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Heavy Quark Mass in PQCD and Heavy Flavor Parton Distributions

Heavy Quark Mass in PQCD and Heavy Flavor Parton Distributions. HeraLhc07 DESY Tung. Outline. A new ( straightforward, systematic ) implementation of the G eneral-mass (GM) QCD formalism; Factorization scheme (Collins) PDF’s and their evolution;

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Heavy Quark Mass in PQCD and Heavy Flavor Parton Distributions

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  1. Heavy Quark Mass in PQCD and Heavy Flavor Parton Distributions HeraLhc07 DESY Tung

  2. Outline • A new (straightforward, systematic) implementation of the General-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 (ACOTc), Phase space, … • Applications to precision global analysis: • New minimal global analysis: CTEQ6.5M + uncertainties(hep-ph/0611254); • 1st focused study of strange distributions: CTEQ6.5Sx(hep-ph/0702268); • 1st study of charm distributions (intrinsic charm?): CTEQ6.5Cx(hep-ph/0701220). • Collaborators: Lai, Nadolsky, Pumplin, Stump, Yuan • Thanks to: Collins, Kretzer, Olness, Schmidt

  3. wa + H.Order The General Mass (GM) PQCD Formalism The Parton Picture: 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. is based on:

  4. S final State parton flavors m(Q) LO NLO NNLO F tot 4-flavorscheme + … O(as2) terms with light quarks only O(as0) terms with light quarks only O(as1) terms with light quarks only mC 3-flavorscheme + … Total Inclusive Structure Functions F tot — Forward Compton Amp.: Only diagrams with HQ lines are shown. * Solid lines: heavy quark; * dashed line: light quark; * subtraction terms to remove overlap are not explicitly shown

  5. SACOTc SACOTc New Implementation of the GM Formalism: F tot • Summing Initial S. partons • Variable-flavor # schemes (3,4,5: depends on Q) • Summing Final S. partons • All flavors allowed by P.S. • Final state HQ on-shell. • Kinematic Constraints: • Mass effects in phase space integration limits; • Rescaling—smooth and physical threshold behavior • Acotc • Wilson Coefficients: • Simplified ACOT (initial state parton mass 0)—more natural parton kinematics and greatly simplified W.C. m O(as0) O(as1) 4-flavorscheme mC 3-flavorscheme N.B. Subtraction terms to remove overlap are not explicitly shown;

  6. NC: Kretzer, Schmidt, wkt (cf. CC: Barnett) When and where do mass effects matter? • In the kinematic phase space: • When c is different from x, and where f(x,Q) is steep in x • (slides) • For Physics quantities that vanish in the zero-mass limit, such as LO Flongitudinal. • In real-life precision phenomenology: • Fixed-target as well as certain HERA data sets—in the low Q2 and relatively small-x region (near HQ thresholds.) This leads to different determination of the non-perturbative PDFs at low (x, Q), which, in turn, lead to modified predictions for physical observables at high energy scale (LHC).

  7. Comparison of GM and ZM Calculations: where in the (x,Q) plane do the differences matter? GM ZM F2(x,Q) low x and Q2 mostly

  8. Comparison of GM and ZM Calculations: where in the (x,Q) plane do the differences matter? FL(x,Q) Much larger ranges of both x and Q2

  9. Remarks • Physical quantities, such as F2, FL, are positive definite and smooth across heavy flavor thresholds; predictions on SFs and Xsecs are extremely stable and robust. • Simplicity of the general formalism + the proper implementation of kinematics underpin these results. The physics of HQ in PQCD is fundamentally simple when organized in a natural way. • This implementation of HQ mass effects serves as the basis of new comprehensive Global Analyses:

  10. Applications of the New Implementation of the GM calculation to Global Analyses(A new generation of “CTEQ PDFs”) • Minimal (conventional) parametrizations;(hep-ph/0611254) • What about an independent strangeness sector?(hep-ph/07021254) • What about anindependent charm sector?(hep-ph/0701254) Apology: in each case: Motivation  bare-bone results(no beef)

  11. New Minimal Analysis: CTEQ6.5M • In conjunction with the comprehensive HERA I (+ Fixed Target and Hadron Collider) data, the new GM calculation Precision global QCD analysis of PDFs under simplifying (conventional) assumptions at Q0: • ; • radiatively generated charm/bottomi.e. no non-perturbative (intrinsic) charm, … etc. Quality of global fit improves in general compared to previous analysis (CTEQ6.1).(“measure”: cf. SF session talk)  CTEQ6.5M + eigenvector uncertainty setsLai, Pumplin, wkt, …

  12. Enhanced quark distributions at x ~ 10-3 CTEQ6.5M + some alternative parametrizations CTEQ6.5M vs. CTEQ6.1M and its error bands

  13. Main deviation from CTEQ6.1 Main deviation from MRST CTEQ6AB MRST04 Alternative, unrealistic, error band (too few parameters) Comparison of CTEQ6.5M (with error band) to previous PDFs CTEQ6.1M

  14. Phenomenological consequences of these differences for the Tevatron and the LHC will be briefly summarized in the SF session. Now, shift focus on the strangeness sector…

  15. dedicated study of the strangeness sector: CTEQ6.5S: • Can now be determined? What is it like? • What can we say about the strangeness asymmetry ? hep-ph/0702268 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. • Inputs that can improve our knowledge of this sector: • NuTeV CC dimuon prod. data (sensitive to s + W  c); • More precise GM QCD calculation of HQ processes.

  16. We obtain bounds on the magnitude of s+: Symmetric strange distribution • New global analysis disfavors ;it suggests that we need >2 indep. new shape parameters for s+(x). • We obtain a range of shape variation of s+(x).

  17. s-(x) x s-(x) Strange Asymmetry • S-(x) was first studied in 2003 as a possible source of the “NuTeV anomaly”. The results were suggestive of <S->.ne.0, 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 

  18. The Charm Content of the Nucleon

  19. 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 top production in DIS (flavor-changing NC) … • Conventional global analysis assume that heavy flavor partons are exclusively “radiatively” generated, i.e. by gluon splitting. • It is natural to ask:What can the improved global analysis reveal about the charm sector of the nucleon parton structure? Is there any evidence for Intrinsic Charm, as suggest by many model considerations?

  20. Scenarios for the Charm parton sector • Radiatively generated c(x,Q0); • Intrinsic (non-perturbative) charm (IC) scenarios: • Sea-like c(x,Q0) — 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, wkt: hep-ph/0701220)

  21. 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. BHPS MC sea-like • A IC component of the nucleon of has important implications for BSM phenomenology at the LHC (cf. talk in SF session) Results: Goodness-of-fit vs. amount of IC (momentum fraction) for the three models 90 % CL

  22. Purely Intrinsic(non-perturbative) Radiatively-dominated at small x, but IC very important at x > 0.1 Rad. Gen. Component grows at small-x Pictures (BHPS model)

  23. Outlook • This is just the beginning. Looking forward to more comprehensive and accurate data from HERA II • With W/Z/g + 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.

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