Heavy Quarks. ... lessons we've learned & future applications. Fred Olness SMU

Transcription

1 Heavy Quarks... lessons we've learned & future applications Fred Olness SMU Conspirators: I Schienbein, S. Berge, P. Nadolsky, Ringberg Workshop J. Y. Yu, J. Owens, J. Morfin, W. Tung, C. Keppel,... 6 October 2008

2 Heavy Quark Production: m = 0: Massless case. Mass plays no dynamic role Well understood. A tale of two scales m = : Infinite case. 2 Mass Decouples. We can forget about this object

3 HISTORY

4 4 Hadroproduction of Beauty at Tevatron Comparison of Run I data with NLO Theory Data is high by factor of 2x or 3x... even given µ variation g c,b g c,b

5 Charm & Beauty Production at HERA CHARM Charm production matches well with NLO calculation BEAUTY Data is high by factor of 2x or 3x 5

6 6 Charm and Beauty Production at LEP Comparison of LEP data with NLO Theory e+ e γ γ c,b Charm is reasonable Bottom data is high by factor of 2x or 3x

7 FUTURE

8 W & Z at LHC: Heavy Quarks play important role d /dy(w+) at Tevatron d /dy(w+) at LHC tot tot ud ud cs us cd y Larger fraction of heavy quarks W/Z are Benchmark Cross Sections... will be measured in early run HEAVY is a relative term cs us cd y 8

9 Calculating Heavy Quarks Part I 9

10 Tevatron: NLO Fixed-Flavor Scheme Leading Order Next to LO Heavy Creation Surprise < Surprise: µ renormalization scale variation NLO / LO Big But,... theory still below data Nason, Dawson, Ellis Beenakker, Kuijf, Van Neerven, Smith 10

11 11 The Basic Contributions to Heavy Flavor Production Heavy Creation Heavy Excitation heavy quark is integral to the proton Variable Flavor Scheme Next to LO Fixed Flavor Scheme Leading Order

12 Calculating Heavy Quarks Part II state of the art 12

13 State of the art HQ Calculations VFN: Variable Flavor Number: Introduce new partonic components when the scale exceeds the heavy quark mass. E.g., charm and bottom are included in the proton at high enough scales Massless MS bar Evolution: Evolution kernels in DGLAP are Mass Independent: f ~ P f. ACOT (Aivazis, Collins, Olness, Tung) A general framework for including the heavy quark components. Phys.Rev.D50: ,1994. S ACOT (Simplified ACOT) ACOT with the simplification that initial state heavy quark masses can be set to zero. Phys.Rev.D62:096007,2000. Prescription: ACOT & S ACOT : As above with a generalized slow rescaling x x(1+(m1+m2)2/q2)... see: R.S. Thorne, W.K. Tung, arxiv: [hep ph] 13

14 Variable Flavor Number: Problem: Heavy Quark introduces new scale:... life gets interesting. 14 Heavy Quark PDFs 2 Q log 2 log M 2 H 2 Solution: Resum Log(M ) in the Heavy Quark PDF's: H ACOT, PRD 50, i.e., as in the ACOT renormalization scheme DIS production of Heavy Quarks DGLAP equation Resums iterative splittings inside the proton r ua Q y v k F D P a He Result: We can describe the full kinematic range from low to high implemented in the CTEQ6HQ PDF's with finite MQ

15 Massless MS-Bar Evolution: Why it is valid 15 f P a a c near threshold (MH~Q) 1 f P g P g a a c 1 f P g P g a 1 P splittings must match Near threshold(mh~q), mass effects cancel between HE and SUB Above threshold(mh<<q), mass effects can be ignored Choice of DGLAP Kernels is a Scheme Choice!!! This is NOT an approximation

16 16 Simplified-ACOT Scheme: S-ACOT Development: Factorization proof extended to Heavy Quark case. Collins (1998) Observation: Simplified ACOT Scheme: Set MH=0 on incoming HQ lines Kramer, Olness, Soper (2000)... MH=0 Result: MH 0 MH=0 MH=0 MH=0 1) Comparable Numerics & 2) Simpler Calculations

17 Simplified-ACOT Scheme: The Numerics Simplified result numerically comparable to full result... what about the analytic result??? 17

18 Simplified-ACOT Scheme: The Analytic Result Which would you prefer to calculate? ACOT S ACOT 18

19 - Prescription: Satisfying the kinematics m1 = x 1 m1 m2 2 Q2 19 m2 F2 Kinematic suppression at threshold x x(1+(0 mc)2/q2) x x(1+(1 mc)2/q2) x x(1+(2 mc)2/q2)

20 20 Results

21 F2 Charm in the threshold region F2 21 c NLO (m=0) ACOT LO S ACOT S ACOT FFS scale (GeV) X=0.1

22 FL Charm in the threshold region S ACOT FFS scale (GeV) S ACOT 22

23 Impact 23

24 24 Heavy Quark Schemes: CTEQ6M, CTEQ6HQ, CTEQ5M Cteq 6.5 Cteq 6HQ Large shift C5M C6M (New DIS & Jet data) Charm PDF tied to gluon (g cc) Small visual difference but... Shift due to both scheme and uncertainty Cteq 6.6 Cteq 6.1 x x Ratio to CTEQ 6.1 x1.5 f(x,q) Gluon 10GeV 2/DOF Set ZEUS H1 TOTAL # pts HQ M 6M GM 6HQ ZM Mixed Schemes S. Kretzer, H.L. Lai, F. I. Olness and W.K. Tung. Phys.Rev.D69:114005,2004

25 Where does it make a difference???... only HERA is sensitive 25 A 3 σ effect HERA experiments sensitive to Mixed scheme Encouraging that C6M and C6HQ are comparable IX ED M ED IX M 6M CT EQ CT EQ 6H Q Encouraging that Mixed schemes yield large 2 Will affect PDFs in region of low x and low Q

26 26 Intrinsic Heavy Quarks

27 Are there Intrinsic Heavy Quarks??? 27 Momentum Fraction c quark 2% b quark 1% CTEQ 6.6 mc mb µ (GeV) Most sensitive near threshold * What happens if we allow the evolution to determine charm? Zero: No intrinsic charm Positive: Intrinsic charm Negative: Inconsistent J. Pumplin, Phys.Rev.D75:054029,2007.

28 Impact of Intrinsic Heavy Quarks Lo Q 28 Hi Q Higgs J. Pumplin, Phys.Rev.D75:054029,2007. W/Z Nadolsky, Phys.Rev.D78:013004,2008.

29 NNLO A proposal for NNLO PDF implementation

30 s as a function of for various flavor numbers At O( s3), not even At 1 loop and 2 loops, continuous at thresholds continuous at thresholds s Log[5 ] mc mb 10 mt m c mb mt 1000

31 f(x, ) as a function of for various flavor numbers 31 Parton Distribution Gluon Not continuous at O( s2) O( s2) Charm Bottom mc mb µ relate N and N+1 PDF's implied relation of C's Note: FFNS ~ N VFNS ~ N+1

32 f(x, ) as a function of for various flavor numbers NNLO b(x, ) g(x, ) 32

33 A Proposal for PDFs NF=4 NNLO NF=5 33 NF=6 NF=3 True For m, N and N+1 Schemes Co exist fa/p(x, Q, NF) Q0 Q0 new M4 NF=3 Freedom to specify NF Requires NF in PDF interface Simplified Numerics match Match at =m Transition at... at M5 M6 transition NF=4 NF=5 NF=6

34 Physical Structure Function A multi flavor scheme is truly a patchwork O( sn+1) 3 mc mb µ * Difference represents the theoretical uncertainty * Gaps will decrease with higher orders (they must as physical quantities) (note: gaps of PDF's and s do not these are unphysical quantities) * If data prefers one scheme optimal perturbative organization * Gaps between schemes reflects limit of theory uncertainty

35 Scheme choices and global fits 35

36 36 Schematic Summary of Schemes TR type schemes Q < mh Q > mh ACOT type schemes constant term Q < mh Q = mh LO LO + + NLO + NLO + NNLO + Q = mh Q > mh + Q = mh + NNLO constant term +

37 37 Are we ready for the LHC... yes... no

38 Inclusive B-Meson Hadroproduction in a GM-VFN 38 GM VFN prediction yields agreement w/ Run II data Contrast FFN w/ old input Kniehl, Kramer, Schienbein, Spiesberger, Phys.Rev.D77:014011,2008.

39 39 Impact of HQ PDFs on W/Z at LHC tot CTEQ % increase in CS d /dy(w+) at LHC (x) ud CTEQ 6.5 CTEQ 6HQ CTEQ 6.1 MSTW Q=1.3 GeV Boson Rapidity x cs us cd y Different Y Distribution... but HQ Uncertainties will feed into LHC Benchmark processes

40 40 Conclusions

41 Conclusions * Historically: Calculation of Heavy Quarks challenging * Significant Progress: New theoretical tools enable reliable calculations Heavy Quarks are included in DGLAP evolution Heavy Quarks masses are included in Global Analysis * Current Challenges Complex at NNLO Heavy Quarks play a more prevalent role at the LHC Need to accommodate these effects and uncertainties to make best use of HERA & Tevatron data. Also, be prepared to cross check using early LHC data Thanks to: I. Schienbein, J. Y. Yu, S. Berge, P. Nadolsky, J. Owens, W. Tung, S. Kretzer, S. Kuhlmann, J. Pumplin, H. Lai, T.Bolton, P. Spentzouris, D. Mason, M. Shaevitz, K. McFarland, U.K. Yang, 41