Small angle (Low Q 2 ) GDH sum rule experiments

Transcription

1 Small angle (Low Q 2 ) GDH sum rule experiments A. Deur Jefferson Lab. Outline: Sum rules, GDH, Bjorken, spin polarizability sum rules; Usefulness and context; Measurements (published, being analyzed, to come); What we learn practically; Perspectives.

2 The Gerasimov-Drell-Hearn Sum Rule A sum rule is a rule (e.g. = ) that relates a sum (e.g. moment of structure functions) to a quantity characterizing the target. GDH sum rule: 16απ 2 Q g1 dx= 0 First spin structure function -2απ 2 2 M 2 Bjorken scaling variable anomalous magnetic moment α: fine structure constant Valid for any kind of target (nucleon, nuclei,...).

3 The Gerasimov-Drell-Hearn Sum Rule A sum rule is a rule (e.g. = ) that relates a sum (e.g. moment(s) of structure function) to a quantity characterizing the target. GDH sum rule: 16απ 2 Q g1 dx= 0-2απ 2 2 M 2 Originally derived for photo-absorption (Q 2 =0) by Gerasimov, Drell, Hearn and others. Generalized to Q 2 16απ >0 by Ji and Osborne: g1 dx= 2απ 2 1 Famous Bjorken sum rule is one aspect of generalized GDH sum rule: At large Q 2 : GDH(proton)-GDH(neutron) Q 2 Bjorken Sum Rule 1 6 s (ln (Q 2 )) π g 1 p- g 1n dx= g a ( )+... Q 2 0 spin-dep. DDVCS

4 Spin polarizabilities sum rules A sum rule is a rule (e.g. = ) that relates a sum (e.g. moment(s) of structure function) to a quantity characterizing the target. Sum rules with higher moments exist, e.g. spin polarizabilities sum rules: x 2 -weighting favors the large-x reactions (resonances, important at low Q 2 ).

5 Interest of the generalized GDH sum rule Sum rule valid at all Q 2 : We can measure g1 dx at different Q 2 and compute the right hand side of the sum rule using different technics: Hadronic degrees of freedoms Chiral perturbation theory ( pt) pqcd Partonic degrees of freedoms Q 2 Lattice QCD Study transition from hadronic to partonic description of strong interaction

6 i.e. study how effective degrees of freedom (hadrons) emerge from fundamental ones (partons). Hadrons (large time and distances) Partons (small time and distances)

7 This is a general phenomenon in nature: When complexity makes the basic degrees of freedom to cumbersome to use, effective ones are used. In addition to their practicality, effective descriptions provide a legitimate description of nature as long a the connection to the basic description is understood. Quantum Hadrodynamic d.o.f: hadrons Fundamental forces: electromagnetic gravitation weak strong force

8 General phenomenon in nature: Chemistry Biology Neurology Psychology Molecular physics d.o.f: atoms, Van der Waals force Atomic physics d.o.f: electrons, nuclei, EM field Nuclear physics d.o.f: hadrons Quantum Hadrodynamic d.o.f: hadrons Fundamental forces: electromagnetic gravitation weak Fundamental particles: quarks, electrons, neutrinos,... strong

9 Existing data Q 2 =0: Mainz-Bohn LEGS Intermediate Q 2 : Jlab Hall A, B & C Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2

10 Existing data INT[GDH(H)] Mainz+Bonn (ub) INT'[GDH(H)] = {Mainz+Bonn}+LEGS! 0 correction Q 2 =0: Mainz-Bohn LEGS Running GDH(p) integral (µb) Intermediate Q 2 : Jlab Hall A & B 1 10 E" (GeV) Proton data GDHp [combined Mainz+Bonn+LEGS] = 208 ±6(stat) ± 14(sys) µb 204 µb GDH(p) Large Q 2 : CERN, SLAC, DESY (Hermes) PRL 102, (09) Q 2

11 ! 1 p (no elastic) g1 dx on proton at intermediate Q Existing data JLab CLAS EG1a JLab CLAS EG1b SLAC E143 HERMES JLab RSS Resonance model GDH slope Q 2 =0: Mainz-Bohn LEGS Heavy Baryon "pt 0 Intermediate Q 2 : Jlab Hall A & B Relativistic "pt Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2 (GeV 2 ) Q 2

12 ! 1 n (no elastic) g1 dx on neutron at intermediate Q Existing data Relativistic "pt JLab Hall C RSS JLab Hall A E94010 HERMES JLab CLAS EG1b SLAC E143 JLab CLAS EG1a Resonance model GDH slope Heavy Baryon "pt Q 2 =0: Mainz-Bohn LEGS -0.1 Intermediate Q 2 : Jlab Hall A & B Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2 (GeV 2 ) Q 2

13 ! 1 p-n Bjorken Sum Existing data EG1b JLab Hall C RSS JLab Hall A E94010/CLAS EG1a CLAS EG1a HERMES E143 E155 pqcd leading twist 0.05 Resonance model Q 2 =0: Mainz-Bohn LEGS 0 Intermediate Q 2 : Jlab Hall A & B Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2 (GeV 2 ) Q 2

14 Spin Polarizabilities proton pt Existing data Phenomenological model pt Q 2 =0: Mainz-Bohn LEGS Intermediate Q 2 : Jlab Hall A & B Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2

15 Spin Polarizabilities proton Existing data neutron Q 2 =0: Mainz-Bohn LEGS Intermediate Q 2 : Jlab Hall A & B Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2

16 Spin Polarizabilities proton Existing data neutron Q 2 =0: Mainz-Bohn LEGS Intermediate Q 2 : Jlab Hall A & B Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2

17 GDH at low Q 2 in: Hall A: E97110, neutron( 3 He) Hall B: EG4, proton & neutron(d) Upcoming results bridge the gap: Q 2 =0: Mainz-Bohn LEGS Intermediate Q 2 : Jlab Hall A, B & C Large Q 2 : CERN, SLAC, DESY (Hermes) Q 2

18 Kinematic coverage Polarized 3 He target Polarized NH3 and ND3 targets E E & E01012 experiments EG1 & EG4 experiments

19 Kinematic coverage Experiment E (Spin-Duality) E E & E01012 experiments EG1 & EG4 experiments

20 Kinematic coverage Experiment E E E & E01012 experiments EG1 & EG4 experiments

21 Kinematic coverage Experiment E E E & E01012 experiments EG1 & EG4 experiments

22 Kinematic coverage Experiment Group EG1: NH 3 & ND 3 E E & E01012 experiments EG1 & EG4 experiments

23 Kinematic coverage Experiment Group EG4: NH 3 & ND 3 E E & E01012 experiments EG1 & EG4 experiments

24 Going to low Q 2 { low beam energy Low Q 2 : and/or forward angle Because we need integrals, our only choice is to work at forward angles. In Hall A: Septum magnets:

25 Going to low Q 2 :{ Low Q 2 : In Hall B: New Cerenkov detector: { low beam energy and/or forward angle Because we need integrals, our only choice is to work at forward angles.

26 Hall A (neutron): Preliminary results on g1 dx! 1 n (no elastic) JLab Hall C RSS JLab Hall A E94010 HERMES JLab CLAS EG1b SLAC E143 JLab CLAS EG1a Resonance model GDH slope Heavy Baryon "pt JLab E97110 (preliminary) Relativistic "pt Preliminary Q 2 (GeV 2 ) Remaining tasks: Finalized: Radiative corrections; Target polarimetry; Acceptance study. Analyze the lowest Q 2 points.

27 Hall A (neutron): Preliminary results on GDH sum

28 Hall A (neutron): Preliminary results on neutron spin polarizabilities

29 Hall B: Preliminary results on difference of polarized cross sections One step away from g1: ~g1 σ -σ. Proton, 2.3 GeV Data (black) normalized to elastic simulation (red) Very preliminary

30 Hall B: Preliminary results on difference of polarized cross sections Proton, 3.0 GeV Very preliminary Not full statistics; Normalized to elastic; No radiative corrections; No detector efficiency; Lowest Q 2 data not included (Scat. angle >10 o data); ND3 to be analyzed.

31 GDH: Study transition from hadronic to partonic description of strong force Examples of practical applications: Low Q 2 : extraction of pt series coefficients;

32 GDH: Study transition from hadronic to partonic description of strong force Examples of practical applications: Low Q 2 : extraction of pt series coefficients;! 1 p-n EG1b JLab Hall C RSS JLab Hall A E94010/CLAS EG1a CLAS EG1a HERMES E143 E155 pqcd leading twist Ex. Bjorken sum: Resonance model 0 Q 2 upper limit: 0.4±0.1 GeV Q 2 (GeV 2 )

33 GDH: Examples of practical applications: Low Q 2 : extraction of pt series coefficients; High Q 2 : extraction of series coefficients (higher twists);

34 GDH: Examples of practical applications: Low Q 2 : extraction of pt series coefficients; High Q 2 : extraction of series coefficients (higher twists); s, the strong coupling constant at large distances (>0.2 fm, i.e. low Q 2 ).! s (r) Lattice QCD AdS/QCD LF Holography AdS/QCD with! s,g1 extrapolation! s,g1 JLab+pQCD+sum rules r (fm) pqcd augmented AdS/QCD + extrapolated CSR! V from! s,g1 using CSR r (fm)

35 Summary/Perspective Two experiments in Hall A & B fill the last gap (low Q 2 ). Data are being analyzed: Hall A data (0.05<Q 2 <0.25 GeV 2 ) will be available in upcoming months; Data at 0.02<Q 2 <0.05 GeV 2 requiring longer analysis; Hall B preliminary data on moments should be available this year. One last missing piece: low Q 2 data on transversally polarized proton. Goal of the next Hall A experiment E (starts Nov ) Low Q 2 data are of high precision. Higher precision data at intermediate and large Q 2 desirable. Hall B EG1b (intermediate Q 2 ) and EG1dvcs (higher Q 2 ); Hall C Sane; 12 GeV, important for the large Q 2 part of this program: Convergence of sum rules; minimize low-x issue; increase Q 2 range; higher precision extraction of higher twists. Polarized HD target in Hall B: precision check of GDH sum rule (Q 2 =0) and may provide a transverse target for electroproduction (Q 2 >0).

36 GDH: Study transition from hadronic to partonic description of strong force Examples of practical applications: Low Q 2 : extraction of pt series coeficients;! 1 p-n EG1b JLab Hall C RSS JLab Hall A E94010/CLAS EG1a CLAS EG1a HERMES E143 E155 pqcd leading twist Ex. Bjorken sum: Resonance model Q 2 (GeV 2 )

37 GDH: Study transition from hadronic to partonic description of strong force Examples of practical applications: Low Q 2 : extraction of pt series coeficients; High Q 2 : extraction of series coeficients;! 1 p-n EG1b JLab Hall C RSS JLab Hall A E94010/CLAS EG1a CLAS EG1a HERMES E143 E155 pqcd leading twist Ex. Bjorken sum: Resonance model Q 2 (GeV 2 )

38 GDH: Study transition from hadronic to partonic description of strong force Examples of practical applications: Low Q 2 : extraction of pt series coeficients; High Q 2 : extraction of series coeficients; g 1 dx= twist twist Q twist-2 =2, Q 2{ Ex. Bjorken sum: g p-n 1 1 dx= g a ( ) Leading twist M 2 (twist 2) 4 = (a 2 + 4d 2 + 2f 2 ) Q 2 9 Leading twist Twist 3 Twist 4 (known from (known from high energy high energy data) data) 6 s (ln (Q 2 )) π { { { 6 Q 4 Higher twists

39 GDH: Study transition from hadronic to partonic description of strong force Examples of practical applications: Low Q 2 : extraction of pt series coeficients; High Q 2 : extraction of series coeficients; Bjorken sum twist coefs E94010+CLAS EG1a CLAS EG1b f 2 p-n JLab CLAS μ 6 /M 4 similar size as f 2 but opposite sign. Overall, higher twist contribution small at Q 2 =1 GeV 2. Bag model f 2 large (similar to leading twist at Q 2 =1 GeV 2 ) in accordance to intuition. Sum rule (2) Sum rule (1) Instanton (2002) Instanton (2006)