1. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 1 PHYS 5326 – Lecture #4 Wednesday, Jan. 31, 2007 Dr. Jae Yu 1.QCD Evolution of PDF 2.Measurement of Sin 2  W 3.Formalism of Sin 2  W in -N DIS 4.Improvements in Sin 2  W 5.Interpretation of Sin 2  W and Its Link to Higgs

2. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 2 Factorization Non-perturbative, infra-red part    kk’      W + (W - ) p ,   } E Had P q= k-k’ q, (  q) xPxP Partonic hard scatter  =f*  p f pp

3. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 3 DGLAP QCD Evolution Equations The evolution equations by D okshitzer- G ribov- L ipatov- A ltarelli- P arisi provide mechanism to evolve PDF’s to any kinematic regime or momentum scale P ij (x/y): Splitting function which describes the probability for a parton i with momentum y get resolved as a parton j with momentum x<y

4. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 4 Feynman Diagrams for Parton Splitting LO: O(  s ) NLO: O(  s 2 )

5. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 5 Standard Model unifies Weak and EM to SU(2)xU(1) gauge theory –Weak neutral current interaction –Measured physical parameters related to mixing parameters for the couplings Neutrinos in this picture are unique because they only interact through left-handed weak interactions  Probe weak sector only –Less complication in some measurements, such as proton structure Electroweak Theory

6. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 6 sin 2  W and -N scattering In the electroweak sector of the Standard Model, it is not known a priori what the mixture of electrically neutral electromagnetic and weak mediator is  This fractional mixture is given by the mixing angle Within the on-shell renormalization scheme, sin 2  W is: Provides independent measurement of M W & information to pin down M Higgs via higher order loop corrections, in comparable uncertainty to direct measurements Measures light quark couplings  Sensitive to other types (anomalous) of couplings In other words, sensitive to physics beyond SM  New vector bosons, compositeness, -oscillations, etc

7. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 7 EW Higher Order Corrections LO GSW requires three parameters: , G F and M Z Higher order corrections bring in dependences to two additional parameters: M Top and M Higgs Z Z t tt qq  W W t qq’ bb WW WW WW WW WW WW WW WW

8. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 8 How is sin 2  W measured? Cross section ratios between NC and CC proportional to sin 2  W Llewellyn Smith Formula:

9. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 9 The Original Experiment Conventional neutrino beam from  /k decays Focus all signs of  /k for neutrinos and antineutrinos Only  in the beam (NC events are mixed) Very small cross section  Heavy neutrino target  e are the killers (CC events look the same as NC events)

10. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 10 Charged Current Events Neutral Current Events How Can Events be Separated? x-view y-view x-view y-view Nothing is coming in!!!   Nothing is going out!!! Event Length

11. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 11 Experimental Variable Define an Experimental Length variable  Distinguishes CC from NC experimentally in statistical manner to theoretical prediction of R Compare experimentally measured ratio

12. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 12 Past Experimental Results The yellow band represents a correlated uncertainty!!

13. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 13 Improvements on Measurements Asses the uncertainties from previous measurements Determine what the sources of largest theoretical and experimental uncertainties are Provide new methods to reduce large uncertainties

14. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 14 sin 2  W Theoretical Uncertainty Significant correlated error from CC production of charm quark (m c ) modeled by slow rescaling mechanism Suggestion by Paschos-Wolfenstein by separating  and  beams:  Reduce charm CC production error by subtracting sea quark contributions  Only valence u, d, and s contributes while sea quark contributions cancel out  Massive quark production through Cabbio suppressed d v quarks only

15. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 15 Improving Experimental Uncertainties Electron neutrinos, e, in the beam fakes NC events from CC interactions –If the production cross section is well known, the effect will be smaller but since majority come from neutral K (K L ) whose x-sec is known only to 20%, this is a source of large experimental uncertainty Need to come up with a beamline that separates neutrinos from anti-neutrinos

16. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 16 Event Contamination and Backgrounds SHORT   CC’s (20%  )  exit and rangeout SHORT e CC’s (5%) e N  eX Cosmic Rays (0.9%) LONG   NC’s (0.7%) hadron shower punch-through effects Hard  Brem(0.2%) Deep  events

17. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 17 Sources of experimental uncertainties kept small, through modeling using and TB data Other Detector Effects Effect Size(  sin 2  W ) Tools Z vert 0.001/inch  +  - events X vert & Y vert 0.001MC Counter Noise0.00035 TB  ’s Counter Efficiency0.0002 events Counter active area0.0025/inch CC, TB Hadron shower length0.0015/cntr TB  ’s and k’s Energy scale0.001/1%TB Muon Energy Deposit0.004 CC

18. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 18 Use well known processes (Ke3: ) Shower Shape Analysis can provide direct measurement e events, though less precise Measurements of e Flux  e from very short events (E >180 GeV) Precise measurement of e flux in the tail region of flux  ~35% more  e in  than predicted Had to require (E had <180 GeV) due to ADC saturation Results in sin 2  w shifts by +0.002 Weighted average used for e   R exp ~0.0005

19. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 19 MC to Relate R exp to R  and sin 2  W Parton Distribution Model –Correct for details of PDF model  Used CCFR data for PDF –Model cross over from short  CC events Neutrino Fluxes  , e,  ,  e in the two running modes  e CC events always look short Shower length modeling –Correct for short events that look long Detector response vs energy, position, and time –Continuous testbeam running minimizes systematics

20. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 20 Thanks to the separate beam  Measure R ’s separately Use MC to simultaneously fit and to sin 2  W and m c, and sin 2  W and  sin 2  W Fit to R exp and R  exp Two parameter fit for sin 2  W and    yields Syst. Error dominated since we cannot take advantage of sea quark cancellation R Sensitive to sin 2  W while R  isn’t, so R  is used to extract sin 2  W and R  to control systematics Single parameter fit, using SM values for EW parameters (   =1)

21. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 21 NuTeV sin 2  W Uncertainties 1-Loop Electroweak Radiative Corrections based on Bardin, Dokuchaeva JINR-E2-86-2 60 (1986 ) 0.00032RLRL 0.00022 0.08  M W (GeV/c 2 ) 0.00162Total Systematic Uncertainty 0.00064Total Physics Model Systmatics 0.00011RadiativeCorrection 0.00005Non-isoscalar target 0.00014Higher Twist 0.00047CC Charm production, sea quarks 0.00063Total Experimental Systematics 0.00018Energy Measurements 0.00046Event Length 0.00039 e flux 0.00135Statistical  sin 2  W Source of Uncertainty Dominant uncertainty

22. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 22 NuTeV vs CCFR Uncertainty Comparisons  Technique worked!  Beamline worked!

23. Wednesday, Jan. 31, 2007PHYS 5326, Spring 2007 Jae Yu 23 Comparison of New sin 2  W Comparable precision but value smaller than other measurements