# Presentation: 035152

## Heavy Quark PDFsc(,2), b(,2)

- Heavy Quark PDFsc(,2), b(,2)

- Stefan Kretzer
**Brookhaven National Laboratory & RIKEN-BNL**

- Review and results of collaborations with:
- F. Olness, H. Lai, C. Schmidt, W.-K. Tung

## What do you get when you dochm = Ctq6Pdf(4,x,Q) bot = Ctq6Pdf(5,x,Q)orcall mrst2001(x,Q, ... ,chm,bot, ...)

- ???

- Short version of a HQ PDF talk

## CTEQ6 error band for HQ PDFs

- Q=10GeV

- xb(x,Q)

- xc(x,Q)

## CTEQ6 error band for HQ PDFs(large {x,Q})

- CTEQ6 error band for HQ PDFs(large {x,Q})

- Q=200 GeV

- xb(x,Q)

- xc(x,Q)

## Comparison CTEQ and MRST

- Comparison CTEQ and MRST

## Guiding questions (from a more inspired brainstorm):

-  What are heavy quark PDFs? (technically and physically / intuitively)
-  How adequate are heavy quark PDFs (for e.g. LHC applications)?
-  How adequate can we make them? (exploring “scheme” ambiguities)
-  How well are HQ PDFs determined from, mostly, HERA data? (approximately the “short version”)
-  Disclaimer:
-  HQ PDF will be integrated (k? independent) PDF.
-  Most of the talk will be DIS oriented. (The ideas are general, tough, and relevant to LHC phenomenology.)

## LHC: Associated         production in MSSM

- LHC: Associated         production in MSSM

- Bottom production feeds Higgs production.

- Dawson, Dicus, Dittmaier, Harlander, Jackson, Kilgore, Krämer,  Orr,  Rainwater, Reina, Spira, Sullivan, Wackeroth, Willenbrock, Zeppenfeld,  ...

## ... or this:

- 2 more general (and practial)  motivations:

- 1) For a lowest order estimate on any  of interest calculate this ...

- ... or this:

## 2) HQ PDFs are needed for (RG consistent) NNLO applications

**1) THE THREE-LOOP SPLITTING FUNCTIONS IN QCD: THE NON-SINGLET CASE.**By _[S. ](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Moch,+S.)__[Moch](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Moch,+S.)_, _[J.A.M. ](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Vermaseren,+J.A.M.)__[Vermaseren](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Vermaseren,+J.A.M.)_, _[A. Vogt](http://www-spires.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Vogt,+A.)_. DESY-04-047, Mar 2004. 29pp. ** _[Temporary entry](http://www-spires.slac.stanford.edu/spires/hep/te.html)_ **
- e--Print Archive: **hep-ph/0403192**

## Warmup:Light quark & gluon PDFs

- q = u,d,s

- P2

- Light quark Propagator / 1/(1-cos )

## Collinear factorization

## In technical terms, local

- or bilocal

- definition of (quark) PDF.

## Heavy quarks

## Heavy Quark Propagator / 1/(1-v cos )

- P2

- Heavy Quark Propagator / 1/(1-v cos )

- introduces no new nonperturbative component. (Unless there is a *significant* amount of intrinsic HQs:                                                  )

## That means HQ PDFs

- can be calculated in perturbation theory up to higher twist [if you want to include HT parts into Q(x)].

- perturbative/extrinsic

- non-perturbative/intrinsic

- Brodsky & Peterson & Sakai

- Collins & TungCollins & OlnessSoper, ACOT, ...

## The Dead Cone

- k?

- k2

- =z k+

- as

- as

- Y. Dokshitzer

## DGLAP resums collinear logs

- DGLAP resums collinear logs

## Schemes (for DIS)

## Schemes are related by a finite, perturbative,  transformation:

- (and analogous for nf=4 ! 5)

- In particular:

- Collins & Tung, Collins & Olness, Soper, ACOT, ...

## Several observables have made us confident in pQCD predictions at Q' mc

- F2(x,Q' mc)
- “high” p? identified particle hadroproduction at (not-so-high) p? ' mc
- ...

- From that perspective one should trust in the **pQCD expansion of HQ production in powers of ********s****(m****c,b****). **The schemes are different ways of arranging the perturbation series.

## Ambiguities(“scheme” definintions)

- Ambiguities(“scheme” definintions)

- Cacciari & Greco & Nason(for hadroproduction)

- _Translation to DIS:_

- Gluon Fusion + Quark Scattering – (overlap) Subtraction    ACOT

- S(implified)-ACOT:Krämer & Olness & Soper

## What do you get as a PDF user?  First of all, acronyms:

-  ACOT (CTEQn, n<6)
-  ACOT() (CTEQ6HQ)$ S(implified)-ACOT
-  Thorne & Roberts (MRST)
-  FOPT (GRV)
-  (Bouza, Chuvakin, Matounine, Smith, and van Neerven: partial NNLO VFNS)

- Need a manual to choose? Choose at all?

## Parametrical order  numerical order

- The curves labeled “PDF”, “BMSN”, and “CSN” deviate by O(m2/Q2). Only those labeled “EXACT” do not resum lnn(Q2/m2).

- Parametrical order  numerical order

- Chuvakin & Smith & van Neerven

## O(sl) for (F2c)CC

- O(sl) for (F2c)CC

- l=2

- l=1

- l=0

- l=2 plus n>2 sn lnn (Q2/m2)

- Buza & van Neerven

## bottom hadroproduction 

- bottom hadroproduction

**F**ixed **O**rder and  **F**ixed **O**rder plus **N**ext-to-**L**eading-**L**og n sn lnn (Q2/m2) results

- Cacciari & Greco & Nason

## MRST fit

- MRST fit
- reminder:CTEQ fit is based on ACOT(), MRST fit is based on Thorne & Roberts

## Quality of CTEQ6HQ fit to F2c data

- X,Q

- X,Q

- 10-4 < x < 10-2
- 2 GeV < Q < 10 GeV

- SK & Lai & Olness & Tung

## GRV description of F2c is based on (f=3, no HQ PDFs) fixed order perturbation theory 

- GRV description of F2*c* is based on (f=3, *no HQ PDFs*) fixed order perturbation theory

- By comparison to data at presently accessible energies, there is no such thing as *THE* BEST SCHEME. Maybe that’s just what we should expect from several “schemes” that are all well tailored (and well defined). We are free to use physics intuition, common sense, and convenience ...

## The HQ PDF ambiguities are another artefact of finite order perturbation theory. They can be fixed from, mostly, kinematic considerations:

***Dynamatics *****of HQ production**

## Kinematical threshold effects from W2=Q2(1/x-1)>4 m2or =x (1+4m2/Q2)<1

- Kinematical threshold effects from W2=Q2(1/x-1)>4 m2or =x (1+4m2/Q2)<1

- Dynamical effects

## Slide 31

## Slide 32

## The threshold problems are intimately related to the “Quark Scattering” process represented by the HQ PDF.

- (And they are not cured by retaining the mass dependence in such a process.)

- ACOT, SK & I. Schienbein ...

## Pair production kinematics ...

- Both         and          vanish at threshold W=2m.

- But
- in the k? ! 0 limit does not!

- ... disfavour a HQ scattering process.

## 2) LL dynamics can be factorized retaining the kinematical threshold condition (explanation 2 slides ahead).

- 1) HQ PDFs do not require a “quark scattering process” (or coefficient function) to do the collinear resummation.
- 2) LL dynamics can be factorized retaining the kinematical threshold condition (explanation 2 slides ahead).

## Roberts & Thorne

- Diagramatically:

## LL dynamics 

- LL dynamics

- can be “factorized”

- retaining the kinematical threshold condition:

- without introducing mass dependence into the evolution equations.

## ACOT()

- ACOT()

- The rescaling variable **** is derived from (and tied to) the DIS process.The logic to retain the threshold kinematics along rescaling prescriptions is general. It is inherent in the underlying gluon pair production process.
- The ACOT() factorization prescription is by no means a unique way of introducing HQ PDFs without violating the threshold (remember e.g. the approach by Roberts and Thorne). I am mostly advocating it as a “variable flavour standard” for its robust efficiency and, not least, simplicity.

- Tung & SK & Schmidt

## Results:

## Slide 40

## HERA kinematic range

## HERA kinematic range

## Back to:chm = Ctq6Pdf(4,x,Q)bot = Ctq6Pdf(5,x,Q) orcall mrst2001(x,Q,upv,dnv,usea,dsea,str,chm,bot,glu)

## CTEQ6 error band for HQ PDFs

- Q=10GeV

- xb(x,Q)

- xc(x,Q)

## CTEQ6 error band for HQ PDFs(large {x,Q})

- CTEQ6 error band for HQ PDFs(large {x,Q})

- Q=200 GeV

- xb(x,Q)

- xc(x,Q)

## Comparison CTEQ and MRST

- Comparison CTEQ and MRST

## Slide 47

## Does this look better than expected?On a second thought, not really. After all, HQ pairs come from gluons, no matter what “scheme”.

## Slide 49

## Gluon distribution at Q=2 GeV

- CTEQ6 with error band

- CTEQ5

- MRST

## Not (too) surprisingly, HQ mass effects impact the light PDFs as well. The dominant effect on the next 2 slides is that light quark PDFs have to compensate the threshold surpression of the HQ contribution. 

## Slide 52

## Slide 53

## Summary:

-  HQ PDFs are conceptually well defined and a convenient tool in pQCD phenomenology.
- They are gluon driven, so their accuracy increases with the scale. At a low scale they are rather ineffective, anyway, i.e. they are neither of much profit nor do they do any damage (if judiciously applied in a way that suppresses their contribution in regions where the physics is not collinear).
-  “Schemes” have to be understood as perturbative ambiguities. We have made a *(very)* easy to implement suggestion for the practical use of HQ PDFs that is based on intuitive and, mostly, kinematical arguments. Despite its simplicity it is robust and efficient. If it is accepted broadly, we can hopefully eliminate the term “scheme” largely from the phenomenology of HQ production (and from related processes at the LHC) and concentrate on the physics issues.
-  One of them is: **How well do we understand bottom production in pQCD?** (Or: “Is bottom production bottom production or sbottom production?”, see  E. Laenen’s overview talk earlier today.) The validity of pQCD for bottom production data is conditio sine non qua for the reliability of *perturbative* HQ PDFs.

## Backup slides

## Neutrino Structure Function

- CTEQ

- MRST

## Slide 57

## Slide 58

## Slide 59

## Slide 60

## Slide 61

## Wish Item:

- With a stable, robust, and simple procedure to incorporate heavy quark mass effects, hopefully a uniform “scheme” is adopted by all groups in future global analysis involving both lepto- and hadro-production processes. Then both experimentalists and theorists can concentrate on the real physics issues facing heavy quark physics, rather than be bewildered by the variety of different, and relatively arbitrary choices of ad hoc prescriptions in the many existing calculations and phenomenological analyses.