EFFECTS OF NEW LEPTONS IN ELECTROWEAK PRECISION DATA
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1 EFFECTS OF NEW LEPTONS IN ELECTROWEAK PRECISION DATA In collaboration with F. del Águila and M. Pérez-Victoria Phys. Rev. D78: , 2008 Depto. de Física Teórica y del Cosmos Universidad de Granada
2 Introduction EWPD are consistent with the SM to a remarkable precision. Only a few discrepancies. Higgs Mass: Best-fit value: LEP2 lower limit (95% C.L.): 2
3 Introduction New leptons modify leptonic observables: May improve the electroweak fit Change the prediction for the Higgs mass New Leptons are predicted in: Grand Unified Theories Models with Extra Dimensions Little Higgs models 3
4 Introduction New Majorana Leptons are proposed in See-saw models to give tiny masses to the SM neutrinos: Type I: Majorana singlet Type III: Majorana triplet They are heavy and we are interested in their effects at energies much smaller than their masses Effective lagrangian approach 4
5 Introduction We classify all the new heavy vector-like leptons that, after EWSB, can mix with the SM neutrinos or charged leptons and compute the effective lagrangian. We analyse their effect in a global fit to EWPD. Extract limits on the mixings between the heavy and the SM leptons. We discuss the interplay between heavy lepton singlets and the Higgs mass. 5
6 Outline Extending the SM with New Leptons Effective Lagrangian Numerical Results New Leptons and the Higgs Mass Conclusions 6
7 Extending the SM with New Leptons Assume that the new vector-like leptons mix at tree level with SM. Renormalizability and SM gauge invariance fixes the quantum number of the new leptons: 7
8 Extending the SM with New Leptons The lagrangian of the theory is given by: Where the light lagrangian is the SM one: The heavy lagrangian involves only the new leptons (η L =1 (Dirac), ½(Majorana)): Finally, the light-heavy interactions: 8
9 Effective Lagrangian Integrate out the new leptons Non-renormalizable interactions contains gauge-invariant local operators of dimension d and give contributions of order to observables. We expect terms of d >6 to give small corrections compared to the experimental precision of current data so we neglect them. We classify the operators in the basis of W. Buchmüller & D. Wyler. Nuc. Phys B268 (1986) ) 9
10 Effective Lagrangian There is only one operator at dimension 5 (Weinberg operator): DL=2 so, in the case of new leptons, can be originated only from Majorana terms (N and S 0 ). After EWSB this operator gives a Majorana mass for the SM neutrinos: 10
11 Effective Lagrangian There are 81 dimension 6 operators preserving B and L. We only find a small subset. Need to use field redefinitions to rewrite the operators in the B&W basis. The dimension six part of the effective lagrangian reads: 11
12 Effective Lagrangian After EWSB these operators modify the NC and CC coupling of SM leptons: As well as the charged lepton masses: Do not contribute to the fits 12
13 Effective Lagrangian Coefficients: 13
14 Effective Lagrangian: Phenomenological constraints Mixing with the new leptons is suppressed when: Mediate Lepton Flavour Violating (LFV) processes. Generate masses for the SM neutrinos. 14
15 Effective Lagrangian: Phenomenological constraints Limits from different processes: LF preserving: constraint diagonal entries of the coefficients. LFV processes: constraint off-diagonal entries of the coefficients (More stringent). Neutrino singlets: Triplets: 15
16 Effective Lagrangian: Phenomenological constraints Looking at the coefficients these can rule out non-lfv limits. To exclude LFV limits impose a strong constraint in definite models. Need a precise alignment of SM charged leptons and new mass eigenstate leptons: Each new fermion multiplet mixes mostly with only one SM lepton flavour. Automatic with the assumption of approximate conservation on lepton family number. 16
17 Effective Lagrangian: Phenomenological constraints Constraints from neutrino masses: For m n to be 1 ev order: L~10 15 GeV if a 5 ~1 Dimension 6 effects are negligible. a 5 ~10-11 if L~1TeV If a 6 is sizeable one has to explain why a 5 is so small. d=5 coefficient: Need of extra particles to cancel dimension 5 effects. 17
18 Effective Lagrangian: Phenomenological constraints Example: 1 singlet quasi-dirac lepton coupled to one SM family. m is the only source of LN violation. Thus, adjusting the LN violating parameter m one can obtain small masses without affecting dimension 6 effects. 18
19 Effective Lagrangian: Fit parameters Dimension six operators coefficients: The fit only constraints the mixings after EWSB. Assuming the mixing of one new lepton to only one SM family: 19
20 Effective Lagrangian: Fit parameters These mixings are directly related to the heavy-light CC couplings: We will present our results in terms of this CC couplings. 20
21 Numerical Results Assumptions: Each new lepton mixes mostly with just one family (avoid LFV constraints) Decoupling between dimension 5 and 6 effects (avoid m n constraints) We perform different fits depending on how we couple the new leptons to the SM particles: One single lepton coupled to one of the three SM families. Three leptons, each coupled to one SM family with independent couplings. Three leptons, each coupled to one SM family with the same coupling (Lepton universality) We impose the LEP2 bound on the Higgs mass: 21
22 Numerical Results Data set used in the fits (SM values for M H =114.4 GeV): 22
23 Numerical Results Data set used in the fits (SM values for M H =114.4 GeV): Different data set if lepton universality is assumed. 23
24 Numerical Results Global fit: 2 χ min / d.o.f. SM 1.46 = 1.42 (Lept. Univ.) 24
25 Numerical Results Upper limit at 90% C.L. and best fit value (minimum): 25
26 Numerical Results Comparison with old limits B.Beckman, J. Gluza,J. Holeczek, J. Syska and M. Zralek Phys. Rev. D 66 (2002) E.Nardi,E. Roulet and D. Tommasini Nucl. Phys. B 386,239 (1992) 26
27 New Leptons and the Higgs Mass SM best fit value for the Higgs mass is in tension with the LEP 2 lower bound. Can new leptons accomodate a heavier Higgs? How? 27
28 New Leptons and the Higgs Mass New Leptons can provide effective oblique corrections. New singlets and triplets mixing with e and/or m affect the extraction of the Fermi constant from the muon lifetime. Since G F is an input, this effect propagates to all observables giving indirect corrections that mimic the ones of the T parameter: If positive can compensate the effect of a heavier Higgs boson. 28
29 New Leptons and the Higgs Mass What leptons can increase the Higgs mass prediction? Sizeable mixing of N coupled to e or m Heavier Higgs is allowed 29
30 New Leptons and the Higgs Mass 90% C.L. Region in the V L Ne -M H parameter space. (N) 30
31 New Leptons and the Higgs Mass 90% C.L. Region in the V L En -M H parameter space. (E) 31
32 New Leptons and the Higgs Mass 90% C.L. Region in the V R en -M H parameter space. (D 1 ) 32
33 New Leptons and the Higgs Mass 90% C.L. Region in the V R E -- e -M H parameter space. (D 3 ) 33
34 New Leptons and the Higgs Mass 90% C.L. Region in the V L en -M H parameter space. (S 0 ) 34
35 New Leptons and the Higgs Mass 90% C.L. Region in the V L En -M H parameter space. (S 1 ) 35
36 New Leptons and the Higgs Mass Best-fit value of the Higgs mass for the SM extension with extra neutral singlets: With the exception of the neutral singlet case, the upper limits on the Higgs mass are similar to the SM one. 36
37 New Leptons and the Higgs Mass Upper limit at 90% C.L. on the Higgs mass: 37
38 Conclusions TeV-scale vector-like leptons with sizeable mixings are compatible with EWPD. We improve the previous bounds on lepton mixings from LF preserving processes. Upper bounds on mixings range from 0.02 to 0.08 at 90 % C.L. If new leptons are weakly coupled, their masses must not be far from the TeV scale. The presence of extra singlets mixing with the 1st and/or 2nd families favours a heavier Higgs: N-m M H =136 GeV, M H <267 GeV (90% C.L.) 38
39 Conclusions Consequences for production and decay at large colliders: Hadron colliders: Heavy leptons produced in pairs except for N which is single produced through mixing. LHC: Majorana N-m with V L Nm >0.054 for M N ~200 GeV (L=30 fb -1 ) e + e - colliders: Production through mixing with 1st family ILC: N-e with V Ne L >0.01 would be observed for M N <400 GeV CLIC:N-e V Ne L >0.01 would be observed for M N <2 TeV 39
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