Determining the Strong Coupling Constant
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Determination of the strong coupling constant αs at the LHC Klaus Rabbertz, KIT Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 1 Outline Introduction 2012: No LHC results yet PDG2012 Jet-like measurements Cross sections Ratios Normalised distributions top-quark pair production W/Z bosons Issues & perspectives Summary & outlook Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 2 Standard Model of Particle Physics Solid matter ... Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 3 Standard Model of Particle Physics Solid matter ... Electromagnetic interaction (magnets, electricity, ...) Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 4 Standard Model of Particle Physics Solid matter ... Electromagnetic interaction (magnets, electricity, ...) Weak interaction (β decays, sun, ...) Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 5 Standard Model of Particle Physics Strong interaction (nuclear forces, ...) Solid matter ... Electromagnetic interaction (magnets, electricity, ...) Weak interaction (β decays, sun, ...) Cush, Wikipedia. … and three fundamental interactions. (no gravity) Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 6 αs(MZ) world average versus time 1st estimate from G. Altarelli Start of FLAG Flavour Lattice Averaging Group +lattice NNLO PDG 2016 +LEP +HERA pre-LEP S. Bethke, arXiv:1907.01435. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 7 αs(MZ) world average versus time 1st estimate from G. Altarelli +lattice NNLO PDG 2016 +LEP +HERA Large theoretical uncertainty from (PDF + αs) on Higgs x sections pre-LEP In particular tTH & gg-Fusion: 7-13% S. Bethke, arXiv:1907.01435. CERN YR, LHC Higgs xs WG. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 8 QCD and asymptotic freedom Nobel prize 2004 Theory: Renormalisation group equation (RGE) Solution of 1-loop equation Running coupling constant D. Gross 'Strong' coupling weak for Q2 → ∞ , i.e. small distances Asymptotic freedom D. Politzer Perturbative methods What happens at large distances? usable Q2 → 0 ? Cannot be answered here! For Q2 → Λ2 perturbation theory not F. Wilczek applicable anymore! Physik Journal 3 (2004) Nr. 12 nobelprize.org Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 9 Unification of couplings? Unification of couplings e.g. in Minimal Supersymmetric Standard Model (MSSM)? We (LHC) are here Need to test RUNNING even – in particular? – when no SUSY found! J. Heisig, DESY Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 10 Jets at the LHC Abundant production of jets: 2 Jets at hadron colliders provide the largest dynamic range ever for αs(Q ) Plus insights into high-pT QCD, the proton structure, non-perturbative and electroweak effects at high Q Proton Structure Proton Structure (PDF) (PDF) Matrix Element Hadrons Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 11 Jets at the LHC Abundant production of jets: Extract αs(MZ), the least precisely known fundamental constant! Proton Structure Proton Structure (PDF) (PDF) Matrix Element Hadrons Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 12 W, Z, top at the LHC High-precision lepton measurements: W, Z, top measurements provide high-precision cross sections Also learn about electroweak parameters, the top mass, and the proton structure Proton Structure Proton Structure (PDF) (PDF) Matrix Element Muons Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 13 Jets at the LHC Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 14 2 Jet cross sections ~ αs Determination of α (M ) in single-parameter fit s Z Test consistency of running of αs(Q) Multi-parameter fit of α (M ) & PDFs s Z Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 15 All inclusive Large transverse momenta Proton Proton Every jet counts ATLAS: EPJC 73 (2013) 2509; JHEP 02 (2015) 153; JHEP 09 (2017) 020; JHEP 05 (2018) 195. Relevant ATLAS & CMS measurements: CMS: PRD 87 (2013) 112002; PRD 90 (2014) 072006; EPJC 75 (2015) 288; EPJC 76 (2016) 265; EPJC 76 (2016) 451; JHEP 03 (2017) 156. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 16 Inclusive jets: cross section Overall agreement with predictions of QCD at NLO over many orders of magnitude in cross section and even beyond 2 TeV in jet pT and for rapidities |y| up to 3 ~ 5 at √s = 2.76, 7, 8, and 13 TeV. Here: anti-kt, R=0.4, 13 TeV Data vs. NLO pQCD x non-pert. x EW corrections Exp. uncertainties for |y| < 0.5 NLO: Ellis, Kunszt, Soper, PRL 69 (1992) 1496; Giele, Glover, Kosower, NPB 403 (1993) 633; Z. Nagy, PRD 68 (2003) 094002. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 17 Inclusive jets: theory corrections anti-kt, R=0.4, 13 TeV, |y| < 0.5 Nonperturbative correction factors: Electroweak correction factors: - estimated from tuned MC event generators - calculated perturbatively - uncertainty of 5 – 15% at pT = 100 GeV - uncertainty small - strongly dependent on jet size R - strongly dependent on jet rapidity y - very important at high p - less important at high pT T EW: Dittmaier, Huss, Speckner, JHEP 11 (2012) 095. Frederix et al., JHEP 04 (2017) 076. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 18 Inclusive jets: theory corrections anti-kt, R=0.4, 13 TeV, |y| < 0.5 Nonperturbative correction factors: Electroweak correction factors: - estimated from tuned MC event generators - calculated perturbatively - uncertainty of 5 – 15% at pT = 100 GeV - uncertainty small - strongly dependent on jet size R - strongly dependent on jet rapidity y - very important at high p - less important at high pT T EW: ALICE, arXiv:1909.09718. Dittmaier, Huss, Speckner, JHEP 11 (2012) 095. See also CMS, SMP-19-003. Frederix et al., JHEP 04 (2017) 076. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 19 Inclusive jets: αs Sensitivity to α (M ) at NLO Χ2 fit of α (M ) for all jet p and |y| bins s Z s Z T - CMS: anti-k R = 0.7 at √s = 8 TeV - In fit: all exp. + PDF + NP uncertainties t - PDFs: CT10 NLO PDF sets for various α (M ) s Z - QCD scale choice: μR = μF = pT,jet Jets @ NNLO not fully used yet in fits @ LHC → in progress Results for ep: → Britzger et al., EPJC79 (2019) 845. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 20 Inclusive jets: αs & PDFs Simultaneous fit of αs & PDFs possible combining HERA DIS & CMS jet data using xFitter Tool Reduced uncertainties of gluon PDF CMS results for α (M ) at NLO s Z Orange shading: external PDF sets Bluish shading: PDF fit incl. HERA data √s lum α (M ) exp NP scale s Z [TeV] [fb-1] PDF +53 7 5.0 0.1185 35 -24 +29 +53 8 19.7 0.1164 -33 -28 +23 +24 7 5.0 0.1192 -19 -39 +19 +22 8 19.7 0.1185 -26 -18 13 (7 TeV) / 18 (8 TeV) Question: How to deal with uncertainty of parameter fit Missing higher orders (aka scale uncertainty) xFitter (HERAFitter): Alekhin et al., EPJC 75 (2015) 304. in PDF fits? First progress → e.g. NNPDF, EPJC79 (2019) 931. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 21 Dijets Large masses Proton Proton ATLAS: JHEP 05 (2014) 059; JHEP 05 (2018) 195. Relevant ATLAS & CMS measurements: CMS: PRD 87 (2013) 112002; EPJC 77 (2017) 746. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 22 Triple-differential dijets Most measurements done with respect to dijet mass * and either max. rapidity |y|max (CMS) or rapidity separation y (ATLAS). One CMS result on α (M ): s Z Illustration of dijet event topologies Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 23 Triple-differential dijets Simultaneous fit of αs & PDFs combining HERA DIS & CMS djet data using xFitter Tool Data over NLO pQCD x non-pert. x EW corrections Reduced uncertainties of gluon PDF √s lum α (M ) exp NP scale s Z [TeV] [fb-1] PDF +53 7 5.0 0.1185 35 -24 +29 +53 8 19.7 0.1164 -33 -28 +23 +24 7 5.0 0.1192 -19 -39 +19 +22 8 19.7 0.1185 -26 -18 16-parameter fit +15 +31 8 19.7 0.1199 -16 -19 Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 24 Multi-jets and αs Higher multiplicity ATLAS: EPJC 75 (2014) 288. Relevant ATLAS & CMS measurements: CMS: EPJC 73 (2013) 2604; EPJC 75 (2015) 186; PAS-SMP-16-008 (2017). Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 25 Jet cross section ratios Determination of α (M ) in single-parameter fit s Z Test running of αs(Q) (reduced PDF dependence) Some reduction in sensitivity But cancellation of many systematic effects More scale choices Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 26 Sensitivity vs. systematic effects Inclusive 3-jet cross section Inclusive 3-jet to inclusive 2-jet cross section ratio Inclusive 2-jet cross section Reduced sensitivity Much reduced systematic uncertainty Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 27 3- to 2-jet ratios M. Wobisch R 3/2 2011 αs = 0.124 αs = 0.106 Fits only above 420 GeV 2 NNPDF CMS: R3/2 - Ratio of inclusive 3- to inclusive 2-jet events - anti-kT R=0.7 √s lum α (M ) exp NP scale → α s Z - Min. jet pT: 150 GeV s [TeV] [fb-1] PDF - Max. rap.: |y| < 2.5 7 5.0 0.1148 23 50 - Data 2011 7 TeV, 8 19.7 0.1150 22 +50 and 2012 8 TeV prel. Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 28 Running of αs(Q) Perform fits in fixed intervals NLO of the chosen scale Q Jet cross sections and ratios Needs an update for latest ATLAS, CMS, & H1 points ... New range explored at LHC Klaus Rabbertz Freiburg, 29.01.2020 GRK 2044 29 Running of αs(Q) Perform fits in fixed intervals NLO of the chosen scale Q → 8 TeV → ATLAS ttbar NNLO Normalised distributions Needs an update for latest ATLAS, CMS, & H1 points ..