QCD studies and Higgs searches at the LHC. part three. Sven-Olaf Moch. DESY, Zeuthen. CALC-2012, Dubna, July

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1 QCD studies and Higgs searches at the LHC part three Sven-Olaf Moch DESY, Zeuthen CALC-212, Dubna, July Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.1

2 Plan Some new results on the heaviest elementary particle Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.2

3 ParticleZoo Abundant production (I) of top-quarks Orders for top-quarks from Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.3

4 ParticleZoo Top-quark decays (II) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.4

5 Top quark production Leading order Feynman diagrams q+ q Q+ Q g+ g Q+ Q NLO in QCD Nason, Dawson, Ellis 88; Beenakker, Smith, van Neerven 89; Mangano, Nason, Ridolfi 92; Bernreuther, Brandenburg, Si, Uwer 4; Mitov, Czakon 8;... accurate to O(15%) at LHC Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.5

6 Top quark production Leading order Feynman diagrams q+ q Q+ Q g+ g Q+ Q NLO in QCD Nason, Dawson, Ellis 88; Beenakker, Smith, van Neerven 89; Mangano, Nason, Ridolfi 92; Bernreuther, Brandenburg, Si, Uwer 4; Mitov, Czakon 8;... accurate to O(15%) at LHC First steps towards higher orders in QCD: explore limits Study of massive QCD amplitudes in high-energy limit s m 2 exploit high-energy factorization in BFKL formalism Partonic threshold s 4m 2 Sudakov logarithms lnβ (velocity of heavy quark β = 1 4m 2 /s) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.5

7 Sudakov logarithms p + k Recall perturbative QCD: calculation of observables as series in α s 1 but: large logarithmic corrections, ln(...) 1 double logarithms (Sudakov) Soft/Collinear regions of phase space p double logarithms from singular regions in Feynman diagrams propagator vanishes for: E g =, soft θ qg = collinear k α s d 4 k 1 (p+k) 2 = 1 (p+k) 2 1 2p k = 1 2E q E g (1 cosθ qg ) 1 α s de g dsinθ qg 2E q E g (1 cosθ qg ) α s ln 2 (...) Improved perturbation theory: resum logarithms to all orders long history of resummation Kidonakis, Sterman 97; Bonciani, Catani, Mangano, Nason 98; Kidonakis, Laenen, S.M., Vogt 1;... Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.6

8 Sudakov logarithms in cross sections Intuitive aspects of higher order corrections lowest order, elastic q t first order correction virtual < (elastic) q q t t bar (I)@ first order correction Brems > (inelastic) q q g t t q t at threshold for t t-creation strong Sudakov-supression inelastic tendency σ exp [ α s ln 2 (1 4m 2 t/s) ] universal factor for parton splittings (leading log accuracy) modelling of MC parton showers Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.7

9 Hadronic reaction p p: recall master equation σ pp t t = ij f i f j ˆσ ij t t initial partons: also Sudakov-supressed bar (II)@ Parton cross section ˆσ ij t t Sudakov-enhancement after mass factorization ˆσ ij t t = σ ln 2 (...) pp t t = e αs f i f ( ) j e α s ln 2 (...) 2 = e+α s ln 2 (...) p p q q t t large double logarithms Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.8

10 sigma Total cross at Tevatron section at Tevatron σ pp t t = ij f i f j ˆσ ij t t 25 L q q [%] L gg [%] L qg [%] Luminosity L ij [1/GeV 2 ] s = 1.96 TeV CTEQ 6.5 µ f = 171 GeV gg qg qq L q q [%] L gg [%] L qg [%] NLO QCD Partonic cross section [pb] µ r = m t = 171 GeV sum gg qq qg qq NLO QCD Hadronic cross section [pb] µ f = µ r = m t = 171 GeV gg qg x 1 Total uncertainty in % s [GeV] % Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.9

11 Top-pair hadro-production NNLO cross section for heavy-quark hadro-production Exact results for channel q q t t Czakon, Mitov as 2 as 3 as β Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.1

12 Top-pair hadro-production NNLO cross section for heavy-quark hadro-production Approximate results for channel qg/gg t t f gg (2,1) exact f gg (2,1) approx f gg (2,1) thresh threshold at s 4m 2 t with logarithms ln(β) in velocity of heavy quark β = 1 4m 2 t /s at nth -order S.M, Uwer 8; Beneke, Czakon, Falgari, Mitov, Schwinn 9 high-energy limit for ρ = 4m 2 t/s 1 Catani, Ciafaloni, Hautmann 91; Ball, Ellis 1; S.M, Uwer, Vogt 12 f (2,) gg approx f (2,) gg thresh η η Sven-Olaf Moch QCD studies and Higgs searches at the LHC p A,B

13 Top Scalescale dependence Theoretical uncertainty from variation of scales µ R,µ F plot with PDF set MSTW 28 (but largely independent on PDFs) mass m t = 173 GeV stable predictions in range µ R,µ F [m t /2,2m t ] 3% σ +1% at LHC 5% σ +3% at Tevatron σ [pb] 75 LHC σ [pb] MSTW 28 NNLO m = 173 GeV Tevatron MSTW 28 NNLO 55 4 m = 173 GeV µ r /µ f LHC µ r /µ f 1 Tevatron Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.11

14 Electroweak corrections Electroweak corrections (ratio of σ EW /σ LO ) Bernreuther, Fücker 5; Kühn, Uwer,Scharf 6 Effect depends on Higgs mass (choices m H = 12GeV,m H = 2GeV,m H = 1GeV) relative weak corrections [%] -1 LHC -1.5 M h = 12 GeV M h = 2 GeV M h = 1 GeV LHC m t [GeV] relative weak corrections [%] 1 Tevatron M h = 12 GeV M h = 2 GeV -1 M h = 1 GeV m t [GeV] Tevatron Tevatron: vanishing contribution for light Higgs LHC: O(2%) with respect to σ LO negative contribution to total cross section σ EW O(1 15) pb Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.12

15 Top-quark pairs with one jet Production of t t+jet at fixed order LHC: large rates for production of t t-pairs with additional jets Scale dependence at LO large g t g t g t g t g t t t g t g g g g g g q t q t q t t t g q g q g q t Feynman diagrams (sample) for t t+ jet production at LO Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.13

16 ( ) [ ] dσ fb dp T,t GeV NLO Production for ttbarjet of t t+ jet at NLO 1 pp t t + jet + X s = 14TeV 15 σ[pb] 1 pp t t+jet+x s = 14TeV p T,jet > 2GeV 1 1 NLO LO 5 NLO (CTEQ6M) LO (CTEQ6L1) K = NLO/LO µ/m t p T,t [GeV] NLO QCD corrections Dittmaier, Uwer, Weinzierl 7-8 scale dependence greatly reduced at NLO corrections for total rate at scale µ r = µ f = m t are almost zero transverse-momentum distributions of top-quark p T,t along with K-factor and scale variation m t /2 µ 2m t Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.14

17 MCatNLO Monte Carlo and parton showers at NLO Merging of fixed order NLO with parton shower Monte Carlo Frixione, Webber 2, Nason 4 combining accuracy of exact hard matrix elements for large angle scattering at NLO with soft/collinear emission of parton shower POWHEG BOX as standard interface to parton shower programs PYTHIA or HERWIG Alioli, Nason, Oleari, Re 1 Production of t t+ jet and parton showers Kardos, Papadopoulos, Trocsanyi 11, Alioli, S.M., Uwer 11 Implementation Event generation with cut on p gen t 1 GeV Alternative option for soft and collinear divergences at Born level: generation of weighted events with Born suppression factor B supp = B F(p t ) Alioli, Nason, Oleari, Re 1 F(p t ) = ( p 2 t p 2 t +(psupp t ) 2 ) n Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.15

18 parton Production shower t t+ jet (I) and parton shower (I) Differential distributions in top-quark s transverse momentum p t T and rapidity y t at LHC7 comparision of NLO, LHEF for POWHEG hardest emission without showering, and POWHEG with shower/hadronization with HERWIG or PYTHIA Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.16

19 parton Production shower t t+ jet (II) and parton shower (II) Differential distributions as function of t t-pair invariant mass m t t and transverse momentum p t t T at LHC7 Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.17

20 Heavy-quark masses QCD Lagrangian L = 1 4 F µνf µν + q(i/d m q )q flavors Covariant derivative D µ = µ +ig s A µ Formal parameters of the theory (no observables) strong coupling α s = gs/(4π) 2 quark masses m q Quantum corrections (loop integrals) require UV renormalization; (scheme dependence): α s asymptotic freedom, running coupling (MS scheme) m q pole mass or running mass (MS scheme) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.18

21 Mass Pole mass renormalization scheme Based on (unphysical) concept of top-quark being a free parton g /p m q Σ(p,m q ) p2 =m 2 q heavy-quark self-energy Σ(p,m q ) receives contributions from regions of all loop momenta also from momenta of O(Λ QCD ) Definition of pole mass ambiguous up to corrections O(Λ QCD ) Running quark masses MS mass definition m(µ R ) realizes running mass (scale dependence) renormalization group equation (mass anomalous dimension γ) ( µ 2 R +β(α s ) ) m(µ α R ) = γ(α s )m(µ R ) s µ 2 R short distance mass probes at scale of hard scattering m pole = m short distance +δm conversion between pole mass and MS mass definition in perturbation theory: m = m(µ R ) (1+a s (µ R )d (1) +a s (µ R ) 2 d (2)) q Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.19

22 RG Scalerunning dependence mass Renormalization group equation for scale dependence strong coupling α s and mass m µ 2 d dµ 2α s(µ) = β(α s ) µ 2 d dµ 2m(µ) = γ(α s)m(µ) Perturbative expansion known to four loops β-function van Ritbergen, Vermaseren, Larin 97 and mass anomalous dimension γ Chetyrkin 97; Larin, van Ritbergen, Vermaseren 97 very good convergence of perturbative series even at low scales Plot at low scales µ = GeV α s (left) and mass ratio m(3gev)/m(µ) (right) running coupling 1. running mass Use of charm-quark mass m c (m c ) is well justified Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.2

23 Illustration for top-quark mass The ILC top-quark mass Pole mass measurements are strongly order-dependent e.g. threshold scan of cross section in e + e collision Beneke, Signer, Smirnov 99; Hoang, Teubner 99; Melnikov, Yelkhovsky 98; Penin, Pivovarov 99; R g Yakovlev 99.2 LO (dotted), NLO (dashed),. NNLO (solid) q 2 GeV Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.21

24 Illustration for top-quark mass The Tevatron top-quark mass Total cross section and different channels of Tevatron analyses (theory uncertainty band from scale variation) Determination of m t from total cross section (slope dσ/dm t ) e.g. DZero 9: NLO m t = ; NNLO m t = ;... (pb) tt σ DØ, L = 1 fb Measured σ tt Nadolsky et al., PRD 78, 134 (28) Cacciari et al., JHEP 9, 127 (28) Moch and Uwer, PRD 78, 343 (28) Top Mass (GeV) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.21

25 The running top-quark mass MS mass definition m(µ R ) realizes running mass (scale dependence) short distance mass probes at scale of hard scattering conversion between pole mass and MS mass definition in perturbation theory: m t = m(µ R ) (1+a s (µ R )d (1) +a s (µ R ) 2 d (2)) Scale dependence greatly reduced Tevatron MSTW 28 NNLO m(m) = 163 GeV σ [pb] 8 σ [pb] LHC MSTW 28 NNLO 6 m(m) = 163 GeV µ r /µ f µ r /µ f Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.22

26 The running top-quark mass MS mass definition m(µ R ) realizes running mass (scale dependence) short distance mass probes at scale of hard scattering conversion between pole mass and MS mass definition in perturbation theory: m t = m(µ R ) (1+a s (µ R )d (1) +a s (µ R ) 2 d (2)) Pole mass scheme for comparison σ [pb] 75 LHC σ [pb] MSTW 28 NNLO m = 173 GeV Tevatron MSTW 28 NNLO 55 4 m = 173 GeV µ r /µ f µ r /µ f Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.22

27 Stability Perturbative in stability MSbar of predictions with M S mass definition Parton cross section for channels q q, gg and qg on-shell scheme for m t = 173 GeV (left) MS scheme for m(m) = 163 GeV (right) qq σ LO and σ NLO for m = 173 GeV 2 qq gg σ LO and σ NLO for m(m) = 163 GeV σ [pb] 15 1 gg σ [pb] qq gg qg 5 qq gg qg s [TeV] s [TeV] Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.23

28 Stability Perturbative in stability MSbar of predictions with M S mass definition Parton cross section for channels q q, gg and qg on-shell scheme for m t = 173 GeV (left) MS scheme for m(m) = 163 GeV (right) MS scheme more emphasis on LO contribution less significance to threshold region at NLO qq σ LO and σ NLO for m = 173 GeV 2 qq gg σ LO and σ NLO for m(m) = 163 GeV σ [pb] 15 1 gg σ [pb] qq gg qg 5 qq gg qg s [TeV] s [TeV] Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.23

29 Top quark s Mmass S mass dependence MSbar Total top-quark cross section as function of m Langenfeld, S.M., Uwer 9 theoretical uncertainity (band) due to variation of µ R [m/2,2m] for fixed set µ F m/2,m,2m Tevatron MSTW 28 NNLO NLO Hathor LHC 7 TeV MSTW 28 NNLO NLO NNLO approx σ [pb] 1 NNLO approx σ [pb] (16 ± 16) pb m(m) Tevatron m(m) LHC Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.24

30 Top quark mass determination Determine top quark mass from Tevatron cross section data σ t t = σ t t = pb D coll. arxiv: pb CDF coll. CDF-note-9913 Fit of m t for individual PDFs (parton luminosity at Tevatron driven by q q) ABM11 JR9 MSTW8 NN21 m MS t (m t ) m pole t (m pole t ) ( ) ( ) ( ) ( ) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.25

31 Top quark cross massection at LHC Check predictions at LHC with s = 7 TeV cross section computation with HATHOR (version 1.3) Aliev, Lacker, Langenfeld, S.M., Uwer, Wiedermann 1 Atlas at s = 7 TeV σ t t = pb Atlas coll. ATLAS-CONF CMS at s = 7 TeV σ t t = pb CMS coll. CMS-PAS-TOP ABM11 JR9 MSTW8 NN21 m MS t (m t ) m pole t (m pole t ) ( ) ( ) ( ) ( ) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.26

32 New Observable Mass measurement with t t + jet-samples Mass determination with new observable Alioli, Fuster, Irles, S.M., Uwer, Vos 12 define normalized-differential t t + jet cross section Upshot dn 3 dρ s (m top,µ,ρ s ) = variable ρ s = 2 m st t+1jet with m = 17GeV and invariant mass of multi-jet system s t t+1jet 1 σ t t+1jet s dn 3 /dρ dσ t t+1jet dρ s (m top,µ,ρ s ) dn 3 (m dρ s p top p p p m top =17 GeV, pdf=cteq6.6, scale variations m /2<µ<2m top top p m top =17 GeV, pdf=mstw28nlo9cl p m top =16 GeV, pdf=cteq6.6 p m top =17 GeV, pdf=cteq6.6,µ,ρ ) using tt+1-jet at NLO s Independent determination of top-quark mass m t alternative to kinematic reconstruction and extraction from total cross section Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.27 ρ s

33 Vacuum Implications (I) on electroweak vacuum Relation between Higgs mass m H and top-quark mass m t condition of absolute stability of electroweak vacuum λ(µ) extrapolation of Standard Model up to Planck scale M P λ(m P ) implies lower bound on Higgs mass m H ( ) m pole ( ) t GeV αs (M m H Z ) GeV.7 ±1. GeV recent NNLO analyses Bezrukov, Kalmykov, Kniehl, Shaposhnikov 12; Degrassi, Di Vita, Elias-Miro, Espinosa, Giudice et a. 12 uncertainity in results due to α s and m t (pole mass scheme) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.28

34 Vacuum (II) T riviality Bound Quantum corrections to the Higgs potential: V (Φ) = λ[φ Φ v2 2 ]2 Corrections to coupling λ 16π 2 dλ d lnq = 24λ2 (3g 2 + 9g 2 12y 2 t )λ g g 2 g g4 6y 4 t + higher order Large mass λ dominated renormalisation group equation (RGE): 16π 2 λ increases with Q dλ d lnq = 24λ2 = λ(q) = M 2 H 2v 2 3 2π 2 M 2 H ln(q/v) Landau pole Λ ve 4π2 v 2 /3M 2 H New Physics must appear before this point to restore stability = For Λ fixed upper bound on M H Triviality No quantum theory for Λ : trivial theory λ =. M.M.Mühlleitner, July 212, Dubna M. Mühlleitner (CALC 212) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.29

35 Vacuum (III) Vacuum Stability Corrections to coupling λ 16π 2 dλ d lnq = 24λ2 (3g 2 + 9g 2 12y 2 t )λ g g 2 g g4 6y 4 t + higher order Small mass y t dominated RGE: 16π 2 dλ d lnq = 6y4 t = λ(q) = λ λ decreases with Q; λ < potential unbounded from below λ = for λ 3 8π 2 y 4 ln Q Q Vacuum stability Λ ve 4π2 M 2 H /3y4 t v2 3 8π 2 y 4 ln Q Q π 2 y 2 ln Q Q New Physics must appear before this point to ensure vacuum stability (no negative λ) = For Λ fixed lower bound on M H M.M.Mühlleitner, July 212, Dubna M. Mühlleitner (CALC 212) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.3

36 Vacuum Implications (IV) on electroweak vacuum Relation between Higgs mass m H and top-quark mass m t ( ) m pole ( ) t GeV αs (M m H Z ) GeV.7 ±1. GeV Uncertainty in Higgs bound due to m t determined in MS scheme m MS t (m t ) = 163.3±2.7 GeV Implications: m t in pole mass scheme: m pole t = 173.3±2.8 GeV bound on m H 129.4±5.6 GeV m pole t [GeV] meta- stable EW vacuum: unstable 95%CL 168 stable M H [GeV] ILC LHC Tev lhc Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.31

37 Vacuum Implications (IV) on electroweak vacuum Relation between Higgs mass m H and top-quark mass m t ( ) m pole ( ) t GeV αs (M m H Z ) GeV.7 ±1. GeV Uncertainty in Higgs bound due to m t determined in MS scheme m MS t (m t ) = 163.3±2.7 GeV Implications: m t in pole mass scheme: m pole t = 173.3±2.8 GeV bound on m H 129.4±5.6 GeV m pole t [GeV] meta- stable EW vacuum: unstable 95%CL 168 stable M H [GeV] ILC LHC Tev lhc Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.31

38 Vacuum (V) G. Isidori (Higgs Hunting 212) Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.32

39 Summary (part III) Top quark theory improved understanding of theory and application of new concepts resummation important for Tevatron and LHC phenomenology Cross sections NNLO predictions for t t NLO corrections to t t+ jet electroweak corrections MS mass definition greatly reduced scale dependence much improved convergence of perturbation theory Sven-Olaf Moch QCD studies and Higgs searches at the LHC p.33