Precision Measurements at Hadron Colliders Hadron Colliders and - - PowerPoint PPT Presentation
Precision Measurements at Hadron Colliders Hadron Colliders and Gl b l A Global Analysis of PDFs l i f PDF C.-P. Yuan Michigan State University February 7, 2011 @ PSI, Switzerland Precision Electroweak Physics at Hadron Colliders
Precision Measurements at Hadron Colliders Hadron Colliders and Gl b l A l i f PDF Global Analysis of PDFs
C.-P. Yuan Michigan State University February 7, 2011 @ PSI, Switzerland
Precision Electroweak Physics at Hadron Colliders Physics of Drell-Yan, W and Z Bosons
Part III
W-boson physics
W-boson production and decay at hadron collider How to measure W-boson mass and width? High order radiative corrections: QCD (NLO, NNLO, Resummation) EW (QED-like, NLO) ResBos and ResBos-A
W-boson production at hadron colliders
parton model PDFs are known from deep inelastic scattering partonic “Born” cross section of
W-boson production at hadron colliders
PDFs: probability of finding a “parton” inside the hadron
fragment ation parton distribu tion parton distribu tion Jet Hard scattering I S R FS R
W
underlying events (from proton remnants)
LO
ISR and FSR: (colored) initial and final states can radiate gluons
( ) ( )
1 ˆ , , 2
A B i A A i B B A B
d d f f d S ξ ξ σ ξ μ ξ μ σ ξ ξ = ⋅
∫
( )
2 A B A A B B
s p p k p l p ξ ξ = + = =
(
)
( ) (
) ( )
3 2 4 4 3
ˆ 2 2 2 d q d q k l q
M
σ π δ π = − −
( ) ( )
( ) ( )
2 2 2 2 2 2 2 2
d d d 1 , , d d d 1 1
A B i A i B A B T A B A B A B T W
f f q y Q S x x Q q Q M
M
ξ ξ σ ξ μ ξ μ ξ ξ π δ δ ξ ξ δ δ = ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⋅ ⋅ ⋅ − ⋅ − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⋅ ⋅ −
∫
2 2 ,
, ,
y y W A B
Q Q Q Q q Q M x e x e S S μ
−
≡ = = = = =
( )
S
α
Fixed order pQCD prediction
( )
( )
( ) ( ) ( )
( )
( ) ( )
2 2 2 2 2 2 2 2 2 2 2 2 2 2
ˆ ˆ d d d , ˆ d d d d , ˆ ˆ d d , ˆ d ,
A i A A T A A j B W B A B j B B B B i A W A B
s f t q y Q S U Q Q T Q f Q M S U Q s f t S T Q Q U Q f Q M S T Q ξ σ σ ξ μ ξ ξ ξ μ δ ξ ξ σ ξ μ ξ ξ ξ μ δ ξ ⎛ ⎞ = ⋅ ⎜ ⎟ + − ⎝ ⎠ ⎛ ⎞ − − − ⎜ ⎟ ⋅ = ⋅ − ⎜ ⎟ + − ⎝ ⎠ ⎛ ⎞ + ⋅ ⎜ ⎟ + − ⎝ ⎠ ⎛ ⎞ − − − ⎜ ⎟ ⋅ = ⋅ − ⎜ ⎟ + − ⎝ ⎠
∫ ∫
2 2 2 2 2 2
, ,
y T y T
T Q q Q S e U Q q Q S e
−
= − + = − +
2 2
ˆ ˆ d 1 ˆ d 16 s t
M
σ π =
( )
2 2
ˆ ˆ
A B A
s S t T Q Q ξ ξ ξ = = − +
( )
1 S
α
M =
( For simplicity, only consider qq→Wg )
( )
2 S
α
Theory Calculations
Horace
Fixed order Perturbative calculations
Less sensitive to Factorization Scale
PDF (parton distribution function) better known
Test QCD in one large scale problem (i.e. )
One large scale observables, e.g., Jet-PT.
MW, can only be accurately described in QCD after including effects of Resummation.
( )
n S
α
μ
T
q
y
~
T
q Q
But the fixed order calculations
Cannot precisely determine at hadron colliders without knowing the transverse momentum of W-boson. Most events fall in the small qT region.
Cannot describe data with small qT of W-boson.
(at NLO)
Shortcoming of fixed order calculation
To describe data Resummation is needed
Dashed: CSS (1,1,1) Solid: CSS (2,2,1) Dotted: Pert ( ) Dot-dashed: Pert ( )
Perturbative
Resummation
QCD Resummation is needed
Resummation calculations agree with data very well
@ Tevatron
Predicted by ResBos: A program that includes the effect of multiple soft gluon emission
W and Z bosons in hadron collisions.
In collaboration with Csaba Balazs, Alexander Belyaev, Ed Berger, Qing-Hong Cao, Chuan-Ren Chen, Zhao Li, Steve Mrenna, Pavel Nadolsky, Jian-Wei Qiu, Carl Schmidt
ResBos
Initial state QCD soft gluon resummation and Final state QED corrections
(Resummation for Bosons)
Drell-Yan V H
including QCD Resummations.
(Spin correlation included)
W ± q
q q q l + ν l + l −
W ±
q q V H
g g H →
t t t
H ,Z γ
V
Jacobin peak sensitive region for measuring : LO NLO : not a good observable
In (ud) c.m. system, Jacobin factor
Transverse momentum of the charged lepton
sensitive region:
: :
Definition:
from overall imbalance unaffected by longitudinal boosts of system not sensitive to tail knows about (direct measurement)
Transverse mass of the W-boson
W Charge Asymmetry: A Monitor of Parton Distribution Functions
Difference between u(x) and d(x) in proton cause and to be boosted in opposite directions
ResBos is also needed for Rapidity distributions
black curve is from ResBos calculation
What’s QCD Resummation?
{ }
2 2
ˆ d ~ 1 d
S S S T
q σ α α α + + +
2
1
T
q
( ) ( )
( )
( ) ( )
2 2 1 2 2 2 1 2 2 3 2 3 5 4 3 2
ˆ d 1 ~ ln d 1 ~ { 1 1 1 }
n n m S n m T T T S T S S
Q q q q L q L L L L L L L L σ α α α α
∞ − = =
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ + + + + + + + + + + + +
∑ ∑
ln
T
Q L q
2
⎛ ⎞ ≡ ⎜ ⎟ ⎝ ⎠
Resummation is to reorganize the results in terms of the large Log’s.
Resummed results:
( )
( ) ( )
{
( )
( )
( ) }
2 3 2 3 5 4 2 2 2 3 3 2 3
d 1 ~ [ 1 ] d [ 1 ] [ 1 ]
S S S T T S S S
L L L L L q q L L L L σ α α α α α α + + + + + + + + + + + + + + + + +
In the formalism by Collins-Soper-Sterman, in addition to these perturbative results, the effects from physics beyond the leading twist is also implemented as [non-perturbative functions].
Determined by A(2) and B(2) Determined by A(3) and B(3)
QCD Resummation
( ) ( )
( )
2 2 ' ' 2 ' '
4 1 , 3 4sin
W W j j j j j j j j W
Q Q kM π α σ θ ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠
∑
( ) ( ) ( )
1 1
, ,
n n n n n n S S n n S n
A A B B C C α α π π α π
∞ ∞ = = ∞ =
⎛ ⎞ ⎛ ⎞ ≡ ⋅ ≡ ⋅ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ ≡ ⋅ ⎜ ⎟ ⎝ ⎠
∑ ∑ ∑
Note: The couplings of gauge bosons to fermions are expressed in the way to include the dominant electroweak radiative
also contain energy-dependent width, as done in LEP precision data analysis.
+
Diagramatically,
As qT → 0
( )
( ) ( )[
] [ ]
( ) ( ) ( ) ( ) }
{ |
2 2 ln 3 4 2 , , , , 2 2 1 d d d d
2 2 , , 2 2 2 \ 2
⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ + ⊗ + ⊗ ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =
← ← → T B B q A A q B B q Q x q q q Q x q q q A A q W T q T
q Q Q x f Q x f Q x f f P f P Q x f Q s T q M Q s Q y q
A Bπ α π δ σ π σ
Exponentiate
To preserve transverse momentum conservation, we have to go to the impact parameter space (b-space) to perform resummation.
→
T
q
Y
Diagramatically, Resummation is doing Monte-Carlo programs ISAJET, PYTHIA, HERWIG contain these physics. ( Note: Arbitrary cut-off scale in these programs to affect the amount of Backward radiation , i.e. Initial state radiation. )
2 2
ln
n m S T
Q q α ⎛ ⎞ ⎜ ⎟ ⎝ ⎠
Resum large terms
2 2 1 2 2 2 1
d 1 ~ ln d d
T
n n m n S m n m T T T q
Q C q y q q σ α
∞ − = = →
⎛ ⎞⋅ ⎜ ⎟ ⎝ ⎠
∑∑
Monte-Carlo Approach
Backward Radiation (Initial State Radiation) Kinematics of the radiated gluon, controlled by Sudakov form factor with some arbitrary cut-off. ( In contrast to perform integration in impact parameter space, i.e., b space. ) The shape of qT (w) is generated. But, the integrated rate remains the same as at Born level ( finite virtual correction is not included ). Recently, there are efforts to include part of higher order effect in the event generator.
Note that the integrated rate is the same as the Born level rate ( ) even though the qT – distribution is different (i.e., not any more).
( )
S
α
( )
2 T
q δ
Event Generators (PYTHIA, HERWIG)
To recover the “K-factor” in the NLO total rate To include the C-Functions
Finite
2
d d d Q y σ ∼
The area under the qT – curve will reproduce the total rate at the order if Y term is calculated to as well.
( )
1 S
α
( )
1 S
α
d d T q σ
T
p
T
q
2
d d d d
T
q y Q σ
Singular
( )
2 T
q δ
2 2 2 2
1 1 ln ,
T T T
Q q q q ⎛ ⎞ ⎜ ⎟ ⎝ ⎠
T
q
Include NNLO in high qT region
implemented through K-factor table which is a function of (Q, qT, y) of the boson, not just a constant value.
ResBos predicts both rate and shape
Precision measurements require accurate theoretical predictions
ResBos-A: improved ResBos by including final state NLO QED corrections
to W and Z production and decay
+
Resum+Born
+ +
Resum+NLO
and denote FQED radiation corrections, which dominates the W mass shift.
Need to consider the recombination effect
Experimental: difficult to discriminate between electrons and photons with a small opening angle Theoretical: to define infra-safe quantities which are independent of long-distance physics Essential feature of a general IRS physical quantity: The observable must be such that it is insensitive to whether n or n+1 particles contributed if the n+1 particles has n-particle kinematics. rejection Procedure @ Tevatron (for electron)
Recombination Effects
infrared-safe
Effects of EW correction decrease significantly after recombination.
W Mass @ CDF Run-2
W→eν transverse mass distribution Statistical error only.
W Boson qT @ D0 Run-2
W Boson qT @ D0 Run-2
Need to study the difference in the intermediate qT region.
ResBos-A (including final state NLO QED corrections) http://hep.pa.msu.edu/resum/code/resbosa/ has not been updated. Why? Because it was not used for Tevatron experiments. The plan is to include final state QED resummation inside ResBos.
Physical processes included in ResBos
W ±
New physics: W’, Z’, H+, A0, H0 …
including gauge invariant set amplitude for Drell-Yan pairs
Physics processes inside ResBos
PYTHIA predicts a different shape (and rate)
Limitations of ResBos
approximation, hence, with limitation.
know what it is good for and what the limitations are.
It could be used to reweight the distributions generated by (PYTHIA) event generator, by comparing the boson (and it decay products) distributions to ResBos predictions.
This has been done for W-mass analysis by CDF and D0)
It does not give any information about the hadronic activities of the event.
Potential of ResBos yet to be explored
asymmetry in Drell-Yan pairs.
ResBos can be used for Matrix Element Method by including resummed kT-dependent parton distribution functions together with higher order matrix element contributions. For example: The coefficients in front of the complete set of angular functions are given by ResBos
ResBos vs D0 Run-2 AFB data
(GeV)
*
M
50 100 150 200 250 300
FB
A
0.2 0.4 0.6 0.8
D0 Data RES
gauge bosons and Higgs bosons at the Tevatron and the LHC.
region but also higher order effect in high qT region, with spin correlations included via gauge invariant set of matrix elements. If you use it, we will keep providing the service to our community. Please send the request to me.
Impact of New CTEQ Parton Distribution Functions to LHC Phenomenology:
W/Z, Top and Higgs Physics
New Physics signal found?
% Difference from NLO QCD with MRSD0 CDF MRSA MRSG CTEQ 2M CTEQ 2ML GRV-94
20 50 100 150 200 250 300 350 400 450GeV Systematic uncertainties
10Excitement at 10 years ago
xT
% Difference from NLO QCD with MRSD0 CDF MRSA MRSG CTEQ 2M CTEQ 2ML GRV-94
20 50 100 150 200 250 300 350 400 450GeV Systematic uncertainties
10% Difference from NLO QCD with MRSD0 CDF MRSA MRSG CTEQ 2M CTEQ 2ML GRV-94
20 50 100 150 200 250 300 350 400 450GeV Systematic uncertainties
10% Difference from NLO QCD with MRSD0 CDF MRSA MRSG CTEQ 2M CTEQ 2ML GRV-94
20 50 100 150 200 250 300 350 400 450GeV Systematic uncertainties
10CDF Run 1A Data (1992-93)
High-x gluon not well known
% Difference from NLO QCD with MRSD0 CDF MRSA MRSG CTEQ 2M CTEQ 2ML GRV-94
20 50 100 150 200 250 300 350 400 450GeV Systematic uncertainties
10ET (GeV)
known …can be accommodated in the Standard Model
Cross sections at the LHC
Experience at the Tevatron is very useful, but scattering at the LHC is not necessarily at the LHC is not necessarily just “rescaled” scattering at the Tevatron Small typical momentum fractions x in many key searches
dominance of gluon and
sea quark scattering sea quark scattering
large phase space for
gluon emission
intensive QCD intensive QCD
backgrounds
Standard Model to wade
BFKL??
through to find the BSM pony
LHC Parton Kinematics
Sensitive to new region of x and Q values. Need better determination of PDFs Need new kind of global analysis, such as “The Combined PDF and PT Fits”
W Lepton Asymmetry, Parton Distributions, and Implications for Collider Physics
C.-P . Yuan
CTEQ - TEA (Tung et al), Michigan State Universityin collaboration with Hung-Liang Lai, Marco Guzzi, Zhao Li, Joey Huston, Pavel Nadolsky, Jon Pumplin BNL @ June 24, 2010
C.-P . Yuan (MSU) BNL June 24, 2010 1 CTEQ-Tung Et Al.: recent activities
Uncertainty induced by αs in the CTEQ-TEA PDF analysis
(arXiv:1004.4624)NLO general-purpose PDF fits
◮ CTEQ6.6 set (published in 2008)→ CT09 → CT10 (to be released) ◮ new experimental data, statistical methods, and parametrization forms
Constraints on new physics PDFs for Event Generators (arXiv:0910.4183) Exploration of statistical aspects (data set diagonalization) and PDF parametrization dependence (Pumplin, arXiv:0909.0268 and
0909.5176) C.-P . Yuan (MSU) BNL June 24, 2010 2 Uncertainty induced by αs in the PDF analyses
Questions addressed:
◮ Two leading theoretical uncertainties in LHC processes are due to αs and the PDFs; how can one quantify their correlation? ◮ Which central αs(MZ) and which error on αs(MZ) are to be used with the existing PDFs? ◮ What are the consequences for key LHC processes (gg → H0, etc.)?
recent activities on this issue:
◮ MSTW (arXiv:0905.3531) ◮ NNPDF (in 2009 Les Houches Proceedings, arXiv:1004.0962) ◮ H1+ZEUS (arXiv:0911.0884)
C.-P . Yuan (MSU) BNL June 24, 2010 3 Our findings (arXiv:1004.4624)
Theorem In the quadratic approximation, the total αs+PDF uncertainty ∆X, with all correlation, reduces to ∆X =
where ∆XPDF is the PDF uncertainty with fixed αs, e.g. uncertainty from 44 CTEQ6.6 PDFs with the same αs(MZ) = 0.118 ∆Xαs = (Xhigh − Xlow)/2 is the αs uncertainty computed with upper/lower αs PDFs, e.g. CTEQ6.6AS PDFs for αs(MZ) = 0.120 and 0.116
Back-up slides: The main idea illustrated; key cross sections tabulated The full proof is given in the paper
C.-P . Yuan (MSU) BNL June 24, 2010 4 CT10 analysis (in progress)
Experimental data Combined HERA-1 neutral-current and charged-current DIS data with 114 correlated systematic effects
◮ replaces 11 separate HERA-1 sets used in the CTEQ6.6 fit
CDF Run-2 and D0 Run-2 inclusive jet production Tevatron Run-2 Z rapidity distributions from both CDF and D0 W electron asymmetry from CDF II and D0 II; W muon asymmetry from D0 II (CT10W set) Other data sets inherited from CTEQ6.6
C.-P . Yuan (MSU) BNL June 24, 2010 5 CT10 analysis (in progress)
Impact of the new HERA data
0.4 0.6 0.8 1 1.2 1.4 1.6 10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.9 New HERA vs Separ. HERA x g(x,Q) Q = 2 GeV, New HERA data (red), separate HERA data (blue) New HERA1Reduction in the uncertainty band at x < 0.001
CT10 analysis (in progress)
Developments in statistical techniques Experimental normalizations Ni are treated on the same footing as other correlated systematic errors
◮ Minimum of χ2 with respect to Ni is found algebraically ◮ normalization shifts are automatically accounted for when producing the eigenvector sets
Set all data weights of 1, unless otherwise specified
◮ do not prefer some experiments over the other experiments ◮ Exception: NMC/BCDMS and Run-2 W asymmetry data (see below)
C.-P . Yuan (MSU) BNL June 24, 2010 5 CT10 analysis (in progress)
Revised functional forms at the input scale More data constraints ⇒more flexible (=less biased) parametrizations for g(x, Q0), d(x, Q0), and s(x, Q0) Rs = limx→0 (s(x) + ¯ s(x)) /
u(x) + ¯ d(x)
the data ⇒large uncertainty in s(x) at x → 0
◮ allow Rs to vary in the fit, but “softly constrain” it by a penalty
The resulting CT10 error bands overlap with the MSTW/NNPDF bands Alternative parametrizations based on Chebyshev polynomials are also explored (Pumplin, arXiv:0909.5176)
C.-P . Yuan (MSU) BNL June 24, 2010 5 More flexible parametrizations
CT10(green) vs. CTEQ6.6(blue) ; PRELIMINARY
105 104 103 0.01 0.02 0.05 0.1 0.2 0.5 0.7 0.6 0.8 1.0 1.2 1.4 x CT66CT6.6M,CT10CT6.6M g at Q2 GeV 105 104 103 0.01 0.02 0.05 0.1 0.2 0.5 0.7 0.5 1.0 1.5 2.0 x CT66CT6.6M,CT10CT6.6M s at Q2 GeVg(x, Q): large uncertainty at x < 10−3, despite tighter constraints by the combined HERA data s(x, Q): wider uncertainty, covers both CTEQ6.6 and MSTW’08
C.-P . Yuan (MSU) BNL June 24, 2010 6 Agreement between data sets
Good overall agreement: χ2/d.o.f. = 1.1 (out of ~2800 data points) Noticable observations on the quality of the fit:
◮ Tevatron single-inclusive jet production: Run-1 and Run-2 sets are moderately compatible (arXiv:0904.2424) ◮ Tevatron Run-2 Z rapidity: D0 well described; CDF acceptable (higher stat.) ◮ Tevatron Run-2 W lepton asymmetry
♦ is precise; constrains d(x)/u(x) at x → 1 ♦ apparently disagrees with existing constraints on d/u, mainly provided by the NMC F d
2 /F p 2 and Run-1 W lepton asymmetrydata; minor tension against BCDMS F d
2 data C.-P . Yuan (MSU) BNL June 24, 2010 7 Agreement between data sets
Reaonable fits to electron (e) asymmetry data are possible without NMC and BCDMS; and vice versa No acceptable fit to D0 II e asymmetry and NMC/BCDMS data can be achieved, if they are included on the same footing Tension between Run-2 e asymmetry and µ asymmetry Good agreement between Run-2 e W asymmetry data and Z y data With special emphasis on D0 II e asymmetry data (weight>1), it is possible to obtain a reasonable agreement for W asymmetry (χ2/d.o.f. = 1 − 2) , with some remaining tension with NMC & BCDMS data, especially at x > 0.4
C.-P . Yuan (MSU) BNL June 24, 2010 8 CT10 family
Two series of PDFs are produced:
◮ CT10: no D0 Run-2 W asymmetry data are included ◮ CT10W: include D0 Run-2 W asymmetry, with an extra weight
C.-P . Yuan (MSU) BNL June 24, 2010 9 CT10 and CT10W fits with Tevatron Run-2 data
PRELIMINARY
Y 0.5 1 1.5 2 2.5 3 (Y) FB ACT10W agrees better with W asy data; has smaller uncertainty than CTEQ6.6 or CT10
C.-P . Yuan (MSU) BNL June 24, 2010 10 d(x, Q)/u(x, Q) at Q = 85 GeV
105 104 103 0.01 0.02 0.05 0.1 0.2 0.5 0.7 0.6 0.8 1.0 1.2 1.4 x Ratio to CTEQ6.6M d/u at Q=85 GeV PRELIMINARY CT10/CT6.6M CT6.6/CT6.6M 105 104 103 0.01 0.02 0.05 0.1 0.2 0.5 0.7 0.6 0.8 1.0 1.2 1.4 x Ratio to CTEQ6.6M d/u at Q=85 GeV PRELIMINARY CT10W/CT6.6M CT6.6/CT6.6MCT10W prefers larger d/u, has smaller uncertainty than CTEQ6.6
CT10 & CT10W predictions for the Tevatron
0.7 0.8 0.9 1 1.1 1.2 1.3 + H CT10 & CT10W predictions for the Tevatron
Y 0.5 1 1.5 2 2.5 3 )/dY (ZPreliminary
70
C.-P . Yuan (MSU) BNL June 24, 2010 13 CT10 & CT10W predictions for the LHC
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 + H CT10 & CT10W predictions for the LHC
σ(W +)/σ(W −) rapidity dist.
Y 0.5 1 1.5 2 2.5 3 3.5 4 ) (w.r.t CTEQ6.6M)CT10W Uncertainty (red) is clearly smaller than that of CT10 & CTEQ6.6. σ(W ±)/σ(Z0) rapidity dist.
Y 0.5 1 1.5 2 2.5 3 3.5 4 ) (w.r.t. CTEQ6.6M) (Z σ ) and d ± (W σ Ratio of d 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 CT10 (Green) CT10W (Red) CTEQ6.6 (Blue) LHC 7 TeV PRELIMINARYCT10 (green) & CT10W (red) uncertainties in central y region are larger than that of CTEQ6.6 (blue), mainly due to larger uncertainty on s distribution.
C.-P . Yuan (MSU) BNL June 24, 2010 15 Summary I
CTEQ6.6AS PDF sets (available in the LHAPDF library): from 4 alternative CTEQ6.6 fits for αs(MZ) = 0.116, .117, .119, .120 sufficient to compute uncertainty in αs(MZ) at ≈68% and 90% C. L., including the world-average αs(MZ) = 0.118 ± 0.002 as an input data point The CTEQ6.6AS αs uncertainty should be combined with the CTEQ6.6 PDF uncertainty as ∆X =
The total uncertainty ∆X reproduces the full correlation between αs(MZ) and PDFs, also applicable to CT10 family and future PDFs.
C.-P . Yuan (MSU) BNL June 24, 2010 16 Summary II
Tevatron Run-2 W asymmetry data... ...become increasingly complete and precise (measurements by both CDF and D0; electron and muon channels) ...cannot be explained based on the d/u ratio provided by the previously existing data Several cross checks of the theoretical calculation for W asymmetry; no problems were found Higher-twist and nuclear corrections in the large-x BCDMS/NMC deuterium data are the usual suspects
( Virchaux and Milsztajn; Alekhin; Accardi et al.)CT10 and CT10W sets of PDFs for practical applications, without and with constraints from the D0 Run-2 W asymmetry
C.-P . Yuan (MSU) BNL June 24, 2010 17 ICHEP 2010 D0 & CDF
[GeV]
Z T
p 20 40 60 80 100 120 Entries/5 GeV 5 10 15 20 25 [GeV]
Z T
p 20 40 60 80 100 120 Entries/5 GeV 5 10 15 20 25
L = 229 nb
ATLAS
=7 TeV) s Data 2010 ( µ µ
[GeV]
T W
p 10 20 30 40 50 60 70 80 Entries / 5 GeV 2 4 6 8 10 12 14 16 18 20 22 [GeV]
T W
p 10 20 30 40 50 60 70 80 Entries / 5 GeV 2 4 6 8 10 12 14 16 18 20 22
= 7 TeV ) s Data 2010 (
QCD
Preliminary ATLAS
L = 16.9 nb
PHYSICAL REVIEW D 73, 052001 (2006) Lam-Tung relation PHYSICAL REVIEW D 16, 2219 (1977)
A2 = A0
(GeV)
Tp
10 20 30 40 50 60 70 80
A
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 RES NLO ) q NLO (q NLO (qg)
Tevatron 1.98 TeV (GeV)
Tp
10 20 30 40 50 60 70 80
1A
0.05 0.1 0.15 0.2 0.25 0.3
RES NLO ) q NLO (q NLO (qg) Tevatron 1.98 TeV y > 1
(GeV)
Tp
10 20 30 40 50 60 70 80
1A
0.02 0.04 0.06 0.08 0.1 RES NLO ) q NLO (q NLO (qg)
Tevatron 1.98 TeV 0 < y < 1
(GeV)
T
p
10 20 30 40 50 60 70 80
2
A
0.02 0.04 0.06 0.08 0.1
RES NLO ) q NLO (q NLO (qg) Tevatron 1.98 TeV
(GeV)
Tp
10 20 30 40 50 60 70 80
4A
0.02 0.04 0.06 0.08 0.1 0.12 0.14
RES NLO ) q NLO (q NLO (qg)
< 116 GeV
Z66 GeV < M Tevatron 1.98 TeV
A2 = A0
Lam-Tung relation
(GeV)
Tp
10 20 30 40 50 60 70 80
A
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
RES NLO ) q NLO (q NLO (qg)
LHC 7 TeV
(GeV)
T
p
10 20 30 40 50 60 70 80
1
A
0.02 0.04 0.06 0.08 0.1 0.12 0.14 RES NLO ) q NLO (q NLO (qg)
LHC 7 TeV y > 1 (GeV)
T
p
10 20 30 40 50 60 70 80
1
A
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 RES NLO ) q NLO (q NLO (qg)
LHC 7 TeV 0 < y <1 (GeV)
T
p
10 20 30 40 50 60 70 80
2
A
0.02 0.04 0.06 0.08 0.1
RES NLO ) q NLO (q NLO (qg)
LHC 7 TeV
D0 collaboration, arxiv: 1002.4594
(GeV)
JJM
200 400 600 800 1000 1200 1400 JJ/dM
< 0.4
max|y|
Scale 0.5 average p
CTEQ6.6 / CT10 CT10 / CT10 CT10W / CT10
(GeV)
JJM
200 400 600 800 1000 1200 1400 JJ/dM
< 0.8
max0.4 < |y|
Scale 0.5 average p
CTEQ6.6 / CT10 CT10 / CT10 CT10W / CT10Setting scale as half average pT of jets makes CTEQ6.6 and CT10/W predictions more consistent with data. Also CT10/W improves the predictions with larger PDF uncertainties.
(GeV)
JJM
200 400 600 800 1000 1200 1400 JJ/dM
< 1.6
max1.2 < |y|
Scale 0.5 average p
CTEQ6.6 / CT10 CT10 / CT10 CT10W / CT10
(GeV)
JJM
200 400 600 800 1000 1200 1400 JJ/dM
< 2.4
max2.0 < |y|
Scale 0.5 average p
CTEQ6.6 / CT10 CT10 / CT10 CT10W / CT10(GeV)
JJM
200 400 600 800 1000 1200 1400 JJ/dM
< 1.2
max0.8 < |y|
Scale 0.5 average p
CTEQ6.6 / CT10 CT10 / CT10 CT10W / CT10(GeV)
JJM
200 400 600 800 1000 1200 1400 JJ/dM
< 2.0
max1.6 < |y|
Scale 0.5 average p
CTEQ6.6 / CT10 CT10 / CT10 CT10W / CT10 M 200 400 600 800 1000 1200 K factor 1.34 1.36 1.38 1.4 1.42 1.44 1.46 1.48 1.5 1.52
CTEQ6.6 MSTW2008
The K factors are almost independent of PDF sets for Tevatron D0 di-jet data.
1900 1950 2000 2050 2100 2150 2200 2250 2300
(fb/GeV)
jj
/dM
20 40 60 80 100 120 140 160 180 200 CT10.00 CT10 PDF uncertainty half scale double scale
di-jet @ LHC 7 TeV < 2200 GeV
jj
2000 GeV < M |y| < 2.8 R = 0.6
280 300 320 340 360 380 400 420
/dy (pb/GeV)
T
/dp
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 CT10.00 CT10 PDF uncertainty half scale double scale
Inclusive Jet @ LHC 7 TeV < 400 GeV
T
310 GeV < p 2.1 < |y| < 2.8 R = 0.6
Top Quark Pair production rates
At Tevatron Run-2, uncertainty Incduced by PDFs is sizable. Uncertainty induced by factorization (and renormalization) scale dependence is large at the LHC. Hence, NNLO calculation Is needed.
Use top quark pair production rate to determine the mass of top quark
What’s top mass?
What’s the top mass in a full event generator such as PYTHIA? generator, such as PYTHIA? NOBODY KNOWS Parton showers generate some higher
but with approximations.
CT10 prediction is about the same as CTEQ6.6 for Higgs production @LHC 7 TeV
ResBos for Higgs Physics
q q V H V
Quark initiated processes: Gluon initiated processes:
at the same order of accuracy as Drell-Yan processes
t t t
H
at the same order of accuracy as Drell-Yan processes consistent with NNLO QCD rate include exact contribution in high PT
( )
2 S
α
arXiv:0909.2305
Shape changes from and variation of scales
( )
2 S
α
( )
2 S
α
( )
1 S
α
H W + W − Predict different shape ResBos vs PYTHIA vs NLO
hep-ph/0509100
b ¯ b H
MSSM Higgs boson
Consistent treatment of initial state parton mass with CTEQ6.6 PDFs, in GM scheme.
(see Sally Dawson’s talk)
Di-Photon Productions
Compare to CDF Run-2 di-Photon data
Costas Vellidis Pheno2010
The cut PT < M is to suppress fragmentation contribution
Compare to CDF Run-2 di-Photon data
Costas Vellidis Pheno2010
The cut PT < M is to suppress fragmentation contribution
Large theoretical uncertainty in fragmentation contribution
arXiv:0704.0001
Backup slides
C.-P . Yuan (MSU) BNL June 24, 2010 18 Details of the CTEQ6.6FAS analysis
Take the “world-average” αs(MZ) = 0.118 ± 0.002 as an input: αs(MZ)|in = 0.118 ± 0.002 at 90% C.L. Find the theory parameter αs(MZ) as an output of a global fit (CTEQ6.6FAS): αs(MZ)|out = 0.118 ± 0.0019 at 90% C.L. The combined PDF+αs uncertainty is estimated as ∆X = 1 2
− X(−)
i2 Problem: each PDF set comes with its own αs⇒ cumbersome A simple workaround exists!
A quadrature sum reproduces the αs-PDF correlation
H.-L. Lai, J. Pumplin
Theorem In the quadratic approximation, the total αs+PDF uncertainty ∆σ
∆X =
where ∆XCTEQ6.6 is the CTEQ6.6 PDF uncertainty from 44 PDFs with the same αs(MZ) = 0.118 ∆Xαs = (X0.120 − X0.116)/2 is the αs uncertainty computed with two central CTEQ6.6AS PDFs for αs(MZ) = 0.116 and 0.120 The full proof is given in the paper; the main idea is illustrated for 1 PDF parameter a1 and αs parameter a2
Illustration of the theorem for 2 parameters
A B D C
∆χ2 =
i,j Hi,jaiaj Physi al basis ai (fo r a2 = 0 )a1
un ertaint ya2 a1 a2
∆χ2 = T 2a1 a2
un ertaint y with a1 ) ( o rrelated∆X2
1 = 1 4 (X(B) − X(D))2∆X2
2 = 1 4 (X(A) − X(C))2 Illustration of the theorem for 2 parameters, cont.
C B D A D C B
a1 a2 y1 y2
∆χ2 = T 2y1 y2
Eigenve to r bases yi , ziz1 z1 z2 z2 ∆χ2 =
i y2 i = i z2 i∆χ2 =
i,j Hi,jaiaj Physi al basis ai∆X2 = 1
4= ∆X2
1 + ∆X2 2 Full and reduced fits with variable αs: cross sections
The full (CTEQ6.6FAS) and reduced (CTEQ6.6+CTEQ6.6AS) methods perfectly agree
C.-P . Yuan (MSU) BNL June 24, 2010 20 For 50 pb^-1 pT(e) > 25 GeV
W Physics at RHIC
( ) / ( )/
e e
d W d R d W d σ η σ η
+ −
=
for CT10/CTEQ6.6M, etc
Preliminary