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10 1. Physical constants 1 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 2005 by P.J. Mohr and B.N. Taylor (NIST). Based mainly on the CODATA Recommended Values of the Fundamental Physical Constants: 2002 by P.J. Mohr and B.N. Taylor, Rev. Mod. Phys. 77, 1 (2005). The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard-deviation uncertainties in the last digits; the corresponding fractional uncertainties in parts per 10 9 (ppb) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). The full 2002 CODATA set of constants may be found at Quantity Symbol, equation Value Uncertainty (ppb) speed of light in vacuum c m s 1 exact Planck constant h (11) J s 170 Planck constant, reduced h/2π (18) J s 170 = (56) MeV s 85 electron charge magnitude e (14) C = (41) esu 85, 85 conversion constant c (17) MeV fm 85 conversion constant ( c) (67) GeV 2 mbarn 170 electron mass m e (44) MeV/c 2 = (16) kg 86, 170 proton mass m p (80) MeV/c 2 = (29) kg 86, 170 = (13) u = (85) m e 0.13, 0.46 deuteron mass m d (16) MeV/c 2 86 unified atomic mass unit (u) (mass 12 C atom)/12 = (1 g)/(n A mol) (80) MeV/c 2 = (28) kg 86, 170 permittivity of free space ɛ 0 =1/µ 0 c Fm 1 exact permeability of free space µ 0 4π 10 7 NA 2 = NA 2 exact fine-structure constant α = e 2 /4πɛ 0 c (24) 10 3 =1/ (46) 3.3, 3.3 classical electron radius r e = e 2 /4πɛ 0 m e c (28) m 10 (e Compton wavelength)/2π λ e = /m e c = r e α (26) m 6.7 Bohr radius (m nucleus = ) a =4πɛ 0 2 /m e e 2 = r e α (18) m 3.3 wavelength of 1 ev/c particle hc/(1 ev) (11) 10 6 m 85 Rydberg energy hcr = m e e 4 /2(4πɛ 0 ) 2 2 = m e c 2 α 2 / (12) ev 85 Thomson cross section σ T =8πre/ (13) barn 20 Bohr magneton µ B = e /2m e (39) MeV T nuclear magneton µ N = e /2m p (21) MeV T electron cyclotron freq./field ωcycl e /B = e/m e (15) rad s 1 T 1 86 proton cyclotron freq./field ω p cycl /B = e/m p (82) 10 7 rad s 1 T 1 86 gravitational constant G N (10) m 3 kg 1 s = (10) c (GeV/c 2 ) standard gravitational accel. g n m s 2 exact Avogadro constant N A (10) mol Boltzmann constant k (24) JK = (15) 10 5 ev K molar volume, ideal gas at STP N A k( K)/( Pa) (39) 10 3 m 3 mol Wien displacement law constant b = λ max T (51) 10 3 m K 1700 Stefan-Boltzmann constant σ = π 2 k 4 /60 3 c (40) 10 8 Wm 2 K Fermi coupling constant G F /( c) (1) 10 5 GeV weak-mixing angle sin 2 θ(m Z )(MS) (15) W ± boson mass m W (29) GeV/c Z 0 boson mass m Z (21) GeV/c strong coupling constant α s (m Z ) (20) in m 1 Å 0.1 nm 1barn m 2 π = e = γ = G 10 4 T 1dyne 10 5 N 1erg 10 7 J 1eV= (14) J 1eV/c 2 = (15) kg kt at 300 K = [ (68)] 1 ev 0 C K esu = 1 C 1 atmosphere 760 Torr Pa The meter is the length of the path traveled by light in vacuum during a time interval of 1/ of a second. At Q 2 =0. AtQ 2 m 2 W the value is 1/128. Absolute lab measurements of G N have been made only on scales of about 1 cm to 1 m. See the discussion in Sec. 10, Electroweak model and constraints on new physics. The corresponding sin 2 θ for the effective angle is (14).

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24 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: QUARKS The u-, d-, and s-quark masses are estimates of so-called currentquark masses, in a mass-independent subtraction scheme such as MS at a scale µ 2GeV.Thec- andb-quark masses are the running masses in the MS scheme. For the b-quark we also quote the 1S mass. These can be different from the heavy quark masses obtained in potential models. u I (J P )= 1 2 ( ) Mass m =1.5 to3.0 MeV [a] Charge = 2 3 e I z =+ 1 2 m u /m d =0.3 to0.6 d I (J P )= 1 2 ( ) Mass m =3to7MeV [a] Charge = 1 3 e I z = 1 2 m s /m d =17to22 m =(m u +m d )/2 = 2.5 to5.5 MeV s I (J P )=0( 1+ 2 ) Mass m =95± 25 MeV [a] Charge = 1 3 e Strangeness = 1 (m s (m u + m d )/2) / (m d m u ) = 30 to 50 c I (J P )=0( ) Mass m =1.25 ± 0.09 GeV Charge = 2 3 e Charm = +1 b I (J P )=0( ) Charge = 1 3 e Bottom = 1 Mass m =4.20 ± 0.07 GeV Mass m =4.70 ± 0.07 GeV (MS mass) (1S mass) Page 1 Created: 7/5/ :38

25 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: t I (J P )=0( ) Charge = 2 3 e Top = +1 Mass m = ± 3.3 GeV [b] (direct observation of top events) Mass m = GeV (Standard Model electroweak fit) p t DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) Wq(q = b, s, d) Wb lν l anything [c,d] ( 9.4±2.4) % τν τ b γ q (q=u,c) [e] < % T = 1 weak neutral current (T1) modes Zq(q=u,c) T1 [f ] < 13.7 % 95% b (4 th Generation) Quark, Searches for Mass m > 190 GeV, CL = 95% (p p, quasi-stable b ) Mass m > 199 GeV, CL = 95% (p p, neutral-current decays) Mass m > 128 GeV, CL = 95% (p p, charged-current decays) Mass m > 46.0 GeV, CL = 95% (e + e, all decays) Free Quark Searches All searches since 1977 have had negative results. Page 2 Created: 7/5/ :38

26 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: NOTES [a]theratiosm u /m d and m s /m d are extracted from pion and kaon masses using chiral symmetry. The estimates of u and d masses are not without controversy and remain under active investigation. Within the literature there are even suggestions that the u quark could be essentially massless. The s-quark mass is estimated from SU(3) splittings in hadron masses. [b] Based on published top mass measurements using data from Tevatron Run-I and Run-II. Including also the most recent unpublished results from Run-II, the Tevatron Electroweak Working Group reports a top mass of ± 1.3 ± 1.9 GeV.Seethenote TheTopQuark inthequark Particle Listings of this Review. [c] l means e or µ decay mode, not the sum over them. [d] Assumes lepton universality and W -decay acceptance. [e] This limit is for Γ(t γ q)/γ(t Wb). [f ] This limit is for Γ(t Zq)/Γ(t Wb). Page 3 Created: 7/5/ :38

27 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: LEPTONS e J = 1 2 Mass m = ( ± ) 10 6 u Mass m = ± MeV me + m e /m < , CL = 90% qe + + q / e e < Magnetic moment µ = ± µ B (g e + g e )/g average =( 0.5 ± 2.1) Electric dipole moment d =(0.07 ± 0.07) e cm Mean life τ > yr, CL = 90% [a] µ J = 1 2 Mass m = ± u Mass m = ± MeV Mean life τ =( ± ) 10 6 s τ µ +/τ µ = ± cτ = m Magnetic moment µ = ± e h/2m µ (g µ + g µ )/g average =( 2.6 ± 1.6) 10 8 Electric dipole moment d =(3.7 ± 3.4) e cm Decay parameters [b] ρ = ± η =0.001 ± (S = 2.0) δ = ± ξp µ =1.003 ± [c] ξp µ δ/ρ > , CL = 90% [c] ξ =1.00 ± 0.04 ξ =0.7 ± 0.4 α/a = (0 ± 4) 10 3 α /A = (0 ± 4) 10 3 β/a = (4 ± 6) 10 3 β /A = (1 ± 5) 10 3 η =0.02 ± 0.08 µ + modes are charge conjugates of the modes below. Page 1 Created: 7/5/ :38

28 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: p µ DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) e ν e ν µ 100% 53 e ν e ν µ γ [d] (1.4±0.4) % 53 e ν e ν µ e + e [e] (3.4±0.4) Lepton Family number (LF ) violating modes e ν e ν µ LF [f ] < 1.2 % 90% 53 e γ LF < % 53 e e + e LF < % 53 e 2γ LF < % 53 τ J = 1 2 Mass m = MeV (m τ + m τ )/m average < , CL = 90% Mean life τ = (290.6 ± 1.0) s cτ =87.11 µm Magnetic moment anomaly > and < 0.013, CL = 95% Re(d τ )= 0.22 to e cm, CL = 95% Im(d τ )= 0.25 to e cm, CL = 95% Weak dipole moment Re(d w τ ) < e cm, CL = 95% Im(d w τ ) < e cm, CL = 95% Weak anomalous magnetic dipole moment Re(α w τ ) < , CL = 95% Im(α w τ ) < , CL = 95% Decay parameters See the τ Particle Listings for a note concerning τ-decay parameters. ρ τ (e or µ) =0.745 ± ρ τ (e) =0.747 ± ρ τ (µ) =0.763 ± ξ τ (e or µ) =0.985 ± ξ τ (e) =0.994 ± ξ τ (µ) =1.030 ± η τ (e or µ) =0.013 ± η τ (µ) =0.094 ± (δξ) τ (e or µ) =0.746 ± (δξ) τ (e) =0.734 ± Page 2 Created: 7/5/ :38

29 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: (δξ) τ (µ) =0.778 ± ξ τ (π) =0.993 ± ξ τ (ρ) =0.994 ± ξ τ (a 1 )=1.001 ± ξ τ (all hadronic modes) = ± τ + modes are charge conjugates of the modes below. h ± stands for π ± or K ±. l stands for e or µ. Neutrals stands for γ s and/or π 0 s. Scale factor/ p τ DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) Modes with one charged particle particle 0neutrals 0K 0 ν τ (85.33±0.08) % S=1.4 ( 1-prong ) particle 0neutrals 0K 0 L ν τ (84.69±0.09) % S=1.4 µ ν µ ν τ [g] (17.36±0.05) % 885 µ ν µ ν τ γ [e] ( 3.6 ±0.4 ) e ν e ν τ [g] (17.84±0.05) % 888 e ν e ν τ γ [e] ( 1.75±0.18) % 888 h 0K 0 L ν τ (12.14±0.07) % S= h ν τ (11.59±0.06) % S= π ν τ [g] (10.90±0.07) % S= K ν τ [g] ( 6.91±0.23) h 1neutralsν τ (37.05±0.12) % S=1.3 h 1π 0 ν τ (ex.k 0 ) (36.51±0.12) % S=1.3 h π 0 ν τ (25.95±0.10) % S= π π 0 ν τ [g] (25.50±0.10) % S= π π 0 non-ρ(770)ν τ ( 3.0 ±3.2 ) K π 0 ν τ [g] ( 4.52±0.27) h 2π 0 ν τ (10.81±0.14) % S=1.5 h 2π 0 ν τ ( 9.47±0.12) % S= h 2π 0 ν τ (ex.k 0 ) ( 9.31±0.12) % S= π 2π 0 ν τ (ex.k 0 ) [g] ( 9.25±0.12) % S= π 2π 0 ν τ (ex.k 0 ), < CL=95% 862 scalar π 2π 0 ν τ (ex.k 0 ), vector < CL=95% 862 K 2π 0 ν τ (ex.k 0 ) [g] ( 5.8 ±2.3 ) h 3π 0 ν τ ( 1.33±0.07) % S=1.1 h 3π 0 ν τ (ex. K 0 ) ( 1.25±0.07) % S=1.1 h 3π 0 ν τ ( 1.17±0.08) % S= π 3π 0 ν τ (ex.k 0 ) [g] ( 1.04±0.08) % S= K 3π 0 ν τ (ex.k 0, η) [g] ( 4.2 ±2.1 ) Page 3 Created: 7/5/ :38

30 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: h 4π 0 ν τ (ex.k 0 ) ( 1.6 ±0.4 ) h 4π 0 ν τ (ex.k 0,η) [g] ( 1.0 ±0.4 ) K 0π 0 0K 0 0γ ν τ ( 1.57±0.04) % S= K 1(π 0 or K 0 or γ) ν τ ( 8.78±0.33) 10 3 < Modes with K 0 s K 0 S (particles) ν τ ( 9.27±0.34) 10 3 S=1.1 h K 0 ν τ ( 1.05±0.04) % S= π K 0 ν τ [g] ( 9.0 ±0.4 ) 10 3 S= π K CL=95% 812 (non-k (892) )ν τ K K 0 ν τ [g] ( 1.53±0.16) K K 0 0π 0 ν τ ( 3.07±0.24) h K 0 π 0 ν τ ( 5.3 ±0.4 ) π K 0 π 0 ν τ [g] ( 3.8 ±0.4 ) K 0 ρ ν τ ( 2.2 ±0.5 ) K K 0 π 0 ν τ [g] ( 1.54±0.20) π K 0 1π 0 ν τ ( 3.2 ±1.0 ) 10 3 π K 0 π 0 π 0 ν τ ( 2.6 ±2.4 ) K K 0 π 0 π 0 ν τ < CL=95% 619 π K 0 K 0 ν τ ( 1.60±0.31) 10 3 S= π K 0 S K 0 S ν τ [g] ( 2.4 ±0.5 ) π K 0 S K 0 L ν τ [g] ( 1.12±0.30) 10 3 S= π K 0 K 0 π 0 ν τ ( 3.1 ±2.3 ) π K 0 S K 0 S π0 ν τ < CL=95% 614 π K 0 S K 0 L π0 ν τ ( 3.1 ±1.2 ) K 0 h + h h 0neutralsν τ < CL=95% 760 K 0 h + h h ν τ ( 2.3 ±2.0 ) Modes with three charged particles h h h + 0neutrals 0K 0 L ν τ (15.22±0.09) % S= h h h + 0neutralsν τ (14.59±0.08) % S= (ex. K 0 S π+ π ) ( 3-prong ) h h h + ν τ ( 9.87±0.08) % S= h h h + ν τ (ex.k 0 ) ( 9.51±0.08) % S= h h h + ν τ (ex.k 0,ω) ( 9.47±0.08) % S= π π + π ν τ ( 9.33±0.08) % S= π π + π ν τ (ex.k 0 ) ( 9.02±0.08) % S= π π + π ν τ (ex.k 0 ), non-axial vector < 2.4 % CL=95% 861 π π + π ν τ (ex.k 0,ω) [g] ( 8.99±0.08) % S= h h h + 1neutralsν τ ( 5.34±0.06) % S=1.1 h h h + 1π 0 ν τ (ex. K 0 ) ( 5.06±0.06) % S=1.1 h h h + π 0 ν τ ( 4.73±0.07) % S= Page 4 Created: 7/5/ :38

31 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: h h h + π 0 ν τ (ex.k 0 ) ( 4.55±0.06) % S= h h h + π 0 ν τ (ex. K 0, ω) ( 2.78±0.08) % S= π π + π π 0 ν τ ( 4.59±0.07) % S= π π + π π 0 ν τ (ex.k 0 ) ( 4.46±0.06) % S= π π + π π 0 ν τ (ex.k 0,ω) [g] ( 2.69±0.08) % S= h h h + 2π 0 ν τ (ex. ( 5.14±0.34) 10 3 S=1.1 K 0 ) h h h + 2π 0 ν τ ( 5.02±0.34) 10 3 S= h h h + 2π 0 ν τ (ex.k 0 ) ( 4.92±0.34) 10 3 S= h h h + 2π 0 ν τ (ex.k 0,ω,η) [g] ( 9 ±4 ) h h h + 3π 0 ν τ [g] ( 2.2 ±0.5 ) K h + h 0neutralsν τ ( 6.79±0.35) 10 3 S= K h + π ν τ (ex.k 0 ) ( 4.86±0.32) 10 3 S= K h + π π 0 ν τ (ex.k 0 ) ( 8.5 ±1.2 ) K π + π 0neutralsν τ ( 5.2 ±0.4 ) 10 3 S= K π + π ( 4.1 ±0.4 ) 10 3 S= π 0 ν τ (ex.k 0 ) K π + π ν τ ( 3.9 ±0.4 ) 10 3 S= K π + π ν τ (ex.k 0 ) [g] ( 3.33±0.35) 10 3 S= K ρ 0 ν τ ( 1.6 ±0.6 ) 10 3 K π + π ν τ K π + π π 0 ν τ ( 1.32±0.14) K π + π π 0 ν τ (ex.k 0 ) ( 7.9 ±1.2 ) K π + π π 0 ν τ (ex.k 0,η) [g] ( 7.3 ±1.2 ) K π + π π 0 ν τ (ex.k 0,ω) ( 3.7 ±0.9 ) K π + K 0neut. ν τ < CL=95% 685 K K + π 0neut. ν τ ( 1.59±0.10) 10 3 S= K K + π ν τ [g] ( 1.53±0.10) 10 3 S= K K + π π 0 ν τ [g] ( 6.1 ±2.0 ) 10 5 S= K K + K 0neut. ν τ < CL=95% 472 K K + K ν τ < CL=90% 472 K K + K π 0 ν τ < CL=90% 346 π K + π 0neut. ν τ < CL=95% 794 e e e + ν e ν τ ( 2.8 ±1.5 ) µ e e + ν µ ν τ < CL=90% 885 Modes with five charged particles 3h 2h + 0neutralsν τ ( 1.02±0.04) 10 3 S= (ex. K 0 S π π + ) ( 5-prong ) 3h 2h + ν τ (ex.k 0 ) [g] ( 8.38±0.35) 10 4 S= h 2h + π 0 ν τ (ex.k 0 ) [g] ( 1.78±0.27) h 2h + 2π 0 ν τ < CL=90% Page 5 Created: 7/5/ :38

32 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: Miscellaneous other allowed modes (5π) ν τ ( 7.6 ±0.5 ) 10 3 S= h 3h + 0neutralsν τ < CL=90% 683 ( 7-prong ) 4h 3h + ν τ < CL=90% 683 4h 3h + π 0 ν τ < CL=90% 612 X (S= 1)ν τ ( 2.95±0.07) % S=1.1 K (892) 0neutrals ( 1.42±0.18) % S= K 0 L ν τ K (892) ν τ ( 1.29±0.05) % 665 K (892) 0 K 0neutralsν τ ( 3.2 ±1.4 ) K (892) 0 K ν τ ( 2.1 ±0.4 ) K (892) 0 π 0neutralsν τ ( 3.8 ±1.7 ) K (892) 0 π ν τ ( 2.2 ±0.5 ) (K (892)π ) ν τ ( 1.0 ±0.4 ) 10 3 π K 0 π 0 ν τ K 1 (1270) ν τ ( 4.7 ±1.1 ) K 1 (1400) ν τ ( 1.7 ±2.6 ) 10 3 S= < CL=90% K (1410) ν τ ( ) K 0 (1430) ν τ < CL=95% 326 K 2 (1430) ν τ < CL=95% 317 ηπ ν τ < CL=95% 798 ηπ π 0 ν τ [g] ( 1.77±0.24) ηπ π 0 π 0 ν τ ( 1.5 ±0.5 ) η K ν τ [g] ( 2.7 ±0.6 ) η K (892) ν τ ( 2.9 ±0.9 ) η K π 0 ν τ ( 1.8 ±0.9 ) η K 0 π ν τ ( 2.2 ±0.7 ) ηπ + π π 0neutralsν τ < CL=90% 744 ηπ π + π ν τ ( 2.3 ±0.5 ) η a 1 (1260) ν τ ηπ ρ 0 ν τ < CL=90% ηηπ ν τ < CL=95% 637 ηηπ π 0 ν τ < CL=95% 559 η (958)π ν τ < CL=90% 620 η (958)π π 0 ν τ < CL=90% 591 φπ ν τ < CL=90% 585 φk ν τ < CL=90% 445 f 1 (1285)π ν τ ( 4.1 ±0.8 ) f 1 (1285)π ν τ ( 1.3 ±0.4 ) 10 4 ηπ π + π ν τ π(1300) ν τ (ρπ) ν τ (3π) ν τ Page 6 Created: 7/5/ :38

33 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: π(1300) ν τ ((ππ) S wave π) ν τ (3π) ν τ < CL=90% h ω 0neutralsν τ ( 2.39±0.09) % S= h ων τ [g] ( 1.99±0.08) % S= K ων τ ( 4.1 ±0.9 ) h ωπ 0 ν τ [g] ( 4.1 ±0.4 ) h ω 2π 0 ν τ ( 1.4 ±0.5 ) h h + ων τ ( 1.20±0.22) Lepton Family number (LF ), Lepton number (L), or Baryon number (B) violating modes L means lepton number violation (e.g. τ e + π π ). Following common usage, LF means lepton family violation and not lepton number violation (e.g. τ e π + π ). B means baryon number violation. e γ LF < CL=90% 888 µ γ LF < CL=90% 885 e π 0 LF < CL=90% 883 µ π 0 LF < CL=90% 880 e K 0 S LF < CL=90% 819 µ K 0 S LF < CL=90% 815 e η LF < CL=90% 804 µ η LF < CL=90% 800 e ρ 0 LF < CL=90% 719 µ ρ 0 LF < CL=90% 715 e K (892) 0 LF < CL=90% 665 µ K (892) 0 LF < CL=90% 660 e K (892) 0 LF < CL=90% 665 µ K (892) 0 LF < CL=90% 660 e η (958) LF < CL=90% 630 µ η (958) LF < CL=90% 625 e φ LF < CL=90% 596 µ φ LF < CL=90% 590 e e + e LF < CL=90% 888 e µ + µ LF < CL=90% 882 e + µ µ LF < CL=90% 882 µ e + e LF < CL=90% 885 µ + e e LF < CL=90% 885 µ µ + µ LF < CL=90% 873 e π + π LF < CL=90% 877 e + π π L < CL=90% 877 µ π + π LF < CL=90% 866 µ + π π L < CL=90% 866 e π + K LF < CL=90% Page 7 Created: 7/5/ :38

34 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: e π K + LF < CL=90% 813 e + π K L < CL=90% 813 e K 0 S K 0 S LF < CL=90% 736 e K + K LF < CL=90% 739 e + K K L < CL=90% 739 µ π + K LF < CL=90% 800 µ π K + LF < CL=90% 800 µ + π K L < CL=90% 800 µ K 0 S K 0 S LF < CL=90% 696 µ K + K LF < CL=90% 699 µ + K K L < CL=90% 699 e π 0 π 0 LF < CL=90% 878 µ π 0 π 0 LF < CL=90% 867 e ηη LF < CL=90% 700 µ ηη LF < CL=90% 654 e π 0 η LF < CL=90% 798 µ π 0 η LF < CL=90% 784 p γ L,B < CL=90% 641 p π 0 L,B < CL=90% 632 p 2π 0 L,B < CL=90% 604 p η L,B < CL=90% 475 p π 0 η L,B < CL=90% 360 Λπ L,B < CL=90% 526 Λπ L,B < CL=90% 526 e light boson LF < CL=95% µ light boson LF < CL=95% Heavy Charged Lepton Searches L ± charged lepton Mass m > GeV, CL = 95% [h] Decay to ν W. L ± stable charged heavy lepton Mass m > GeV, CL = 95% Page 8 Created: 7/5/ :38

35 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: Neutrino Properties See the note on Neutrino properties listings in the Particle Listings. Mass m < 2 ev (tritium decay) Mean life/mass, τ/m > 300 s/ev, CL = 90% (reactor) Mean life/mass, τ/m > s/ev (solar) Mean life/mass, τ/m > 15.4 s/ev, CL = 90% (accelerator) Magnetic moment µ < µ B, CL = 90% (reactor) Number of Neutrino Types Number N =2.994 ± Number N = 2.92 ± 0.06 width) (Standard Model fits to LEP data) (Direct measurement of invisible Z Neutrino Mixing The following values are obtained through data analyses based on the 3-neutrino mixing scheme described in the review Neutrino mass, mixing, and flavor change by B. Kayser in this Review. sin 2 (2θ 12 )= =( ) 10 5 ev 2 m 2 21 The ranges below for sin 2 (2θ 23 )and m 2 32 correspond to the projections onto the appropriate axes of the 90% CL contours in the sin 2 (2θ 23 )- m 2 32 plane. sin 2 (2θ 23 ) > 0.92 m 2 32 =1.9 to ev 2[i] sin 2 (2θ 13 ) < 0.19, CL = 90% Page 9 Created: 7/5/ :38

36 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: Heavy Neutral Leptons, Searches for For excited leptons, see Compositeness Limits below. Stable Neutral Heavy Lepton Mass Limits Mass m > 45.0 GeV, CL = 95% (Dirac) Mass m > 39.5 GeV, CL = 95% (Majorana) Neutral Heavy Lepton Mass Limits Mass m > 90.3 GeV, CL = 95% (Dirac ν L coupling to e, µ, τ; conservative case(τ)) Mass m > 80.5 GeV, CL = 95% (Majorana ν L coupling to e, µ, τ; conservative case(τ)) NOTES [a] This is the best limit for the mode e νγ. The best limit for electron disappearance is yr. [b] See the Note on Muon Decay Parameters in the µ Particle Listings for definitions and details. [c] P µ is the longitudinal polarization of the muon from pion decay. In standard V A theory, P µ =1andρ = δ = 3/4. [d] This only includes events with the γ energy > 10 MeV. Since the e ν e ν µ and e ν e ν µ γ modes cannot be clearly separated, we regard the latter mode as a subset of the former. [e] See the relevant Particle Listings for the energy limits used in this measurement. [f ] A test of additive vs. multiplicative lepton family number conservation. [g] Basis mode for the τ. [h] L ± mass limit depends on decay assumptions; see the Full Listings. [i] The sign of m 2 32 is not known at this time. The range quoted is for the absolute value. Page 10 Created: 7/5/ :38

37 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: GAUGE AND HIGGS BOSONS γ I (J PC ) = 0,1(1 ) Mass m < ev Charge q < e Mean life τ =Stable g or gluon I (J P )=0(1 ) Mass m =0 [a] SU(3) color octet W J =1 Charge = ±1 e Mass m = ± GeV m Z m W = ± GeV m W + m W = 0.2 ± 0.6 GeV Full width Γ = ± GeV Nπ ± =15.70 ± 0.35 NK ± =2.20 ± 0.19 Np =0.92 ± 0.14 Ncharged =19.41 ± 0.15 W modes are charge conjugates of the modes below. p W + DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) l + ν [b] (10.80± 0.09) % e + ν (10.75± 0.13) % µ + ν (10.57± 0.15) % τ + ν (11.25± 0.20) % hadrons (67.60± 0.27) % π + γ < % D + s γ < % c X (33.4 ± 2.6 ) % c s (31 )% invisible [c] ( 1.4 ± 2.8 ) % Page 1 Created: 9/15/ :44

38 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: Z J =1 Charge = 0 Mass m = ± GeV [d] Full width Γ = ± GeV Γ ( l + l ) = ± MeV [b] Γ ( invisible ) = ± 1.5 MeV [e] Γ ( hadrons ) = ± 2.0 MeV Γ ( µ + µ ) /Γ ( e + e ) = ± Γ ( τ + τ ) /Γ ( e + e ) = ± [f ] Average charged multiplicity Ncharged =20.76 ± 0.16 (S = 2.1) Couplings to leptons g l V g l A = ± = ± g ν e =0.53 ± 0.09 g ν µ =0.502 ± Asymmetry parameters [g] A e = ± A µ =0.142 ± A τ =0.143 ± A s =0.90 ± 0.09 A c =0.670 ± A b =0.923 ± Charge asymmetry (%) at Z pole =1.71 ± 0.10 FB =4± 7 =9.8 ± 1.1 =7.07 ± 0.35 =9.92 ± 0.16 A (0l) FB A (0u) A (0s) FB A (0c) FB A (0b) FB Page 2 Created: 9/15/ :44

39 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: Scale factor/ p Z DECAY MODES Fraction (Γ i /Γ) Confidence level (MeV/c) e + e ( ±0.004 ) % µ + µ ( ±0.007 ) % τ + τ ( ±0.008 ) % l + l [b] ( ±0.0023) % invisible (20.00 ±0.06 ) % hadrons (69.91 ±0.06 ) % (uu +cc )/2 (11.6 ±0.6 ) % (dd +ss +bb )/3 (15.6 ±0.4 ) % cc (12.03 ±0.21 ) % bb (15.12 ±0.05 ) % b bbb ( 3.6 ±1.3 ) 10 4 ggg < 1.1 % CL=95% π 0 γ < CL=95% ηγ < CL=95% ωγ < CL=95% η (958)γ < CL=95% γγ < CL=95% γγγ < CL=95% π ± W [h] < CL=95% ρ ± W [h] < CL=95% J/ψ(1S)X ( ) 10 3 S=1.1 ψ(2s)x ( 1.60 ±0.29 ) 10 3 χ c1 (1P)X ( 2.9 ±0.7 ) 10 3 χ c2 (1P)X < CL=90% Υ(1S) X+Υ(2S) X +Υ(3S) X Υ(1S)X < CL=95% Υ(2S)X < CL=95% Υ(3S)X < CL=95% (D 0 /D 0 )X (20.7 ±2.0 ) % D ± X (12.2 ±1.7 ) % D (2010) ± X [h] (11.4 ±1.3 ) % D s1 (2536) ± X ( 3.6 ±0.8 ) 10 3 D sj (2573) ± X ( 5.8 ±2.2 ) 10 3 D (2629) ± X searched for B + X ( 6.03 ±0.15 ) % ( 1.0 ±0.5 ) 10 4 B 0 s X ( 1.55 ±0.13 ) % B + c X searched for Λ + c X ( 1.54 ±0.33 ) % b -baryon X ( 1.51 ±0.26 ) % anomalous γ +hadrons [i] < CL=95% Page 3 Created: 9/15/ :44

40 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: e + e γ [i] < CL=95% µ + µ γ [i] < CL=95% τ + τ γ [i] < CL=95% l + l γγ [j] < CL=95% q q γγ [j] < CL=95% ν νγγ [j] < CL=95% e ± µ LF [h] < CL=95% e ± τ LF [h] < CL=95% µ ± τ LF [h] < CL=95% pe L,B < CL=95% p µ L,B < CL=95% Higgs Bosons H 0 and H ±,Searchesfor H 0 H 0 Mass m > GeV, CL = 95% H 0 1 in Supersymmetric Models (m H 0 <m 1 H 0) 2 Mass m > 89.8 GeV, CL = 95% A 0 Pseudoscalar Higgs Boson in Supersymmetric Models [k] Mass m > 90.4 GeV, CL = 95% tanβ >0.4 H ± H ± Mass m > 79.3 GeV, CL = 95% See the Particle Listings for a Note giving details of Higgs Bosons. Heavy Bosons Other Than Higgs Bosons, Searches for Additional W Bosons W with standard couplings decaying to e ν, µν Mass m > 800 GeV, CL = 95% W R right-handed W Mass m > 715 GeV, CL = 90% (electroweak fit) Page 4 Created: 9/15/ :44

41 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: Additional Z Bosons Z SM with standard couplings Mass m > 825 GeV, CL = 95% (p p direct search) Mass m > 1500 GeV, CL = 95% (electroweak fit) Z LR of SU(2) L SU(2) R U(1) (with g L = g R ) Mass m > 630 GeV, CL = 95% (p p direct search) Mass m > 860 GeV, CL = 95% (electroweak fit) Z χ of SO(10) SU(5) U(1) χ (with g χ =e/cosθ W ) Mass m > 690 GeV, CL = 95% (p p direct search) Mass m > 781 GeV, CL = 95% (electroweak fit) Z ψ of E 6 SO(10) U(1) ψ (with g ψ =e/cosθ W ) Mass m > 675 GeV, CL = 95% (p p direct search) Mass m > 366 GeV, CL = 95% (electroweak fit) Z η of E 6 SU(3) SU(2) U(1) U(1) η (with g η =e/cosθ W ) Mass m > 720 GeV, CL = 95% (p p direct search) Mass m > 619 GeV, CL = 95% (electroweak fit) Scalar Leptoquarks Mass m > 256 GeV, CL = 95% (1st generation, pair prod.) Mass m > 298 GeV, CL = 95% (1st gener., single prod.) Mass m > 202 GeV, CL = 95% (2nd gener., pair prod.) Mass m > 73 GeV, CL = 95% (2nd gener., single prod.) Mass m > 148 GeV, CL = 95% (3rd gener., pair prod.) (See the Particle Listings for assumptions on leptoquark quantum numbers and branching fractions.) Axions (A 0 ) and Other Very Light Bosons, Searches for The standard Peccei-Quinn axion is ruled out. Variants with reduced couplings or much smaller masses are constrained by various data. The Particle Listings in the full Review contain a Note discussing axion searches. The best limit for the half-life of neutrinoless double beta decay with Majoron emission is > years (CL = 90%). Page 5 Created: 9/15/ :44

42 Citation: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: NOTES [a] Theoretical value. A mass as large as a few MeV may not be precluded. [b] l indicates each type of lepton (e, µ, andτ), not sum over them. [c] This represents the width for the decay of the W boson into a charged particle with momentum below detectability, p< 200 MeV. [d] TheZ-boson mass listed here corresponds to a Breit-Wigner resonance parameter. It lies approximately 34 MeV above the real part of the position of the pole (in the energy-squared plane) in the Z-boson propagator. [e] This partial width takes into account Z decays into ν ν and any other possible undetected modes. [f ] This ratio has not been corrected for the τ mass. [g]herea 2g V g A /(g 2 V +g2 A ). [h] The value is for the sum of the charge states or particle/antiparticle states indicated. [i]seethez Particle Listings for the γ energy range used in this measurement. [j]form γγ =(60± 5) GeV. [k] The limits assume no invisible decays. Page 6 Created: 9/15/ :44