HERA RESULTS AND DGLAP EVOLUTION: THEORY AND PHENOMENOLOGY STEFANO FORTE UNIVERSITÀ DI MILANO & INFN GLASMA WORKSHOP BNL, MAY 9, 2010

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1 HERA RESULTS AND DGLAP EVOLUTION: THEORY AND PHENOMENOLOGY STEFANO FORTE UNIVERSITÀ DI MILANO & INFN GLASMA WORKSHOP BNL, MAY 9,

2 SUMMARY SMALL Ü RESUMMATION: WHERE DO WE STAND? ß Ö ÙÑÑ Ø ÓÒ Ó Ä È ÚÓÐÙØ ÓÒ ß Ó Æ ÒØ ÙÒØ ÓÒ ß Ô Ý Ð Ó ÖÚ Ð ØÖÙØÙÖ ÙÒØ ÓÒ FIXED ORDER DGLAP FROM HERA TO LHC ß ÙÖÖ ÒØ Ô ÖØÓÒ Ø ß À Ê Ø Ú º ÖÓÒ Ø BEYOND FIXED ORDER: EVIDENCE? ß ÓÑ ØÖ Ð Ò Ò Ä È ß Ú Ø ÓÒ ÖÓÑ Ä È Ò À Ê Ø

3 SMALL Ü RESUMMATION

4 SMALL Ü PHYSICS FROM THE PERTURBATIVE END THE NNLO CORRECTIONS THEORY THE COEFFICIENT Ä FUNCTION Î ÖÑ Ö Ò ÎÓ Ø ¾¼¼ µ ÅÓ PHENOMENOLOGY THE BEST FIT GLUON ¾¼¼ µ Gluon LO, NLO and NNLO Ñ ØÛ 5 Q = GeV Q =5 GeV NLO fit 5 NNLO fit LO fit g(,q Q = GeV 5 Q = GeV 4 g(,q 3 PERTURBATIOMN THEORY UNSTABLE LEADING LOG APPROX POOR

5 ¾µ Ü ½µ «ÐÒ µ Ü µ ÐÒ ¾ Ü ¾µ ÐÒ Ü ½µ ÐÒ WHY WE SHOULD WORRY ABOUT SMALL X: PERTURBATIVE INSTABILITY: THE SINGLET SPLITTING FUNCTION ÜÈ «Üµ Ü ¼ ½µ ½ ««¾ ½µ ¾ « NNNLO Ø Ñ Ø µ.35.3 ÜÈ «Üµ (Æ ¼, «¼ ¾.5. LO, NLO.5..5 NNLO e+5 e+6 ½ Ü

6 WHY WE SHOULD WORRY ABOUT SMALL X: THE IMPACT AT LHC CORRELATION BETWEEN PDFS AND THE Ï TOTAL CROSS SECTION.5 TEVATRON CTEQ6.6: correlation betweens tot and fh,q=85. GeVL pp - fi WX,!! s=.96 TeV dūg u d s c b Ì É ¾¼¼ µ.5 LHC Correlation betweens W HLHCLand fh,q=85. GeVL Correlation Correlation dūg u d s c b UNCERTAINTIES ON SMALL Ü PDFS PROPAGATE TO INCLUSIVE OBSERVABLES

7 DIS RESUMMED PHENOMENOLOGY ÊÓ Ó ¾¼½¼ Ò ÔÖÓ Ö µ SMALL Ü RESUMMATION: WHERE DO WE STAND? SUBLEADING LEVEL ÃÄ ¹ Ò¹Ä Ô ØÓÚ µ SMALL Ü TERMS IN DGLAP RESUMMED TO ALL ORDERS AT THE LEADING AND NONTRIVIAL LEVEL FOR HQ PHOTO & Ø Ò ÐÓÒ ELECTROPRODUCTION ½; DIS Ø Ò À ÙØÑ ÒÒ µ; HQ HADROPRODUCTION ÐРú ÐÐ À ÙØÑ ÒÒ ¼½µ; Å ÖÞ Ò ÐÐ Ð Ù º º Î Ò GG HIGGS ¼ µ; Å ÖÞ Ò DRELL YAN SMALL Ü CORRECTIONS TO HARD CROSS SECTIONS KNOWN AT THE LEADING ÐÐ ¼ µ; ISOLATED PHOTON Ò ½¼µ TWO ALTERNATIVE APPROACHES TO DGLAP RESUMMATION: SMALL Ü RESUMMATION OF DGLAP ÐØ Ö ÐÐ ÐÐ º º µ ß INCLUSION INTO BFKL OF FIXED ORDER DGLAP ß & SUBSEQUENT NUMERICAL DECONVOLUTION OF RESUMMED DGLAP SPLITTING ÐÓÒ ÓÐ Ö Ë Ð Ñ Ëµ FUNCTION STABLE PERTURBATIVE EXPANSION OF THE RESUMMED DGLAP SPLITTING FUNCTION UP TO NLO WITH Ò ¼ Ë ËØ ØÓ ¼¾ ¼ µ: ß DGLAP BFKL MATCHING THROUGH SUITABLE DOUBLE BFKL+GLAP EXPANSION ÐÐ º º ¾¼¼¼µ ß COLLINEAR/ANTICOLLINEAR GLUON EMISSION SYMMETRY Ë Ð Ñ µ RUNNING COUPLING Ë ¼½µ ß EXTENSION TO HARD COEFFICIENT FUNCTIONS OF SMALL Ü RUNNING COUPLING ÐÐ ¼ µ RESUMMATION COEFFICIENT FUNCTIONS AND DGLAP EVOLUTION ¼ µ EXTENSION TO Ò ¼ AND SCHEME INDEPENDENT MATCHING OF DIS

8 RESUMMATION: GENERAL FEATURES THE SPLITTING FUNCTION (Ò ¼ FIXED COUPLING RUNNING COUPLING RESUMMED EXPANSION CONVERGES RAPIDLY ESPECIALLY WITH RUNNING COUPLING BEHAVIOUR FOR Ü ½¼ ¾ VERY STABLE CAREFUL MATCHING OF SMALL Ü RUNNING COUPLING TERMS REQUIRED Û Ø ËË Ü ¼ ¾ ÓÑÔ Ö DOMINANT QUALITATIVE BEHAVIOUR: DIP (SUPPRESSION OF SPLITTING FUNCTION AT Ü MEDIUM SMALL

9 RESUMMATION: GENERAL FEATURES SMALL Ü BEHAVIOUR SINGULARITY IN ANOM. DIM. AT Æ «µ ASYMPT. SMALL Ü POWER Ü «SMALL Ü POWER VS. «SLOPE OF THE SPLITTING FUNCTION.. GLAP NLO P rc,res NLO P Bateman (P log(/ ¼ µ º ÖÙ Ù Ð ¼ µ EXPANSION SUBLEADING TERMS (SYM. + R.C. MANDATORY FOR STABLE PERTURBATIVE AT Ü (Ü LARGE ¼ ¾ SPLITTING FUNCTION COINCIDES WITH NLO GLAP SMALL INTERCEPT & CURVATURE DETERMINE RESUMMED BEHAVIOUR Ü

10 THE SPLITTING FUNCTION MATRIX LO (DASH, NLO, NNLO, RESUMMED (É ¼ ÅË RESUMMED (ÅË Ò, «¼ ¾ ¼ µ

11 THE COEFFICIENT FUNCTION MATRIX NLO, NNLO, RESUMMED (É ¼ ÅË RESUMMED (ÅË Ò, «¼ ¾ ¼ µ

12 HOW DO THE INITIAL PDFS CHANGE? KEEP ¾ & Ä FIXED AT É ¼ GEV COMPUTE à ܵ Õ Ò Û Ü É ¾ ¼ µ ÕÆÄÇ Ü É ¾ ¼ µ Ò Û Ü É ¾ ¼ µ ÆÄÇ Ü É ¾ ¼ µ NNLO, É RESUMMED ¼ ÅË, ÅË RESUMMED GLUON QUARK ¼ µ EFFECT OF RESUMMATION COMPARABLE TO NNLO RESUMMED SUPPRESSION DUE TO LARGER COEFFICIENT FUNCTIONS SCHEME DEPENDECE REASONABLE (LARGELY CANCELS BETWEEN HARD COEFFN. & SPLITTING FUNCTION

13 HOW DO PDFS CHANGE WITH SCALE? KEEP ¾ & Ä FIXED AT É ¼ GEV COMPUTE à ɵ Õ Ò Û Ü É ¾ µ Õ ÆÄÇ Ü É ¾ µ Ò Û Ü É ¾ µ ÆÄÇ Ü É ¾ µ NNLO, É RESUMMED ¼ ÅË, RESUMMED Ü ½¼ ÅË; ½¼ ½¼ GLUON QUARK ¾ ¼ µ EVOLUTION WASHES OUT THE DIFFERENCES

14 É ¾ µ ÆÄÇ ¾ Ü É ¾ µ Ò Û Ä Ü É¾ µ ÆÄÇ Ä Ü É ¾ µ Ü NNLO, É RESUMMED ¼ ÅË, RESUMMED Ü ½¼ ÅË; ½¼ ½¼ ¾ THE EFFECT ON PHYSICAL OBSERVABLES KEEP ¾ & Ä FIXED AT É ¼ ¾ GEV à ɵ COMPUTE ¾ Ò Û Ä ¾ EFFECT OF RESUMMATION COMPARABLE TO NNLO ¼ µ RESUMMED SUPPRESSION DUE TO DIP IN EVOLUTION & PDF LOW SCALE SCHEME DEPENDENCE SMALLER THAN FOR PDFS EVOLUTION WASHES OUT THE DIFFERENCES

15 FIXED ORDER DGLAP PHENOMENOLOGY

16 Å ¾ µ È Ê ½ Ü Ñ Ò Ü ½ Ü ¾ ½ Ü ½ µ ¾ Ü ¾ µ Õ Õ Ü ½ Ü ¾ Å ¾ CURRENT PDF SETS 9 LHC parton kinematics ÄÀ Ò Ñ Ø Ø ÓÖ ÐÓ Ð Ø ÆÆÈ ¾º¼µ NNPDF. dataset 8, = (M/4 TeV ep(±y Q = M M = TeV ] [ GeV / p / M Q 6 5 T NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H DYE65 DYE886 CDFWASY CDFZRAP DZRAP CDFRKT DRCON M = GeV M = GeV M = TeV y = HERA fied target THREE NLO GLOBAL PDF SETS AVAILABLE (CTEQ6.6, MSTW8, NNPDF. Q (GeV 6 DIS AND HADRONIC (JETS, DRELL YAN, Ï AND PRODUCTION DATA COMBINED COLLIDER (ZEUS, H, D, CDF AND FIXED TARGET (NMC, BCDMS, CHORUS, NUTEV, TEVATRON EXXX

17 DETERMINING PDF AND THERI UNCERTAINTIES THE MONTE CARLO APPROACH (NNPDF 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 FIT STOPS WHEN QUALITY OF FIT TO RAN DOMLY SELECTED VALIDATION DATA (NOT FIT TED STOPS IMPROVING Eperimental Data MC generation NN parametrization Fi i=,...,ndata NMC,BCDMS,SLAC,HERA,CHORUS... Fi( Fi( qnet( qnet( TRAINING Fi(N- EVOLUTION Fi(N qnet(n- qnet(n REPRESENTATION OF PROBABILITY DENSITY

18 DETERMINING PDF AND THERI UNCERTAINTIES THE MONTE CARLO APPROACH (NNPDF 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 FIT STOPS WHEN QUALITY OF FIT TO RAN DOMLY SELECTED VALIDATION DATA (NOT FIT TED STOPS IMPROVING CAN DETERMINE BOTH 68C.L.& g (, Q NNPDF. - 68% CL NNPDF. - -σ Individual Replicas -

19 PARAMETRIZATION UNCERTAINTIES CROSS VALIDATION 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 OPTIMAL FITTING FIT TO DATA

20 THE BEST FIT IS NOT AT THE MINIMUM OF THE ¾ PARAMETRIZATION UNCERTAINTIES CROSS VALIDATION 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 OVERFITTING FIT TO DATA

21 STANDARD CANDLES: WHERE DO WE STAND? LHC 7 TEV HIGGS (Å ½¾¼ GEV TOP σ( H, m H = GeV [pb].5.5 PDF4LHC benchmarks - LHC 7 TeV CTEQ6.6 NNPDF. MSTW8 a s =.8 a s =.9 a s =.9 a s =.9 a s =. σ(tt [pb] PDF4LHC benchmarks - LHC 7 TeV CTEQ6.6 NNPDF. MSTW8 a s =.8 a s =.9 a s =.9 a s =.9 a s = PDF4LHC benchmarks - LHC 7 TeV Ï CTEQ6.6 NNPDF. MSTW8 a s =.8 a s =.9 a s =.9 a s =.9 a s = PDF4LHC benchmarks - LHC 7 TeV Ï CTEQ6.6 NNPDF. MSTW8 a s =.8 a s =.9 a s =.9 a s =.9 a s =...98 PDF4LHC benchmarks - LHC 7 TeV CTEQ6.6 NNPDF. MSTW8 a s =.8 a s =.9 a s =.9 a s =.9 a s =. σ(w + B W [nb] σ(w - B W [nb] σ(z B Z [nb] GLOBAL FITS (MSTW, NNPDF, CTEQ IN GOOD MUTUAL AGREEMENT (CENTRAL VALUE & UNCERTAINTY CHOICE OF «VALUE IMPORTANT

22 Distribution of χ COMPATIBILITY: A FIRST LOOK DIS DATA VS. HADRONIC DATA NNPDF. for sets NMC-pd NMC SLACp SLACd NO OBVIOUS MUTUAL TENSION BETWEEN DIS AND HADRONIC DATA CDFRKT DRCON BCDMSp BCDMSd HERA-NCep HERA-NCem HERA-CCep HERA-CCem CHORUSnu CHORUSnb FLH8 NTVnuDMN NTVnbDMN Z6NC Z6CC DYE65 DYE886p DYE886r CDFWASY CDFZRAP DZRAP SOME INTERNAL DATA INCONSISTENCIES (NMC DIS DATA, CDF Ï AND RAPIDITY DISTRIBUTIONS REASONABLE DISTRIBUTION OF ¾ VALUES

23 ¾ Õ ½µ Õ ¾µ Õ ½µ ½µ Õ ¾µ ¾µ ¾ µ ¾ µ Õ µ Ö Ô Æ IF TWO MC SETS EXTRACTED FROM SAME UNDERLYING DISTRIBUTION, THEN ½ Æ Ö Ô COMPATIBILITY: DETAILED TESTS GLOBAL FITS INCLUDE DATASETS IN DISPARATE KINEMATIC REGIONS MUTUAL CONSISTENCY µ TEST OF DGLAP EVOLUTION INCONSISTENT DATA µ NO IMPROVEMENT IN PDF ACCURACY CAN TEST BY COMPARING FITS TO DIFFERENT DATA SUBSETS A USEFUL TOOL: DISTANCE BETWEEN PDF SETS ¾ ½µ Õ ½µ ¾ ¾µ Õ ¾µ ¾ µ Õ µ ½ MEAN PDF EXTRACTED FROM MONTECARLO SET OF SIZE Æ Ö Ô FLUCTUATES WITH STANDARD DEVIATION

24 ¾ ØÓØ ¼º ½º¼¼ ¼º ¼Ê¾ ÇÆ º¾½ º ¾ ¼º ¼ º½ º½¾ ¾º¼¾ Ê È ¼º ¼º ¼º ¼ Ê È COMPATIBILITY: OLD HERA DATA VS. COMBINED HERA DATA Á˹À Ê ÓÐ ÁË ÆÆÈ ¾º¼ NNPDF. dataset ½º½¾ ½º¾¼ ½º¾½ ¼º ¼º ¼º ÆÅ ¹Ô ½º ½º ½º ÆÅ ½º ½º ½º ËÄ ½º¾ ½º¾ ½º¾ ÅË.96.3 ½º½ À Ê Á ½º½¾ ½º½ ½º½ ÀÇÊÍË ½º ½º ½ ½º ÄÀ½¼ ¼º ½ ¼º ½ ¼º ÆÌÎ ÅÆ ½º ½º ¼ ½º ½ Í˹À¾ ¼º ¼º ½ ¼º ¼ ʾÃÌ ] [ GeV / p / M 6 5 T 4 3 NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H DYE65 DYE886 CDFWASY CDFZRAP DZRAP CDFRKT DRCON Q ¾º ¾º¾ ½º¾ ¾¼º ¾ ½ º¼ ½º Ï Ë Distance between central values 7 Distance between central values PDFS UNCHANGED, MARGINAL IM PROVEMENT IN GLUON QUALITY OF FIT TO FIXED TARGET DIS UNCHANGED SLIGHT DETERIORATION IN QUALITY OF FIT TO HERA DATA d[ q(,q ] Σ g T 3V S s+ s- NNPDF.-DIS vs..-dis-heraold Σ g T 3V Distance between PDF uncertainties NNPDF.-DIS vs..-dis-heraold d[ q(,q ] Σ g T 3V S s+ s- NNPDF.-DIS vs..-dis-heraold e Σ g T 3V Distance between PDF uncertainties NNPDF.-DIS vs..-dis-heraold S s+ S s+ (MARGINALLY INADEQUATE THEORY µ COULD BE EVIDENCE FOR d[ σ q (,Q ] 3 s- d[ σ q (,Q ] 3 s e-5....

25 ¾ ØÓØ ½º ¼ ½º ½º ½ Í˹À¾.9.79 ¼º ¼ ʾÃÌ ¾º¾ ¾º ½º¾ ½ º¼ ½ º½ ½º Ï Ë º½¾ º ½ ¾º¼¾ Ê È ¼º ¼º ¼º ¼ Ê È COMPATIBILITY: DIS DATA VS. JET DATA ÁË ÁË Â Ì ÆÆÈ ¾º¼ NNPDF. dataset ½º¾¼ ½º½ ½º¾½ 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 ] [ GeV / p / M 6 5 T 4 3 NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H DYE65 DYE886 CDFWASY CDFZRAP DZRAP CDFRKT DRCON Q..93 ¼º ¼Ê¾ ÇÆ º ¾ ½¼º ¼º ¼ EVEN WHEN NOT µ FITTED Ü LARGE GLUON WELL DETERMINED BY SCALING VIOLATIONS! HIGH Ì JET DATA WELL REPRODUCED GLUON ACCURACY SIGNIFICANT IMPROVEMENT IN LARGE Ü g (, Q NNPDF. - DIS NNPDF. - DIS + JET OTHER PDFS UNCHANGED

26 ¾ ØÓØ ½º ¼ ½º ½º ½ Í˹À¾ ¼º ½ ¼º ¼º ¼ ʾÃÌ COMPATIBILITY: DIS+JETS VS. DRELL YAN (AND Ï DATA ÁË ÁË Â Ì ÆÆÈ ¾º¼ NNPDF. dataset ½º¾¼ ½º½ ½º¾½ 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 ] [ GeV / p / M 6 5 T 4 3 NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH8 NTVDMN ZEUS-H DYE65 DYE886 CDFWASY CDFZRAP DZRAP CDFRKT DRCON Q VERY SUBSTANTIAL IMPROVEMENT IN NNPDF. DIS+JET NNPDF.. NNPDF. DIS+JET NNPDF. FIT QUALITY WHEN DATA µ INCLUDED SOME PDF COMBINATIONS POORLY DE TERMINED WITHOUT THESE DATA HUGE IMPROVEMENT IN SEA ASYM (, Q T V (, Q Ù & STRANGENESS SIGNIFICANT IMPROVEMENT IN TOTAL.7.6 NNPDF. DIS+JET NNPDF..3 NNPDF. DIS+JET NNPDF. VALENCE ( È Õ Õ µ & ISOTRIPLET (Ù Ù µ (, Q S (, Q s

27 COMPATIBILITY: DIS VS. HADRONIC DATA AGAIN A SENSITIVE TEST: IS THE IMPACT OF A DATASET INDEP. OF THE DATA IT IS ADDED TO?...TO DIS DATA ADDING JET DATA......TO DIS+DY DATA NNPDF. DIS NNPDF. DIS+JET. NNPDF. DIS NNPDF. DIS+JET NNPDF. NNPDF. DIS+DY. NNPDF. NNPDF. DIS+DY g (, Q.3.. V (, Q.6.4 g (, Q.3.. V (, Q TO DIS DATA ADDING DRELL YAN DATA......TO DIS+JET DATA NNPDF. DIS. NNPDF. DIS.5.45 NNPDF. DIS+JET. NNPDF. DIS+JET.4.35 NNPDF. DIS+DY NNPDF. DIS+DY.4.35 NNPDF. NNPDF (, Q T 3.5. V (, Q.6 (, Q T 3.5. V (, Q NNPDF. DIS NNPDF. DIS+DY.4.3 NNPDF. DIS NNPDF. DIS+DY NNPDF. DIS+JET NNPDF..4.3 NNPDF. DIS+JET NNPDF (, Q S. (, Q s -. (, Q S.4.3 (, Q s

28 COMPATIBILITY: DIS VS. HADRONIC DATA AGAIN A SENSITIVE TEST: IS THE IMPACT OF A DATASET INDEP. OF THE DATA IT IS ADDED TO?...TO DIS DATA ADDING JET DATA......TO DIS+DY DATA NNPDF. DIS NNPDF. DIS+JET. NNPDF. DIS NNPDF. DIS+JET NNPDF. NNPDF. DIS+DY. NNPDF. NNPDF. DIS+DY g (, Q.3.. V (, Q.6.4 g (, Q.3.. V (, Q TO DIS DATA ADDING DRELL YAN DATA......TO DIS+JET DATA NNPDF. DIS. NNPDF. DIS.5.45 NNPDF. DIS+JET. NNPDF. DIS+JET.4.35 NNPDF. DIS+DY NNPDF. DIS+DY.4.35 NNPDF. NNPDF (, Q T 3.5. V (, Q.6 (, Q T 3.5. V (, Q NNPDF. DIS NNPDF. DIS+DY.4.3 NNPDF. DIS NNPDF. DIS+DY NNPDF. DIS+JET NNPDF..4.3 NNPDF. DIS+JET NNPDF (, Q S. (, Q s -. (, Q S.4.3 (, Q s YES: PERFECT COMPATIBILITY!

29 BEYOND FIXED ORDER DGLAP?

30 * É ¾ ¼ WHAT ABOUT GEOMETRIC SCALING? W.R. TO Ü Ü É¾ µ ¼ STRUCTURE FUNCTION DATA SCALE p σ γ tot HERA data, <. ËØ ØÓ ÓÐ ¹ ÖÒ Ø ÃÛ Ò ¾¼¼½µ EVIDENCE FOR NONLINEAR EVOLUTION? (RECOMBINATION, SATURATION,... DOES DGLAP FAIL?? FOR É ¾ ½¼ GEV ¾ τ

31 * É ¾ ¼ DOES DGLAP FAIL?? FOR É ¾ ½¼ GEV ¾ WHAT ABOUT GEOMETRIC SCALING? W.R. TO Ü Ü É¾ µ ¼ STRUCTURE FUNCTION DATA SCALE ËØ ØÓ ÓÐ ¹ ÖÒ Ø ÃÛ Ò ¾¼¼½µ EVIDENCE FOR NONLINEAR EVOLUTION? (RECOMBINATION, SATURATION,... p σ γ tot HERA data, <. DAS prediction BUT DOUBLE LOG SOLUTION TO LO (LINEAR DGLAP ( DAS ALSO SCALES! CAN ALSO BE SHOWN ANALYTICALLY τ ÓÐ º º ¾¼¼ µ

32 * É ¾ ¼ DOES DGLAP FAIL?? FOR É ¾ ½¼ GEV ¾ WHAT ABOUT GEOMETRIC SCALING? W.R. TO Ü Ü É¾ µ ¼ STRUCTURE FUNCTION DATA SCALE ËØ ØÓ ÓÐ ¹ ÖÒ Ø ÃÛ Ò ¾¼¼½µ EVIDENCE FOR NONLINEAR EVOLUTION? (RECOMBINATION, SATURATION,... p σ γ tot HERA data, <. DAS prediction BUT DOUBLE LOG SOLUTION TO LO (LINEAR DGLAP ( DAS ALSO SCALES! CAN ALSO BE SHOWN ANALYTICALLY QF(λ HERA data DAS prediction 4 τ ÓÐ º º ¾¼¼ µ CAN DETERMINE OPTIMAL SCALING FROM QUALITY FACTOR ANALYSIS Ð Ø Ðº ¾¼¼ µ µ OBSERVED AGREES WITH DAS : DGLAP PREDICTS GEOMETRIC SCALING A FINER TEST NEEDED TO REVAL DEVIATIONS FROM DGLAP! λ

33 BEYOND DGLAP: TESTING FOR DEVIATIONS IDEA: Ð ¾¼¼ µ ÓÐ º º ÊÓ Ó ¾¼½¼µ CUT OUT DATA IN THE DANGEROUS (SMALL REGION DETERMINE PDFS IN THE SAFE Ü (LARGE É AND REGION ¾ EVOLVE BACKWARDS AND COMPARE TO DATA

34 BEYOND DGLAP: TESTING FOR DEVIATIONS IDEA: Ð ¾¼¼ µ ÓÐ º º ÊÓ Ó ¾¼½¼µ BACKWARD EV. VS DATA CUT OUT DATA IN THE DANGEROUS (SMALL REGION DETERMINE PDFS IN THE SAFE Ü (LARGE É AND REGION ¾ EVOLVE BACKWARDS AND COMPARE TO DATA OLD HERA DATA DAT/TH DIST: NO CUT DAT/TH DIST: CUT =3.5 GeV F (,Q Fit without cuts Fit with A cut =.5 Fit with A cut =.5 Data BACKWARD EVOLVED FIT LIES SYSTEMATICALLY BELOW DATA DATA AT LOW Ü AND É ¾ SHOW LESS EVOLUTION THAN PREDICTED BY NLO DGLAP IF Ü LOW É AND DATA INCLUDED, THE FIT MANAGES TO COMPENSATE BY READJUSTING THE ¾ PDFS

35 BACKWARD EV. VS DATA NEW (COMBINED HERA DATA DAT/TH DIST: NO CUT DAT/TH DIST: CUT =3.5 GeV F (,Q Fit with A cut Data Fit without cuts =.5 =.5 Fit with A cut DATA AT LOW Ü AND É ¾ SHOW LESS EVOLUTION THAN PREDICTED BY NLO DGLAP BACKWARD EVOLVED FIT LIES SYSTEMATICALLY BELOW DATA WITH MORE PRECISE DATA, THE FIT NO LONGER MANAGES TO COMPENSATE BY READJUSTING THE PDFS: EVEN FULL FIT LIES BELOW DATA DETERIORATION IN FIT QUALITY: ¾ VS SLICES QUALITY OF UNCUT FIT DETERIO RATES IN LOW REGIONS POOR AS DECREASES QUALITY OF CUT FIT INCREASINGLY

36 DEVIATIONS FROM DGLAP: SHOULD WE WORRY? (THEORY OBSERVED DEVIATION FROM DGLAP CANNOT BE DUE TO MISSING NNLO TERMS: DATA EVOLVE LESS THAN NLO WHILE NNLO EVOLVES MORE THAN NLO RES. É ¼, RES. ÅË, NNLO PERTURBATIVE RESUMMATION HAS THE RIGHT SIGN AND ROUGH SIZE SATURATION OR MORE GENERALLY HIGHER TWIST (POWER SUPPRESSED EFFECTS MIGHT ALSO REDUCE EVOLUTION NOTE: SOUGHT FOR EVIDENCE IS SUP PRESSED (É SCALE DEPENDENCE, RE GARDLESS OF THE ¾ GROWTH Ü ¼ µ

37 DEVIATIONS FROM DGLAP: SHOULD WE WORRY? (PHENOMENOLOGY LHC STANDARD CANDLES (4 TEV Ï DEPENDENCE ON CUT TOP REMOVING DATA FROM DANGEROUS REGION LEADS TO INCREASED PDF UNCERTAINTIES IMPACT ON LHC STANDARD CANDLES MODERATE COULD HAVE SOME EFFECT ON LESS INCLUSIVE OBSERVABLES ÓÐ º º ÊÓ Ó ½¼µ HIGGS ( GEV RAP. DISTN Fit without cuts Fit with A cut =.5 d σ Z dmdy y DETERMINATION OF ««FROM SCALING VIOLATION MAY BE BIASED DOWNWARDS (WEAKER EVOLUTION ARTIFICIALLY SMALLER «BIAS STRONGER AT NNLO MSTW ( SEE A CHANGE OF SIGMA FROM NLO TO NNLO ¼ ½¾¼¾ ¼ ¼¼½¾ «¼ ¼¼½ TO «¼ ½½ ½ ¼ ¼¼½

38 YESTERDAY ¾ JUST BEFORE THE HERA START (99 WHAT S BEHIND THE CORNER? =5 GeV (, Q p F.8 TODAY ¾ AND PDF UNCERTAINTIES NNPDF. NNPDF. NNPDF. DATA Q / GeV TOMORROW THE LHC AND LHEC KINEMATICS LHC Eperiments (4TeV: Atlas and CMS Atlas and CMS rapidity plateau LHeC TEVATRON Eperiments: D Central+Fwd. Jets CDF/D Central Jets HERA Eperiments: H and ZEUS Fied Target Eperiments: NMC BCDMS E665 SLAC NLO DGLAP WORKS EXCEEDINGLY WELL IN THE HERA REGION PHENOMENOLOGY AT ± ACCURACY AT THE LHC IS POSSIBLE ONE PERCENT ACCURACY IS BEHIND THE CORNER, MAY BE NECESSARY FOR DISCOVERY AND REQUIRES GOING BEYOND NLO NLO REQUIRES RESUMMATION TO STABILIZE IT AT LOW Ü ß TO MAKE IT ACCURATE AT LOW É ¾ ß INSIGHT INTO PERTURBATIVE QCD BEYOND FIXED ORDER BEHIND THE CORNER, BUT MAY REQUIRE LHEC+LHC

39 EXTRAS

40 Ù Ð Ó ÄÇ Ä Ø ÄÇ Ä ¼ ØÓ Ø ÖÑ Ó ÓÖ Ö ÆÄÇ Ä Ò ÓÒÚ Ö ÐÝ ÙÔ ¼ THE DOUBLE LEADING EXPANSION «¼ Ƶ «Æ µ «Æ «Ò Æ «¼ ŵ «Å µ «µ Å «Ò Å «½ Ƶ «Æ «¾ Æ ¾ ½ Æ ««½ ŵ «Å «¾ Å ¾ ½ Å «DUALITY HOLDS ORDER BY ORDER IN THE DOUBLE LEADING EXPANSION:

41 DOUBLE LEADING EVOLUTION ² Ð Ò Ò ÜØßØÓßÐ Ò Ä ÖÒ Ð Å ¼ ««Å «Å «¾ ž «Å µ Å ¼µ ½ MOMENTUM CONSERVATION ½µ ¼

42 µ Å ¼µ ½ ² Ð Ò Ò ÜØßØÓßÐ Ò MOMENTUM CONSERVATION ½µ ¼ DOUBLE LEADING EVOLUTION Å ¼ ««Å «Å «¾ Å ¾ «Å Ä ÖÒ Ð THE DL KERNEL HAS A WELL BEHAVED PERTURBATIVE EXPANSION DL IS CLOSE TO LLÉ THE RESULT FOR Æ ¾ ¼ Å ¼ ¾, LL½ Ü CLOSE Å ½ ¾ TO FOR

43 DOUBLE LEADING EVOLUTION ² Ð Ò Ò ÜØßØÓßÐ Ò Ä ÖÒ Ð Å ¼ ««Å «Å «¾ ž «Å µ Å ¼µ ½ PERTURBATIVE EXPANSION STABILIZED IN Å ¼ REGION MOMENTUM CONSERVATION ½µ ¼

44 Å µ Ä ÖÒ Ð Ð Ò ² Ò ÜØßØÓßÐ Ò DOUBLE LEADING EVOLUTION MOMENTUM CONSERVATION! ½µ ¼ µ Æ ¼µ ½ ««Å «Å ¾ «¾ «Å Å Å ¼

45 Å µ Å «µ Å µ DIS KINEMATIC VARIABLES ɾ Ü ¾ É ¾ É ¾ ¾ THE SECOND INGREDIENT: EXCHANGE SYMMETRY DIAGRAMS FOR ÐÒ ½ Ü EVOLUTION KERNEL Å µ ½½ Ê ¾ É ¾ É ¾ É ¾ Å É ¾ ¾ µ SYMMETRIC UPON INTERCHANGE OF INITIAL AND FINAL PARTON VIRTUALITIES COLLINEAR RES. OF POLES ANTICOLLINEAR RES. OF POLES ½ ½ Å ½ Å É ¾ ¾ Å ½ Å SYMMETRY BREAKING Ñ ÐРܵ RUNNING OF THE COUPLING «É ¾ µ BOTH CAN BE DETERMINED EXACTLY

46 SYMMETRIZED EXPANSION THE KERNEL MOMENTUM CONSERVATION + SYMMETRYµ ALWAYS HAS A MINIMUM SYMMETRIC VARIABLES LO, NLO SYMMETRIC RE SUMMED CLOSE TO EACH OTHER IS AN ENTIRE FCTN (QUADRATIC APPROX. IS EXCELLENT! RESUMMED NLO HIGHER THAN LO

47 SYMMETRIZED EXPANSION THE KERNEL MOMENTUM CONSERVATION + SYMMETRYµ ALWAYS HAS A MINIMUM ASYMMETRIC VARIABLES LO, NLO SYM. CLOSE TO EACH OTHER AP LO, NLO SYM. CLOSE TO CURVATURE & INTERCEPT SAME IN SYM. & ASYM. VARIABLES RESULT DETERMINED BY MOM. CONS. + SYM. AMBIGUITIES MINIMAL, (CFR. ABF VS. CCSS BUT MATCHING TO GLAP CRUCIAL

48 Å Æ Å µ Æ Å µ À¼ Å µ ¼ «Æ Å µ Å THE THIRD INGREDIENT: RUNNING COUPLING THE RUNNING OF THE COUPLING «Øµ «½ ¼ «Ø ÐÒ É¾ (Ø IS LEADING É LOG, BUT NEXT TO LEADING LOG ½ ¾ Ü UPON M MELLIN ¾ Ü TRANSFORMATION (ÐÒ EVOLUTION ص BECOMES AN OPERATOR: ««Å µ «¾ ½ ¼ «¾ EVOLUTION EQUATION ÓÖ Æ Åµ Û Ø ºº À ¼ ŵ µ «½

49 Å Æ Å µ Æ Å µ À¼ Å µ ¼ «Ø Å µ ¼ Æ µ ÜÔ Æ Å µ Å THE THIRD INGREDIENT: RUNNING COUPLING THE RUNNING OF THE COUPLING «Øµ «½ ¼ «Ø ÐÒ É¾ (Ø IS LEADING É LOG, BUT NEXT TO LEADING LOG ½ ¾ Ü UPON M MELLIN ¾ Ü TRANSFORMATION (ÐÒ EVOLUTION ص BECOMES AN OPERATOR: ««Å µ «¾ ½ ¼ «¾ EVOLUTION EQUATION ÓÖ Æ Åµ Û Ø ºº À ¼ ŵ µ «½ GOOD NEWS: DUALITY STILL HOLDS AT NLO& BEYOND «Øµ Ê «««µ «µ WITH MATCHED ANOMALOUS DIMENSION AND B.C ص «Øµ Ƶ «Øµ Ƶ «Øµ ¼ «Øµ Ƶ «Øµ ¼ µ ¾ «Øµ Ƶ Ç «Øµ ¼ µ «¼ «Æµ ¼ Ƶ «½µ ¼ ¼ Ƶ «¼ µ ¾ ¾µ ¼ Ƶ Ç «¼ µ, ¼ FIXED COUPLING DUAL

50 THE THIRD INGREDIENT: RUNNING COUPLING «µ ¾ ½ Å Æ Å µ Å Ò ÆÄÇ ÓÙ Ð Ð Ò ÄÇ Ê Ø ÖÑ THE RUNNING OF THE COUPLING «Øµ «½ ¼ «Ø ÐÒ É¾ (Ø IS LEADING É LOG, BUT NEXT TO LEADING LOG ½ ¾ Ü UPON M MELLIN ¾ Ü TRANSFORMATION (ÐÒ EVOLUTION ص BECOMES AN OPERATOR: ««Å µ «¾ ½ ¼ «¾ EVOLUTION EQUATION ÓÖ Æ Å µ Û Ø ºº À ¼ Å µ µ «½ Å µ Æ Å µ À¼ Å µ ¼ «Æ BAD NEWS: PERTURBATIVE INSTABILITY NLO R.C. CORRECTION NOT UNIFORMLY SMALL AS Ü ¼: «µ È «µ È

51 Æ «½ Æ «½ ½ RUNNING COUPLING DUALITY THE OPERATOR APPROACH: DUAL KERNEL INVERSION ««Æ µµ Æ ««Å µµ Å ACTING ON Æ Å µ DUALITY STILL HOLDS TO ALL ORDERS!: CAN DETERMINE ( AS A FUNCTIONAL OF FIXED COUPLING DUAL ( : Ø ÄÇ Ù Ò ¼ Æ «½ Ù Æ «½ ¼ Å µ ¼ Ó Æ ¼ ¼¼ Æ «½ ¼ Æ «½ ¾ RESULTS UP TO NLO FOR, NNNLO FOR ÒÐÙ Ò ½ Ø ÖÑ µ PERTURBATIVE SERIES OF UNSTABLE R.C. CORRNS. CAN BE RESUMMED

52 QUADRATIC KERNEL «Å µ «µ ½ ¾ «µ Å Å µ ¾ Õ Æ Øµ» à ¾ «Æ µ ¼ «Øµ «Æ µ EXACT ASYMPTOTIC SOLUTION ASYMPTOTIC BEHAVIOUR CONTROLLED BY MINIMUM OF Å µ RIGHTMOST SING. OF Æ µ CAN SOLVE EXACTLY WITH «LINEARIZED «µ, µ IN TERMS OF BATEMAN à FUNCTION ܵ: THE EFFECTIVE RESUMMED KERNEL ½, DEPEND ON «Æ TRHOUGH, ASYMPTOTIC LEADING LOG SMALL Ü SE RIES RESUMMED BRANCH CUT IN REPLACED BY SIMPLE POLE

53 Ö ÆÄÇ «Øµ Ƶ ÆÄÇ «Øµ Ƶ «Øµ Ƶ «Øµ Ƶ «Øµ Ƶ ¼ «Øµ Ƶ Ñ Ø «Øµ Ƶ ÑÓÑ «Øµ Ƶ PUTTING EVERYTHING TOGETHER THE RESUMMED ANOMALOUS DIMENSION: Ö Ô ÖØ Ö Ô ÖØ ÆÄÇ «Øµ Æ µ CONTAINS ALL TERMS WHICH ARE UP TO NLO IN THE DOUBLE LEADING EXPANSION, SYMMETRIZED (SO ITS DUAL HAS A MINIMUM «Øµ Æ µ RESUMS THE SERIES OF SINGULAR RUNNING COUPLIG CORRECTIONS «Øµ Æ µ, «Øµ Æ µ ¼ «Øµ Æ µ ARE DOUBLE COUNTING SUBTRACTIONS BETWEEN THE PREVIOUS TWO ÑÓÑ SUBTRACTS SUBLEADING TERMS WHICH RUIN MOMENTUM CONSERVATION Ñ Ø SUBTRACTS ANY CONTRIBUTION WHICH DEVIATES FROM NLO GLAP AND AT Æ LARGE DOESN T DROP AT LEAST AS ½ Æ

54 THE SPLITTING FUNCTION MATRIX Ô Ò Ò Ò ¼ Ò NLO, NNLO, RESUMMED Ò GROWS Ò GROWS

55 THE SPLITTING FUNCTION MATRIX Ô Ò Ò «¼ ½ ¼ ½ ¼ ¾ ¼ ¾ ¼ «NLO, NNLO, RESUMMED «GROWS «GROWS

56 DOUBLE SCALING OF HERA DATA R F σ ALL HERA DATA WITH Ü ¼ ¼ AND ½¼ É ¾ ¾ GEV ¾ INCLUDED (Æ NEW COMBINED HERA DATA USED SLOPE: MEASURED ¾ ¼ ¼, PREDICTED ¾

57 * É ¾ ¼ DOES DGLAP FAIL?? FOR É ¾ ½¼ GEV ¾ RUNNING COUPLING GEOMETRIC SCALING W.R. TO ÐÒ ÐÒ É¾ STRUCTURE FUNCTION DATA SCALE Ô ÐÒ Ü Ü ¼ µ ËØ ØÓ ÓÐ ¹ ÖÒ Ø ÃÛ Ò ¾¼¼½µ EVIDENCE FOR NONLINEAR EVOLUTION? (RECOMBINATION, SATURATION,... p σ γ tot HERA data, <. DAS prediction BUT DOUBLE LOG SOLUTION TO LO (LINEAR DGLAP ( DAS ALSO SCALES! CAN ALSO BE SHOWN ANALYTICALLY QF(λ HERA data DAS prediction 4 τ ÓÐ º º ¾¼¼ µ CAN DETERMINE OPTIMAL SCALING FROM QUALITY FACTOR ANALYSIS Ð Ø Ðº ¾¼¼ µ µ OBSERVED AGREES WITH DAS : DGLAP PREDICTS GEOMETRIC SCALING A FINER TEST NEEDED TO REVAL DEVIATIONS FROM DGLAP! λ