Running quark and lepton masses

Running quark and lepton masses ------Tables of updated values Shun Zhou MPI für Physik, München Based on the work: Z.Z. Xing, H. Zhang & S.Z., Phys. Rev. D 77, 113016 (2008) 48 th Winter School on Theoretical Physics in Schladming, 27 Feb.- 6 Mar., 2010

Outline Fermion Mass Problems: Origin and Hierarchy Running Fermion Masses: below the EW Scale Running Fermion Masses: above the EW Scale Useful Tables and Summary

Higgs boson? LHC Gauge symmetry breaking Origin of fermion masses Physics beyond the Standard Model? Origin of neutrino masses (Seesaw models?) Flavor mixing patterns (large or small mixing angles?) Fermion mass hierarchy (quark-lepton symmetry?) de Gouvea, 2004

u MSSM e d s c t ν e μ b ν μ τ Georgi & Glashow, 1974 ν τ Fritzsch & Minkowski, 1975 Mass Models at the High energy scales Mass Values at the Low energy scale Renormalization Group Equations (RGEs) Gell-Mann & Low, 1954 Callan, 1970; Symanzik, 1970

Theoretical Predictions of Fermion Masses Fermion Masses Extracted from Experimental Data Fermion masses from the PDG 2006 HQET, LQCD, SR Running Masses m(μ) χpt, Lattice QCD, Sum Rules Direct measurements t Hooft scale Manohar & Sachrajda, 2008 Review on Quark Masses, PDG Pole Masses

Remarks: 1. Unlike the leptons, quarks are confined in hadrons. Therefore, quark masses cannot be measured directly. They are indirectly determined from their influence on the properties of hadrons. 2. When talking about quark masses, one should keep in mind that they are defined in a specific theoretical framework, and thus scheme-dependent. For example, the constituent quark masses in the quark models.

Leutwyler, arxiv: 0911.1416

Leutwyler, arxiv: 0911.1416

Running Fermion Masses: below the EW scale Goal: running quark and lepton masses m(μ) at the EW scale μ=mz Formula: (1) RGEs for the strong coupling constant and quark masses t Hoof, 1972 Number of active quarks Gross & Wilczek, 1973; Politzer, 1973 van Ritbergen, Vermaseren & Larin, 1997 Chetyrkin, 1997; van Ritbergen, Vermaseren & Larin, 1997

Formula: (1) RGEs for the strong coupling constant and quark masses Solution of quark masses Chetyrkin, 1997; Chetyrkin & Steinhauser, 1999; Melnikov & van Ritbergen, 2000 Formula: (2) Matching conditions for the strong coupling and masses Mz=91.2 GeV μ=mb(mb) = 4.2 GeV μ=2 GeV nq = 5 nq = 4 Flavor threshold μ=mc(mc) = 1.25 GeV

Formula: (2) Matching conditions for the strong coupling and masses Chetyrkin, Kniehl & Steinhauser, 1998; Chetyrkin, Kuehn & Steinhauser, 2000

Formula: (3) Relation between running mq(μ) and pole masses Mq Chetyrkin & Steinhauser, 1999; Melnikov & van Ritbergen, 2000 K (2) c = 11.21 K (2) b = 10.17 K (2) t = 9.13 K (3) c = 123.8 K (3) b = 101.5 K (3) t = 80.4 Formula: (4) RGEs for α and running masses of charged leptonsm (μ) l Arason et al., 1992

Strategy: (1) Input values from the PDG 2006; (2) Runningmatching-running scheme for the evaluation of quark masses μ(5)=mb(mb) = 4.20 GeV Mz=91.186 GeV μ(4)=mc(mc) = 1.25 GeV nq = 4 μ(5)=mb(mb) = 4.20 GeV Mz=91.186 GeV nq = 5 nq = 6

Running Fermion Masses: above the EW scale Goal: running fermion masses m(μ) at the TeV scale, the seesaw scale and the GUT scale, both in the SM and in the MSSM (1) We adopt the seesaw model for neutrino masses, so neutrinos are assumed to be Majorana particles; (2) Above the EW scale, we define fermion masses as mf = yf v, where yf are the eigenvalues of Yukawa couplings and v is the vev; (3) We use two-loop RGEs for Yu, Yd, Yl, but one-loop RGE for effective neutrino coupling matrix κ. mq(mz) Yu & Yd Machack & Vaughn, 1984; Antusch et al., 2002, 2005; Mei & Xing, 2004; Mei, 2005 Gauge couplings Yl & κ θ12 = 33.8 deg θ23 = 45.0 deg θ13 ~ 0 δ=ρ=σ = 0 (A) m1 = 0.001 ev, m1 < m2 < m3 (B) m1 = 0.2 ev, m1< m2 < m3

Xing, Zhang & Zhou, Phys. Rev. D 77, 113016 (2008) Mathematica code RunDec, by Chetyrkin, Kuehn & Steinhauser, 2000

Xing, Zhang & Zhou, Phys. Rev. D 77, 113016 (2008) In the SM with MH = 140 GeV

Xing, Zhang & Zhou, Phys. Rev. D 77, 113016 (2008) In the SM with MH = 140 GeV

MSSM with tan β = 10 MSSM with tan β = 50

Summary 1. The origin of fermion masses, the fermion mass hierarchy and flavor mixing patterns are still big puzzles in particle physics. New physics beyond the SM is expected so much. 2. The models for fermion masses are usually constructed at the high-energy scales, e.g. the TeV and GUT scales. The predictions should be confronted with experimental data. 3. Starting with the latest values given by PDG, we have evaluated the running quark and lepton masses at the EW, TeV, Seesaw, GUT scales, in the SM and MSSM.