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Perturbative Aspects of Top Mass Reconstruction

Perturbative Aspects of Top Mass Reconstruction. Based on work with: Sean Fleming, Sonny Mantry and Iain Stewart (hep-ph/0703207) … more work in progress. Outline.

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Perturbative Aspects of Top Mass Reconstruction

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  1. Perturbative Aspects of Top Mass Reconstruction Based on work with: Sean Fleming, Sonny Mantry and Iain Stewart (hep-ph/0703207) … more work in progress LCWS 2007, Desy , May 30 - June 3, 2007

  2. Outline • Motivation. Why do we want a precision ? • Theory issues for reconstruction. • Factorization theorem for and invariant mass distribution in electron-positron annihilation ( ) • Summary • Effective Field Theories for top jets: SCET & HQET • Derivation Factorization at LO in • Phenomenology • Radiative Corrections LCWS 2007, Desy , May 30 - June 3, 2007

  3. Top Quark is Special ! • Heaviest known quark (related to SSB?) • Important for quantum effects affecting many observables • Very unstable, decays “before hadronization” ( ) Top Quark Mass at the Tevatron Combined measurement (March 2007) 1% precision ! How shall we theorists judge the error ? What is the theoretical error ? What mass is it ? LCWS 2007, Desy , May 30 - June 3, 2007

  4. Methods at Tevatron Template Method Not easy to answer the questions because of complicated dependence on the top quark mass Dynamics Method from Aurelio Juste LCWS 2007, Desy , May 30 - June 3, 2007

  5. Need for a precise Top mass Electroweak precision observables Mass of Lightest MSSM Higgs Boson • Best precision possible wanted. • Mass definition (with small error) needs to be well defined. (Which mass has 0.1 GeV uncertainty ?) LCWS 2007, Desy , May 30 - June 3, 2007

  6. Direct Measurement Methods Miquel, Martinez; Boogert, Gounaris Threshold Scan Invariant Mass Reconstruction Chekanov, Morgunov What mass? pole mass? (color triplet !) The top quark does not live by itself ! LCWS 2007, Desy , May 30 - June 3, 2007

  7. Theory Issues for • definition of jet observables • initial state radiation • final state radiation • underlying events • color reconnection & soft gluon interactions • beam remnant • parton distributions • summing large logs • relation to Lagrangian short distance mass First step: we will study and the issues LCWS 2007, Desy , May 30 - June 3, 2007

  8. Conceptual Goals • relate top jet observables with a given Lagrangian mass (define suitable short-distance mass with good convergence properties What mass is measured? ) • proof of factorization of dynamics at different length scales ( What has to be computed by theorists ? ) • combined treatement of top production & decay • separate perturbative from non-perturbative effects • hopefully better understand & reduce theoretical & experimental uncertainties Tool: Sequence of Effective Field Theories LCWS 2007, Desy , May 30 - June 3, 2007

  9. Basic Idea Hemisphere invariant mass distribution SOFT JET JET SOFT Dijet Event Integrate out m boosted HQET SCET Isgur, Wise Jets with Jets with LCWS 2007, Desy , May 30 - June 3, 2007

  10. Scheme of EFT’s boosted in n direction boosted in n direction _ Program technically analogous to combination of threshold resummation ( ) & method of unstable particle EFT Korshemsky, Sterman, etal. Fadin, Khoze Beenacker etal., Beneke, etal. Reisser, AH LCWS 2007, Desy , May 30 - June 3, 2007

  11. Soft-Collinear Effective Theory Degrees of freedom Light-cone coordinates quark fields gluon fields Leading order Lagrangian (n-collinear) massive SCET: Leibovich etal, Rothstein LCWS 2007, Desy , May 30 - June 3, 2007

  12. Soft-Collinear Effective Theory Top pair production current one-loop matching • agrees with massless SCET • known to Gehrmann etal LCWS 2007, Desy , May 30 - June 3, 2007

  13. Soft-Collinear Effective Theory QCD Cross Section Integrate out hard fluctuations at Q SCET Cross Section (LO in m/Q) factorization of asymptotic final states LCWS 2007, Desy , May 30 - June 3, 2007

  14. Soft-Collinear Effective Theory Factorization: soft-collinear decoupling Factorization and Soft field redefinition: soft-collinear decoupling Hemisphere mass constraint LCWS 2007, Desy , May 30 - June 3, 2007

  15. SCET Cross Section SCET factorization formula we find: Korchemsky, Sterman Jet functions: • perturbative • depends on • insensitive to hemisphere constraints Soft function: • non-perturbative • renormalized due to UV divergences • governs massless dijet thrust and jet mass distributions • depends on hemisph. constr. LCWS 2007, Desy , May 30 - June 3, 2007

  16. Boosted HQET SCET factorization formula Lower virtuality of jet function: ultracollinear Jet functions: one-loop matching Only low energy fluctuations are relevant for the resonance region. LCWS 2007, Desy , May 30 - June 3, 2007

  17. Factorization Theorem Everything computable in perturbation theory except for S_hemi (which is known from massless event shapes) Ultracollinear jet functions: • at tree level: • describes perturbative contributions to the invariant mass distributions • top width acts as IR-cutoff. • computable for any given Lagrangian mass Breit-Wigner only at tree level ! LCWS 2007, Desy , May 30 - June 3, 2007

  18. How general is the approach? Why Q>>m is crucial • top and antitop boosted in opposite directions, . top and antitop jet axes and can be defined . allows factorization • combinatorial background, wrong assignment suppressed by ILC: ok for LHC: probably ok for tops with Tev: ? LCWS 2007, Desy , May 30 - June 3, 2007

  19. Other Mass Prescriptions We don’t have to assume a hemisphere mass definition: • any jet algorithm that combines soft particles with the hard jets from the top decay • wide cone definition that contains the top/antitop jet axes and top decay products (collinear radiation off top) Different soft function, same factorization formula [The soft functions for most cases at unknown at this time and migh need to be fitted together with the top mass, determined from MC’s or by other means.] LCWS 2007, Desy , May 30 - June 3, 2007

  20. Summation of logs • low energy scales of jet functions and soft function can differ • RG-evolution of jet and soft functions individually involve plus functions and convolutions • different possibilities to set up RG-evolution LCWS 2007, Desy , May 30 - June 3, 2007

  21. Summation of logs LCWS 2007, Desy , May 30 - June 3, 2007

  22. Short-distance Top Jet Mass • One-loop: shift in the pole scheme 300 MeV • shift in the pole scheme contains renormalon • jet mass scheme: defined such that peak located at the mass to all orders What mass is measured? Answer: the one that gives the best convergence in the theoretical expansion. LCWS 2007, Desy , May 30 - June 3, 2007

  23. LO Numerical Analysis Jet functions: Soft function: Fit to heavy jet mass distribution Korchemsky, Tafat hep-ph/0007005 LCWS 2007, Desy , May 30 - June 3, 2007

  24. LO Numerical Analysis Double differential invariant mass distribution: Non-perturbative effects shift the peak to higher energies and broaden the distribution. LCWS 2007, Desy , May 30 - June 3, 2007

  25. LO Numerical Analysis Single differential distribution: Non-perturbative effects shift the peak to higher energies and broaden the distribution. LCWS 2007, Desy , May 30 - June 3, 2007

  26. LO Numerical Analysis Different invariant mass prescriptions/soft functions: Fairly precise determination of jet mass from determination of Q-dependence of the peak position and extrapolation Q to zero LCWS 2007, Desy , May 30 - June 3, 2007

  27. Perturbative corrections LL LL+ PRELIMINARY LCWS 2007, Desy , May 30 - June 3, 2007

  28. Summary & Outlook • established factorization theorem for invariant mass distributions: separation of perturbative and non-perturbative effects • applicable for many other systems and setups: (any colored unstable particle, W mass reconstruction, etc..) • exact and systematic relation of peak to a Lagrangian mass: What mass is measured ? “Jet-mass” • resummation of large logarithms • soft gluon color reconnection power suppressed • Here: • Planned: renormalons W mass Q/m ~ 2 (large p_T) more loops different mass definitions (cone, k_T) LCWS 2007, Desy , May 30 - June 3, 2007

  29. Backup Slides LCWS 2007, Desy , May 30 - June 3, 2007

  30. ILC Simulations Reconstruction for all-hadronic events at the LC Chekanov; Morgunov hep-ex/0301014 Q dependence of observed width Dependence on parton shower, hadronization, jet algorithms Not relevant once soft function is known LCWS 2007, Desy , May 30 - June 3, 2007

  31. Event Shapes e.g. Thrust distribution on the peak region: Chekanov; Morgunov hep-ex/0301014 LCWS 2007, Desy , May 30 - June 3, 2007

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