Advances in Global QCD Analysis and Impact on LHC Phenomenology Hung-Liang Lai Taipei Municipal University of Sinica, Nov. 23, 2007 In collaboration with: Belyaev, Huston, Nadolsky, Pumplin, Stump, Tung, Yuan (Michigan State Univ., Univ. of Washington & TMUE)

Outline  Global QCD Analysis in brief  Heavy quark mass effects and CTEQ PDFs ( References: JHEP 0702:053; PRD 75:054029; JHEP 0704:089 (2007) )  Impact on LHC phenomenology (paper in preparation)  New advances (ongoing): (a) extended to NNLO (b) combined Pt resummation + PDF global analysis

The many faces of QCD in Hadron Collider Physics hadrons leptons, hadrons partons, gauge bosons, new particles (universal) parton Distributions SM physics: PQCD & EW jet algorithms hadronization models: MC programs frag. functions New physics scenarios Asymptotic Freedom and Factorization of QCD: L.D. S.D. L.D. QCD enters in all aspects of HCP.

Global QCD Analysis of Parton Structure of the Nucleon Intrinsic interest: QCD dynamics at short distance, PQCD; fundamental structure of the nucleon (non- perturbative) — QCD dynamics at the confinement scale; Practical importance: essential ingredient that connects the hadron world to the parton world for all SM and New physics processes in hadron colliders. (Crucial to understand both the signal and the background of most processes of interest.)

universal, extracted by global analysis Theory Input

NuTev

Experimental input (continued) ( ) (DIS jets, heavy quark prod. …)

Kinematics of Parton variables LHC Tevatron QCD (DGLAP) evolution Predictive power of global analysis of PDFs is based on the renormalization group properties of the universal Parton Distributions f(x,Q).

Recent works on Heavy quark mass effects and CTEQ 6.x PDFs

Heavy quark mass effects and CTEQ PDFs A new systematic implementation of the G eneral-mass (GM) QCD formalism; Factorization scheme (Collins)  PDF’s and their evolution;  Mass-dependence of hard cross section (SACOT) Final States, on-shell kinematics …  Rescaling (ACOT  ), Phase space, … Applications: precision global analysis: CTEQ6.5M + uncertainties ( JHEP 0702:053, 2007 ) ; 1 st focused study of strange distributions: CTEQ6.5Sx ( JHEP 0704:089, 2007 ) ; 1 st study of charm distributions (intrinsic charm?): CTEQ6.5Cx ( PRD 75:054029, 2007 ).

The General Mass (GM) PQCD Formalism Factorization Thm (valid order-by-order, to all orders of PQCD) Conventional proofs: assume Zero Mass (ZM) partons; Collins (85-97): FacThm proof is independent of the mass parameters in PQCD—General Mass (GM) case. aa  H.Order The Parton Picture: is based on:

Where do mass effects matter? For Physics quantities that vanish in the zero-mass limit, such as LO F longitudinal. In the kinematic phase space: When  is substantially different from x, and where f(x,Q) is steep in x NC: Kretzer, Schmidt, Tung (cf. CC: Barnett) In real-life precision phenomenology: Certain HERA data sets—in the low Q region (H1NCe+9697X and ZeusNCe+9697X) This leads to different determination of the non- perturbative PDFs at low Q, which, in turn, lead to modified predictions for physical observables at high Q.

Comparison of GM and ZM Calculations: where in the (x,Q) plane do the differences matter? F 2 (x,Q) GM ZM low Q 2 mostly

Comparison of GM and ZM Calculations: where in the (x,Q) plane do the differences matter? F L (x,Q) Much larger ranges of both x and Q 2

Remarks Physical quantities, such as F 2, F L, are positive definite and smooth across heavy flavor thresholds. Simplicity of the general formalism + the new implementation (including proper kinematics) underpin these results. This combination serves as the basis of new comprehensive Global Analyses: conventional parametrizations; independent strangeness sector; independent charm sector

Applications of the New Implementation of the GM calculation to Global Analysis In conjunction with the comprehensive HERA I (+ Fixed Target and Hadron Collider) data, the new GM calculation  Precision global QCD analysis of PDFs under conventional assumptions at Q 0 : ; radiatively generated charm/bottom i.e. no non-perturbative (intrinsic) charm, … etc.  CTEQ6.5M + eigenvector uncertainty sets (Tung,Lai,Belyaev,Pumplin,Stump,Yuan: JHEP 0702:053, 2007)

CTEQ6.5M vs. CTEQ6.1M and its error bands Enhanced quark distributions at x ~ CTEQ6.5M + some alternative parametrizations

Comparison of CTEQ6.5M (with error band) to previous PDFs CTEQ6.1MMRST04 CTEQ6AB Alternative, unrealistic, error band (too few parameters) Main deviation from CTEQ6.1 Main deviation from MRST

Strange parton content of the nucleon Surprisingly little is known so far about the strangeness sector of the parton structure of the nucleon: generally assume it is known that r ~ 0.5, with large uncertainties. dedicated study of the strangeness sector: CTEQ6.5S: Can now be determined? What is it like? What can we say about the strangeness asymmetry ? (Lai, Nadolsky,Pumplin,Stump,Tung,Yuan: JHEP 0702:089, 2007) Inputs that can improve our knowledge of this sector: NuTeV CC dimuon prod. data (sensitive to charm prod.) More precise GM QCD calculation of HQ processes.

Symmetric strange distribution New global analysis disfavors ; it suggests that, with current experimental constraints, we need at least one new shape parameters for s + (x). More may be needed with improved experimental input.

Symmetric strange distribution We obtain bounds on the magnitude of s + : We obtain a range of shape variation of s + (x).

Strange Asymmetry S - (x) was first studied in 2003 as a possible source of the “NuTeV anomaly. The results were suggestive, but not conclusive. Has the situation improved, due to recent advances? Results of current study: Current global analysis does not require a non-zero s - (x). If non-zero, the range on its magnitude: —the same as in the 2003 study. A range on its shape is found  s - (x) x s - (x)

The Charm Content of the Nucleon Conventional global analysis assume that heavy flavor partons are exclusively “radiatively” generated, i.e. by gluon splitting. This assumption/ansatz more or less agrees with existing data on production of charm; but it is natural to ask: What can current global analysis reveal about the charm sector of the nucleon parton structure? Why should we care about c(x,Q)? Intrinsic interest: the structure of the nucleon; Practical interests: collider phenomenology, especially beyond the SM, e.g.  Charged Higgs production, c + s-bar --> H + ;  Single b’ production, g+c  b’+W ;  Single top production in DIS (flavor-changing NC) …

Scenarios for the Charm parton sector Radiatively generated c(x,Q 0 ); Intrinsic (non-perturbative) charm (IC) scenarios: Sea-like c(x,Q 0 ) — similar to light quark seas light-cone model scenarios:  Model of Brodsky etal (BHPS);  Meson-cloud model (MC) ( similar, except c.ne. cbar for the latter). First results … (Pumplin, Lai, Tung: PRD75:054029, 2007)

Results: A IC component of the nucleon of has important implications for BSM phenomenology at the LHC 90 % CL Goodness-of-fit vs. amount of IC (momentum fraction) for the three models In the range : Current global analysis does not require IC; For (assuming IC exists, as is natural in the models), our analysis sets a useful upper bound ; Light-cone model guesstimates,, are within this bound.

Purely Intrinsic (non-perturbative) Pictures (BHPS model) Two components in parity Radiatively-dominated at small x, but IC very important at x > 0.1

Outlook This is just the beginning. Looking forward to more comprehensive and accurate data from HERA II With W/Z/  + tagged heavy flavor events at the hadron colliders, we can get direct information on s/c/b quark distributions; Challenges at the Tevatron and the LHC=>=>=> c-quark and b-quark are important phenomenologically in the physics program at LHC for exploring beyond the SM scenarios.

Nearly completed: CTEQ6.6 PDFs  While in the process of consistent implementation of GM-NNLO, we gain minor improvement of the GM-NLO codes as well.  Independent parametrization of strange distribution is included in the general-purpose PDF sets. Therefore, 22 free PDF parameters (vs. 20 in CTEQ6.1 and 6.5)  Extended x range (down to ) for providing wider LHC simulation.  To be released in accompany with LHC phenomenology study.

Impact of new CTEQ PDFs on LHC Phenomenology

CTEQ6.1 LHC Luminosities: ratios to CTEQ6.5M Main deviation from CTEQ6.1 U-quark distribution: ratio to CTEQ6.5M (2 GeV) CTEQ6.1 CTEQ6.5 error band For small s-hat, q-qbar luminosity is 5 – 10 % higher than previous estimates; q-g luminosity is just within the error band; g-g luminosity is within the band; The uncertainty bands narrow somewhat at large s-hat, but are otherwise similar to before.

Impact of CTEQ6.5M,S,C PDF’s on  tot ’s at LHC +

Example: a beyond SM process  tot ( ) Tevatron LHC

New advances (ongoing works)

Extension to NNLO  For vast majority of applications, NLO is generally sufficient, since experimental errors and other sources of uncertainties largely outweigh the NNLO corrections. Still, there are inevitable demands to push for higher order.  QCD Evolution kernal at NNLO has been available in the market.  Hard cross sections for most essential processes are available as well. We have recently extended the implementation up to NNLO and detailed study is underway.

Transverse momentum distribution plays an important role in precision DY, W/Z, top, and Higgs phenomenology at hadron colliders, both in SM and BSM. In PQCD, p T resummation is required to describe the transverse momentum distribution in the most important physical region L QCD < p T < M W /Z/t/H. The resummation calculation depends on a small number of non-perturbative (Sudakov) parameters that must be determined by fitting DY and W/Z production data. d  /dp t | Z CDF & D0 BLNY 02 Typical example: Combined pt resummation …

Combined p T resummation and PDF global QCD analysis So far, the studies of p T and PDF degrees of freedom are entirely segregated, although physically they are not. To achieve high accuracy in precision W/Z, top, and Higgs physics, an integrated approach is imperative; e.g. the reliable estimate of the “PDF uncertainty” in precision M W measurement. Higgs discovery, with appropriate p t -cut to enhance signal/background ratio.

Combined p T resummation and PDF global QCD analysis Difficulty in combining p T resummation calculation and PDF global QCD analysis: deadly combination of p T resummation calculation is complicated (multiple convolution integral), hence computationally costly; global QCD analysis typically requires thousands of iterations to optimize PDF, and Sudakov, parameters. This difficulty has recently been overcome: Combined global analysis involving Sudakov and PDF parameters simultaneously can now be done; An active program of systematic investigation of precision DY, W/Z, top, and Higgs phenomenology has begun. (Lai, Nadolsky, Tung, Yuan, …)

Preliminary indications: base set of expts (e.g. DIS + …) perfect fit bad fit a priori acceptable fit (e.g. 90 % CL ) Fixed target DY and collider W/Z p t distribution data  n = 1 By iteratively improving the fit to the combined data sets, the p t data will help constrain PDF degrees of freedom not probed before in traditional global analyses. The new degrees of freedom so constrained could have important implications for precision measurements, such as M W and Higgs production.

Summary  Our knowledge of PDFs and its uncertainty is crucial for hadron collider physics.  Heavy quark mass effects are noticeable, even at high scale, and thus have impact on LHC study.  The amount of intrinsic charm could be important on some new Physics scenarios at LHC.  Combined PDF+Pt analysis is expected to have impact on our understanding of Mw and Higgs measurements.