Download Slides - Indico

QCD Factorization for Top
Quark Mass Reconstruction
André H. Hoang
Max-Planck-Institute for Physics
Munich
Based on:
S. Fleming, S. Mantry, I.W. Stewart, AHH, hep-ph/0703207
I.W. Stewart, AHH, arXiv:0709.3519
S. Fleming, S. Mantry, I.W. Stewart, AHH, arXiv:0709.2079
EuroFlavor 07, Orsay , Nov 14-16, 2007
Outline
•
Why do we want a precision
•
Methods for top mass determinations
•
Factorization theorem for
? What kind of precision.
and
electron-positron annihilation (




•
invariant mass distribution in
)
EFT derivation of Factorization at LO in
Top mass determination to better than
Which top mass is (not) measured ?
NLL order analysis
Summary
André H. Hoang - 2
EuroFlavor 07, Orsay , Nov 14-16, 2007
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 ?
André H. Hoang - 3
EuroFlavor 07, Orsay , Nov 14-16, 2007
Need for a precise Top mass
Fit to electroweak precision observables
causes half of
error in predicted
André H. Hoang - 4
EuroFlavor 07, Orsay , Nov 14-16, 2007
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?
André H. Hoang - 5
EuroFlavor 07, Orsay , Nov 14-16, 2007
Methods at Tevatron
Template Method
Not easy to address both issues:
• complicated mass dependence
• systematics (expansion scheme) unclear
Dynamics Method
• effects of radiative corrections (NLO)
• might or might not be numerically relevant
• kinematics yet unresolved conceptual problem
from Aurelio Juste
(theoretically)
André H. Hoang - 6
EuroFlavor 07, Orsay , Nov 14-16, 2007
Basic Methods
Miquel, Martinez;
Threshold Scan
ILC
Boogert, Gounaris
“threshold masses”
Invariant Mass Reconstruction
•
•
•
•
•
Tev +LHC + ILC
data available soon
measures different top mass ?
uncertainties (much) more involved
many different methods available
error around 1 GeV challenging
André H. Hoang - 7
EuroFlavor 07, Orsay , Nov 14-16, 2007
Reconstruction Methods
Plain Method:
Kinematic Fit:
•
•
•
•
•
•
•
Atlas study:
Borjanovic etal
Major error sources:
W reconstruction + b tagging
Inv. mass from
100.000 events after cuts
reconstruct entire event
impose constraints ( e.g.
vary unknows freely
Lepton + Jets
)
o
b jet energy scale:
o
FSR jets:
o
b jet energy scale:
o
FSR jets:
Continuous Jet Definition:
•
•
•
Large
plain method for varying cone size:
take weighted average
FSR error reduced
event shape-like !
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
o UE:
strong sensitivity to soft jets + Underlying Events
Mass scale calibrations (W mass)
André H. Hoang - 8
o
calibration
EuroFlavor 07, Orsay , Nov 14-16, 2007
ILC: Ideal Study Case
•
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)
André H. Hoang - 9
EuroFlavor 07, Orsay , Nov 14-16, 2007
Factorization Theorem
Fleming, Mantry, Stewart, AH
hep-ph/0703207
SOFT
QCD
JET
JET
SCET
bHQET
SOFT
LO
factorization
theorem
JET
André H. Hoang - 10
JET
SOFT
EuroFlavor 07, Orsay , Nov 14-16, 2007
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.)
André H. Hoang - 11
EuroFlavor 07, Orsay , Nov 14-16, 2007
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
André H. Hoang - 12
EuroFlavor 07, Orsay , Nov 14-16, 2007
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
André H. Hoang - 13
EuroFlavor 07, Orsay , Nov 14-16, 2007
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
André H. Hoang - 14
EuroFlavor 07, Orsay , Nov 14-16, 2007
Soft-Collinear Effective Theory
Factorization: soft-collinear decoupling
Factorization and Soft field
redefinition: soft-collinear
decoupling
Hemisphere mass
constraint
André H. Hoang - 15
EuroFlavor 07, Orsay , Nov 14-16, 2007
SCET Cross Section
SCET factorization formula
a la Korchemsky, Sterman
including top mass and width effects
Jet functions:
•
•
•
perturbative
depends on
insensitive to hemisphere
constraints
Soft function:
•
•
•
•
André H. Hoang - 16
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
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
André H. Hoang - 17
EuroFlavor 07, Orsay , Nov 14-16, 2007
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
André H. Hoang - 18
EuroFlavor 07, Orsay , Nov 14-16, 2007
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
André H. Hoang - 19
Korshemsky, Sterman, etal.
Bauer, Manohar, Wise, Lee
Short distance top mass
can (in principle) be
determined to better
than
.
EuroFlavor 07, Orsay , Nov 14-16, 2007
Summation of Logs

Wilson coefficients
André H. Hoang - 20
and
sum local double logs
EuroFlavor 07, Orsay , Nov 14-16, 2007
Summation of Logs


low energy scales of jet functions and soft function differ
RG-evolution of jet and soft functions individually involve plus functions
André H. Hoang - 21
EuroFlavor 07, Orsay , Nov 14-16, 2007
Soft Function Model beyond LL
Stewart, AH
arXiv: 0709.3519
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
Korchemsky,Sterman, Tafat ‘00
glue partonic tail to model function (absorbs partonic information partially into
)
Bosch, Lange, Neubert, Paz ‘04
André H. Hoang - 23
EuroFlavor 07, Orsay , Nov 14-16, 2007
Soft Function Model beyond LL
Stewart, AH
arXiv: 0709.3519
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
André H. Hoang - 24
EuroFlavor 07, Orsay , Nov 14-16, 2007
Soft Function Model beyond LL
Stewart, AH
arXiv: 0709.3519
partonic soft function:
soft function model:
normalized model function
→ gapped soft model:
→ renormalon subtraction scheme:
André H. Hoang - 25
EuroFlavor 07, Orsay , Nov 14-16, 2007
Soft Function Model beyond LL
Stewart, AH
arXiv: 0709.3519
first moment renormalon-free
with renormalon
subtraction
without renormalon
subtraction
André H. Hoang - 26
EuroFlavor 07, Orsay , Nov 14-16, 2007
Can one measure the Pole Mass ?
Message: The pole mass
is not accessible !
André H. Hoang - 27
EuroFlavor 07, Orsay , Nov 14-16, 2007
Short-distance Top Jet Mass
•
•
•
Top Jet mass is a scheme where
we expect that a pert. analysis
contains the least theoretical
uncertainties.
André H. Hoang - 29
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
2-loop analysis
talk by I. Scimemi
EuroFlavor 07, Orsay , Nov 14-16, 2007
NLL Numerical Analysis
Soft function model:
Fit to heavy jet mass
distribution
Korchemsky, Tafat
hep-ph/0007005
André H. Hoang - 30
EuroFlavor 07, Orsay , Nov 14-16, 2007
NLL Numerical Analysis
Double differential invariant mass distribution:
Non-perturbative effects shift the peak by +2.4 GeV
and broaden the distribution.
André H. Hoang - 31
EuroFlavor 07, Orsay , Nov 14-16, 2007
NLL Numerical Analysis
LL vs. NLL distribution
•
•
Jet vs. Pole mass scheme
NLL corrections large for normalization
NLL corr. reduce scale-dependence
André H. Hoang - 32
EuroFlavor 07, Orsay , Nov 14-16, 2007
NLL Numerical Analysis
Scale-dependence of peak position
•
•
Jet mass scheme: significanly better perturbative behavior.
Renormalon problem of pole scheme already evident at NLL.
André H. Hoang - 33
EuroFlavor 07, Orsay , Nov 14-16, 2007
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 Qdependence of the peak position
and extrapolation Q to zero
André H. Hoang - 34
EuroFlavor 07, Orsay , Nov 14-16, 2007
NLL Predictions for Thrust
NLL thrust distribution for massive quark jets
top (bottom) mass
from event shape
distributions
André H. Hoang - 35
EuroFlavor 07, Orsay , Nov 14-16, 2007
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
→ …..
André H. Hoang - 37
EuroFlavor 07, Orsay , Nov 14-16, 2007