CTEQ-TEA Parton distribution functions and α s

Transcription

1 CTEQ-TEA Parton distribution functions and α s C.-P. Yuan Michigan State University in collaboration with H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. Nadolsky, J. Pumplin, and D. Stump Alphas Workshop, MPI Munich Feb 9, 2011 C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

2 CTEQ-Tung Et Al.: recent activities Uncertainty induced by α s in the CTEQ-TEA PDF analysis (PRD, arxiv: ) New PDFs for collider physics CTEQ6.6 set (published in 2008) CT09 CT10, CT10W (PRD, arxiv: ) new experimental data, statistical methods, and parametrization forms PDFs for Event Generators (JHEP, arxiv: ) Exploration of statistical aspects and PDF parametrization dependence (PRD, arxiv: and ) C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

3 Uncertainty in α s in the CTEQ-TEA PDF analysis arxiv: Two leading theoretical uncertainties in LHC processes are due to α s and the PDFs These are not independent uncertainties; 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.)? C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

4 Uncertainty in α s in the CTEQ-TEA PDF analysis arxiv: Recent activity to examine these questions, e.g.: MSTW (arxiv: ) α s (M Z ) is an output of the global fit (constrained by the hadronic scattering only) several sets of error PDFs, each with its own α s (M Z ) value lengthier calculations The α s uncertainty and PDF uncertainty are inseparable NNPDF (in 2009 Les Houches Proceedings, arxiv: ): α s (M Z ) = ± is taken as an input α s PDF correlation is examined with 1000 PDF replicas and found to be small H1+ZEUS (arxiv: ): sensitivity of the HERAPDF set to δα s (M Z ) = ±0.002 is explored C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

5 Our findings Total PDF+α s errors X are the same when found (a) from a full fit with floating α s, or (b) by adding X P DF and X αs in quadrature g at Q 2 GeV CT6.6AS CT6.6M CT6.6AS CT6.6M x c at Q 2 GeV x black CTEQ6.6 PDF uncertainty Blue filled PDF+α s uncertainty of the fit with floating α s (M Z ) Green hatched PDF+α s uncertainty added in quadrature Also, agreement in cross section predictions C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

6 Our findings Total PDF+α s errors X are the same if found either from a full fit with floating α s, or by adding X P DF and X αs in quadrature g at Q 2 GeV 1.4 CT6.6AS CT6.6M CT6.6AS CT6.6M x c at Q 2 GeV This agreement is a rigorous consequence of the quadratic approximation for χ x C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

7 Details of the CTEQ6.6FAS analysis Take the world-average α s (M Z ) = ± as an input: α s (M Z ) in = ± 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 = ± at 90% C.L. The combined PDF+α s uncertainty is estimated as X = ( ) X (+) i X ( ) 2 i 2 i=1 Problem: each PDF set comes with its own α s cumbersome A simple workaround exists! C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

8 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 = XCT 2 EQ6.6 + X2 α s, where X CT EQ6.6 is the CTEQ6.6 PDF uncertainty from 44 PDFs with the same α s (M Z ) = X αs = (X X )/2 is the α s uncertainty computed with two central CTEQ6.6AS PDFs for α s (M Z ) = and The full proof is given in the paper; the main idea is illustrated for the α s parameter a 0 and 1 PDF parameter a 1 C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

9 Illustration of the theorem for 2 parameters C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

10 Illustration of the theorem for 2 parameters, cont. C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

11 PDF and α s uncertainties for gg H and t t production 11.2 Higgs production (M =120 GeV) at 7 TeV H σ(pp H+X) [pb] α S (M ) Z tt production (m =171 GeV) at 14 TeV t 910 σ(pp tt+x) [pb] α S (M ) Z C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

12 Full and reduced fits with variable α s : cross sections The full and reduced methods perfectly agree C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

13 Correlations between α s and PDFs Correlation cosine cos φ between the best-fit α s (M Z ) and PDFs, plotted as a function of the momentum fraction x. cos φ cos φ CT6.6FAS: correlation ofα s M Z with f a x,q g x,q 2 GeV x,q 2 GeV c x,q 2 GeV x CT6.6FAS: correlation ofα s M Z with f a x,q g x,q 85 GeV x,q 85 GeV c x,q 85 GeV b x,q 85 GeV x solid gluon PDF; anticorrelated at x 0.01; from HERA NC-DIS dashed singlet PDF; correlated at x 0.4; from BCDMS and NMC NC-DIS dashed-dotted heavy quark (c, b) PDFs; correlated at x ; from HERA At large Q, these correlations are reduced by PDF evolution, except heavy-quark PDFs. C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

14 Full fit with floating α s in CT10.AS Series The Minimal χ 2 found from a full fit with floating α s in CT10.AS series χ CT α s (M ) Z The χ 2 = 100 range (at 90% C.L.) is ± which is a rather weak constraint as compare to the world-average α s (M Z ) = ± C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

15 Summary CTEQ6.6AS and CT10.AS PDF sets (available in LHAPDF): from 4 alternative CTEQ6.6 fits ( for α s (M Z ) = 0.116, 0.117, 0.119, sufficient to compute uncertainty in α s (M Z ) at 68% and 90% C. L., including the world-average α s (M Z ) = ± as an input data point The CTEQ6.6AS α s uncertainty should be combined with the CTEQ6.6 PDF uncertainty as X = XCT 2 EQ6.6 + X2 CT EQ6.6AS The total uncertainty X reproduces the full correlation between α s (M Z ) and PDFs A larger range (from to 0.123) of α s (M Z ) for CT10/W.AS series is given at C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

16 Backup slides C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,

17 NMCF d 2 /F p 2 and F p 2 data vs. α s Minimal χ 2 from a full fit with floating α s in CT10.AS series. NMC F2 Ratio data χ 2 NMC F2 proton data χ CT α s CT α s We did not find a significant effect of NMC F2 d/f p 2 data on α s, though a smaller value is mildly preferred. (χ 2 is close to the number of data points, which is 123.) NMC F p 2 data prefers a larger α s, but χ 2 is much larger than the number of data points, which is 201.) We will examine the NMC reduced cross section (instead of F 2 ) in the next version of CTEQ-TEA fits. C.-P. Yuan (MSU) Alphas Workshop, MPI Munich Feb 9,