Current Issues and Challenges in Global Analysis of Parton Distributions DIS06TsukubaTung

Outline Challenges for Global QCD Analysis in the era of HERA II, Tevatron Run II, and LHC New Experimental Input to Current Global Analysis of PDFs More Precise Theoretical Calculations needed to meet these challenges Recent Results and Work in Progress (CTEQ):  Implications of PDF uncertainties on Physical Applications;  A new implementation of the general PQCD formalism with quark mass effects. This is applied to a comprehensive global analysis, including the full HERA I total and semi- inclusive cross section data sets with correlated errors;  Close examination of new fixed-target experimental data (NuTev, E866) and large-x behavior of PDFs; Summary and Outlook

Challenges for Global QCD Analysis —from here to LHC Gluon Distribution; Small-x and Large-x behavior of all distributions; Strange distribution; Charm and bottom distributions; Quantifying uncertainties of all PDFs. In spite of steady progress in over 20 years of global analysis of PDFs, it is surprising how much knowledge is still missing on the parton structure of the nucleon ! A successful LHC program depends on making substantial improvement on most of these fronts.

Some recent “CTEQ” work (2005–) NLO PQCD is stable for Collider phenomenology (Huston, Pumplin, Stump, wkt. JHEP 0506:080,2005) ; LHC phenomenology: Uncertainties of the inclusive Higgs production cross section at the Tevatron and the LHC (Belyaev, Pumplin, Yuan, wkt. JHEP 0601:069,2006); (PDF uncertainties can be larger than commonly estimated “theoretical uncertainties”, depending on the Higgs mass.) CTEQ6A,B series of PDFs: for physical applications that are sensitive to  s. (Pumplin, Belyaev, Huston, Stump, wkt. JHEP 0602:032,2006 ) ;

Uncertainties of the inclusive Higgs production cross section at the Tevatron and the LHC (Belyaev, Pumplin, Yuan, wkt. JHEP 0601:069,2006) vs. T Enhanced bbA-coupling in MSSM

CTEQ6A,B PDFs for a series of  s (Pumplin, Belyaev, Huston, Stump, wkt: JHEP 0602:032,2006 ) * Curves:  s = – ; * Shaded areas: uncertainty band based on CTEQ6 error analysis for fixed a s = Many applications. One example: (Realistic range: between blue lines.)

New Experimental Input to Current Global Analysis Extensive HERA I data sets (complete?) on  total inclusive NC and CC cross sections, covering a wide range of kinematic phase space;  semi-inclusive (tagged heavy flavor) cross sections: charm and bottom;  semi-inclusive jet cross sections. (Note: out go the SFs, F 1,2,3 ; in come the xSec’s!) Fixed-target Experiments (Last of the kind?)  NuTeV DIS S.F.s and cross sections;  E866 DY pp and pd cross sections (finally?). New Tevatron Data on W/Z production, jet production, … etc.

Available HERA Data Sets for Current Global Analysis (by our reckoning) H1  CCe+9497X  CCe+9900X  CCe-9899X  (NCe+9497X ?)  NCe+9697X  NCe+9900X  NCe-9899X  NCe-9900X  NCe+9697F 2 c  NCe+9900Xc  NCe+9900Xb ZEUS  CCe+9497X  CCe+9900X  CCe-9899X  NCe+9697X  NCe+9900X  NCe-9899X  NCe+9697F 2 c  NCe+9890F 2 c Wow! (both in coverage and in accuracy.) Just wait until HERA II data come along!

“New” Precision Global Analysis ( S. Belyaev, H.L. Lai, J. Pumplin, D. Stump, wkt, C.P. Yuan) Data: Full HERA I total-inclusive and semi-inclusive heavy flavor cross sections with correlated errors + F.T. DIS + DY + Tevatron Jet; Theoretical tool: New implementation of General Mass Variable-Flavor-Number-Scheme factorization formalism of Collins for consistency + recent SAcot, Acot- , … practical prescriptions for efficiency. (cf. talk in the joint HQ/SF session, wkt). ——————————— Sorry! DIS jet inclusive not yet implemented. (  Jon Pumplin) NLO for now. Extension to order  s 2 is “straightforward”, given the perturbative approach. “New” Phenomenology work always trail frontier Theory and Experimental advances (examplified by the plenary talks), by yeas!

Results Excellent fit to 32 sets of data—CTEQ6C0: Details in the  2 analysis are dependent on: (i) using the xSec data (vs. SFs); and (ii) using CorSysErr’s. (representative plots.) Comparison of CTEQ6.1M and CTEQ6C0 PDFs; (representative plots) Where do mass effects matter? (H1NCe+9697X, ZeusNCe+9697X) —low Q 2 data.

NC e X H1 ZEUS

H1 Zeus NC e X

Pull Plots: NC e X H1 Zeus Close to normal distribution. N.B. This is after correlated SysErr’s have been taken into account! The shifts for individual SysErr’s are generally ~ 1.

Lines: theory (fits); Red points: raw data points; Blue points: data points shifted by optimal correlated SysErr. (usually within 1  ) H1 CC e X Comparison to CC data

CC e X ZEUS

Where does the General Mass Formalism make a difference? Compare with CTEQ6.1M (ZM) ZM Low Q 2 bins, of course. GM H ZEUS data show the same effects

Charm Production S.F. and xSec. Zeus NC e F 2 C Only show comparison with 1 (out of 4) data set—will re-visit this comparison in Talk in joint SF & HQ session, which concerns the theoretical basis, and heavy flavor physics.

An interesting application of the GM formalism and the precision global analysis: The first phenomenological study of “Is there room in the nucleon for intrinsic charm?” or “How well can available data constrain the charm content of the nucleon?” Talk in the joint HQ/SF session, wkt

Comparison of New PDF (CTEQ6C0) with previous PDFs (CTEQ6.1 and its uncertainty band) Space only permit a very brief comparison: Gluon at two scales New PDFs lie within the previously estimated uncertainty bands. After a new round of careful study, the new uncertainty bands should be narrower, due to improvements on both theory and experiment.

“New” Fixed Target Data for Global Analysis NuTeV:  extensive and anti- F 2,3 & cross section data;  Interest: Experimental: extracted F 2,3 data indicates discrepancies with CCFR results at large x; Theoretical: new data pull the PDFs in the opposite direction compared to the E866 results! E866:  Measurement of pp and pd DY cross sections;  Interest: Preliminary results (hep-ex/ ) indicated discrepancies with existing PDFs;

Study of Large-x Behavior of PDFs (Kuhlmann, Morfin, Olness, Owens, Stump) E866 pp and pd cross sections  Preliminary results (hep-ex/ )  CTEQ studies (deuteron corr. + other effects)  Final results ?? NuTeV and anti- scattering data  Comparison of F 2 vs. theory NuTeV (Tzanov) CTEQ study (nuclear corr., quark mass effects)  Comparison of cross section data vs. theory Petti & Kulagin (emphasizes nuclear correction) CTEQ study (nuclear corr., quark mass effects)

E866 “ The results imply that the u quark distributions in CTEQ6 and MRST2001 are overestimated as x  1. —hep-ex/ These.. discrepancies.. imply that future PDF fits will see a substantial correction to the u and d quark distributions at large x.” Reports by E866 in subsequent conferences indicate that improved radiative corrections seem to reduce the discrepancy, but it has not completely gone away.… stay tuned. CTEQ group have studied possible sources for this discrepancy, particularly deuteron target corrections. Results were inclusive.

F 2 Measurement Isoscalar ν-Fe F 2 NuTeV F 2 is compared with CCFR and CDHSW results - the line is a fit to NuTeV data All systematic uncertainties are included All data sets agree for x<0.4. At x>0.4 NuTeV agrees with CDHSW At x>0.4 NuTeV is systematically above CCFR Tzanov, DIS2005 Notable NuTeV Results

Our Attempts to Incorporate the NuTeV Structure Function, F 2,3, data in the Global Analysis Find this data set “incompatible” with the other data sets in the global analysis—with our usual assumptions; Total  2 of the NuTeV data set unacceptably high; shape discrepancy clearly seen; Tried to: (i) vary nuclear target corrections; (ii) include target and heavy quark mass effects, … None of these help; some make things worse. However, it is more preferable to directly compare theory with the cross section data !

Kulagin and Petti Caution: 2, out of many, energy bins (total # data points > 1000); details impossible to see in these plots.

NuTeV xSec. data compared to a typical fit: This is only an impression plot; Data with different E are superimposed; Error bars are shown only for two bins; Overall  2 is 1140 / 1170 pts. However, CorSysErr not yet included; the devil may be in the details.

Can Nuclear Corrections Help? For each x, data are combined and errors are weighted; See a systematic x- dependent deviation that cannot be reduced substantially by nuclear correction models.

Our Attempts to Incorporate the Full NuTeV Cross section data in the Global Analysis The situation improves! Total  2 of the NuTeV data set becomes acceptable— not too different from 1 /dof ; However, upon closer examination, a clear shape discrepancy persists; Tried to: (i) vary nuclear target corrections; (ii) include target and heavy quark mass effects, … None of these help; some make things worse. Therefore, we believe the compatibility of this measurement with the other data sets in the global analysis within the conventional PQCD framework remains an open question.

Summary and Outlook The impressive consistency between the improved theoretical calculation and much improved HERA input on DIS NC, CC & heavy flavor production (and other F.T. and hadron collider processes) provides a new basis for performing precision phenomenology within and beyond the SM. A lot of work remains to be done to pin down the full parton structure of the nucleon (particularly gluon, s, c, b); HERA II and Tevatron Run II data can contribute substantially to fill the gaps. More specifically, With more accurate data on CC cross sections, we gain additional (clean) handles for differentiating up and down types of quarks; Direct F Long measurement in the cards? With W/Z/  + tagged heavy flavor events at the hadron colliders, we can get direct information on s/c/b quark distributions; …. LHC physics is waiting for these advances …

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Reserve Slides

Comments on NNLO In the perturbative approach, for the total inclusive S.F.s and cross sections, once a comprehensive NLO calculation is in place, it is “straightforward” to include known NNLO corrections additively. Extending global analysis to NNLO is certainly desirable, but not necessarily urgent for current applications, since experimental errors for most measured quantities, as well as other sources of uncertainties (such as parametrization, power-law corrections …), largely outweigh the NNLO corrections. Additional note: unlike total inclusive F 2,L, quantities such as ”F 2 c ” are not well defined theoretically at NNLO and beyond. (It is not infra-red safe!) It is rather misleading to talk about a true “NNLO theory” of F 2 c (except within the 3-flv scheme, which has a very limited range of applicability).