# Presentation: 494843

## 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.

## 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 (→PRL)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 (→EPJC)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, ...

## Outline:

-  The NuTeV anomaly: pQCD to O(<1%)  accuracy?
-  Observables:
-  Paschos-Wolfenstein relation
-  Cross section ratios
-  pQCD Corrections: NLO, masses
-  non-perturbative corrections (nucleon parton structure):
-  strangeness asymmetry
-  constraints and phenomenological extraction (dimuon events)
-  impact on the “anomaly”
-  (the rest of it: isospin violations, ...)
-  Conclusions and outlook

## NuTeV Anomaly

- NuTeV _*Anomaly*_

- SLAC E158:Parity Violation in Møller Scattering

- Atomic Parity Violation

## NuTeV Anomaly

-  Global EWWG fit

- (Gambino)

## 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

- “'”        “=”

## Paschos-Wolfenstein à la NuTeV

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

**K. McFarland @ Win03**

## Is based on a LO MC model?

- The correlations in a simultaneous fit to Rexp and Ranti-exp are essentially the same as in R-

- Is based on a LO MC model?

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

## 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!

## Model-independency

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

## “Technical” (“standard”) Effects

- (briefly)

## Calculable corrections: NLO and O(1GeV) masses

- Q/GeV

- [s, (s / 2 )]

- 1GeV2 / Q2

- XBJ: valence region

## OPE for DIS in a nutshell(twist =2)

- Target mass corrections

- (Nuclear) target dependence

- NLO corrections&charm production

- OPE for DIS in a nutshell(twist =2)

## 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

## Remarks on the evaluation of

- s dE dx dy d1,2,3
- i convolution variables from NLO and TMC corrections
-  6 dimensional MC integral (VEGAS)
-  can be reduced to 1,2 by moment technique
-  5 dimensions to integrate at high numerical precision
- In the approximation of (i) neglecting DGLAP evolution (ii) MW,Z ! 1 limit of the boson propagator (iii) overlooking the hadronic energy cut this boils down to second moments of PDFss01 dx x q(x)

- (Davidson et al., Moch & McFarland, Dobrescu & Ellis)

## An unexpected correction:

-  Lepton mass terms (e.g. structure function F5) are suppressed byd  / (m2/S) F5
-  But F5 measures the quark number density q(x),not momentum density xq(x)
-  Consider the academic limit E ! 1Then typically x' MW,Z2/S
-  So the F5 term is “only” suppressed by  (m2/S) (S/ MW,Z2) = (m2/MW,Z2)That is small but constant
-  Again, this is an academic limit. But the lesson is true that lepton mass terms are “not quite as small as one would think”.
-  The shift in             that is caused by the m2/S terms, is of the order of the experimental precision.

## Digested results on “standard” corrections:

-  NLO, TMC, and m corrections (& PDF uncertainties)
-  have insignificant impact on R- and R
-  have significant impact (of the order of the experimental error) on Ranti-
-  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 (which is ongoing).

## “Physical” (“new”) results

- on the NuTeV anomaly
- and on parton structure

## SM:   Corrections to the P-W Relation Due to Strangeness Asymmetry, Isospin Violation, ... etc.

- CCFR-NuTeV: PR D65, 111103 (2002)

## 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:

## Reminder:

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

## 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

## Paolo Gambino @ Lepton Photon 2003:

- Kretzer, Olness, Pumplin, Stump,Tung et al.

## 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)

## DGLAP

## NuTeV

*NuTeV*

- ....

## ..... experimental input continued

## Slide 30

## “CTEQ” Global Analysis

- Same ingredients as “CTEQ6” analysis (preceding 4 slides)
- Add CCFR-NuTeV dimuon data (next slide)
- 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 comparing theory with data.

## Portrait of charm (produced in an active iron target)

- Portrait of charm (produced in an active iron target)

## 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).

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

## 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-].(NLO results are underway.)

## 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.)

## Typical fit results

- Vs. Bjorken x

## 5 representative fits obtained using LM method

## The Lagrange Multiplier Method in Global Analysis

- [S-]

## Lagrangian multiplier results for [S-]:

- Lagrangian multiplier results for [S-]:

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

- § 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 around by about 0.15%.

## What about different results by  CCFR-NuTeV? And the BPZ analysis (of inclusive X-secs)?

- BPZ:  large-x peak of s-(x) not natural; 2 oscillations not supported by theoretical expectations

- Under reconsideration by the collaboration

## 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)s01 dx f(x)=0            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 conclusins 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 P-W (see “standard” part of the talk), 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*.

- The NuTeV result has triggered a lot of investigatons of “small” effects in parton structure.