the LHC Miha Nemevšek ICTP, Trieste with Maiezza, Melfo, Nesti, Senjanović, Tello, Vissani and Zhang Balkan Workshop 2011, Donji Milanovac

2. LHC a neutrino machine? Neutrino mass is an experimentally established fact for BSM physics. Might as well be @ TeV (hierarchy) A phenomenological hint may already be here

3. Neutrino mass and BSM Facts Questions 2 ∆mS,A & θA,S,13 Mass scale & hierarchy At least two massive light CP phases neutrinos Dirac or Majorana LHC may play a crucial role Low-high energy interplay becomes important The theory of neutrino mass?

4. Origin of mν Standard Model νL only, mν = 0 h h y2v2 Effective theory OW =y ⇒ mν = Λ Λ High scale TeV Typical in GUTs Theory: GUT remnant Indirect, LHC of little use Phenomenological Neutrino mass and the LHC

5. UV completions of OW Renormalizable theory = seesaw scenarios Fermionic singlet Bosonic triplet Fermionic triplet I II III h h h h h h ∆ ν S ν ν T0 ν ν ν Type I+III Triplet predicted at TeV by a minimal SU(5) with 24F Neutrino mass matrix through decays Bajc, Senjanović ’06 Oscillations-collider connection Bajc, MN, Senjanović ’07

6. UV completions of OW Fermionic singlet Bosonic triplet Fermionic triplet I II III h h h h h h ∆ ν S ν ν T0 ν ν ν Type I+II Predicted by a minimal LR symmetric theory Singlet is gauged, type I required by anomalies Triplet breaks the LR symmetry - type II May need to be light →

7. Left-Right symmetry νL νR , WL ↔ , WR eL eR Parity restoration at high scales Pati, Salam ’74 Mohapatra, Pati ’75 Spontaneously broken Mohapatra, Senjanović ’75 Minkowski ’77 Origin of the seesaw mechanism Senjanović ’79 Senjanović, Mohapatra ’80

8. Minimal LR Model SU (2)L × SU (2)R × U (1)B−L LR symmetric Higgs sector, parity invariant L Φ(2, 2, 0), ∆L (3, 1, 2), ∆R (1, 3, 2) First stage @ TeV Second stage @ 100 GeV 0 0 v1 0 ∆R = Φ = vR 0 0 v2 eiα ∆L ≡ vL = 0 vL = λ v 2 /vR Breaks SU (2)R and Lepton number MW ∝ v ≡ 2 2 v1 + v2 , mD ∝ v MWR = g vR , mN = y vR

9. Mass spectra ˜ ˜ LY = L (YΦ Φ + YΦ Φ) R + T L Y∆L ∆L L + T R Y∆R ∆R R + h.c. Dirac terms Majorana terms MD = v1 YΦ + v2 e ˜ YΦ , MνR −iα = vR Y∆R M = iα ˜ v2 e YΦ + v1 YΦ MνL T = vL Y∆L − MD MνR MD −1 C: YΦ = YΦ T , Y∆L,R = Y∆R,L ∗ Mass eigenstate basis † ∗ † ∗ † M =U Lm U R, MνL = UνL mν UνL , MνR = UνR mN UνR ∗ C:U L = UR

10. The Interactions g New Gauge: Lcc = √ νL VL † W ¯ / L ¯ † / + νR VR W R R 2 T ++ New Scalar: L∆++ = eR Y ∆R eR g ∗ † Y = VR mN VR MWR ∗ Flavor ﬁxed in type II: VR = VL Remember; two angles, one limit, no phases

11. The Interactions g New Gauge: Lcc = √ νL VL † W ¯ / L ¯ † / + νR VR W R R 2 T ++ New Scalar: L∆++ = eR Y ∆R eR g ∗ † Y = VR mN VR MWR Flavor ﬁxed in type II: VR = oL ly! ∗ Vn xam ple E Remember; two angles, one limit, no phases LHC could eventually measure these

12. Bounds on the LR scale Theoretical bounds since ’81 Beall et al. ’81...Zhang et al. ’07 A recent detailed study, including CP violation Maiezza, Nesti, MN, Senjanović ’10 C : MWR > 2.5 TeV P : MWR > 3.2 − 4.2 TeV Direct searches Dijets MWR > 1.51 TeV CMS 1107.4771 Light neutrino MWR > 2.27 TeV CMS PAS EXO-11-024 LHC is here! L ≈ 2.5 fb −1

13. Left-Right @ LHC Most interesting channel: l l j j Keung, Senjanović ’83 LNV at colliders p WR i Gauge production: s-channel, VR iα p Nα W nearly on-shell VR jα j Clean, no missing energy WR j Reconstructs W and N masses j Information on the ﬂavor

14. Limits from the LHC MN, Nesti, Senjanović, Zhang ’11 1000 1.64` 1000 1.64` 800 800 D0: dijets 2 D0: dijets 2 GeV 3 GeV 600 600 4 4 3 MNΜ MN 400 400 200 200 1 L 33.2pb L 34pb 1 0 0 800 1000 1200 1400 1600 1800 800 1000 1200 1400 1600 1800 March MWR GeV MWR GeV High N inaccessible due to jets, low N due to isolation This year: L = 0.1(1) fb −1 : MWR > 1.6(2.2) TeV Electron and muon channel essentially the same

15. Limits from the LHC CMS PAS EXO-11-002 MN, Nesti, Senjanović, Zhang ’11 CMS Preliminary CMS Preliminary MNe [GeV] MNµ [GeV] MNe > MWR 240 pb-1 at 7 TeV 1.64` MNµ > MWR 240 pb-1 at 7 TeV 1200 1000 Observed 1200 1000 Observed 1.64` Expected Expected 800 800 D0: dijets 1000 1000 2 D0: dijets 2 GeV 3 GeV 600 600 4 4 3 800 800 MNΜ MN 400 400 200 600 600 200 1 L 33.2pb L 34pb 1 Excluded by Tevatron Excluded by Tevatron 0 0 800 1000 1200 1400 1600 1800 400 400 800 1000 1200 1400 1600 1800 March MWR GeV MWR GeV 200 200 High N inaccessible due to jets, low N due to isolation 0 0 This year: L = 0.1(1) fb 800 1000 1200 1400 1600 −1 : MWR > 1.6(2.2) TeV 800 1000 1200 1400 1600 July MWR [GeV] MWR [GeV] Electron and muon channel essentially the same

16. Low/high energy interplay Majorana mass term dominance ∗ MνR = vR Y MνL = vL Y Implications for masses and mixings ∗ ∗ mN ∝ mν UνR = UνL ⇒ VR = VL mN 2 2 − mN 1 2 mν2 2 − mν1 2 Hierarchy probe = ±0.03 mN 3 2 − mN 1 2 mν3 2 − mν1 2 @ LHC i mN i mcosm = ∆m2 A , Cosmo-oscillations |mN3 2 − m2 2 | N -LHC link

17. 0ν2β and cosmology 1.01 Majorana mass implies 0ν2β Vissani ’99 0.1 0.1 inverted Gerda, Cuore, Majorana,... |mee| in eV 0.01 0.01 Review by Rodejohann ’11 normal ν Claim of observation 10−3 0.001 |mν | ee 0.4 eV 10−4 −4 10 4 4 Klapdor-Kleingrothaus ’06, ’09 10 10 0.001 0.001 0.01 0.01 0.1 0.1 1 1 lightest neutrino mass in eV

18. 0ν2β and cosmology 1.01 Cosmological bounds mν < 0.17 eV 0.1 0.1 inverted Seljak et al. ’06 |mee| in eV WMAP alone 0.01 0.01 normal ν mν < 0.44 eV 10−3 0.001 Hannestad et al. ’10 10−4 −4 10 4 4 If conﬁrmed, a hint for NP 10 10 0.001 0.001 0.01 0.01 0.1 0.1 1 1 Vissani ’02 lightest neutrino mass in eV

19. New Diagrams for 0ν2β Mohapatra, Senjanović ’81 n p n p n p WR W WR VR eα e e e (YL )ee (YR )ee WR Nα VR eα e vL ∆L ∆L e vR ∆R ∆R e W WR WR n p n p n p ∝ 1/mN ∝ mν ∝ mN Large? Tiny Subdominant? In agreement with cosmology?

20. 0ν2β : the new contribution e LR mixings small e e e ;N ´L;R sin ξ < MW /MWR < 10 −3 c WL;R WL;R WL;R WL;R mD 0 A A A A A A ZX Z`1 X Z`2 X ZX Z`1 X Z`2 X 4 2 2 1 2 mN j MW µ c HNP = GF VR ej + 4 JRµ JR eR eR mN j m2∆ MWR Type II: VR = VL ∗ ∆L suppressed: mν /m∆ 1 LFV: mN /m∆R < 1 The gauge contribution is dominant

21. 0ν2β : the total contribution LHC accessible regime ee 2 |mν+N | ≡ lightest mN in GeV ee 2 ee 2 1. 1.0 1 10 100 400 500 |mν | + |mN | 0.5 Interference small normal inverted |mee | in eV 0.1 Reversed role of 0.05 hierarchies ν +N 0.01 No tension with 0.005 MWR = 3.5 TeV cosmology largest mN = 0.5 TeV 10−3 0.001 −4 A light mN < MWR 10 4 10 0.001 0.001 0.01 0.01 0.1 1 lightest neutrino mass in eV No cancellations

22. LHC and 0ν2β Suppose NP is a must for 0ν2β ; θ13 0 α = 2(ϕ2 − ϕ1 ) ee 2 2 iα 2 2 |Mν+N | = |mν1 cos θ12 + mν2 e sin θ12 | + 4 2 2 MW 1 2 1 iα 2 p 4 cos θ12 + e sin θ12 MWR mN 1 mN 2

23. LHC and 0ν2β Suppose NP is a must for 0ν2β ; θ13 0 α = 2(ϕ2 − ϕ1 ) 1000 1000 1000 1000 Normal Hierarchy Normal Hierarchy 500 MWR = 3.5TeV, α = 0 500 500 MWR = 3.5TeV, α = π 500 ee ee |Mν+N | |Mν+N | 200 200 200 200 mN1 in GeV mN1 in GeV 0.05 ee 2 2 0.05 iα 2 2 |Mν+N | = |mν1 cos θ12 + m e 100 100 100 ν2 100 sin θ12 | + 0.1 0.1 50 50 4 50 50 2 0.2 2 MW 1 2 1 0.2iα 2 20 20 p0.4 4 cos θ12 + 20 0.4 sin θ12 20 e MWR mN 1 mN 2 10 10 0.6 10 10 0.6 1.0 1.0 55 5 5 10−4 0.0001 0.001 0.001 0.01 0.01 0.1 0.1 1 1 10−4 0.0001 0.001 0.001 0.01 0.01 0.1 0.1 1 1 lightest neutrino mass in eV lightest neutrino mass in eV jj : mN 50 GeV v : mN / 20 GeV LHC: j : mN 20 GeV / E : mN 3 − 7 GeV

24. LHC and 0ν2β Suppose NP is a must for 0ν2β ; θ13 0 α = 2(ϕ2 − ϕ1 ) 1000 1000 1000 1000 1000 1000 Inverted Hierarchy 1000 1000 Normal Hierarchy Inverted Hierarchy Normal Hierarchy 500 MWR = 3.5TeV, α = 0 500 500 500 3.5TeV, α = 0 500 MWR = 3.5TeV, α = π 500 MWR = 3.5TeV, α = π 500 500 ee |Mν+N | ee ee |Mν+N | |Mν+N | 200 200 200 0.05 200 200 200 200 mN1 in GeV 200 mN in GeV mN1 in GeV mN11 in GeV 0.05 ee 2 2 0.05 iα 2 2 |M 100 100 100 0.1 ν+N | = |mν1 cos θ12 + m e 100 100 100 100 |M ee ν2 ν+N | sin θ12 | + 0.1 0.1 50 50 50 0.2 4 50 50 50 50 0.05 2 0.2 2 M W 1 2 1 2 0.2iα 0.1 20 20 p 0.4 4 cos θ12 + 20 0.4 sin θ12 20 20 20 e 20 0.4 0.6 M WR mN 1 mN2 0.2 10 10 0.6 10 10 10 10 0.6 10 1.0 0.4 1.0 1.0 0.6 55 5 55 50.0001 10−4 0.0001 0.001 0.001 0.001 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 11 11 10−4 10−4 0.0001 0.001 0.001 0.001 0.001 0.01 0.01 0.01 0.01 0.1 0.1 0.1 0.1 1 1 1 1 lightest neutrino mass in eV neutrino mass in eV lightest neutrino mass in eV lightest neutrino mass in eV jj : mN 50 GeV v : mN / 20 GeV LHC: j : mN 20 GeV / E : mN 3 − 7 GeV

25. Lepton Flavor Violation Cirigliano et al ’04 LFV rates computable: type II (or LHC) Raidal, Santamaria ’97 µ Y∆µe e T →3 tree ∆++ L,R VL mN /m∆ VL e Y∆ ∗ ee e γ † → γ loop ∆++ ∆++ VL mN /m∆ VL µ Y∆µi c Y∆ ∗ e i ie µL Y∆ Y∆ ∗ eL L (νL ) ∆++ (∆+ ) ∆++ (∆+ ) † µN− eN log VL mN /m∆ VL L L L L γ, ZL , ZR N N

26. Combined LFV constraints Muonic and tau channels Tello, MN, Senjanović, Vissani ’10 Varying PMNS constrains mN /m∆ < 1 5.0 5.0 5. absolute bound from LFV 5. absolute bound from LFV 1.0 1. 1.0 1. mN/m∆ mN/m∆ 0.5 0.5 0.5 0.5 0.1 0.1 0.1 0.1 0.05 always allowed by LFV 0.05 0.05 always allowed by LFV 0.05 MWR = 3.5TeV MWR = 3.5TeV 0.01 4 Inverted Hierarchy 0.01 4 Normal Hierarchy 0.01 0.01 10−4 10 0.001 0.001 0.01 0.01 0.1 0.1 1 1 10−4 10 0.001 0.001 0.01 0.01 0.1 0.1 1 1 lightest neutrino mass in eV lightest neutrino mass in eV

27. Triplet searches 2001 2003 2003 2004 2004 2005 2006 2008 2008 2011 2011 2011 350 313 300 250 200 LHC 150 156 m 146 141 144 150 136 118.4 114 98.5 97.3 100 100 Delphi CDF CDF CDF H1 D0 CDFII D0 CMS CMS Opal L3 50 ΤΤ ΜΜ e&Μ 0 eΜ ΜΜ eΤ ΜΤ April July 0 2001 2003 2003 2004 2004 2005 2006 2008 2008 2011 2011 2011

28. Gauge Production √ ∆+ / 2 ∆++ ∆= √ ∆0 −∆+ / 2 Pair-wise through Z, γ ∗ ∗ ∆+ ∆++ ∆0 γ ,Z ∗ γ ,Z Z ∆− ∆−− ∆0 Associated via W ± ∆±± ± ∆± W W GeV ∆ ∆0

29. Gauge Production √ 2.00 ∆+ / 2 ∆++ LHC @ 7 TeV ∆= √ 1.00 ∆0 −∆+ / 2 0.50 Pair-wise through Z, γ ∗ solid=LO 0.20 Z dashed=NLO Σ pb 0 ∗ ∆+ ∆++ ∆ γ ,Z ∗ γ ,Z 0.10 0.05 ∆− ∆−− K-factor =1.3 ∆0 0.02 Associated via W 100 120W ± 140 ∆±± 160 180 ± ± 200 ∆ red = assoc. W M TeV GeV ∆ ∆0 blue=pair.

30. Decay Phase Diagram m∆ U ∗ mν U † m3 v∆ 2 Γ∆→ ∝ Γ∆→V V ∝ ∆ 4 Γ∆→∆ V ∝ ∆m5 /m4 W v∆ v a) b) c) Decays a) Leptonic ∆→ Tiny v∆ b) Gauge boson ∆→VV Large v∆ c) Cascade ∆→∆V Mass split D0: pair-production only, CMS degenerate mass

31. Decay Phase Diagram 100.0 50.0 ∗ Cascade 2 Decay m∆ U mν U † m3 v∆ Γ∆→ ∝ Γ∆→V V ∝ ∆ 4 Γ∆→∆ V ∝ ∆m5 /m4 W v∆ v a) b) c) 10.0 Decays M GeV 5.0 a) Leptonic ∆→ Tiny v∆ 1.0 Leptonic Decay b) Gauge boson 0.5 ∆→VV Large v∆ Gauge c) Cascade ∆→∆V Mass split Boson Decay D0: pair-production only, 6 10 10 10 8 10 CMS degenerate mass 10 4 0.01 1 v GeV

32. Mass splits The general potential 2 † 2 † T ∗ V =− mH H H + m∆ Tr∆ ∆ + (µH iσ2 ∆ H + h.c.)+ † 2 † c2 † 2 λ1 (H H) + λ2 (Tr∆ ∆) + λ3 Tr(∆ ∆) + † † † † α H H Tr∆ ∆ + β H ∆∆ H Splits components by v 2; there is a sum rule 2 2 2 2 2 m∆ + − m∆++ m∆ 0 − m∆ + β v /4 c mS mA = m∆ 0 v2 Only two mass scales govern the spectrum up to O v∆ 2

33. Electroweak Precision Tests EWPT calculated for the first time Melfo, MN, Nesti, Senjanović, Zhang ’11 Oblique parameters suffice (Yukawa small by LFV) m 200 GeV 100 T parameter 80 T positive definite, controlled by 60 mass splits GeV 40 68 20 95 Heavy Higgs=negative T m 99 Bottom-line m 0 20 O(10 GeV) splits allowed 40 100 200 300 400 500 600 Cascade region opens up... mh GeV

34. Type II Roadmap Melfo, MN, Nesti, Senjanović, Zhang ’11 100 100 Sum Rule Sum Rule β<3 c Direct search Direct search 50 50 LHC 980 pb 11 LHC 980 pb CMS data GeV GeV v 10 66 GeV v 10 GeV EWPT 0 0 CMS-PAS- mh 300GeV m m HIG-11-007 LE m LEP m 50 50 EWPT Light Higgs P mh 130GeV Sum Rule & Sum Rule & 100 100 Z width Z width mh = 130 GeV c 0 0 100 100 200 200 300 300 400 400 500 500 600 600 700 700 mm GeV GeV

35. Type II Roadmap Melfo, MN, Nesti, Senjanović, Zhang ’11 100 Sum Rule β<3 c Direct search 50 LHC 980 pb 1 CMS data GeV v 10 6 GeV EWPT 0 CMS-PAS- mh 300GeV m HIG-11-007 LE m 50 Heavy Higgs P Sum Rule & 100 Z width mh = 300 GeV c 0 100 200 300 400 500 600 700 m GeV

36. Conclusions 0ν2β signal may require new physics at TeV Left-Right symmetry @ LHC a natural example no tension with cosmology, precision data or LFV links oscillations, cosmology and the LHC Exclusions with fairly low luminosity and 7 TeV LHC may observe LNV and in turn connect it to low energy rates, both LNV and LFV

37. Thank you.

38. Higgs decay Heavy Higgs decay: a way to probe α Akeroyd, Moretti ’11 mh > 2m∆ Br(h → W W ) 100 2 Γh→∆++ ∆−− ∝ α 1.5 2 Γh→∆+ ∆− ∝ (α + β/2) 1.0 Α 0.5 Higgs Br’s change 10 0.0 ++ 150 200 300 500 Easy to search if ∆ Mh GeV Hidden if ∆0 Melfo, MN, Nesti, Senjanović, Zhang ’11

39. A global picture MN, Nesti, Senjanović, Zhang ’11 1000 1 L 33.2pb 500 4 1.64` D0: dijets 3 2 100 GeV 0Ν2 50 Β H M jet EM activity MN Τ N 1 mm 10 Displaced Vertex 5 ΤN 5 m CMS Missing Energy 1 1000 1500 2000 2500 3000 MWR GeV

40. Non-minimal case CKM CKM∗ Minimal case: gL = gR C : VL = VR Maiezza, Nesti, MN, Senjanović ’10 1.4 1.2 95% CL gR gL 1.0 0.8 0.6 mN = 500 GeV 1200 1300 1400 1500 1600 1700 1800 MWR GeV

41. And the WR ? Less important, loop suppressed no log enhancement ﬂavor structure always mN < MWR † VL mN /MWR VL Still, future µ N − e N useful J-PARC and Fermilab could probe the mediator Cirigliano, Kitano, Okada, Tuzon ’09 even CP phases if LR Bajc, MN, Senjanović ’09

42. Role of θ13 Flavor structure in muon-electron transitions iα A(µ → 3e) ∝ −mN1 + exp mN2 sin 2θ12 cos θ23 2 iα 2 2 mN1 cos θ12 + exp mN2 sin θ12 /m∆++ µ → 3e insensitive to θ13 ∆m2 13 N ∆m2 A(µ → e) ∝ S sin 2θ12 cos θ23 + eiδ sin θ13 sin θ23 m2 ++ ∆ 2∆m2A µ − e conversion and µ → eγ depend a lot

43. Role of θ13 Impact of non zero Θ13 0.200 Flavor structure in muon-electron transitions T2K sin2Θ12 cosΘ23 ei∆ sinΘ13 sinΘ23 0.100 sin2 2Θ13 0.11 iα Minos → 3e) A(µ 0.050 ∝ −mN1 + exp mN2 sin 2θ12 cos θ23 2 iα 2 sin2 2Θ13 20.04 mN1 cos θ12 + exp mN2 sin θ12 /m∆++ 0.020 µ → 3e insensitive to θ13 0.010 Θ13 0 ∆m2 13 N 0.005 ∆m2 A(µ → e) ∝ S sin 2θ12 cos θ23 + eiδ sin θ13 sin θ23 m2 ++ 2∆m2 2 mA 2 A mS 2 ∆ 2 4 0.002 sin 2Θ13 8x10 0.001 µ − e conversion and Π → eγ depend a lot 0 µ 2 Π 3Π 2Π 2 ∆

M. Nemevsek - Neutrino Mass and the LHC

M. Nemevsek - Neutrino Mass and the LHC

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