Calculations of γz corrections-box diagrams. Carl E. Carlson William and Mary Intense Electron Beams Workshop June17-19, 2015, Cornell

Transcription

1 Calculations of γz corrections-box diagrams 1 Carl E. Carlson William and Mary Intense Electron Beams Worksho June17-19, 2015, Cornell

2 Toics PV in e scattering and QWeak A startling (at least in 2009) calculation It may be settled But we would like to be sure How PVDIS can hel 2

3 relevant for today Parity violating (PV) electron scattering Usually, olarized electron, unolarized target Parity violation exists in SM, from (small at low energy) Z-exchange e g A e e Usually reort (R,L = helicity of electron) g V Z A PV = R L R + L 3

4 QWeak---from elastic e scatt. At LO, asymmetry comes from interference between hoton exchange and Z-boson exchange, e e g A e g V Z For Q 2 ->0,! LO only, A PV = G F 4 2 Q2 Q P W Q,LO W = 1 4 sin2 W For later, JLab QWeak runs at E elec =1.165 GeV, Q 2 = GeV 2 Mainz (P2 at MESA) lans for E elec = 150 MeV 4

5 QWeak Interesting because of HO corrections, e.g., e e Z Z + W Z W + f Z _ f + W W 1 4 sin 2 W "1" "1" Changes balance between 1 and 4sin 2 W. 1 4 sin 2 W 1 4 (Q 2 ) sin 2 W 1 4 sin 2 W(Q 2 ) Thus, sin 2 W runs or evolves with Q 2. If SM comlete---article content and interactions known--- evolution can be recisely calculated. 5

6 SM sin 2 θ W evolution Each exeriment is differently sensitive to otential new hysics 6S 7S 133 Cs atomic transition Parity violating moller scattering neutrino dee-inelastic scattering cross-sections (controversial hadronic corrections not included) Standard Model electroweak fit with uncertainty Colliders Mark Dalton First direct measurement of roton weak charge DNP, Fall If SM correct, result from QWeak will lie on curve. If not... Precision needed! 6 Beringer et al. (PDG), Phys. Rev. D86, (2012)

7 and still more data will come From PDG, or from Erler, , with future hoes sin 2 θ W (μ) SM ublished ongoing roosed Q W Q W(Ra) KVI (Cs) Boulder Mainz Q Weak Z f γ JLab SLAC E158 Q W (e) MOLLER JLab Q Weak JLab PVDIS 6 GeV PVDIS NuTeV ν-dis screening Z W γ JLab SOLID LEP 1 SLC anti-screening Tevatron CMS μ [GeV] W 7

8 Reort: QWeak has data 4% of total data (full(qweak(dataset( exected(recision) Q W ()* (using(only(4%(of( Qweak(dataset) *(Uses(electroweak(radia<ve(correc<ons(from(Erler,(Kurylov,(RamseyCMusolf,(PRD(68,(016006((2003).( 8 from Mark Dalton, APS/DNP meeting, Fall 2012 Publ.: PRL 111 (2013) 14,

9 But there are other corrections Correction to 1 4 sin 2 W(0) Troublesome box Q W = (1 + + e) Q,LO W + e + WW + ZZ + Re Z Corrections to the Z- boson and hoton vertices Well understood box corrections 9

10 γ-z Box k k 1 k k k 1 k q q q q (Dashed line for Z.) Only one heavy roagator. Low momenta dominate loo. Both vector and axial Z-roton coulings contribute. Abbreviated γz V and γz A. 10

11 Now starts a story Big note: γz V (E) is odd in E; γz A is even in E (electron beam en.) (Crossing symmetry argument.) Old days (< 2009), calculated basic box at threshold E=0. Thought actual E low enough to use this result. k k 1 k Z (+ reverse and crosses) Still old days: Dumed γz V. Defacto just γz A. (Will hardly talk about it today.) 11

12 γ-z Box Gorchtein and Horowitz (PRL 102, (2009)) had insight to calculate the amlitude disersively DR calculate whole amlitude form imaginary art. Imaginary art comes when intermediate states on shell. Like inelastic amlitude squared, i.e., for DIS. Squares given and measured as structure functions F i. Only roblem: F i γγ measured, not the interference term F i γz. 12

13 Maybe a roblem Gorchtein-Horowitz first estimate of γz V (the thing that was suosed to be zero) was twice the size of the rojected exerimental uncertainty of the Q Weak exeriment.! Peole got busy. 13

14 Vector box lots today Hall et al. PRD 88, (2013) Carlson and Rislow PRD 83, (2011) Gorchtein et al. PRC 84, (2011) Central values close Differences come from the treatment of the structure functions BTW, we combined errors directly, Hall et al. in quadrature. Could reeat: Re V Z(E =1.165 GeV) (5.6 ± 0.36) 10 3 (5.7 ± 0.52) 10 3 (5.4 ± 2.0)

15 Why not be hay? Where from came results? Resonance contributions: basically from fit of Bosted and Christy for F i γγ modified using NR quark model (Rislow and me) Isosin rotations and neutron data (GHRM, Hall et al.), getting /n ratio from PDG, finessing Q 2 deendence As above, getting resonant amlitudes and Q 2 deendence from MAID fits (Rislow and me, later attemt) 15

16 Data lots and functions The Bosted-Christy fits are good. Samle: 2nd lot shows difference F i γγ to F i γz F 2 HQ 2,WL Q 2 = GeV W HGeVL F2HQ 2,WL 0.4 Q 2 = GeV gg F 2 gz F W HGeVL 16

17 Basic relation Note on isosin rotations 2 R + J Z V µ =(1 4 sin 2 W) R + J µ R 0 J µ n R + s µ s Neglect contribution of strange quark (A4, G0, HAPPEX) Need two things: Proton electromagnetic matrix elements GHRM get them from identifiable resonance terms in Christy-Bosted fit (as we did also) and then need neutron matrix elements. GHRM obtain matrix elements at Q 2 = 0 from PDG, form n/ ratios, and then use above relation. Omitted Q 2 deendence in n/ ratios. Can also get resonance electroroduction amlitudes from MAID. Above is for resonances. Background, both under (in) resonance region and above resonance region still to be discussed. 17

18 Note on non-resonant contributions The difficult region is low Q 2 and high W We took Christy-Bosted background, got guidance from scaling region to argue that for the γz version was between 2/3 and 3/3 of the γγ values. GHRM took two γγ fits to HERA and ZEUS data (much higher energies) and extraolated to the suort region for the resent case. Difference between the two extraolations gave the bulk of their uncertainty. 18

19 Think of something! Although results similar, they come after doing some integrals, and there are regions where the integrands are fairly different. The interference structure functions F i γz actually are measurable. Use Parity Violating Dee Inelastic Scattering (PVDIS). 19

20 PVDIS, es. in res. reg. + Z PVDIS asymmetry directly deends on F i γz A PVDIS = g e G F Q 2 A 2 2 xy 2 F Z y x 2 y 2 M 2 Q 2 xy 2 F y F Z 2 + ge V g e A y x 2 y 2 M 2 Q 2 F 2 y 2 2 xf Z 3 x = Q 2 /2m ν ; y = ν/e ; g e A = -½ ; g e V = -½+2sin 2 θ W with unlimited data can obtain all F γz i (ν,q 2 ) with some data, can check other models for γz V, resonance region dominates integrals 20

21 A PVDIS = 3G F Q for context scaling region write F i γz in terms of quark distribution functions, 2C 1u (u A +ū A ) C 1d (d A + d A + s A + s A )+Y 2C 2u (u A ū A ) C 2d (d A da ) Y (y) = 4(u A +ū A )+d A + d A + s A + s A 1 (1 y)2 1+(1 y) 2, C 1q =2g e Ag q V, C 2q =2g e V g q A Scaling region is x 1, y 1, Y 1, antiquark and strange distributions 0, and for deuteron, u A = d A, A PVDIS = 3G F Q C 1u C 1d +2C 2u C 2d 5 The C 1 s are better known, can test BSM for C 2 s. 21

22 PVDIS in res. reg. APVDIS g A e G FQ ΠΑ For sarser data case, here are redictions from existing models, E 6 GeV Q GeV 2 Black CB Red Mod I Blue Mod II Green MAID W GeV 22 this is roton target CB = CQM modified Christy-Bosted F 1,2 γγ fit Model I, II = GHRM based results MAID from isosin rotated MAID & n EM fits Vertical dashed line = 6 GeV PVDIS ext. oint JLab ext has some ublic data in scaling region

23 deuteron redictions and data for the deuteron, there is PVDIS data in the resonance region: Wang et al., PRL 111, (2013) Calc: Rislow and me, PRD 85, (2012), Matsui et al. (2005); Gorchtein et al. (2011); Hall et al (2013). Hall, Blunden, Melnitchouk, Thomas, Young, PRD88, 0 (m)/ Q 2 (GeV -2 ) d A PVDIS E = 6 GeV Q 2 = 1.1 GeV 2 Black=CQM Red=GHRM Green=MAID W (GeV) W eff (GeV)

24 general statements regarding data also want data on roton more recise useful: lower Q 2 (few tenths GeV 2 ) and high W. This is where the background disagreements lie. 24

25 Summary The world is saved maybe regarding the γz corr. to Q Weak. I.e., γz V now calculated. About (8.1±1.4)% of Q W at E elec =1.165 GeV. Proortional to E elec. Not discussed here: γz A also now calculated w/o guesswork certain log terms About (6.3±0.6%) of Q W at E elec threshold. Small deendence on E elec. Might still like to imrove. For goal of 1% or better measurement of QWeak (Mesa), energy is about 1/6 of JLab exeriment, and corrections and error in γz V scale with energy. PVDIS can hel shrink uncertainty limits. 25

26 Beyond the end 26

27 Cuss and kinks A smoother view, albeit from year 2000 Czarnecki & Marciano 27

28 Comments on γz A For some of integral, F 3 γz is in resonance region. No e.m. analog (arity violating). Get by fits to neutrino resonance region data (Lalakulich et al., 06) but there is no data or by quark modeled modifications of e.m. case. Published results (BMT) are with first. Rislow and I have done the second. Not wildly different overall for γz A although noticeably different for resonance art alone. Adds to uncertainty. 28