# Presentation: 205906

## Strangeness Asymmetry of the Nucleon and other QCD Aspects of the NuTeV Anomaly

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

- Collaboration with:
-  M.-H. Reno
-  CTEQ: F. Olness, J. Pumplin, D. Stump, and W.-K. Tung, et al.

- Strangeness Asymmetry of the Nucleon and other SM  Aspects of the NuTeV Anomaly

## Comprehensive Review Article:

-  “The parton structure of the Nucleon and Precison Measurement of the Weinberg Angle in Neutrino Scattering”BNL-NT-03-16= RBRC-328=hep-ph/0312322 with F. Olness, D. Stump, J. Pumplin, M.H. Reno, and W.-K. Tung
-  “Neutrino Dimuon Production and the Strangeness Asymmetry of the Nucleon” BNL-NT-03-17= RBRC-329=hep-ph/0312323 with CTEQ
-  “Target Mass Corrections to Electroweak Structure Functions and Perturbative Neutrino Cross Sections”PRD 69, 034002 (2004)with M.H. Reno

- _Comprehensive Review Article_:
-  “Old and New Physics Interpretation of the NuTeV Anomaly”JHEP 0202:37 (2002)S. Davidson, S. Forte, P. Gambino, N. Rius, and A. Strumia

- _Additional Related Work_:
-  T. Londergan & A.W. Thomas, MRST, K. McFarland & S. Moch, B. Dobrescu & R.K. Ellis, K. Diener & S. Dittmaier & W. Hollik, S. Kumano, J. Qiu & I. Vitev, F.G. Cao & A.I. Signal, S. Brodsky & B. Ma, S.A. Kulagin, ...

## NuTeV Anomaly

- NuTeV _*Anomaly*_

- SLAC E158:Parity Violation in Møller Scattering

- Atomic Parity Violation

- SM fit:
- Talk by S. Roth

## The “NuTeV Anomaly”

- The NuTeV             measurement:

- SM explanation(s) or Signal for New Physics?

- PRL 88, (2002)

## “'”        “=” 

- Long Event ' Charged Current Event
- Short Event ' Neutral Current Event

- “'”        “=”

## Theorist’s Observables

- EW radiative corrections
- Non-isoscalarity (Fe)
- NLO QCD and masses
- “**physical**” (“new”) effects:
- Higher twist
- Nuclear effects (A' 56)

- Paschos-Wolfenstein:
- Parton model
- Isoscalar target

-  Cross section ratios

**Notes:**
Check what’s in the SM fit!

## Is based on a LO MC model?

- The correlations in a simultaneous fit to         are essentially the same as in          .

- Is based on a LO MC model?

- Has to await an experimental reanalysis (NLO QCD, electroweak corrections, ...)

## Model-independency

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

## “Technical” (“standard”) Effects

- (NLO QCD & electroweak , very briefly)

## twist =2

-  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

## Digested results on “standard” QCD corrections:

-  NLO, TMC, and m corrections (& PDF uncertainties)
-  shift             by an amount that is of the order of the experimental accuracy for            (<1%).
-  shift             by an amount that is negligible compared to the experimental error attributed to                (<1%).
-  [Seeming discrepancies with analytic NLO estimates by Bogdan Dobrescu and Keith Ellis (hep-ph/0310154) have been understood.]
-  These results do not permit reliable conclusions on the signficance of the anomaly: *None of the above R’s is actually measured.* *Only **NuTeV** can come to a definitive answer.*
-  The results do indicate that *the corrections have to be considered in an experimental reanalysis.*

## Electroweak Corrections

- In the NuTeV measurement of the Weinberg angle in neutrino DIS electroweak corrections have been applied according to:

- Recently, these corrections have been reevaluated in Diener & Dittmaier & Hollik hep-ph/0310364.DDH analyze only     , not       .

- An investigation of electroweak corrections is limited by the same constraints as the investigation of NLO QCD corrections – that the “theory observables” do not really match with the NuTeV Monte Carlo fit.

## Digested results on electroweak corrections:

- Digested results on electroweak corrections:

- Different q ! q  factorization schemes:
- DDH:BD:

## “Physical” (“new”) results

- on the NuTeV anomaly
- and on parton structure

## Corrections to R-— for the moment:                               

-  Let’s neglect cuts / exp. Issues: ideal Paschos-Wolfenstein relation [and look for big effects that are unaffected by O(30%) detector effect corrections]
-  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:

## Theoretical expectations:S. Brodsky & B.-Q. Ma (1996)p !  K+ fluctuation

- Theoretical expectations:S. Brodsky & B.-Q. Ma (1996)p !  K+ fluctuation

- Phys. Lett. B381 (1996)

- More recent results:F.G. Cao & A.I. Signal (2003)A.W. Thomas & W. Melnitchouk & F.M. Steffens (2000)...
- And phenomenology from:V. Barone & C. Pascaud & F. Zomer (2000)

## 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

## Reminder:

- [S-] is not a local operator.
- (Higher, uneven moments are.)

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

- Add CCFR-NuTeV dimuon data
- Allow a non-symmetric strangeness sector:

- “CTEQ” Global Analysis

***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***.

## Charged Current neutrinoproduction of charm

- s

- c

- W+

- g

-  Data from CCFR/NuTeV (see D. Mason’s talk) determine the strange sea within a CTEQ global analysis.
-  NLO corrections 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).

- T. GottschalkM. Glűck, E. Reya, SKAivazis, Collins, Olness, Tung

- LO

- NLO

## 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

## The results on the last 3 slides suggest that the perturbative NLO effects will be small compared to the non-perturbative uncertainties in [S-].

## Typical fit results

- Vs. Bjorken x

## Lagrangian multiplier results for [S-]:

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

- NuTeV/CCFR data

- Other (less) sensitive data

## Further uncertainties:

-  LO $ NLO PDF analysis
-  charm mass
-  charm fragmentation and decay
- Are considered in our estimate for the range of [S-] (! conclusions).
- The general features of the LM parabola stay the same,  the minimum wanders within a range that is consistent with the width of the 2 vs. [S-] parabola.

## Future prospects for [S-]?

-  CC charm @ HERA: ditto
-  Lattice:The moment [S-] itself does not correspond to a local operator.Higher, uneven moments  (n=3,5,...)can be related to local operators and could presumably clarify the sign of the x! 1 behaviour, though not the magnitude of [S-].
-  Semi-Inclusive DIS (eRHIC)?

- Future prospects for [S-]?

- s

- g

- c

- W

- Baur, Halzen, Keller, Mangano, Riesselmann

## MRST analysis of isospin violations:

- uvn(x)=dvp(x)+ f(x)with s01 dx f(x)=0  finds  f(x) < 3-10 %  (8 x)

- Best fit value of  removes half of the discrepancy with the SM. Within a permissible variation of 2MRST
- -0.007 <  sin W < 0.007the full 3  are covered.

- Martin, Roberts, Stirling, Thorne

## Main conclusions of the CTEQ strangeness analysis

- However, the strong _interplay_ between the existing _experimental_ constraints and the global _theoretical_ constraints, particularly the # sum rule, places quite robust limits on acceptable values of the strangeness asymmetry momentum integral [S-].

## Implication on the NuTeV anomaly

- We estimate that -0.001 < [S-] < 0.004. A sizable negative [S-] is disfavored by both dimuon and other inclusive data.

- We have done a NLO calculation of the Paschos-Wolfenstein relation, using the new CTEQ PDFs.
- According to this calculation, a value of [S-] < 0.0017 (central value) can reduce the NuTeV anomaly from a 3  effect to 1.5 ; a value of [S-] ~ 0.003 – 0.004 would then reduce it to within 1 . The actual effect on the NuTeV measurement must await re-analysis by the experimental group, correcting current flaws, extending to NLO, as well as taking into account global constraints.
- The variation of [S-] underestimates the full uncertainties (isospin, higher twist, ...). Again, a definitive answer will have to come from NuTeV.
*The bounds of current uncertainty studies suggest that the dimuon data, the Weinberg angle measurement and other global data sets used in QCD parton structure analysis can all be consistent with the SM*.

## Status (theory) of the NuTeV anomaly

- The cross section ratios          that are closely related to the NuTeV extraction of the Weinberg angle have been thoroughly reevaluated by many authors under  several SM corrections:
-  pQCD corrections (NLO & masses)
-  electroweak corrections
-  nucleon parton structure uncertainties
-  The exact impact of the corrections on the extraction of sin2 W cannot be quantified in theory because of the involved Monte Carlo / detector effects in modeling “long” and “short” events in the NuTeV experiment. The closely related theoretical observables receive corrections that are of the order of the assigned experimental errors or bigger. Partonic uncertainties (strangeness asymmetry, ...) do even survive in the ideal Paschos-Wolfenstein ratio.
-  These effects have, so far, not been assigned a systematic error in the NuTeV  value of sin2 W. Claims that they cancel in the NuTeV (LO Monte Carlo) analysis procedure are a posteriori and have not been substantiated by an analysis that takes them into account ab initio. The corresponding programs are available from the authors. Before a careful re-assessment of all theoretical uncertainties (pQCD & non-pQCD & electroweak) the 3  discrepancy with the SM cannot be taken at face value.

## }

- An afterthought on S(emi)I(inclusive)DIS:
-  Current fragmentation into strange hadrons:is challenging for all the non-strange background fragmentation channels. A good knowledge of the corresponding FFs would be required.
-  An asymmetry between strange and anti-strange target fragmentation / fracture products might be more promising? Energy conservation:

- x

- z

- (1-x)

- 1

- M

## **** Backup Slides ****

## Paschos-Wolfenstein à la NuTeV

- NuTeV result:
- Statistics dominate uncertainty
- Standard model fit (LEPEWWG):
**0.2227 ********0.00037, a** 3 discrepancy

**K. McFarland @ Win03**

## Quality of fit to the neutrino dimuon data

- x ' 0.02 -- 0.3      Q2/GeV2 ' 2. -- 50.(Data points are color-coded according to x; for each x, they are ordered in y.)

## 5 representative fits obtained using LM method

## The Lagrange Multiplier Method in Global Analysis

- [S-]

## Slide 40

## Slide 41