1. QCD Factorization for Top Quark Mass Reconstruction
Based on:
S. Fleming, S. Mantry, I.W. Stewart, AHH, hep-ph/
I.W. Stewart, AHH, arXiv:
S. Fleming, S. Mantry, I.W. Stewart, AHH, arXiv:
EuroFlavor 07, Orsay , Nov 14-16, 2007
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2. Outline Why do we want a precision ? What kind of precision.
Methods for top mass determinations
Factorization theorem for and invariant mass distribution in electron-positron annihilation ( )
Summary
EFT derivation of Factorization at LO in
Top mass determination to better than
Which top mass is (not) measured ?
NLL order analysis
EuroFlavor 07, Orsay , Nov 14-16, 2007

3. Top Quark is Special ! Heaviest known quark (related to SSB?)
Important for quantum effects affecting many observables
Very unstable, decays “before hadronization” ( )
1% precision !
How shall we theorists judge the error ?
What is the theoretical error ?
What mass is it ?
EuroFlavor 07, Orsay , Nov 14-16, 2007

4. Need for a precise Top mass
Fit to electroweak precision observables
causes half of error in predicted
EuroFlavor 07, Orsay , Nov 14-16, 2007

5. Need for a precise Top mass
Mass of Lightest MSSM Higgs Boson
5 Higgs bosons:
How to reduce theoretical and experimental errors?
What mass scheme does the central value refer to?
EuroFlavor 07, Orsay , Nov 14-16, 2007

6. Methods at Tevatron Template Method Dynamics Method
Not easy to address both issues:
complicated mass dependence
systematics (expansion scheme) unclear
effects of radiative corrections (NLO)
might or might not be numerically relevant
kinematics yet unresolved conceptual problem
Dynamics Method
from Aurelio Juste
(theoretically)
EuroFlavor 07, Orsay , Nov 14-16, 2007

7. Basic Methods ILC Tev +LHC + ILC Threshold Scan
Miquel, Martinez;
Boogert, Gounaris
ILC
Threshold Scan
“threshold masses”
Tev +LHC + ILC
Invariant Mass Reconstruction
data available soon
measures different top mass ?
uncertainties (much) more involved
many different methods available
error around 1 GeV challenging
EuroFlavor 07, Orsay , Nov 14-16, 2007

8. Reconstruction Methods
Lepton + Jets
Atlas study:
Borjanovic etal
Plain Method:
W reconstruction + b tagging
Inv. mass from
events after cuts
Major error sources:
b jet energy scale:
FSR jets:
Kinematic Fit:
reconstruct entire event
impose constraints ( e.g )
vary unknows freely
b jet energy scale:
FSR jets:
Continuous Jet Definition:
plain method for varying cone size:
take weighted average
FSR error reduced
event shape-like !
Large Events:
select events with
top pair back-to-back decay products in different hemispheres
large cone size around top/antitop jet axes:
and from in-cone momenta
strong sensitivity to soft jets + Underlying Events
Mass scale calibrations (W mass)
UE:
calibration
EuroFlavor 07, Orsay , Nov 14-16, 2007

9. ILC: Ideal Study Case Resonance region: ILC at large c.m. energy:
No beam remnant : all soft radiation can be assigned to top or antitop
Resonance region:
ILC at large c.m. energy:
Dijet limit: QCD factorization á la Korchemsky/Sterman
related to thrust and heavy jet mass event shapes
set up similar to Chekanov/Morgunov experimental analysis (based on k_T jet algorithm)
unstable particle effective theory method (Fadin, Khoze; Beenaker etal, Beneke etal, Reisser,AH)
EuroFlavor 07, Orsay , Nov 14-16, 2007

10. Factorization Theorem
Fleming, Mantry, Stewart, AH
hep-ph/
SOFT
QCD
JET
JET
SCET
bHQET
SOFT
LO factorization theorem
JET
JET
SOFT
EuroFlavor 07, Orsay , Nov 14-16, 2007

11. Step 1: Factorization in SCET
Integrate out Q
Invariant mass fluctuations
Jet functions still contain large logs in peak region:
top decay products (b,W) still appear as explicit d.o.f.
applicable to massless jet event shapes (thrust, etc.)
EuroFlavor 07, Orsay , Nov 14-16, 2007

12. Soft-Collinear Effective Theory
Degrees of freedom
Light-cone coordinates
quark fields
gluon fields
Leading order Lagrangian (n-collinear)
massive SCET:
Leibovich etal,
Boos, Feldmann, Mannel etal
EuroFlavor 07, Orsay , Nov 14-16, 2007

13. Soft-Collinear Effective Theory
Top pair production current
one-loop matching
agrees with massless SCET
known to
Kramer, Lampe ’87
Matsuura, v.d. March, v. Neerven ’88, ‘89
Gehrmann, Huber, Maitre ‘05
EuroFlavor 07, Orsay , Nov 14-16, 2007

14. 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
EuroFlavor 07, Orsay , Nov 14-16, 2007

15. Soft-Collinear Effective Theory
Factorization: soft-collinear decoupling
Factorization and Soft field redefinition: soft-collinear decoupling
Hemisphere mass constraint
EuroFlavor 07, Orsay , Nov 14-16, 2007

16. SCET Cross Section SCET factorization formula Jet functions:
a la Korchemsky, Sterman
including top mass and width effects
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.
EuroFlavor 07, Orsay , Nov 14-16, 2007

17. Step 2: Factorization in boosted HQET
integrate out the top mass
Jet functions without large logs in peak region:
top decay “integrated out” (unstable particle EFT)
soft function S unchanged
EuroFlavor 07, Orsay , Nov 14-16, 2007

18. boosted HQET bHQET Lagrangian: two copies of HQET (top+antitop)
residual mass term:
for pole mass
total top width:
- Inclusive treatment of top decay
- wrong mass assignment suppressed
Jet functions:
one-loop matching of jet functions
EuroFlavor 07, Orsay , Nov 14-16, 2007

19. Factorization Theorem
Jet functions:
perturbative, any mass scheme
depends on
Breit-Wigner at tree level
Soft function:
non-perturbative
renormalized due to UV divergences
also governs massless dijet thrust and jet mass event distributions
Short distance top mass can (in principle) be determined to better than
Korshemsky, Sterman, etal.
Bauer, Manohar, Wise, Lee
EuroFlavor 07, Orsay , Nov 14-16, 2007

20. Summation of Logs Wilson coefficients and sum local double logs
EuroFlavor 07, Orsay , Nov 14-16, 2007

21. Summation of Logs
low energy scales of jet functions and soft function differ
RG-evolution of jet and soft functions individually involve plus functions
EuroFlavor 07, Orsay , Nov 14-16, 2007

22. Soft Function Model beyond LL
Stewart, AH arXiv:
partonic soft function:
soft function non-perturbative (distribution in the peak region) model function
partonic contributions required for OPE for moments and predictions in the tail
absorb partonic information fully into model parameters
glue partonic tail to model function (absorbs partonic information partially into )
Korchemsky,Sterman, Tafat ‘00
Bosch, Lange, Neubert, Paz ‘04
EuroFlavor 07, Orsay , Nov 14-16, 2007

23. Soft Function Model beyond LL
Stewart, AH arXiv:
partonic soft function:
soft function model:
normalized model function
consistent OPE for predictions of moments or in the tail
has renormalon: ambiguity in partonic zero-point
Gardi ‘00
affects first power correction
EuroFlavor 07, Orsay , Nov 14-16, 2007

24. Soft Function Model beyond LL
Stewart, AH arXiv:
partonic soft function:
soft function model:
normalized model function
gapped soft model:
renormalon subtraction scheme:
EuroFlavor 07, Orsay , Nov 14-16, 2007

25. Soft Function Model beyond LL
Stewart, AH arXiv:
first moment renormalon-free
with renormalon subtraction
without renormalon subtraction
EuroFlavor 07, Orsay , Nov 14-16, 2007

26. Can one measure the Pole Mass ?
Message: The pole mass is not accessible !
EuroFlavor 07, Orsay , Nov 14-16, 2007

27. Short-distance Top Jet Mass
One-loop: shift in the pole scheme 250 MeV
shift in the pole scheme contains renormalon
jet mass scheme: defined such that peak located at the mass to all orders
Top Jet mass is a scheme where we expect that a pert. analysis contains the least theoretical uncertainties.
2-loop analysis
talk by I. Scimemi
EuroFlavor 07, Orsay , Nov 14-16, 2007

28. NLL Numerical Analysis
Soft function model:
Fit to heavy jet mass distribution
Korchemsky, Tafat
hep-ph/
EuroFlavor 07, Orsay , Nov 14-16, 2007

29. NLL Numerical Analysis
Double differential invariant mass distribution:
Non-perturbative effects shift the peak by +2.4 GeV and broaden the distribution.
EuroFlavor 07, Orsay , Nov 14-16, 2007

30. NLL Numerical Analysis
LL vs. NLL distribution
Jet vs. Pole mass scheme
NLL corrections large for normalization
NLL corr. reduce scale-dependence
EuroFlavor 07, Orsay , Nov 14-16, 2007

31. NLL Numerical Analysis
Scale-dependence of peak position
Jet mass scheme: significanly better perturbative behavior.
Renormalon problem of pole scheme already evident at NLL.
EuroFlavor 07, Orsay , Nov 14-16, 2007

32. NLL Numerical Analysis
Q-dependence of peak position
different soft models
different treatment for soft particles between jets
Fairly precise determination of jet mass from determination of Q-dependence of the peak position and extrapolation Q to zero
EuroFlavor 07, Orsay , Nov 14-16, 2007

33. NLL Predictions for Thrust
NLL thrust distribution for massive quark jets
top (bottom) mass from event shape distributions
EuroFlavor 07, Orsay , Nov 14-16, 2007

34. Summary & Outlook
established factorization theorem for invariant mass distributions: separation of perturbative and non-perturbative effects for the ILC
applicable for many other systems and setups (e.g. squarks)
exact and systematic relation of peak to a Lagrangian mass: What mass is measured ? “Jet-mass”
resummation of large logarithms
NNLL analysis on the way
extension to LHC
other applications:
massless/massive event shapes (electron-positron)
hadron collider event shapes
…..
EuroFlavor 07, Orsay , Nov 14-16, 2007