To recover the “K-factor” in the NLO total rate To include the C-Functions σ d ∼ 2 d d Q y σ d ⎛ ⎞ 2 1 1 Q ln ⎜ ⎟ , 2 d d d q y Q 2 2 2 ⎝ ⎠ q q q T T T T Finite q Singular σ d T ( ) δ d T 2 q q T p q 0 T T The area under the q T – curve will reproduce the total rate at ( ) ( ) α 1 α 1 the order if Y term is calculated to as well. S S
Include NNLO in high q T region • To improve prediction in high q T region • To speed up the calculation, it is implemented through K-factor table which is a function of (Q, q T , y) of the boson, not just a constant value. ResBos predicts both rate and shape of distributions.
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+NLO Resum+Born + + + 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. Procedure @ Tevatron (for electron) rejection
Recombination Effects Effects of EW correction decrease significantly after recombination. infrared-safe
W Mass @ CDF Run-2 W → e ν transverse mass distribution Statistical error only.
W Boson q T @ D0 Run-2
W Boson q T @ D0 Run-2 Need to study the difference in the intermediate q T region.
Where is it? • ResBos : http://hep.pa.msu.edu/resum/ • Plotter : http://hep.pa.msu.edu/wwwlegacy 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 ± γ including gauge invariant set amplitude , Z for Drell-Yan pairs H γγ , , ZZ WW New physics: W ’ , Z ’ , H + , A 0 , H 0 …
Physics processes inside ResBos
PYTHIA predicts a different shape (and rate)
Limitations of ResBos • Any perturbative calculation is performed with some approximation, hence, with limitation. • To make the best use of a theory calculation, we need to know what it is good for and what the limitations are. It does not give any information about the hadronic activities of the event. 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)
Potential of ResBos yet to be explored • E.g., in the measurement of forward-backward asymmetry in Drell-Yan pairs. ResBos can be used for Matrix Element Method by including resummed k T -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 A FB data 0.8 0.6 0.4 0.2 FB A 0 D0 Data -0.2 RES -0.4 -0.6 50 100 150 200 250 300 M (GeV) * � Z/
Conclusion • ResBos is a useful tool for studying electroweak gauge bosons and Higgs bosons at the Tevatron and the LHC. • It includes not only QCD resummation for low q T region but also higher order effect in high q T 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? x T Excitement at 10 years ago 150 150 150 150 150 % Difference from NLO QCD with MRSD0 � % Difference from NLO QCD with MRSD0 � % Difference from NLO QCD with MRSD0 � % Difference from NLO QCD with MRSD0 � % Difference from NLO QCD with MRSD0 � 10 5 10 5 10 5 10 5 10 5 nb/GeV nb/GeV nb/GeV nb/GeV nb/GeV 10 4 10 4 10 4 10 4 10 4 125 125 125 125 125 1/ �� d 2 � /(dE T d � ) d � 1/ �� d 2 � /(dE T d � ) d � 1/ �� d 2 � /(dE T d � ) d � 1/ �� d 2 � /(dE T d � ) d � 1/ �� d 2 � /(dE T d � ) d � 10 2 10 2 10 2 10 2 10 2 CDF CDF CDF CDF CDF 100 100 100 100 100 NLO QCD NLO QCD NLO QCD NLO QCD NLO QCD 1 1 1 1 1 75 75 75 75 75 -2 -2 -2 -2 -2 10 10 10 10 10 -4 -4 -4 -4 -4 10 10 10 10 10 50 50 50 50 50 -6 -6 -6 -6 -6 10 10 10 10 10 GeV GeV GeV GeV GeV 0 0 0 0 0 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 25 25 25 25 25 0 0 0 0 0 -25 -25 -25 -25 -25 CDF CDF CDF CDF CDF CTEQ 2M CTEQ 2M CTEQ 2M CTEQ 2M CTEQ 2M MRSA � MRSA � MRSA � MRSA � MRSA � CTEQ 2ML CTEQ 2ML CTEQ 2ML CTEQ 2ML CTEQ 2ML MRSG MRSG MRSG MRSG MRSG GRV-94 GRV-94 GRV-94 GRV-94 GRV-94 -50 -50 -50 -50 -50 CDF Run 1A Data (1992-93) 20 20 20 20 20 Systematic uncertainties Systematic uncertainties Systematic uncertainties Systematic uncertainties Systematic uncertainties 0 0 0 0 0 0 0 0 0 0 50 50 50 50 50 100 100 100 100 100 150 150 150 150 150 200 200 200 200 200 250 250 250 250 250 300 300 300 300 300 350 350 350 350 350 400 400 400 400 400 450 450 450 450 450 GeV GeV GeV GeV GeV E T (GeV) Phys. Rev. Lett. 77, 438 (1996) High-x gluon not well known 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 � or to summarize,…lots of BFKL?? Standard Model to wade 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 P T Fits”
W Lepton Asymmetry, Parton Distributions, and Implications for Collider Physics C.-P . Yuan CTEQ - TEA (Tung et al), Michigan State University in 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 α s 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 α s in the PDF analyses � Questions addressed: ◮ Two leading theoretical uncertainties in LHC processes are due to α s and the PDFs; how can one quantify their correlation? ◮ Which central α s ( M Z ) and which error on α s ( M Z ) are to be used with the existing PDFs? ◮ What are the consequences for key LHC processes ( gg → H 0 , 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 α s + PDF uncertainty ∆ X , with all correlation, reduces to � ∆ X 2 ∆ X = PDF + ∆ X 2 α s , where � ∆ X PDF is the PDF uncertainty with fixed α s , e.g. uncertainty from 44 CTEQ6.6 PDFs with the same α s ( M Z ) = 0 . 118 � ∆ X α s = ( X high − X low ) / 2 is the α s uncertainty computed with upper/lower α s PDFs, e.g. CTEQ6.6AS PDFs for α s ( M Z ) = 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 g(x,Q) Q = 2 GeV, New HERA data (red), separate HERA data (blue) c(x,Q) Q = 2 GeV, New HERA data (red), separate HERA data (blue) 1.6 1.6 New HERA1 New HERA1 Separ. HERA Separ. HERA 1.4 1.4 New HERA vs Separ. HERA New HERA vs Separ. HERA 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 10 -5 10 -4 10 -3 10 -5 10 -4 10 -3 0.01 0.02 0.05 0.1 0.2 0.5 0.9 0.01 0.02 0.05 0.1 0.2 0.5 0.9 x x Reduction in the uncertainty band at x < 0.001 C.-P . Yuan (MSU) BNL June 24, 2010 5
CT10 analysis (in progress) Developments in statistical techniques � Experimental normalizations N i are treated on the same footing as other correlated systematic errors ◮ Minimum of χ 2 with respect to N i 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, Q 0 ) , d ( x, Q 0 ) , and s ( x, Q 0 ) u ( x ) + ¯ � � � R s = lim x → 0 ( s ( x ) + ¯ s ( x )) / ¯ d ( x ) is not constrained by the data ⇒ large uncertainty in s ( x ) at x → 0 ◮ allow R s to vary in the fit, but “softly constrain” it by a penalty on χ 2 to satisfy 0 . 4 < R s < 1 � 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 g at Q � 2 GeV CT66 � CT6.6M,CT10 � CT6.6M 1.4 1.2 g ( x, Q ) : large uncertainty at 1.0 x < 10 − 3 , despite tighter 0.8 constraints by the combined 0.6 HERA data 10 � 5 10 � 4 10 � 3 0.01 0.02 0.05 0.1 0.2 0.5 0.7 x s at Q � 2 GeV CT66 � CT6.6M,CT10 � CT6.6M 2.0 s ( x, Q ) : wider uncertainty, 1.5 covers both CTEQ6.6 and 1.0 MSTW’08 0.5 10 � 5 10 � 4 10 � 3 0.01 0.02 0.05 0.1 0.2 0.5 0.7 x C.-P . Yuan (MSU) BNL June 24, 2010 6
Agreement between data sets � Good overall agreement: χ 2 /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 2 /F p provided by the NMC F d 2 and Run-1 W lepton asymmetry data; 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 ( χ 2 /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
D0 II electron Asymmetry (0.75 fb -1 )
CT10 and CT10W fits with Tevatron Run-2 data PRELIMINARY 0.2 0.2 0 0 l l p > 25 GeV p > 25 GeV T T (Y) (Y) -0.2 → → ν p p W l +X S =1.96 TeV -0.2 → → ν FB FB p p W l +X S =1.96 TeV A A -0.4 -0.4 D0 Electron D0 Electron CDF Electron CDF Electron -0.6 -0.6 CT10 (Green) CT10W (Green) CTEQ6.6 (Red) CTEQ6.6 (Red) -0.8 -0.8 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Y Y 0.3 0.3 0.2 0.2 0.1 0.1 → → ν (Y) p p W l +X S =1.96 TeV (Y) → → ν p p W l +X S =1.96 TeV 0 0 FB FB p l > 35 GeV A A T p l > 35 GeV D0 Electron -0.1 -0.1 T D0 Electron CDF Electron CDF Electron CT10W (Green) -0.2 CT10 (Green) -0.2 CTEQ6.6 (Red) CTEQ6.6 (Red) -0.3 -0.3 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 Y Y CT10W 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 d/u at Q=85 GeV d/u at Q=85 GeV PRELIMINARY PRELIMINARY CT10/CT6.6M CT10W/CT6.6M 1.4 1.4 CT6.6/CT6.6M CT6.6/CT6.6M Ratio to CTEQ6.6M Ratio to CTEQ6.6M 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 10 � 5 10 � 4 10 � 3 0.01 0.02 0.05 0.1 0.2 0.5 0.7 10 � 5 10 � 4 10 � 3 0.01 0.02 0.05 0.1 0.2 0.5 0.7 x x CT10W prefers larger d/u, has smaller uncertainty than CTEQ6.6 or CT10 C.-P . Yuan (MSU) BNL June 24, 2010 11
CT10 & CT10W predictions for the Tevatron PRELIMINARY → 0 gg H (250) → 0 gg H (160) → 0 CTEQ6.6 gg H (120) t t CT10 + W Z CT10W Z’ (600) Z’ (300) + W ’ (600) + W ’ (300) Tevatron 1.96 TeV t (s-channel) t (t-channel) HZ + HW - HW + H 0.7 0.8 0.9 1 1.1 1.2 1.3 C.-P . Yuan (MSU) BNL June 24, 2010 12
CT10 & CT10W predictions for the Tevatron 70 70 60 60 50 )/dY Preliminary 40 0 (Z -1 CDF Tevatron II 2.1 fb � 30 d CT10 (Green) 20 CT10W (Red) CTEQ6.6 (Blue) 10 0 0 0.5 1 1.5 2 2.5 3 Y � C.-P . Yuan (MSU) BNL June 24, 2010 13
CT10 & CT10W predictions for the LHC PRELIMINARY → 0 gg H (250) → 0 gg H (160) CTEQ6.6 → 0 gg H (120) CT10 t t - W + CT10W W Z Z’ (600) LHC 7 TeV Z’ (300) + W ’ (600) + W ’ (300) t (s-channel) t (t-channel) HZ + HW - HW + H 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 C.-P . Yuan (MSU) BNL June 24, 2010 14
CT10 & CT10W predictions for the LHC σ ( W ± ) /σ ( Z 0 ) rapidity dist. ) (w.r.t. CTEQ6.6M) σ ( W + ) /σ ( W − ) rapidity dist. 1.06 ) (w.r.t CTEQ6.6M) LHC 7 TeV 1.04 1.6 PRELIMINARY 1.02 1.4 1 0 (Z LHC 7 TeV 1.2 σ PRELIMINARY ) and d 0.98 - (W σ 1 0.96 ) and d CT10 (Green) ± (W CT10W (Red) CT10 (Green) 0.94 σ 0.8 Ratio of d CTEQ6.6 (Blue) + CT10W (Red) (W 0.92 σ 0.6 CTEQ6.6 (Blue) Ratio of d 0 0.5 1 1.5 2 2.5 3 3.5 4 Y 0.4 0 0.5 1 1.5 2 2.5 3 3.5 4 Y CT10 (green) & CT10W (red) uncertainties in central y region CT10W Uncertainty (red) is are larger than that of CTEQ6.6 clearly smaller than that of (blue), mainly due to larger CT10 & CTEQ6.6. 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 α s ( M Z ) = 0 . 116 , . 117 , . 119 , . 120 � sufficient to compute uncertainty in α s ( M Z ) at ≈ 68% and 90% C. L., including the world-average α s ( M Z ) = 0 . 118 ± 0 . 002 as an input data point � The CTEQ6.6AS α s uncertainty should be combined with the CTEQ6.6 PDF uncertainty as � ∆ X 2 CTEQ 6 . 6 + ∆ X 2 ∆ X = CTEQ 6 . 6 AS � The total uncertainty ∆ X reproduces the full correlation between α s ( M Z ) 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
High precision W/Z data @Tevatron ICHEP 2010 D0 & CDF
LHC W/Z data • Need more integrated luminosity (at least of the order of 100 1/pb) to make precision tests using W/Z data.
Measurements of Drell-Yan @ LHC 7 TeV 25 25 Entries/5 GeV Entries/5 GeV � -1 ATLAS Preliminary L = 229 nb 20 20 Data 2010 ( s =7 TeV) Z � µ µ 15 15 10 10 5 5 0 0 0 0 20 20 40 40 60 60 80 80 100 100 120 120 Z Z p p [GeV] [GeV] T T 22 22 Entries / 5 GeV Entries / 5 GeV Data 2010 ( s = 7 TeV ) 20 20 W e � � 18 18 QCD 16 16 W � � � 14 14 ATLAS Preliminary 12 12 � -1 L = 16.9 nb 10 10 8 8 6 6 4 4 2 2 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 W W p p [GeV] [GeV] T T
Predictions from different PDF sets
Angular function in Drell-Yan process A 2 = A 0 Lam-Tung relation PHYSICAL REVIEW D 16, 2219 (1977) PHYSICAL REVIEW D 73, 052001 (2006)
0.3 0.8 Tevatron 1.98 TeV 0.7 Tevatron 1.98 TeV 0.25 y > 1 0.6 0.2 0.5 RES RES NLO 1 0 0.15 A 0.4 NLO A NLO (q q ) NLO (q q ) NLO (qg) NLO (qg) 0.3 0.1 0.2 0.05 0.1 0 0 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 p (GeV) p (GeV) T T 0.1 0.1 Tevatron 1.98 TeV Tevatron 1.98 TeV 0.08 0.08 0 < y < 1 0.06 0.06 0.04 RES 0.02 NLO 1 0.04 A 2 NLO (q q ) -A 0 NLO (qg) 0 A 0.02 -0.02 RES NLO -0.04 0 NLO (q q ) -0.06 NLO (qg) -0.02 -0.08 0 10 20 30 40 50 60 70 80 p (GeV) -0.1 T 0 10 20 30 40 50 60 70 80 p (GeV) T 0.14 Tevatron 1.98 TeV A 2 = A 0 0.12 0.1 Lam-Tung relation 0.08 4 A 0.06 0.04 RES NLO 66 GeV < M < 116 GeV Z NLO (q q ) 0.02 NLO (qg) 0 0 10 20 30 40 50 60 70 80 p (GeV) T
0.8 LHC 7 TeV 0.14 LHC 7 TeV 0.7 y > 1 0.12 0.6 RES 0.5 0.1 NLO RES NLO (q q ) NLO 0 0.4 A NLO (q q ) NLO (qg) 0.08 1 NLO (qg) A 0.3 0.06 0.2 0.04 0.1 0.02 0 0 10 20 30 40 50 60 70 80 p (GeV) 0 T 0 10 20 30 40 50 60 70 80 p (GeV) T 0.02 LHC 7 TeV 0.018 0 < y <1 0.016 RES 0.014 NLO 0.012 NLO (q q ) NLO (qg) 1 0.01 A 0.008 0.006 0.1 0.004 0.08 LHC 7 TeV 0.002 0.06 0 0 10 20 30 40 50 60 70 80 0.04 p (GeV) T 0.02 2 -A 0 0 A -0.02 RES -0.04 NLO NLO (q q ) -0.06 NLO (qg) -0.08 -0.1 0 10 20 30 40 50 60 70 80 p (GeV) T
Di-jet at Tevatron • Large scale dependence • PDF uncertainty CT10 and CTEQ6.6 differ from MSTW with larger uncertainty
D0 Di-jet Invariant Mass distributions D0 collaboration, arxiv: 1002.4594
1.6 1.6 Scale 0.5 average p of jets Scale 0.5 average p of jets T T 1.4 1.4 0.4 < |y| < 0.8 |y| < 0.4 max max 1.2 1.2 JJ JJ /dM /dM 1 1 � � Ratio of d Ratio of d 0.8 0.8 CTEQ6.6 / CT10 0.6 0.6 CTEQ6.6 / CT10 CT10 / CT10 CT10 / CT10 0.4 0.4 CT10W / CT10 CT10W / CT10 0.2 0.2 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 M (GeV) M (GeV) JJ JJ 1.8 1.8 Scale 0.5 average p of jets Scale 0.5 average p of jets 1.6 1.6 T T 1.2 < |y| < 1.6 1.4 0.8 < |y| < 1.2 1.4 max max JJ JJ /dM /dM 1.2 1.2 � � Ratio of d Ratio of d 1 1 0.8 0.8 CTEQ6.6 / CT10 0.6 CTEQ6.6 / CT10 0.6 CT10 / CT10 CT10 / CT10 0.4 0.4 CT10W / CT10 CT10W / CT10 0.2 0.2 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 M (GeV) M (GeV) JJ JJ 2.4 2.5 Scale 0.5 average p of jets 2.2 Scale 0.5 average p of jets T T 2 2.0 < |y| < 2.4 2 1.6 < |y| < 2.0 max 1.8 max JJ JJ CTEQ6.6 / CT10 /dM /dM 1.6 CT10 / CT10 � 1.5 � 1.4 Ratio of d Ratio of d CT10W / CT10 1.2 1 1 0.8 CTEQ6.6 / CT10 0.6 CT10 / CT10 0.5 0.4 CT10W / CT10 0.2 200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400 M (GeV) M (GeV) JJ JJ Setting 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.
The NLO K factors for di-jet invariant mass distribution 1.52 CTEQ6.6 1.5 1.48 MSTW2008 1.46 K factor 1.44 1.42 1.4 1.38 1.36 1.34 200 400 600 800 1000 1200 M jj The K factors are almost independent of PDF sets for Tevatron D0 di-jet data.
Theory uncertainties on jets @ LHC 7TeV 200 0.5 di-jet @ LHC 7 TeV 180 2000 GeV < M < 2200 GeV 0.45 jj |y| < 2.8 R = 0.6 160 0.4 CT10.00 140 /dy (pb/GeV) CT10 PDF uncertainty 0.35 (fb/GeV) half scale double scale 120 0.3 Inclusive Jet @ LHC 7 TeV 100 0.25 jj /dM 310 GeV < p < 400 GeV T T 80 /dp 0.2 2.1 < |y| < 2.8 � R = 0.6 d � 60 d 0.15 CT10.00 CT10 PDF uncertainty 40 0.1 half scale 20 0.05 double scale 0 0 1900 1950 2000 2050 2100 2150 2200 2250 2300 280 300 320 340 360 380 400 420 PDF uncertainty dominates. Can further constrain PDFs.
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 order corrections in the event shape order corrections in the event shape, but with approximations.
Higgs predictions with different PDF sets CT10 prediction is about the same as CTEQ6.6 for Higgs production @LHC 7 TeV
This is an exciting era for High Energy Physics Thank You!
Backup Slides
ResBos for Higgs Physics q V Quark initiated processes: V q H • Rate and shape: � at the same order of accuracy as Drell-Yan processes t t Gluon initiated processes: t H • Rate and shape: � at the same order of accuracy as Drell-Yan processes � consistent with NNLO QCD rate ( ) α 2 � include exact contribution in high P T S
( ) α 2 S ( ) α 1 S W + H W − arXiv:0909.2305 ( ) α 2 Shape changes from S and variation of scales
Predict different shape ResBos vs PYTHIA vs NLO hep-ph/0509100 b Consistent treatment of initial H state parton mass with CTEQ6.6 MSSM Higgs boson PDFs, in GM scheme. ¯ b (see Sally Dawson’s talk)
Di-Photon Productions
Compare to CDF Run-2 di-Photon data Costas Vellidis Pheno2010 The cut P T < M is to suppress fragmentation contribution
Compare to CDF Run-2 di-Photon data Costas Vellidis Pheno2010 The cut P T < 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” α s ( M Z ) = 0 . 118 ± 0 . 002 as an input : α s ( M Z ) | in = 0 . 118 ± 0 . 002 at 90% C.L. � Find the theory parameter α s ( M Z ) as an output of a global fit (CTEQ6.6FAS): α s ( M Z ) | out = 0 . 118 ± 0 . 0019 at 90% C.L. � The combined PDF+ α s uncertainty is estimated as � 22+1 � ∆ X = 1 � 2 � X (+) − X ( − ) � � � i i 2 i =1 � Problem: each PDF set comes with its own α s ⇒ cumbersome � A simple workaround exists!
A quadrature sum reproduces the α s -PDF correlation H.-L. Lai, J. Pumplin Theorem In the quadratic approximation, the total α s + PDF uncertainty ∆ σ of the CTEQ6.6FAS set, with all correlation, reduces to � ∆ X 2 CTEQ 6 . 6 + ∆ X 2 ∆ X = α s , where � ∆ X CTEQ 6 . 6 is the CTEQ6.6 PDF uncertainty from 44 PDFs with the same α s ( M Z ) = 0 . 118 � ∆ X α s = ( X 0 . 120 − X 0 . 116 ) / 2 is the α s uncertainty computed with two central CTEQ6.6AS PDFs for α s ( M Z ) = 0 . 116 and 0 . 120 The full proof is given in the paper; the main idea is illustrated for 1 PDF parameter a 1 and α s parameter a 2
Physi al basis a i Illustration of the theorem for 2 parameters ∆ χ 2 = � i,j H i,j a i a j a 2 a 2 A un ertaint y un ertaint y (fo r a 2 = 0 ) ( o rrelated D with a 1 ) a 1 a 1 B ∆ χ 2 = T 2 a 1 a 2 C 4 ( X ( B ) − X ( D )) 2 1 = 1 4 ( X ( A ) − X ( C )) 2 ∆ X 2 ∆ X 2 2 = 1
Eigenve to r bases y i , z i Physi al basis a i Illustration of the theorem for 2 parameters, cont. ∆ χ 2 = � ∆ χ 2 = � i y 2 i z 2 i = � i,j H i,j a i a j i a 2 y 2 z 2 y 2 z 1 A y 1 D ����� ����� z 1 ����� ����� A z 2 ����� ����� D ����� ����� a 1 y 1 ����� ����� B ����� ����� ∆ χ 2 = T 2 C B C ( X ( A ) − X ( C )) 2 + ( X ( B ) − X ( D )) 2 � ∆ X 2 = 1 � 4 = ∆ X 2 1 + ∆ X 2 2
Full and reduced fits with variable α s : cross sections The full (CTEQ6.6FAS) and reduced (CTEQ6.6+CTEQ6.6AS) methods perfectly agree C.-P . Yuan (MSU) BNL June 24, 2010 20
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