# Presentation: 744409

## PDF aspects of sin2 W  in pQCD:  strange sea quark asymmetry 

- PDF aspects of sin2 W  in pQCD:  strange sea quark asymmetry

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

- Collaboration with:
-  M.-H. Reno
-  CTEQ: F. Olness, W.-K. Tung et al.
-  D. Mason (NuTeV)

## Instead of Introduction:

- 15 minutes are short.
- I will make claims.
- We will have discussions.

## PRL 88, (2002) aka the NuTeV anomaly:“Having precisely determined R and Ranti-, and their predicted values as a function of electroweak parameters (...)”

## Model-independency

- Model cross sections provide model parameters.
- Theory cross sections provide theory parameters.

## R-(QCD): Model-independent corrections

- R-(QCD): Model-independent corrections

-  NLO=O(s) corrections for light and charm quarks
-  O(mc2n/Q2n)

-  Target mass corrections to ew structure functions along the OPE (Georgi & Politzer) approach:O(MN2n/Q2n)
-  NLO DGLAP

- M.H. Reno, SK (2003)

-   scaling @ NLO

- twist =2

- (! M.H. Reno’s talk)

##  The Paschos-Wolfenstein Relation and its approximations

-  The Paschos-Wolfenstein Relation and its approximations

- Structure functions F1,2,3 are not proportional to one another
- Next-to-Leading Order QCD
- Target Mass Corrections
-  A  2 Z for target material
- Isospin violation
- Single charm threshold and CKM in CC scattering
- Sea quark / anti-quark asymmetry
- strangeness
- (charm)

- All approximations

- Include NLO and TM corrections only:NLO & TMC modify physical effects, do not generate new effects

*Mathematica* # lines: 6→1

## Corrections to R-— for the moment:                               

-  Let’s neglect cuts / exp. Issues: ideal Paschos-Wolfenstein relation
-  Let’s neglect evolution / scale dependence
-  Let’s neglect NLO corrections
-  Let’s assume the target material (mostly Fe) is isoscalar and that isospin is exact
-  Let’s assume mc=0
-  Let me focus on the quark / antiquark asymmetry for strange sea quarks

## Then:

- _Then_:

- is not protected by any symmetry:

## What do we know about                 ?

- Before any data, two things:
-                                          (exact sum rule )_oscillation_)
-                                          (positivity)

- For more information, we have to ask data:
-  ***dimuon production***:                           (CCFR, NuTeV, ...)
-  further (weak) constraints:
-  s g ! c W- background to sign-selected W production (“W charge asymmetry”) at the Tevatron

## “CTEQ” Global Analysis

- Same ingredients as “CTEQ6” analysis
- Add CCFR-NuTeV dimuon data
- Allow a non-symmetric strangeness sector:

***Parametrization*** of the Strangeness sector (at some* Q=Q**0*)

- Where x0 is to be determined by the condition [s-]=0.
***Sum rule and positivity are then satisfied***.

## Strangeness Structure of the Nucleon: Dimuon Production in        Scattering

- Process that provides the most direct (LO) constraints on the strangeness sector of the parton structure of the nucleon.

*(d* is Cabibbo suppressed)

- Modeling needed for com-paring theory with data.

## NLO corrections

- s

- c

- W+

- g

- for dimuon production are not yet included in current CTEQ analysis (to meet the LO acceptance correction model).
- NLO corrections become sizable at high energy (HERA) but are well behaved for fixed target scattering (CCFR/NuTeV).

## CC charm: LO/NLO stability

- NLO: T. Gottschalk
-           M. Glűck, E. Reya, SK
-           ACOT

- PDF ­
- hard scattering

## CC charm: LO/NLO stability

- NLO: M. Glűck, E. Reya, SK

- PDF ­
- hard scattering ­
- fragmentation

## Differential production cross section and acceptance

- D. Mason, F. Olness, SK

- d 

- z

- rapidity

- Acceptance vs. rapidity

- Acceptance vs. z

## From the last 3 slides, I argue that the acceptance correction model will not be different either on a LO or NLO basis!(! discussion session)

## Typical fit results

- Vs. Bjorken x

## But remember: The most closely correlated quantity is the moment [S-]:

- But remember: The most closely correlated quantity is the moment [S-]:

- Rule of thumb:
- The 3  anomaly corresponds to
- [S-] £ 100 ' 0.5

- § data

- Other (less) sensitive data

## Future prospects for [S-]?

-  CC charm @ HERA: ditto
-  Lattice:The moment [S-] does not correspond to a local operator and can, therefore, not be evaluated on the lattice.Higher, noninteger moments  (n=3,5,...)can be related to local operators but could presumably clarify the sign of the x! 1 behaviour at best, not the magnitude of [S-].

- Future prospects for [S-]?

- s

- g

- c

- W

- Baur, Halzen, Keller, Mangano, Riesselmann

## MRST analysis of isospin violations:

- uvn(x)=dvp(x)+ f(x)

- Best fit value of  removes 1-1.5  of the discrepancy.
- A permissible variation of 2MRST covers the full 3  .

- (! T. Londergan’s talk)

## Low Q2 : s d  (Q2-Q2min) 

| Q2min |  | anti- |
| --- | --- | --- |
| 0  | 100% | 100% |
| 0.5 GeV2 | 99% | 98% |
| 1.0 GeV2 | 98% | 95% |
| 2.0 GeV2 | 95% | 89% |
| 5.0 GeV2 | 86% | 73% |

- (Contribution from the low Q2 region. Percentages based on the CC DIS process)

## Conclusions

-  The **central fit value** of CTEQ for [S-] is positive – decreasing the anomaly. The central value depends sensitively on model details and spurious higher order terms.
-  The **uncertainty** of [S-] is data driven and allows a broad range of values for [S-] within CTEQ global QCD analysis (incl. § production data). Additionally, MRST finds a broad range of isospin violations (of reasonable magnitude) that cannot be excluded. Taken together, **within the parameter space (and from the perspective) of global QCD analysis, the consistency of NuTeV neutrino scattering data with other hard scattering data and with the standard model seems possible**.
-  In the near future, the relevant parameters will unlikely be determined to a substantially better accuracy. This is an unfortunate mismatch of the uncertainties of the QCD theory - which relates R- to sin2 - and the high statistical accuracy of the NuTeV measurment.
-  Parallel to discussing [S-] etc., my suggestion for the workshop is ***to discuss / re-think systematic errors***.