Precision determination of the top-quark mass Sven-Olaf Moch Universit¨ at Hamburg ————————————————————————————————————– Theoretical Physics Seminar , Liverpool, Mar 04, 2015 Sven-Olaf Moch Precision determination of the top-quark mass – p.1
Introduction (I) Classical mechanics • Mass is defined as product of density and volume of matter • classical concept Sven-Olaf Moch Precision determination of the top-quark mass – p.2
Introduction (I) Classical mechanics • Mass is defined as product of density and volume of matter • classical concept • The quantity of matter is that which arises jointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass. Newton Sven-Olaf Moch Precision determination of the top-quark mass – p.2
Introduction (I) Classical mechanics • Mass is defined as product of density and volume of matter • classical concept • The quantity of matter is that which arises jointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass. Newton Atomic theory • Mass is conserved Lavoisier • Mass of body is sum of mass of its constituents M ( X ) = N A m a ( X ) Avogadro Sven-Olaf Moch Precision determination of the top-quark mass – p.2
Introduction (II) Kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Orginal des Bureau International des Poids et Mesures • International prototype kilogram (IPK): made in 1889, 39 mm high, alloy of platinum and iridium Sven-Olaf Moch Precision determination of the top-quark mass – p.3
Introduction (II) Kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Orginal des Bureau International des Poids et Mesures • International prototype kilogram (IPK): made in 1889, 39 mm high, alloy of platinum and iridium Special relativity • Equivalence principle E = mc 2 Einstein Sven-Olaf Moch Precision determination of the top-quark mass – p.3
Introduction (II) Kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Orginal des Bureau International des Poids et Mesures • International prototype kilogram (IPK): made in 1889, 39 mm high, alloy of platinum and iridium Special relativity • Equivalence principle E = mc 2 Einstein Standard Model • Higgs boson gives mass to matter fields via Higgs-Yukawa coupling • large top-quark mass m t Sven-Olaf Moch Precision determination of the top-quark mass – p.3
Quantum field theory QCD • Classical part of QCD Lagrangian − 1 � 4 F a µν F µν L = + q i (i / ¯ D − m q ) ij q j b flavors • field strength tensor F a µν and matter fields q i , ¯ q j • covariant derivative D µ,ij = ∂ µ δ ij + i g s ( t a ) ij A a µ • Formal parameters of the theory (no observables) • strong coupling α s = g 2 s / (4 π ) • quark masses m q • Parameters of Lagrangian have no unique physical interpretation • radiative corrections require definition of renormalization scheme Challenge • Suitable observables for measurements of α s , m q , . . . • comparison of theory predictions and experimental data Sven-Olaf Moch Precision determination of the top-quark mass – p.4
Coupling constant renormalization • Running coupling constant α s from radiative corrections, e.g. one loop – anti-screening (color charge of g ) – screening (like in QED) • QCD beta function µ 2 d dµ 2 α s ( µ ) = β ( α s ) running coupling • perturbative expansion α s ( µ ) 0.40 to four loops van Ritbergen, Vermaseren, Larin ‘97 0.35 • very good convergence of perturbative series 0.30 even at low scales 0.25 µ 1.0 1.5 2.0 2.5 3.0 Sven-Olaf Moch Precision determination of the top-quark mass – p.5
Quark mass renormalization • Heavy-quark self-energy Σ( p, m q ) i + + + . . . = Σ Σ Σ p − m q − Σ( p, m q ) / QCD g • QCD corrections to self-energy Σ( p, m q ) t • dimensional regularization D = 4 − 2 ǫ • one-loop: UV divergence 1 /ǫ (Laurent expansion) � µ 2 � ǫ � � � � �� Σ (1) , bare ( p, m q ) = α s − C F 1 3 C F 1 ( / p − m q ) ǫ + fin. + m q ǫ + fin. m 2 4 π q • Relate bare and renormalized mass parameter m bare = m ren + δm q q q = + + + . . . Σ ren ( p, m q ) ( Z ψ − 1) / p − ( Z m − 1) m q Sven-Olaf Moch Precision determination of the top-quark mass – p.6
Quark mass renormalization • Heavy-quark self-energy Σ( p, m q ) i + + + . . . = Σ Σ Σ p − m q − Σ( p, m q ) / W EW sector • EW corrections to top-quark self-energy t t • on-shell intermediate (virtual) W -boson b • m t complex parameter with imaginary part Γ t = 2 . 0 ± 0 . 7 GeV • Γ t > 1 GeV: top-quark decays before it hadronizes Sven-Olaf Moch Precision determination of the top-quark mass – p.6
Mass renormalization scheme Pole mass • Based on (unphysical) concept of top-quark being a free parton • m ren coincides with pole of propagator at each order q � � p − m pole p − m q − Σ( p, m q ) / → / � q � / p = m q • Definition of pole mass ambiguous up to corrections O (Λ QCD ) • heavy-quark self-energy Σ( p, m q ) receives contributions from regions of all loop momenta – also from momenta of O (Λ QCD ) • bound from lattice QCD: ∆ m q ≥ 0 . 7 · Λ QCD ≃ 200 MeV Bauer, Bali, Pineda ’11 MS scheme • MS mass definition • one-loop minimal subtraction � 1 � = m q α s δm (1) 4 π 3 C F ǫ − γ E + ln 4 π q • MS scheme induces scale dependence: m ( µ ) Sven-Olaf Moch Precision determination of the top-quark mass – p.7
Running quark mass Scale dependence • Renormalization group equation for scale dependence • mass anomalous dimension γ known to four loops Chetyrkin ‘97; Larin, van Ritbergen, Vermaseren ‘97 � � µ 2 ∂ ∂µ 2 + β ( α s ) ∂ m ( µ ) = γ ( α s ) m ( µ ) ∂α s • Plot mass ratio m t (163 GeV ) /m t ( µ ) running top quark mass 1.00 m ( µ ) 0.99 0.98 0.97 0.96 90 100 110 120 130 140 150 160 µ Sven-Olaf Moch Precision determination of the top-quark mass – p.8
Scheme transformations • Conversion between different renormalization schemes possible in perturbation theory • Relation for pole mass and MS mass • known to four loops in QCD Gray, Broadhurst, Gräfe, Schilcher ‘90; Chetyrkin, Steinhauser ‘99; Melnikov, v. Ritbergen ‘99; Marquard, Smirnov, Smirnov, Steinhauser ‘15 • EW sector known to O ( α EW α s ) Jegerlehner, Kalmykov ‘04; Eiras, Steinhauser ‘06 • example: one-loop QCD � � 4 � �� � µ 2 1 + α s ( µ ) m pole = m ( µ ) 3 + ln + . . . m ( µ ) 2 4 π Sven-Olaf Moch Precision determination of the top-quark mass – p.9
Top-quark mass What is the value of the top-quark mass ? mt = ? Sven-Olaf Moch Precision determination of the top-quark mass – p.10
Some Answers 17 -1 -1 Tevatron+LHC m combination - March 2014, L = 3.5 fb - 8.7 fb top int ATLAS + CDF + CMS + D0 Preliminary ± CDF RunII, l+jets 172.85 1.12 ± ± (0.52 0.49 0.86) -1 L = 8.7 fb int ± CDF RunII, di-lepton 170.28 3.69 ± (1.95 3.13) -1 L = 5.6 fb int CDF RunII, all jets ± 172.47 2.01 ± ± (1.43 0.95 1.04) -1 L = 5.8 fb int miss CDF RunII, E +jets ± 173.93 1.85 ± ± T (1.26 1.05 0.86) -1 L = 8.7 fb int ± D0 RunII, l+jets 174.94 1.50 ± ± (0.83 0.47 1.16) -1 L = 3.6 fb int D0 RunII, di-lepton ± 174.00 2.79 ± ± (2.36 0.55 1.38) -1 L = 5.3 fb int ± ATLAS 2011, l+jets 172.31 1.55 ± ± (0.23 0.72 1.35) -1 L = 4.7 fb int ATLAS 2011, di-lepton ± 173.09 1.63 ± (0.64 1.50) -1 L = 4.7 fb int ± CMS 2011, l+jets 173.49 1.06 ± ± (0.27 0.33 0.97) -1 L = 4.9 fb int ± CMS 2011, di-lepton 172.50 1.52 ± (0.43 1.46) -1 L = 4.9 fb int CMS 2011, all jets ± 173.49 1.41 ± (0.69 1.23) -1 L = 3.5 fb int ± χ 2 173.34 0.76 ± ± / ndf =4.3/10 World comb. 2014 (0.27 0.24 0.67) χ 2 prob.=93% ± ± ± Comb. 173.20 0.87 Previous Tevatron March 2013 (Run I+II) (0.51 0.36 0.61) ± 173.29 0.95 ± ± (0.23 0.26 0.88) LHC September 2013 total ( stat. iJES syst. ) 1 165 170 175 180 185 m [GeV] top Sven-Olaf Moch Precision determination of the top-quark mass – p.11
World combination Experiment: ATLAS, CDF, CMS & D0 coll. 1403.4427 mt = 173.34 ± 0.76 GeV Sven-Olaf Moch Precision determination of the top-quark mass – p.12
World combination Experiment: ATLAS, CDF, CMS & D0 coll. 1403.4427 mt = 173.34 ± 0.76 GeV In all measurements considered in the present combination, the analyses are calibrated to the Monte Carlo (MC) top-quark mass definition. Sven-Olaf Moch Precision determination of the top-quark mass – p.12
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