Calculations of γz corrections

Transcription

1 Calculations of γz corrections Carl E. Carlson William and Mary γz box(ing) workshop, Dec , 2013, JLab

2 Our relevant papers Contributions from γz box diagrams to parity violating elastic ep scattering, Rislow & Carlson, Phys.Rev. D83 (2011) Resonance Region Structure Functions and Parity Violating Deep Inelastic Scattering, Carlson & Rislow, Phys.Rev. D85 (2012) Modification of electromagnetic structure functions for the γz-box diagram, Rislow & Carlson, Phys.Rev. D88 (2013)

3 Weak Charge of the Proton e p QwP extracted from parity-violating, ep scattering: A PV = R L R + L Lowest order diagrams e g A and result: e Z p g V p A PV = Lowest order definition of QwP : G F 4 p 2 Q2 Q p W Q p,lo W = 4ge Ag p V =1 4 sin2 W 3

4 One-loop result e Z Z Z W W f + + p p p p J Z J Z J e Z W W Z _ f + + W W p J J J 3 =J Z +2 sin 2 J W Q p W =(1+ + e) 1 4 sin 2 W + 0 e + WW + ZZ + Z 4

5 Running Weinberg Angle (Czarnecki and Marciano) Only Pinched Part Degrassi and Sirlin, PRD 46, 3104 (1992) 5

6 Running Weinberg Angle Czarnecki and Marciano Running Int. J. Mod. Phys. A15, 2365 (2000) Erler and Langacker Particle Data Group (2012) 6

7 Weak Charge Extrapolation Weak Charge Extrapolation (PRL 99, (2007)) In O p A/A 0! Q " Q 2 B( Q 2, =0) W #! This Experiment!$$$$HAPPEX "$$$SAMPLE $$$PVA4 %$$$G0 SM (prediction) #!! 0.0 " Q [GeV] 7 Data Rotated to the Forward-Angle Limit!! C1u + C1d FIG. 3. The co constants C 1u The more horiz 7 straint on the more vertical (b isting Q 2 < 0.6

8 γz Box Definition: For WW or ZZ boxes, two heavy propagators enough to ensure contributing momenta are big. Calculate w/pqcd. Here, one heavy propagator not enough. Low momenta in loop, perturbative calculation unreliable.: 8

9 γz Box Gorchtein and Horowitz (PRL 102, (2009)) had insight to calculate the amplitude dispersively Optical theorem, 9

10 γz Box equations Imaginary part Dispersion relations, 10

11 γz Box equations Imaginary part Dispersion relations, Structure Functions must be modeled. Labels proton current. 11

12 Vector Boxes

13 Vector box plots Hall et al. PRD 88, (2013) Carlson and Rislow PRD 83, (2011) Gorchtein et al. PRC 84, (2011) Differences come from the treatment of the structure functions 13

14 Us We divided up the energy regions and modified the structure functions. functions. W (GeV) 2.5 Capella et al. (Phys. Lett. B 337, 358 (1994)) (modified) Christy and Bosted (PRC 81, (2010)) (modified) CTEQ (PRD 82, (2010)) 14 8 Q 2 (GeV) 2

15 Evaluation in scaling region Calculated directly using PDFs We use CTEQ Alternative Hall et al. use ABM11 (PRD 86, (2012)) 15

16 Evaluation in resonance region All later calculations modify Christy-Bosted electromagnetic fits. (May also use MAID.) CB fit have 7 resonances and a smooth background Resonances modified by corrective ratio: ; 16

17 Vector Cres Definition of structure functions: Cres in terms of helicity amplitudes: 17

18 Vector Cres We constructed helicity amplitudes using SU(6) wave functions: Phenomenological constraints used to fit A and B: = = -1 for Q 2 = 0 +1 for high Q 2 18

19 Cres for D13(1520) SU(6) wave function for proton: Helicity amplitudes Spatial Flavor Spin 19

20 Cres for D13(1520) A and B relations for D13(1520): Λ found by comparing amplitudes to MAID: 20

21 Our vector Cres 21

22 R & C Background Correction In limit where all light quarks (u, d, s) are equally likely: In valence quark limit (d and 2 u s): We took their average as the correction: 22

23 Alternative resonance analysis Isospin rotate neutron amplitudes: Rewrite neutral current 23

24 C res calculated using PDG photoproduction data GHRM used PDG data at Q2 = 0, dropped relative Q 2 dependence. Can also use MAID to obtain neutron amplitudes, at all Q2. 24

25 Cres Effect on γz Box res Solid: Constituent Quark Model of Carlson and Rislow Blue: PDG (used by Gorchtein et al. and Hall et al.) Red: MAID (Eur.Phys.J.ST 198, 141 (2011)) Green: MAID without Roper Resonance 25

26 Axial Box Analyses

27 Axial Box Calculations Blunden et al. PRL 107, (2011) Carlson and Rislow PRD 88, (2013) 27

28 Comments on γz A The γz V just discussed compares to γz quoted on old days. Pure coincidence. This was just for γz A. γz A can be calculated anew. With the DR treatment there are no logs to guess arguments of. Notes A Z (E) = 2 E >0 E de E 2 E 2 Im A Z (E ) Not zero at threshold The E makes high energies important Most of result comes from scaling region for F3 γ Z, where it can be obtained reliably 28

29 Current Axial Box Results Blunden et al. PRL 107, (2011) Carlson and Rislow PRD 88, (2013) 29

30 Same split of regions functions. W (GeV) CTEQ (modified) CTEQ (PRD 82, (2010)) 2 Christy and Bosted (PRC 81, (2010)) (modified) 8 Q 2 (GeV) 2 30

31 Evaluation of Axial Structure Function Scaling region High W, low Q 2, CTEQ 31

32 Resonance Region: Blunden et al. use Lalakulich et al. (PRD74,014009) for F3 Fewer resonances than the Christy Bosted fit: fits for D13(1520), P11(1440), P33(1232), and S11(1535) We continue modifying the Christy Bosted fit. 32

33 Rislow & Carlson Axial Cres 33

34 R & C Background Correction Smooth background Average 5/3 34

35 Axial Box Contributions Blunden et al. PRL 107, (2011) Carlson and Rislow PRD 88, (2013) (Overall results already given) 35

36 Summary The world is saved (almost), regarding the γz corr. to Q Weak. I.e., γz V now calculated. About (8.1±1.4)% of Q W p at E elec =1.165 GeV. Proportional to E elec. γz A also now calculated w/o guesswork on logs About (6.3±0.6%) of Q W p at E elec threshold. Small dependence on E elec. For goal of 1% or better measurement of Q Weak (P2 at Mesa), energy is about 1/6 of JLab experiment, and corrections and error in γz V scale with energy. Would like to improve γz A but believe this is very manageable 36

37 Post summary: APV With one-photon exchange, A Born PV where where A Born A Born M R L G FQ 2 p R L 4 ABorn E ABorn A 2 G Ep 2 G Mp 2 E 2g e A GZ Ep G Ep ; ABorn M q 2g e V A Born A G Z A G Mp 2ge A GZ Mp G Mp 37

38 May also have 2-photon exchange whence, A PV G FQ 2 p 4 2 A E A M A A A 0 M A0 A p jg 0 Ep j2 jg 0 Mp j G Mp Re G0 Ap where A 0 A 2ge V 1 GZ A Re G0 Ap q A 0 M 2ge A G Z M Re G0 Ap : 38

39 plot I.e., there are effective modifications to electromagnetic GE and GM, plus a new e.m. form factor, here called GA Calculated (estimated) mid-last-decade, 1.03 A P V ( 1 γ+2γ) / A P V ( 1γ ) Q 2 = 2 GeV 2 Q 2 = 5 GeV 2 Q 2 = 9 GeV ε Reference: Afanasev and me, PRL 94, (2005). 39