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On the Status of α s

On the Status of α s. Insights and Open I ssues. André Hoang, Faculty for Physics University of Vienna. Content. World Average of α s. What this talk it NOT about:. Lattice. Tau Decays. PDF fits. Jets. Content. World Average of α s. What this talk it NOT about:. Aims:.

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On the Status of α s

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  1. On the Status of αs Insightsand Open Issues André Hoang, Faculty for Physics University of Vienna

  2. Content World Average of αs What this talk it NOT about: Lattice Tau Decays PDF fits Jets XX DIS-Workshop, University of Bonn, March 26-30, 2012

  3. Content World Average of αs What this talk it NOT about: Aims: • Point out recent developments • Provide some insight into some tricky points and open issues • Motivate to push foward precise αs determinations This talk attempts to be objective, but certainly won’t ! Apologies to those whose work is not mentioned and missing references ! Some material in this talk taken from presentations given at the Workshop “Precision Measurements of αs” (MPI, Munich, February 9-11, 2012) XX DIS-Workshop, University of Bonn, March 26-30, 2012

  4. Content • Introduction • LatticeSimulations • 𝛕-decays • Eventshapesand Jet Rates • DIS • Conclusions XX DIS-Workshop, University of Bonn, March 26-30, 2012

  5. Strong Coupling: Theory SU(3) gauge theory: / • SU(3) gauge symmetry does not fix strong coupling and quark masses • QCD parameters are renormalized quantities and NOT physical • Values are fixed by BSM short-distance physics XX DIS-Workshop, University of Bonn, March 26-30, 2012

  6. Strong Coupling: Theory RG-evolution: _ • Standard scheme: MS defined within dim reg • 4-loop precision available β3 : Vermaseren, Larin, v.Ritbergen 1997 Czakon 2004 Decoupling: • Defined within an nf-flavor effective theory • Massive quarks integrated out • 4-loop precision available Schröder, Steinhauser 2005 Chetyrkin, Kühn, Sturm 2005 Theory error smaller than most other uncertainties. XX DIS-Workshop, University of Bonn, March 26-30, 2012

  7. Strong Coupling: Theory Asymptotic freedom: • αs perturbative only for scales larger than 1 GeV • Currently we are only capable determining αs from processes where perturbation theory dominates. • Parameter equivalent to αs • Frequently used to as a synonym for the scale of hadronization/confinement in dimensional counting XX DIS-Workshop, University of Bonn, March 26-30, 2012

  8. Strong Coupling: Theory IR-Sensitivity: • dim reg perturbation theory in gauge theories leads to enhanced sentivity to scales • „Renormalons“ • Conceptual origin of the OPE Wilson’s OPE: (cutoff regulator) • Cleanest separation of short and long distance contributions • renormalon-free • EXTREMELY cumbersome for precision computations XX DIS-Workshop, University of Bonn, March 26-30, 2012

  9. Strong Coupling: Theory IR-Sensitivity: • dim reg perturbation theory in gauge theories leads to enhanced sentivity to scales • „Renormalons“ • Perturbation theory only valid within OPE OPE in MS: dim. reg. • High precision calculations manageable • Renormalons can degrade perturbative behavior • „Non-perturbative effects“ – and also „Duality Violation“ XX DIS-Workshop, University of Bonn, March 26-30, 2012

  10. Lattice QCD • QCD without gauge-fixing and ghosts • Functional integrals formulated numerically on a finite Euklidean space-time lattice: size Ns3 x N3 x a4 • Demanding: technical+conceptualimplementationofvirtualquarks (seaquarks): 4-fold replication on finite lattice • Large scaleseparation vs. finite lattice: EffectiveTheories • Chirallimitwithstaggeredfermions: • 2(light)+1(strange) fermions: state-of-the-art Staggered (4th root of det) Wilson Domain-wall fast numerically, coneptually less clear clean conceptually, expensive e.g. heavy quark masses: HQET, NRQCD Lattice spacing small: Symanzik improved action considered meaningful, but all results need to be checked with other fermion formulations XX DIS-Workshop, University of Bonn, March 26-30, 2012

  11. Lattice QCD αs-determinations: • tune lattice to observed hadron spectrum • Compute quantities on the lattice that can also be computed with perturbation theory („lattice replaces experiment“) fix lattice parameters as fct of a • small Wilson loops (compare to lattice p.th.) • Current correlators (lattice + continuum p.th.) • Adler function (lattice + contiuum p.th.) • QCD energy in cylinder (lattice p.th.) HPQCD JLQCD PACS-CS ALPHA XX DIS-Workshop, University of Bonn, March 26-30, 2012

  12. Lattice QCD Bethke 2011 αs-determinations: Results live from their consistency within well-developed methods. World average dominated by lattice results. Is that it ? Any reason to go on ? - YES ! • Results should be cross checked (from lattice and other methods) • Finding the origin of disagreement to other methods motivates dedicated studies Ability to make precision measurements reflects the true understanding of the method of theory. XX DIS-Workshop, University of Bonn, March 26-30, 2012

  13. 𝝉 Decay Total hadronic 𝝉 width: Braaten, Narison, Pich 1992 Related to absorptive part of V and AV current correlators non-perturb. corr. (OPE) electroweak corr. O(αs4) : Baikov, Chetyrkin, Kühn 2008 QCD corrections Contour-improved (CIPT) Fixed-order (FOPT) • Resums large βn-logs to all orders • Improved convergence • Treats all corrections on equal footing • Smaller scale-dependence XX DIS-Workshop, University of Bonn, March 26-30, 2012

  14. 𝝉 Decay Contour-improved (CIPT) Fixed-order (FOPT) • Resums large βn-logs to all orders • Improved convergence • Well behaved • Treats all corrections on equa footing • Smaller scale-dependence • Well behaved Typical results at O(αs4) [lots of literature] Studies based on models of asymptotic behavior of the perturbative series do not favor any expansion Beneke, Jamin 2008 Descots-Genon 2010 Beneke, Jamin XX DIS-Workshop, University of Bonn, March 26-30, 2012

  15. 𝝉 Decay Contour-improved (CIPT) Fixed-order (FOPT) • Resums large βn-logs to all orders • Improved convergence • Well behaved • Treats all corrections on equa footing • Smaller scale-dependence • Well behaved Typical results at O(αs4) [lots of literature] Studies based on models of asymptotic behavior of the perturbative series do not favor any expansion Beneke, Jamin 2008 Descots-Genon 2010 Expansion look well, BUT ARE close to being unstable. Common variation methods unreliable to estimate perturbative error. What is the theoretical handle that explains the discrepancy ? XX DIS-Workshop, University of Bonn, March 26-30, 2012

  16. 𝝉 Decay Boito, Cata, Golterman, Jamin, Maltman, Osborne, Peris 2011 Duality Violation: m𝝉 not sufficiently heavy such that OPE (p.th. + condensates) is justified at very high precision (resonances not sufficient “smeared” out) (recall: OPE = expansion in ) model (no first principle computation possible) parameters must be fitted Behavior of non-perturbative effects in the Minkowskian region data XX DIS-Workshop, University of Bonn, March 26-30, 2012

  17. 𝝉 Decay Boito, Cata, Golterman, Jamin, Maltman, Osborne, Peris 2011+2012 CIPT Duality Violation: CIPT CIPT FOPT FOPT Discrepancy reconciled at the cost of larger errors. FOPT 2010 (old status) 2011 2012 with duality violation old data with duality violation updated data Bethke 2011 Uncertainties from spread of central values. XX DIS-Workshop, University of Bonn, March 26-30, 2012

  18. Eventshape Distributions (e+e-) Single variable measure of global topology properties of hadronic events (primary ) Variable zero for final state (2 back-to-back zero mass jets) Thrust: Heavy jet mass 𝞀H: Heavier of the invariant masses of all particle in the 2 hemispheres w.r. to the thrust axis C-parameter: Jet broadening: y23: Transition value between 2 and 3 jets (Durham jet algorithm) XX DIS-Workshop, University of Bonn, March 26-30, 2012

  19. Eventshape Distributions (e+e-) Perturbation theory: IR-save & perturbatively inclusive (e.g. thrust) Korshemski, Sterman perturbative perturbative 𝞀H, C: similar to thrust B: Gehrmann-DeRidder, Gehrmann, Glover, Heinrich 2007 High precision era: partonic Monte-Carlo program Weinzierl 2009 XX DIS-Workshop, University of Bonn, March 26-30, 2012

  20. Eventshape Distributions (e+e-) Fixed-Order and log summation: • NNLO (fixed-order) • NNLO + NLL (classic resummation) • NNLO + N3LL (SCET factorization) Catani ea; Dokshitzer ea all eventshapes 𝝉, 𝞀H. (B) Non-perturbative Effects (tail): • MC: hadron mode – partonic mode • Power corrections from data Problem of MC-estimate: • Hadronization corrections in MC are not in the scheme needed for calculations based on NNLO corrections (MSbar+dim reg) • MC estimates much too small (tiny ! Few % for αs) Abbate, Fickinger, Hoang, Mateu, Stewart 2010 XX DIS-Workshop, University of Bonn, March 26-30, 2012

  21. Eventshape Distributions (e+e-) Only 3 NNLO-based analyses left : Gavin Salam Davison, Webber 2009 (all event shapes_ Abbate, Fickinger, Hoang, Mateu, Stewart 2010 (thrust) Gehrmann, Jaquier, Luisoni 2010 (all event shapes) Jet rates All results for are low !! XX DIS-Workshop, University of Bonn, March 26-30, 2012

  22. Eventshape Distributions (e+e-) Abbate, Fickinger, Hoang, Mateu, Stewart 2010 • Central values for ɑs decrease with order • Very good convergence XX DIS-Workshop, University of Bonn, March 26-30, 2012

  23. Eventshape Distributions (e+e-) NEW: PRELIMINARY Abbate, Fickinger, Hoang, Mateu, Stewart to appear • SCET analyses for other event shapes needed ! XX DIS-Workshop, University of Bonn, March 26-30, 2012

  24. DIS and PDF fits Alekhin, Blümlein, Moch 2012 • Central values for ɑs decrease NLO to NNLO • All below the world average. XX DIS-Workshop, University of Bonn, March 26-30, 2012

  25. Conclusions • Ability to make precise measurements of the strong coupling reflects our understanding and control of QCD in various areas. • High precision measurements and methods claiming very small theoretical uncertainties HAVE TO BE challenged and questioned. Even new and difficult-to-be-answered questions should be asked. • Why do jet observables all seem to give low αs with NNLO included ? • Eventually: measurements of αs at the LHC What does this mean ? Maybe NNNLO helps ? XX DIS-Workshop, University of Bonn, March 26-30, 2012

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