PARTON DISTRIBUTIONS AT THE DAWN OF THE LHC

Transcription

1 PARTON DISTRIBUTIONS AT THE DAWN OF THE LHC STEFANO FORTE UNIVERSITÀ DI MILANO & INFN ICHEP PARIS, JULY,

2 PDFS FOR THE SPS (984) PDFS: 5 YEARS OF PROGRESS YEARS OF VALENCE PDFS.5.5 post-hera EHLQ84 DuOw84 MoTu9 KMRS9 CTQM MRSA95 GRV94 CTQ4M MRS98 C6.M MRST Alekhin StrAsy u() at Q = GeV f(,q) * a (-) b pre-hera (Scale is linear in /3 ).5 D quark at Q = GeV post-hera EHLQ84 DuOw84 MoTu9 KMRS9 CTQM MRSA95 GRV94 CTQ4M MRS98 C6.M MRST Alekhin StrAsy f(,q) * a (-) b pre-hera (Scale is linear in /3 ) GHR VS DUKE OWENS W. K. TUNG, 4 HADRON COLLIDERS CIRCA 985 µ QUALITATIVE QCD: DISCOVERY PHYSICS DIS AT NMC AND HERA µ QUANTITATIVE QCD: PRECISION PHYSICS HADRON COLLIDERS CIRCA µ PRECISION QCD NEW PHYSICS

3 PDFS: TOWARDS LHC PHYSICS THE HIGGS CROSS SECTION FIRST PDFS WITH UNCERTAINTIES σ(gg H) [pb] s = 4 TeV MH [GeV] MRST CTEQ Alekhin CURRENT GLOBAL PDF SETS MSTW8 NNPDF. CTEQ6.6 GG luminosity S = (7 TeV) M H [GeV] MSTW8 NNPDF. CTEQ6.6 GG luminosity S = (4 TeV) PDFS WITH ERROR ( 3) Ì É ÅÊËÌ ÐÓ Ðµ Ð Ò Á˵ WIDELY DIFFERENT UNCERTAINTY ESTIMATES UNSATISFACTORY AGREEMENT WITHIN UNCERTAINTIES ÓÙ ÖÖ ¾¼¼ µ ¾ ½¼¼ (CTEQ); ¼ (MRST); (ALEKHIN) ½ ÐÙÓÒ ÐÙÑ ÒÓ Ø PDF uncertainty - Ratio to MSTW8 PDF uncertainty - Ratio to MSTW M H [GeV] THREE GLOBAL (DIS+HADRONIC) PDF SETS AVAILABLE REASONABLE AGREEMENT OF CEN TRAL VALUES & UNCERTAINTIES À ÖÓ Ø ÓÒ Ñ ÖØ Ò Ø Ðº ¾¼½¼µ

4 AN ONGOING EFFORT HERALHC (4 8): A WORKSHOP TO TRANSFER KNOWN HOW FROM HERA TO THE LHC COMMUNITY PDF4LHC (8 ONGOING): A PERMANENT WORKING GROUP TO PROVIDE GUIDANCE ON PDF TO LHC EXPERIMENTS AND PHENOMENOLOGY ØÛÓ ÓÒ ¾¼¼ ¹¾¼¼ ¾¼¼ ¹¾¼¼ µ ÓÙÖ ÔÐ Ò ÖÝ Ñ Ø Ò Ú Ñ ¹Ø ÖÑ Ò ß ÖÓÙÔ Ñ Ø Ò ÛÓÖ Ò ØÛÓ ÊÆ» Ë Ö ÔÓÖØ Ý ÐÐÓÛ ÓÓ µ ß ARXIV:93.386º HEP PH/6 HEP PH/63 ÕÙ ÖØ ÖÐÝ Ñ Ø Ò ½¼ Ò Ò ÔØ ÓÒ Ò ÖÙ ÖÝ ¾¼¼ ß Û Ø ØØÔ»»ÛÛÛº ÔºÙк ºÙ»Ô л Ò ß ØØÔ»»Û ºØ Ö Ð º» Ò ÜºÔ Ô Ø ØÐ È ÄÀ ÏÁÃÁ Ö ÓÙÖ Û Ú Ð Ð ß ÖÙ Ø ÙÐ ÒØ Ö Ø ÓÒ Û Ø Ø ÄÀ À ÖÓ Ë Ø ÓÒ Ï

5 CURRENT PDF SETS Å ¾ µ È Ê ½ ÜÑ Ò Ü ½ ܾ ½ Ü ½µ ¾ Ü ¾µ Õ Õ Ü½Ü¾ Å ¾ LHC parton kinematics NNPDF. dataset 9 8, = (M/4 TeV) ep(±y) Q = M M = TeV Ø ÓÖ ÐÓ Ð Ø ÆÆÈ ¾º¼µ Q / M / p T [ GeV ] NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H DYE65 DYE886 CDFWASY CDFZRAP DZRAP CDFRKT DRCON M = GeV M = TeV y = M = GeV HERA fied target ÄÀ Ò Ñ Ø Q (GeV ) CTEQ6.6: GLOBAL, NLO, VFN WITH HQ MASS, SEVERAL «VALUES MSTW8: GLOBAL, NLO & NNLO, VFN WITH HQ MASS, SEVERAL «VALUES NNPDF.: GLOBAL, NLO, VFN WITHOUT HQ MASS, SEVERAL «VALUES ALEKHIN ABKM: DIS+SOME DY, NLO & NNLO, BMSN (FFN), SINGLE «VALUE HERAPDF.: ONLY HERA DATA, NLO, VFN WITH HQ MASS, SEVERAL «VALS. SETS BASED ON MODEL ASSUMPTIONS (GRV/GJR, STATISTICAL PDFS,...)

6 FEATURES, TRADEOFFS AND CHOICES DATA; ABKM, GJR GLOBAL DIS+ FIXET TARGET DY; HERAPDF: HERA ONLY STATISTICAL TREATMENT: CTEQ HESSIAN WITH TOLERANCE; MSTW HESSIAN WITH DYNAMICAL TOLERANCE; HERAPDF, ABKM, GJR, STANDARD HESSIAN; NNPDF MONTE CARLO (ALSO STUDIED BY HERAPDF) POLYNOMIALS; GJR: DITTO + VALENCELIKE ASSUMPTION; NNPDF NEURAL NETS; CHEBYSHEV POLYNOMIALS STUDIED BY HERAPDF; HEAVY QUARKS:CTEQ: GM VFN (SACOT SCHEME); MSTW: GM VFN (ACOT+TR SCHEME); NNPDF: ZM VFN, PRELIM: GM VFN (FONLL A SCHEME); ABKM: (Æ FFN MATCHED WITH BMSN SCHEME); GJR: FFN ) (Æ PERTURBATIVE ORDER:CTEQ: NLO, BUT DY LO WITH K FACTORS; MSTW: NNLO, BUT DY LO WITH K FACTORS; NNPDF FULL NLO; ABKM, GJR: FULL NNLO «VALUE:CTEQ, NNPDF: EXTERNAL PARAMETER, SEVERAL VALUES AVAILABLE; MSTW: FITTED, BUT ALSO VARIABLE AS EXT.PARAMETER; ABKM, GJR: FITTED, NOT VARIABLE AS EXT. PARAMETER THE PDF4LHC RECOMMENDATION DATASET:CTEQ, MSTW, NNPDF FIXED TARGET AND COLLIDER, È AND È È PARTON PARAMETRIZATION:CTEQ, MSTW, HERAPDF Ü «½ ܵ AT NLO, ENVELOPE OF CTEQ, MSTW, NNPDF AT NNLO, MSTW WITH UNCERTAINTY RESCALED MY MSTWNLO/NLOENVELOPE

7 DATASET: WHY GLOBAL FITS? IMPACT OF DRELL YAN DATA ON THE NNPDF. FIT ¾ ØÓØ NNPDF. dataset ÁË ÁË Â Ì ÆÆÈ ¾º¼ ½º½ ½º¾½ ½º¾¼ ¼º ¼º ¼º ÆÅ ¹Ô ½º ½º ½º ÆÅ ½º ½º ½ ½º ËÄ ½º¾ ½º¾ ½º¾ ÅË ½º½ ½º½ ½º½ À Ê Á ½º½ ½º½½ ½º½ ÀÇÊÍË ½º ½ ½º ½º ÄÀ½¼ ¼º ½ ¼º ¼º ÆÌÎ ÅÆ ½º ¼ ½º ½º ½ Í˹À¾ Q / M / p T [ GeV ] NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H DYE65 DYE886 CDFWASY CDFZRAP DZRAP CDFRKT DRCON.5.45 NNPDF. DIS+JET. NNPDF. DIS+JET FIT QUALITY WHEN DATA µ INCLUDED SOME PDF COMBINATIONS POORLY DE TERMINED WITHOUT THESE DATA VERY SUBSTANTIAL IMPROVEMENT IN SIGNIFICANT IMPROVEMENT IN TOTAL VALENCE ( Õ µ) & ISOTRIPLET µ) È Õ Ù (Ù HUGE IMPROVEMENT IN SEA ASYM & STRANGENESS Ù T3 (, Q ) NNPDF..8 V (, Q ).6.4. NNPDF NNPDF. DIS+JET NNPDF. DIS+JET.7.3 NNPDF. NNPDF..6.5 S (, Q ) ).4 s - (, Q

8 STATISTICAL TREATMENT: HESSIAN APPROACH CTEQ TOLERANCE CRITERION & MSTW DYNAMICAL TOLERANCE STANDARD ¾ ½ BANDS TOO NARROW µ LARGE DISCREPANCIES FOR INDIVIDUAL EXPERIMENTS CTEQ TOLERANCE PLOT FOR 4TH EIGENVEC. DYNAMICAL µ SEPARATELY DETERMINED FOR EACH HESSIAN EIGENVECTOR 4 Eigenvector 4 3 GLOBAL MSTW TOLERANCE MINIMUM VS GLOBAL ¾ ¾ 3 TOLERANCE µ ENVELOPE OF UNCERTAINTIES OF EXPERIMENTS ÓÐÐ Ò ÈÙÑÔÐ Ò ¾¼¼½ distance BCDMSp BCDMSd Ha Hb ZEUS NMCp NMCr CCFR CCFR3 E65 CDFw E866 Djet CDFjet MSTW TOLERANCE PLOT FOR 3TH EIGENVEC. Eigenvector number 3 MSTW 8 NLO PDF fit BCDMS BCDMS NMC NMC NMC E665 E665 SLAC F SLAC ed µp F µd F µp F µd F µn/µp µp F µd F ep F NMC/BCDMS/SLAC FL E866/NuSea pp DY E866/NuSea NuTeV pd/pp DY νn F νn F νn 3 νn 3 νn µµx NuTeV νn µµx H ep 97- ZEUS ep 95- H ep 99- ZEUS ep 99- H/ZEUS ep F H ep 99- jets NC σr σr NC σr CC CC σr charm incl. ZEUS ep 96- incl. jets D II pp incl. jets CDF II pp incl. jets D II W lν asym. CDF II W lν asym. D II Z rap. CDF II Z rap. Distance = χ global % C.L. 68% C.L. 68% C.L. 9% C.L. global 5 Tolerance T = χ MSTW 8 NLO PDF fit Eigenvector number 5 (MRST) + 5 (CTEQ) + (MRST) (CTEQ) - - NC H ep 97- σ r NuTeV ν N µµx CCFR ν N µµx E866/NuSea pd/pp DY 3 NuTeV ν N F NuTeV ν N µµx BCDMS µd F BCDMS µp F NC ZEUS ep 95- σ r NC ZEUS ep 95- σ r SLAC ed F E866/NuSea pd/pp DY D II W lν NuTeV ν N F 3 NuTeV ν N F asym. E866/NuSea pd/pp DY CCFR ν N µµx E866/NuSea pd/pp DY NC H ep 97- σ r NuTeV ν N µµx NC H ep 97- σ r NMC µd F NuTeV ν N µµx E866/NuSea pd/pp DY NuTeV ν N µµx D II W lν NuTeV ν N µµx asym. BCDMS µd F NC H ep 97- σ r BCDMS µd F NC H ep 97- σ r E866/NuSea pd/pp DY E866/NuSea pp DY NMC µd F NC H ep 97- σ r CCFR ν N µµx NuTeV ν N µµx D II W lν asym. NC H ep 97- σ r 3 NuTeV ν N F

9 STATISTICAL TREATMENT: MONTE CARLO APPROACH BASIC IDEA: MONTE CARLO SAMPLING OF THE PROBABILITY MEASURE IN THE (FUNCTION) SPACE OF PDFS Eperimental Data Fi i=,...,ndata NMC,BCDMS,SLAC,HERA,CHORUS... START FROM MONTE CARLO SAMPLING OF DATA SPACE EACH PDF NEURAL NETWORK PARAMETRIZED BY 37 PARAMETERS Å ¾ (NNPDF.: PARMS) INFINITE NUMBER PARAMETERSµ OF CAN REP RESENT ANY FUNCTION MC generation Fi() Fi() Fi(N-) Fi(N) TRAINING EVOLUTION FIT STOPS WHEN QUALITY OF FIT TO RAN DOMLY SELECTED VALIDATION DATA (NOT FIT TED) STOPS IMPROVING NN parametrization qnet() qnet() qnet(n-) qnet(n) REPRESENTATION OF PROBABILITY DENSITY

10 STATISTICAL TREATMENT: MONTE CARLO APPROACH BASIC IDEA: MONTE CARLO SAMPLING OF THE PROBABILITY MEASURE IN THE (FUNCTION) SPACE OF PDFS START FROM MONTE CARLO SAMPLING OF DATA SPACE EACH PDF NEURAL NETWORK PARAMETRIZED BY 37 PARAMETERS Å ¾ (NNPDF.: PARMS) INFINITE NUMBER PARAMETERSµ OF CAN REP RESENT ANY FUNCTION CAN DETERMINE BOTH 68C.L.& ) g (, Q NNPDF. - 68% CL NNPDF. - -σ Individual Replicas FIT STOPS WHEN QUALITY OF FIT TO RAN DOMLY SELECTED VALIDATION DATA (NOT FIT TED) STOPS IMPROVING

11 PARTON PARAMETRIZATION: HESSIAN UNCERTAINTIES EXPLORING THE SPACE OF PARAMETERS IN HESSIAN APPROACH CAN VARY THE FUNCTIONAL FORM, ASSUMPTIONS, STARTING SCALE DONE IN THE HERAPDF. FIT: VARIATION OF STRANGENESS FRACTION, Ü LARGE BEHAVIOUR, HIGHER ORDER POLYNOMIAL TERMS ORTHOGONAL POLYNOMIALS OLD IDEA (PARISI, SOURLAS, 978; ZOMER 996): EXPAND PDFS OVER BASIS OF ORTHOGONAL POLYNOMIALS GLAZOV, RADESCU, 9: COUPLED TO MONTE CARLO METHOD NO TOLERANCE ( ¾ ½), UNCERTAINTY DOUBLED LENGTH PENALTY TO STABILIZE THE FIT Ð ÞÓÚ Ê Ù ¾¼¼ µ

12 PARTON PARAMETRIZATION: NNPDF UNCERTAINTIES CROSS VALIDATION OPTIMAL FITTING REPLICAS ARE FITTED TO A DATA SUBSET A DIFFERENT SUBSET OF DATA USE FOR EACH REPLICA OPTIMAL FIT WHEN FIT TO VALIDATION (CONTROL) DATA STOPS IMPROVING ¾ FIT TO DATA

13 PARTON PARAMETRIZATION: NNPDF UNCERTAINTIES CROSS VALIDATION THE BEST FIT IS NOT AT THE MINIMUM OF THE ¾ OVERFITTING REPLICAS ARE FITTED TO A DATA SUBSET A DIFFERENT SUBSET OF DATA USE FOR EACH REPLICA OPTIMAL FIT WHEN FIT TO VALIDATION (CONTROL) DATA STOPS IMPROVING ¾ FIT TO DATA

14 HEAVY QUARKS: AN OLD PROBLEM s dspdf in units of shcteq66ml LHC,NLO MANY FITS(CTEQ<6, NNPDF, ALEKHIN<9) TREAT CHARM AS MASSLESS ABOVE µ THRESHOLD ZMVFN SCHEME COMBINED MATCHED SCHEMES AVAILABLE SINCE LONG (ACOT94, FONLL98) INCLUDING CHARM MASS ALONG WITH LL RESUMMATION; ALTERNATIVE TR/TR PROCEDURE IMPLEMENTED SINCE 98 IN MRST WHEN CTEQ IMPLEMENTED ACOT IN 8, SURPRISING CHANGECTEQ6 CTEQ6.5 IN Ï, & AGREEMENT WITH MRST SPOILED (LATER RESTORED) W + W - Z W + h HL W - h HL tt - H7L ggfi h HL h + HL KNNLO CTEQ6.6 CTEQ6. IC-Sea RECENT PROGRESS: THE LES HOUCHES 9 BENCHMARKS FONLL PRESCRIPTION RECENTLY ALSO IMPLEMENTED FOR DIS, AVAILABLE Ç «TO µ (LIKE TR/TR, ACOT ONLY TO Ç «µ) ¾ Ç «µ FONLL, ACOT COINCIDE EXACTLY, TR DIFFERS BY SUBLEADING µµ É INDEP. TERM ¾ Ñ Ç «¾ VARIOUS PRESCRIPTIONS FOR HANDLING SUBLEADING TERMS ( SCALING ): DIFFERENCES SIZABLE ÊÓ Ó Ø Ðº ¾¼½¼µ Æ ÓÐ Ý Ø Ðº ¾¼¼ µ

15 HEAVY QUARKS: NEW PROBLEMS IMPACT OF SUBLEADING TERMS SIZABLE CLOSE TO THRESH OLD DIFFERENCE BETWEEN DIFFERENT PRESCRIPTIONS (ACOT SCALING, FONLL DAMPING, MSTW MATCHING) AS LARGE AS DIFFERENCE BETWEEN FFN (NO DGLAP RESUM MATION FOR CHARM) AND ZMVFN (NO CHARM MASS) THE SOLUTION: GO UP ONE ORDER IF EVERYTHING AT ONE EXTRA ORDER IN «, DIFFERENCES MINOR IN FONLL, CAN COMBINE Ç «¾ µ TREATMENT OF HQ WITH STANDARD Ç «µ NLO TREATMENT OF LIGHT µ QUARKS EXCELLENT APPROX TO FULL º º Ä Ò Ò Æ ÓÒ RESULT DUCTION COEFF. FCTNS. COMPUTED Ö Ò ÙÑ RECENT PROGRESS: Ç «µ MASSLESS LIMIT OF HQ PRO ÊÓ Ó ¾¼½¼µ ÐĐÙÑÐ Ò ÃÐ Ò ¾¼¼ µ

16 NNLO CORRECTIONS E-65 (Y=) NNLO (±σ) NLO M 5 dσ/d(m)/d(y)/(- ).5 (nbgev 4 ) Q =9 GeV DIS/DY(±σ) DIS(±σ) (ū+d - )/ LO+Ã FACTORS MSTW NNLO TREATS DIS AT NNLO, JETS AT NLO, DRELL YAN AT ALEKHIN SERIES FITS GENUINELY NNLO, BUT ONLY DIS+ TWO FIXED TARGET DY EXPERIMENTS INCLUDED BUT IMPACT NOT NEGLIGIBLE... WHY NOT INCLUDED? CONVOLUTIONS ARE HARD! NNPDF IS AT NLO Ð Ò Å ÐÒ ÓÚ È ØÖ ÐÐÓ ¾¼¼

17 PROBLEM: NNLO NEEDED FOR STANDARD CANDLES EXAMPLE: THE W CHARGE ASYMMETRY ÖÖ Ö Ö ÞÞ Ò ¾¼½¼ Ø Ò NNLO CORRECTIONS VISIBLY IMPROVE AGREEMENT WITH DATA EFFECT ON MATRIX ELEMENT COMPARABLE TO EFFECT ON PDFS, BUT IN DIFFERENT REGIONS

18 TOWARDS NNLO TOOLS: GRID BASED METHODS AT NLO ORIGINAL IDEA EXPANSION OF PDFS ON BASES OF POLYNOMIALS (PASCAUD, ZOMER, THE GRID IDEA (CARLI, SALAM, SIEGERT 5) PRECOMPUTE CONVOLUTION WITH BASIS FUNCTIONS EXPAND PDF OVER BASIS CONVOLUTIONS REDUCED TO LINEAR COM BINATIONS MATRIX MULTIPLICATION REPRESENT PDFS ON INTERPOLATED GRID BASIS FCTNS INTERPOLATING FCTNS (IF MONTE CARLO USED, BASIS FCTNS WEIGHTS FOR MC INTEGRAL) DO CONVOLUTIONS OVER BASIS FUNCTIONS GRID CAN BE OPTIMIZED SOME IMPLEMENTATIONS:. FastKernel METHOD ˉ² FASTNLO: FAST INTERFACE FOR JET CROSS SEC ÃÐÙ Ê ÖØÞ ÏÓ ¾¼¼ µ TIONS ˉ³ ˉ⁴ E65 E886p SPACE COMPUTATION OF GLAP GREEN FUNCTIONS, INTERFACED TO FASTNLO FOR JETS AND TO SUIT FASTKERNEL: GRID METHOD INTERFACED TO N y E886r Wasy Zrap ABLE ÆÆÈ ¾¼½¼µ FAST DY APPLGRID: OPTIMIZED GRID, POTENTIALLY UNIVER SAL INTERFACE, IMPLEMENTED FOR JETS, W AND Z PRODUCTION ÖÐ Ø Ðº ¾¼½¼µ.6.4 σgrid / σstandard N bins =5, Int.: (5, 5, ); a = ; W N bins =5, Int.: (5, 5, ); a = 3; W η N bins =5, Int.: (5, 5, ); a = 4; W N =5, Int.: (5, 5, ); a = 5; W bins <.5 positron PDF PDF PDF PDF = = = = p positron T (GeV)

19 «: AN OUTSTANDING PROBLEM NEW GLOBAL «DETERMINATION BY BETHKE (9): ¼ ½½ ¼ ¼¼¼ «ADOPTED BY PDG WEB UPDATE (9) τ-decays (N3LO) Quarkonia (lattice) Υ decays (NLO) DIS F (N3LO) DIS jets (NLO) e + e jets & shps (NNLO) electroweak fits (N3LO) e + e jets & shapes (NNLO)...3 α s (Μ Z ) WHAT S THE PROBLEM? N LO DETERMINATION ÐĐÙÑÐ Ò ĐÓØØ Ö Ù«ÒØ ¾¼¼ µ FROM NONSINGLET SCALING ¼ ½½ ¼ ¼¼¾ VIOLATIONS: «¼ ½½ (NLO: ¼ ¼¼¾) AT THREE «FROM AVERAGE DO WE UNDERSTAND HIGHER ORDERS? MSTW () SEE A CHANGE OF SIGMA FROM NLO TO NNLO TO ¼ ½¾¼¾ ¼ ¼¼½¾ ¼ ¼¼½ «¼ ½½ ½ ¼ ¼¼½ «DO WE UNDERSTAND EXTRAPOLATION? IF TRUNCATED MOMENTS ARE USED (NO ASSUMPTIONS) NLO RESULT FROM NONSINGLET SCALING VIOLATIONS º º Ø Ðº IS «¼ ½¾ ¼ ¼¼ ¼ ¼¼ ¾¼¼¾µ WE NEED A BELIEVABLE «CONSERVATIVE AVERAGE FOR PHENOMENOLOGY ÓÐ Ö Ñ ÙÖ Ñ ÒØ ÒÓØ ÒÐÙ Ù Ó ºººØ Ö Ð Ö ººº ÙÒ ÖØ ÒØ

20 WHERE DO WE STAND? LHC STANDARD CANDLES Ï TOP GLOBAL FITS IN GOOD MUTUAL AGREEMENT CHOICE OF «VALUE IMPORTANT Ï º Ï ØØ ¾¼½¼µ

21 WHERE DO WE STAND? PARTON LUMINOSITIES QUARK QUARK GLUON GLUON THE HIGGS CROSS SECTION ÑÀ ½¾¼ GEV: DIFFERENT GROUPS..5 THE PDF4LHC RECIPE different values of αs(mz) eact pdf+αs uncertainties NNPDF. CTEQ6.6 MSTW8nlo PDF4LHC recipe º Ï ØØ ¾¼½¼µ º Ï ØØ ¾¼½¼µ R LHC 7 TeV normalized to MSTW8 pdf+αs 68% C.L. mh (GeV) ENVELOPE TAKES CARE OF POORLY UNDERSTOOD DISAGREEMENTS º Î Ò ¾¼½¼µ

22 WHERE ARE WE GOING? THEORETICAL UNCERTAINTIES UNCERTAINTIES: CAN BE COMBINED IN QUADRATURE WITH PDF UNCERTAINTIES Ä Ø Ð «¾¼½¼µ; AVAILABLE FOR CTEQ, HERAPDF, MSTW, NNPDF Ì É Ñ: MSTW8 IN PROGRESS: DEPENDENCE ON & MASS Ñ : NNPDF, CTEQ Ratio to MSTW 8 NLO Charm quark distribution at Q = 4 GeV MSTW 8 NLO (9% C.L.) m c m c =.3 GeV =.5 GeV NEEDED: RESUMMATION: SMALL Ü REGION AT HERA, LARGE REGION FOR FIXED TARGET DY ORDERS: RENORMALIZATION AND FACTORIZATION SCALE VARIATION HEAVY QUARKS: MATCHING SCHEME VARIATION

23 CONCLUSION THIS IS JUST THE BEGINNING!

24 EXTRAS

25 WHERE IS THE HESSIAN UNCERTAINTY COMING FROM? WHY DOES ONE NEED LARGE TOLERANCES? DATA INCOMPATIBILITY ÈÙÑÔÐ Ò ¾¼¼ µ CAN REDIAGONALIZE : DIAGONALIZE SIMULTANEOUSLY FOR TOTAL AND TH ¾ EXPT COMPATIBILITY OF EACH EXPT WITH µ GLOBAL FIT FUNCTIONAL BIAS ÈÙÑÔÐ Ò ¾¼¼ µ IF PARM. NOT GENERAL ENOUGH, GLOBAL MIN. IS NOT TRUE MIN. ONE VARIATION ABOUT FAKE MIN CORRESP. TO LARGE VARIATION ¾ USE OF CHEBYSHEV POLYNOMIALS SUGGESTS MOST GENERAL PARM. WITHIN ½¼ OF CTEQ6.6 PARM. ¾ STUDY DISTRIBUTION OF DISCREPANCIES APPROX. GAUSSIAN WITH UNCERTAINTIES RESCALED BY µ ¾ ½¼ FOR 9%C.L.

26 WHERE IS THE MONTE CARLO UNCERTAINTY COMING FROM? FIT TO REPLICAS VS RANDOM SUBSET OF CENTRAL VAL.S LIGHT QUARKS ¾ REPLICAS CENTRAL V..3.3 ¾ GLUE STRANGE UNCERTAINTY ON DATA ONLY REDUCED BY. µ EXPT. UNCERTAINTIES UNDERESTIMATED OR UNDERLYING INCOMPRESSIBLE UNCERTAINTY Ö ÔÐ º Ú Ð º QUALITY OF FIT &PDFS UNCHANGED REDUCTION OF ¾ Ö Ô BY FACTOR ¾ µ FLUCTUATIONS ABOUT TRUE VALUE HALVED

27 WHERE IS THE MONTE CARLO UNCERTAINTY COMING FROM? CENTRAL VALUES: VARYING PARTITION VS FIXED PARTITION REPLICAS CENTRAL VALUE FIXED PARTITION ¾ 4 GLUE CTEQ6.6 MRSTE 3 NNPDF. Current fit ¾ Ö Ô ¾ ¼ ¾ ½ ¼ ¾¼ ½ ¼ ¾ Ø QUALITY OF FIT UNCHANGED ¾ Ö Ô UNCHANGED µ CENTRAL FIT UNCHANGED UNCERTAINTY ON PREDICTION (I.E. ON PDFS) REDUCED FUNCTIONAL UNCERTAINTY MORE THAN HALF OF UNCERTAINTY DUE TO FUNCTIONAL FORM : ¼ ¼ SMALLER FOR HERA DATA Ø REMAINING UNCERTAINTY ROUGHLY SCALES WITH DATA UN CERTAINTY: ¼ ¼¼ CENT.; Ø ¼ ¼¼ REP. Ø Ü Ô ÖØ Ø ÓÒ Ö ÙÐØ Ó Ø Ò Ú Ö Ò ÓÚ Ö «Ö ÒØ Ó Ó Ô ÖØ Ø ÓÒ ½¼¼ Ö ÔÐ µ ÑÓÖ Ô ÖØ Ø ÓÒ Ò ÓÖ ÙÖ Ø Ö ÙÐØ g (, Q ) - VALENCE.4 CTEQ6.6 MRSTE. NNPDF. Current fit.8 VT (, Q ) TRIPLET.5 CTEQ6.6 MRSTE.4 NNPDF. Current fit.3 T3 (, Q ) STRANGE.3 CTEQ6.6.5 MRSTE NNPDF. Current fit..5 s+ (, Q )

28 WHY UNCERTAINTIES ARE IMPORTANT: THE NUTEV ANOMALY... Æ µ Ê ÈÏ Æ µ Æ µ µ Ë µ Í PASCHOS WOLFENSTEIN RATIO CAN BE MEASURED IN NEUTRINO DIS RESULT DEPENDS ON EW MIXING ANGLE, VALENCE ISOSPIN BREAKING (WITH ISOSINGLET TARGET), STRANGENESS VALENCE MOMENTUM ASYMMETRY STRANGENESS VALENCE MOMENTUM ASSUMED BY NUTEV TO µ VANISH THREE DISCREPANCY WITH GLOBAL FIT ½ ¾ Ò ¾ Ï Æ µ É ½ Ò¾ Ï

29 WHY UNCERTAINTIES ARE IMPORTANT: THE NUTEV ANOMALY... Æ µ Ê ÈÏ Æ µ Æ µ µ Ë µ Í PASCHOS WOLFENSTEIN RATIO CAN BE MEASURED IN NEUTRINO DIS RESULT DEPENDS ON EW MIXING ANGLE, VALENCE ISOSPIN BREAKING (WITH ISOSINGLET TARGET), STRANGENESS VALENCE MOMENTUM ASYMMETRY STRANGENESS VALENCE MOMENTUM ASSUMED BY NUTEV TO µ VANISH THREE DISCREPANCY WITH GLOBAL FIT...IS GONE Determinations of the weak miing angle sin θ W ONCE UNCERTAINTY ON STRANGENESS ASYM METRY KEPT INTO ACCOUNT (DIS ONLY FIT: NNPDF.) THE EFFECT LOSES STATISTICAL SIGNIFICANCE IF HADRONIC DATA INCLUDED (NNPDF. GLOBAL FIT), STRANGENESS ASYMMETRY DE TERMINED QUITE ACCURATELY CORRECTED RESULT IN IMPRESSIVE AGREEMENT WITH SM GLOBAL FIT NuTeV NuTeV NuTeV EW fit + NNPDF. [S - ] + NNPDF. [S - ] ½ ¾ Ò ¾ Ï Æ µ É ½ Ò¾ Ï ÆÆÈ ¾º¼ ¾¼½¼µ sin θw