1. Stefan Kretzer Brookhaven National Laboratory & RIKEN-BNL
Neutrino-Production of Charm and the Strangeness Asymmetry of the Nucleon
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.
1/2/2019

2. Comprehensive Review Article:
Based on:
“The parton structure of the Nucleon and Precison Measurement of the Weinberg Angle in Neutrino Scattering” BNL-NT-03-16= RBRC-328=hep-ph/ 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/ with CTEQ
“Target Mass Corrections to Electroweak Structure Functions and Perturbative Neutrino Cross Sections” PRD 69, (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, …

3. Charged Current neutrinoproduction of charm:W+ c g s LO
NLO
Probes the strangeness sector of the nucleon sea.
Is a well understood process at NLO.

4. Strangeness Structure of the Nucleon: Dimuon Production in Scattering
P. Spentzouris, next talk n, n -
Process that provides the most direct (LO) constraints on the strangeness sector of the parton structure of the nucleon.
# of events:
(d is Cabibbo suppressed)
Modeling needed for comparing theory with data.

5. CC charm: LO/NLO stability
PDF ­
hard scattering
NLO: T. Gottschalk
M. Glűck, E. Reya, SK
ACOT

6. CC charm: LO/NLO stability
PDF ­
hard scattering ­
fragmentation
NLO: M. Glűck, E. Reya, SK

7. Differential production cross section and acceptance
D. Mason, F. Olness, SK
Acceptance vs. rapidity
d  z
rapidity
Acceptance vs. z

8. But there is more to it …

9. NuTeV Anomaly Atomic Parity Violation
SLAC E158: Parity Violation in Møller Scattering

10. The “NuTeV Anomaly” The NuTeV measurement:
PRL 88, (2002)
It was inspired by, and is related (but not identical) to, the Paschos-Wolfenstein (1973) Ratio: (isoscalar target, …)
NuTeV
LEP EWWG
a 3.1  discrepancy

11. 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

12. Then:
is not protected by any symmetry:

13. Phys. Lett. B381 (1996)
Theoretical expectations: S. Brodsky & B.-Q. Ma (1996) p !  K+ fluctuation
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)

14. 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

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

16. “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=Q0)
Where x0 is to be determined by the condition [s-]=0.
Sum rule and positivity are then satisfied.

17. Charged Current neutrinoproduction of charm
T. Gottschalk M. Glűck, E. Reya, SK Aivazis, Collins, Olness, Tung W+ c g s LO
NLO
Data from CCFR/NuTeV (see P. Spentzouris’ 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).

18. Detailed investigation of NLO corrections suggest that the perturbative higher order effects will be small compared to the non-perturbative uncertainties in [S-].

19. Quality of fit to the neutrino dimuon data
x ' Q2/GeV2 ' (Data points are color-coded according to x; for each x, they are ordered in y.)

20. Typical fit results
Vs. Bjorken x
positive [S-]

21. Lagrangian multiplier results for [S-]:
NuTeV/CCFR data
Other (less) sensitive data
Rule of thumb:
The 3  anomaly corresponds to
[S-] £ 100 ' +0.5

22. 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.

23. Future prospects for [S-]?
W and associated charm (jet) production: Tevatron, RHIC, LHC But statistics (efficiency driven) and high scale are unlikely to permit to access a small asymmetry.
CC 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)? g c s W
Baur, Halzen, Keller, Mangano, Riesselmann

24. Main conclusions of the CTEQ strangeness analysis
By including neutrino-production of charm and by fully exploring the allowed parameter space in a global QCD analysis, we now have a good general picture of the status of the strangeness sector of nucleon structure.
Experimental constraints on are still relatively weak. There are large uncertainties in any specific region of x, as seen from the wide range spanned by the fits. Because of other sources of uncertainties, the band of possible s-(x) values is considerably wider.
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-].

25. Implication on the NuTeV anomaly
We estimate that < [S-] < A sizable negative [S-] is disfavored by both dimuon and other inclusive data.
Implication on the NuTeV anomaly
We have done a NLO calculation of the Paschos-Wolfenstein relation, using the new CTEQ PDFs.
According to this calculation, a value of [S-] < (central value) can reduce the NuTeV anomaly from a 3 s effect to 1.5 s; a value of [S-] ~ – would then reduce it to within 1 s. 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.

26. **** Backup Slides ****

27. 5 representative fits obtained using LM method
Normalized c2 values
Processes having some sensitivity to s-
Processes having no sensitivity to s- (majority)

28. The Lagrange Multiplier Method in Global Analysis
Neutrino dimuon prod. data sets
Other data sets
[S-]
Constrained fits using modified c2 function:
and vary l over an appropriate range.