PARTON DISTRIBUTIONS AT THE DAWN OF THE LHC S TEFANO F ORTE U - PowerPoint PPT Presentation

PARTON DISTRIBUTIONS AT THE DAWN OF THE LHC S TEFANO F ORTE U NIVERSIT ` A DI M ILANO & INFN CTEQ-MC NET SUMMER SCHOOL L AUTERBAD , J ULY 30, 2010

SUMMARY LECTURE II: ISSUES AND RECENT DEVELOPMENTS � PDF UNCERTAINTIES { MONTE CARLO VS HESSIAN : GAUSSIAN UNCERTAINTIES { TOLERANCE { PARTON PARAMETRIZATION � THEORETICAL ISSUES { HEAVY QUARKS { HIGHER ORDERS � THE STATE OF THE ART { LHC STANDARD CANDLES { THEORETICAL UNCERTAINTIES ?

PDF UNCERTAINTIES

� ) � ) WHAT IS A ONE - � UNCERTAINTY ? MSTW/CTEQ: THE SPREAD OF PDF S WITHIN AN ACCEPTABLE TOLERANCE 2 � STANDARD 1 BANDS TOO NARROW ) LARGE DISCREPANCIES FOR INDIVIDUAL � � = EXPERIMENTS 2 � MINIMUM i 2 � VS GLOBAL Collins, Pumplin 2001

� ) WHAT IS A ONE - � UNCERTAINTY ? MSTW/CTEQ: THE SPREAD OF PDF S WITHIN AN ACCEPTABLE TOLERANCE CTEQ TOLERANCE CRITERION & 2 � STANDARD 1 BANDS TOO NARROW ) LARGE DISCREPANCIES FOR INDIVIDUAL � � = EXPERIMENTS � TOLERANCE ) ENVELOPE OF UNCERTAINTIES OF EXPERIMENTS CTEQ TOLERANCE PLOT FOR 4 TH EIGENVEC . Eigenvector 4 40 30 BCDMSp BCDMSd CCFR2 CCFR3 CDFjet 20 NMCp CDFw ZEUS NMCr 2 D0jet E605 E866 H1a H1b � MINIMUM i 10 2 distance 0 � VS GLOBAL � 10 � 20 � 30 Collins, Pumplin 2001

MSTW/CTEQ: THE SPREAD OF PDF S WITHIN AN ACCEPTABLE TOLERANCE � DYNAMICAL � TOLERANCE � STANDARD Collins, VS GLOBAL MINIMUM EXPERIMENTS CTEQ TOLERANCE CRITERION & MSTW DYNAMICAL TOLERANCE Pumplin � � i 2 2 2001 � � ) SEPARATELY DETERMINED FOR EACH HESSIAN EIGENVECTOR ) ENVELOPE OF UNCERTAINTIES OF EXPERIMENTS 2 = ∆ χ Eigenvector number 13 2 Distance = global 1 BANDS TOO NARROW -20 -15 -10 WHAT IS A ONE - � UNCERTAINTY ? 10 15 20 MSTW TOLERANCE PLOT FOR 13 TH EIGENVEC . -5 0 5 distance CTEQ TOLERANCE PLOT FOR 4 TH EIGENVEC . µ µ � 30 � 20 � 10 BCDMS BCDMS p F p F 10 20 30 40 2 2 µ µ 0 BCDMS BCDMS d F d F 2 2 µ µ NMC NMC p F p F 2 2 µ µ NMC NMC d F d F BCDMSp 2 2 µ µ µ µ NMC NMC n/ n/ p p µ µ BCDMSd E665 E665 p F p F 2 2 µ µ E665 E665 d F d F 2 2 H1a SLAC ep F SLAC ep F 2 2 SLAC ed F SLAC ed F 2 2 H1b NMC/BCDMS/SLAC F NMC/BCDMS/SLAC F L L E866/NuSea pp DY E866/NuSea pp DY MSTW 2008 NLO PDF fit ZEUS E866/NuSea pd/pp DY E866/NuSea pd/pp DY ν ν NuTeV NuTeV N F N F 2 2 NMCp ν ν CHORUS CHORUS N F N F 2 2 Eigenvector 4 ν ν NuTeV NuTeV N xF N xF NMCr 3 3 ν ν CHORUS CHORUS N xF N xF 3 3 ν ν → → µ µ µ µ CCFR CCFR N N X X CCFR2 ν ν → → µ µ µ µ NuTeV NuTeV N N X X σ σ NC NC CCFR3 H1 ep 97-00 H1 ep 97-00 r r σ σ ZEUS ep 95-00 ZEUS ep 95-00 NC NC r r σ σ CC CC E605 H1 ep 99-00 H1 ep 99-00 r r σ σ CC CC ZEUS ep 99-00 ZEUS ep 99-00 r r charm charm CDFw H1/ZEUS ep F H1/ZEUS ep F 2 2 ) LARGE DISCREPANCIES FOR INDIVIDUAL H1 ep 99-00 incl. jets H1 ep 99-00 incl. jets E866 ZEUS ep 96-00 incl. jets ZEUS ep 96-00 incl. jets ∅ ∅ D D II p II p p p incl. jets incl. jets D0jet CDF II p CDF II p p p incl. jets incl. jets ∅ ∅ → → ν ν D D II W II W l l asym. asym. CDFjet → → ν ν CDF II W CDF II W l l asym. asym. ∅ ∅ D D II Z rap. II Z rap. CDF II Z rap. CDF II Z rap. 90% C.L. 68% C.L. 68% C.L. 90% C.L. ∆ χ 2 Tolerance T = global -20 -15 -10 10 15 20 -5 0 5 σ NC σ NC 1 1 H1 ep 97-00 H1 ep 97-00 r r µ 2 2 ν → µ µ NMC d F NuTeV N X 2 GLOBAL MSTW TOLERANCE ν → µ µ ν → µ µ 3 3 CCFR N X NuTeV N X 4 4 E866/NuSea pd/pp DY E866/NuSea pd/pp DY MSTW 2008 NLO PDF fit ν NuTeV N xF ν → µ µ 5 5 NuTeV N X 3 ν → µ µ ν → µ µ 6 6 NuTeV N X NuTeV N X µ BCDMS d F ∅ → ν 7 7 D II W l asym. 2 µ µ 8 8 BCDMS p F BCDMS d F 2 2 σ NC σ NC 9 9 ZEUS ep 95-00 H1 ep 97-00 r r 10 11 12 13 14 15 16 17 18 19 20 10 11 12 13 14 15 16 17 18 19 20 µ BCDMS d F SLAC ed F 2 2 σ NC σ NC ZEUS ep 95-00 H1 ep 97-00 r r E866/NuSea pd/pp DY E866/NuSea pd/pp DY ν NuTeV N xF E866/NuSea pp DY 3 µ ∅ → ν NMC d F D II W l asym. 2 Eigenvector number ν NuTeV N F σ NC H1 ep 97-00 2 r ν → µ µ E866/NuSea pd/pp DY CCFR N X ν → µ µ ν → µ µ CCFR N X NuTeV N X ∅ → ν E866/NuSea pd/pp DY D II W l asym. σ σ H1 ep 97-00 NC H1 ep 97-00 NC r r ν → µ µ ν NuTeV N xF NuTeV N X 3 - - + + 100 50 50 100 (MRST) (MRST) (CTEQ) (CTEQ)

WHAT IS A ONE - � UNCERTAINTY ? NNPDF: THE CENTRAL 68% OF THE MC DISTRIBUTION OF PDF S Example: the gluon distribution in the NNPDF1.0 set 4 4 N rep =25 N rep =100 3 3 2 2 2 ) 2 ) xg(x,Q 0 xg(x,Q 0 1 1 0 0 -1 -1 -2 -2 1e-05 0.0001 0.001 0.01 0.1 1 1e-05 0.0001 0.001 0.01 0.1 1 x x $ PROBABILITY DISTRIBUTION OF PDF S � ENSEMBLE OF REPLICAS $ MEAN ; UNCERTAINTY � EXPECTED CENTRAL VALUE $ STANDARD DEVIATION � ANY FEATURES OF DISTRIBUTION CAN BE DETERMINED ( C . L . INTERVALS , CORRELATIONS ...)

(Pumplin, 2009) � � � 2 � � 2 � � = 10 WHERE IS THE UNCERTAINTY COMING FROM? WHY DOES ONE NEED LARGE TOLERANCES ? DATA INCOMPATIBILITY (Pumplin, 2009) 2 FOR � C AN “ REDIAGONALIZE ”: DIAGONALIZE SIMULTANEOUSLY � i – TH EXPT TOTAL AND ) COMPATIBILITY OF EACH EXPT WITH GLOBAL FIT � STUDY DISTRIBUTION OF DISCREPANCIES � APPROX . 2 GAUSSIAN WITH UNCERTAINTIES RESCALED BY ) 2 10 FOR 90% C . L . � � �

WHERE IS THE UNCERTAINTY COMING FROM? WHY DOES ONE NEED LARGE TOLERANCES ? DATA INCOMPATIBILITY (Pumplin, 2009) 2 FOR � C AN “ REDIAGONALIZE ”: DIAGONALIZE SIMULTANEOUSLY � i – TH EXPT TOTAL AND ) COMPATIBILITY OF EACH EXPT WITH GLOBAL FIT � STUDY DISTRIBUTION OF DISCREPANCIES � APPROX . 2 GAUSSIAN WITH UNCERTAINTIES RESCALED BY ) 2 10 FOR 90% C . L . � � � FUNCTIONAL BIAS (Pumplin, 2009) � IF PARM . NOT GENERAL ENOUGH , GLOBAL MIN . IS NOT TRUE MIN . � ONE - � VARIATION ABOUT FAKE MIN CORRESP . 2 VARIATION TO LARGE � � USE OF CHEBYSHEV POLYNOMIALS SUGGESTS 2 “ MOST GENERAL ” PARM . WITHIN 10 OF � � = CTEQ6.6 PARM .

� � PARAMETRIZATION UNCERTAINTIES ? NONGAUSSIAN BEHAVIOUR ? LOGNORMAL VS . GAUSSIAN THE HERALHC BENCHMARK (F eltesse, Glazo v, Rades u + NNPDF 2008) � TRY EXPERIMENTAL SYSTEMATICS GIVEN BY EITHER GAUS - SIAN OR LOGNORMAL DISTRIBUTION -1 -0.5 0 0.5 1 1.5 2 2.5 3 ( BENCHMARK ) HERAPDF, � REPEAT WITH MONTECARLO LOGNORMAL OR GAUSSIAN , IN EITHER CASE DETERMINE UN - CERTAINTY EITHER WITH HESSIAN OR MONTECARLO -1 -0.5 0 0.5 1 1.5 2 2.5 3 LOGNORMAL : HESS . VS MC GAUSSIAN : HESS . VS MC Fit vs H1PDF2000, Q 2 = 4. GeV 2 Fit vs H1PDF2000, Q 2 = 4. GeV 2 10 10 xG(x) xG(x) 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 1 10 10 10 10 1 x x � NO DIFFERENCE BETWEEN LOGNORMAL , GAUSSIAN , MC, HESSIAN

PARAMETRIZATION UNCERTAINTIES ? NONGAUSSIAN BEHAVIOUR ? LOGNORMAL VS . GAUSSIAN THE HERALHC BENCHMARK (F eltesse, Glazo v, Rades u + NNPDF 2008) � TRY EXPERIMENTAL SYSTEMATICS GIVEN BY EITHER GAUS - SIAN OR LOGNORMAL DISTRIBUTION -1 -0.5 0 0.5 1 1.5 2 2.5 3 ( BENCHMARK ) HERAPDF, � REPEAT WITH MONTECARLO LOGNORMAL OR GAUSSIAN , IN EITHER CASE DETERMINE UN - CERTAINTY EITHER WITH HESSIAN OR MONTECARLO � COMPARE TO NNPDF FIT TO SAME DATA -1 -0.5 0 0.5 1 1.5 2 2.5 3 NNPDF LOGNORMAL : HESS . VS MC GAUSSIAN : HESS . VS MC Fit vs H1PDF2000, Q 2 = 4. GeV 2 Fit vs H1PDF2000, Q 2 = 4. GeV 2 10 10 10 xG(x) xG(x) 9 9 8 8 8 7 7 ) 6 2 = 4 GeV 6 6 5 5 2 0 x g (x, Q 4 4 4 3 3 2 2 2 1 1 0 0 0 -4 -3 -2 -1 -4 -3 -2 -1 10 10 10 10 1 10 10 10 10 1 x x -3 -4 -2 -1 10 10 10 10 1 x � NO DIFFERENCE BETWEEN LOGNORMAL , GAUSSIAN , MC, HESSIAN � SIZABLE DIFFERENCE WR TO FLEXIBLE NNPDF PARAMETRIZATION

PARAMETRIZATION UNCERTAINTIES ? EXPLORING THE SPACE OF PARAMETERS : HESSIAN APPROACH � IN H ESSIAN APPROACH CAN VARY THE FUNCTIONAL FORM , ASSUMPTIONS , STARTING SCALE HERAPDF1.0 FIT : � DONE IN THE VARIATION OF STRANGENESS FRACTION , LARGE x BEHAVIOUR , HIGHER ORDER POLYNOMIAL TERMS 2 � NO TOLERANCE ( � � 1 ), UNCERTAINTY = DOUBLED ORTHOGONAL POLYNOMIALS � OLD IDEA (P ARISI , S OURLAS , 1978; Z OMER 1996): EXPAND PDF S OVER BASIS OF ORTHOGONAL POLYNOMIALS � G LAZOV , R ADESCU , 2009: COUPLED TO M ONTE C ARLO METHOD � LENGTH PENALTY TO STABILIZE THE FIT (Glazo v, Rades u, 2009)