Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction
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Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction. E00-108 experiment in Hall C, 10 (!) days of beam time PAC-30 Proposal E12-06-104, approved for 40 days with A- per PAC-36 PAC-34 Proposal PR12-09-017, conditionally approved

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Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction

E00-108 experiment in Hall C, 10 (!) days of beam time

PAC-30 Proposal E12-06-104, approved for 40 days with A- per PAC-36

PAC-34 Proposal PR12-09-017, conditionally approved

Rolf Ent, Hall C Summer Workshop, August 27, 2010

  • Semi-Inclusive Deep Inelastic Scattering & the Parton Model

  • E00-108 Results: The Onset of the Parton Model

  • General Pion Electro-production Formalism

    • - Bridging the Formalism and the High-Energy “Factorized” Viewpoint

  • 12 GeV Examples: R in SIDIS & transverse momentum dependence


  • Sidis flavor decomposition
    SIDIS – Flavor Decomposition Semi-Inclusive Pion Electroproduction

    DIS probes only the sum of quarks and anti-quarks  requires assumptions on the role of sea quarks

    Solution: Detect a final state hadron in addition to scattered electron

    SIDIS

     Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

    (M,0)

    (e,e’)

    Mx2 = W2 = M2 + Q2 (1/x – 1)

    (For Mm small, pm collinear with g, and Q2/n2 << 1)

    (e,e’m)

    Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z)

    z

    z = Em/n

    Mx2 = W’2


    Sidis flavor decomposition1
    SIDIS – Flavor Decomposition Semi-Inclusive Pion Electroproduction

    DIS probes only the sum of quarks and anti-quarks  requires assumptions on the role of sea quarks

    Solution: Detect a final state hadron in addition to scattered electron

    SIDIS

     Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

    Measure inclusive (e,e’) at same time as (e,e’h)

    • Leading-Order (LO) QCD

    • after integration over pT

    • and f

    • NLO: gluon radiation mixes

    • x and z dependences

    : parton distribution function

    : fragmentation function


    How Can We Verify Factorization? Semi-Inclusive Pion Electroproduction

    • Neglect sea quarks and assume no pt dependence to parton distribution functions

    • Fragmentation function dependence drops out in Leading Order

    [sp(p+) + sp(p-)]/[sd(p+) + sd(p-)]

    = [4u(x) + d(x)]/[5(u(x) + d(x))]

    ~ sp/sd independent of z and pt

    [sp(p+) - sp(p-)]/[sd(p+) - sd(p-)]

    = [4u(x) - d(x)]/[3(u(x) + d(x))]

    independent of z and pt,

    but more sensitive to assumptions


    E00-108: Onset of the Parton Model Semi-Inclusive Pion Electroproduction

    GRV & CTEQ,

    @ LO or NLO

    Good description for p and d targets for 0.4 < z < 0.65

    (Note: z = 0.65 ~

    Mx2 = 2.5 GeV2)

    Closed (open) symbols reflect data after (before) events from coherent r production are subtracted


    p Semi-Inclusive Pion Electroproduction

    quark

    E00-108: Onset of the Parton Model

    Collinear Fragmentation

    Seq2q(x) Dqp(z)

    (Deuterium data)

    factorization

    (Resonances cancel (in SU(6)) in D-/D+ ratio extracted from deuterium data)


    E00-108: Onset of the Parton Model Semi-Inclusive Pion Electroproduction

    Solid (open) symbols are after (before) subtraction of diffractive r events

    Solid curve is a naïve parton model calculation assuming CTEQ5M parton distribution functions at NLO and BKK fragmentation functions

    Overall, one finds good agreement, but there are detailed differences in the cross section measurements (also for the deuterium target)

    x = 0.4

    x = 0.4


    E00-108: Onset of the Parton Model Semi-Inclusive Pion Electroproduction

    Solid (open) symbols are after (before) subtraction of diffractive r events. Blue symbols are old Cornell measurements.

    Solid curve is a naïve parton model calculation assuming CTEQ5M parton distribution functions at NLO and BKK fragmentation functions

    Agreement with the naïve parton model expectation is always far better for ratios, also for D/H, Al/D, or ratios versus z or Q2.


    SIDIS Formalism Semi-Inclusive Pion Electroproduction

    General formalism for (e,e’h) coincidence reaction w. polarized beam:

    [A. Bacchetta et al., JHEP 0702 (2007) 093]

    (Y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

    If beam is unpolarized, and the (e,e’h) measurements are fully integrated over f, only the FUU,T and FUU,L responses, or the usual transverse (sT) and longitudinal (sL) cross section pieces, survive.


    R = Semi-Inclusive Pion ElectroproductionsL/sTin DIS

    • RDIS is in the naïve parton model related to the parton’s

    • transverse momentum: R = 4(M2x2 + <kT2>)/(Q2 + 2<kT2>).

    • RDIS 0 at Q2  ∞ is a consequence of scattering

    • from free spin-½ constituents

    • Of course, beyond this, at finite Q2, RDIS sensitive to

    • gluon and higher-twist effects

    • No distinction made up to now between diffractive and

    • non-diffractive contributions in RDIS

    • RDISH = RDISD, to very good approximation (experimentally)

      • - from formal point of view they should differ! (u not equal to d at large x + evolution in Q2,H = spin-1/2 and D = spin-1, at low Q2)


    p Semi-Inclusive Pion Electroproduction

    quark

    R = sL/sTin (e,e’p) SIDIS

    Knowledge on R = sL/sT in SIDIS is essentially non-existing!

    • If integrated over z (and pT, f, hadrons), RSIDIS = RDIS

    • RSIDIS may vary with z

    • At large z, there are known contributions from exclusive

    • and diffractive channels: e.g., pions from D and r p+p-

    • RSIDIS may vary with transverse momentum pT

    • Is RSIDISp+ = RSIDISp- ? Is RSIDISH = RSIDISD ?

    • Is RSIDISK+ = RSIDISp+ ? Is RSIDISK+ = RSIDISK- ? We measure kaons too! (with about 10% of pion statistics)

    • RSIDIS = RDIS test of dominance of quark fragmentation

    “A skeleton in our closet”

    Seq2q(x) Dqp(z)


    R = Semi-Inclusive Pion ElectroproductionsL/sT in SIDIS (ep  e’pX)

    Cornell data of 70’s

    Conclusion: “data both consistent with R = 0 and R = RDIS”

    RDIS

    Some hint of large R at large z in Cornell data?

    RDIS (Q2 = 2 GeV2)


    p Semi-Inclusive Pion Electroproduction

    quark

    So what about R = sL/sT for pion electroproduction?

    “Deep exclusive scattering” is the z  1 limit of this “semi-inclusive DIS” process

    “Semi-inclusive DIS”

    Seq2q(x) Dqp(z)

    Here, R = sL/sT ~ Q2(at fixed x)

    RSIDIS RDIS disappears with Q2!

    Planned scans in z at Q2 = 2.0 (x = 0.2) and 4.0 GeV2 (x = 0.4)  should settle the behavior of sL/sT for large z.

    Not including a comparable systematic uncertainty:

    ~1.6%

    Example of 12-GeV projected data assuming RSIDIS = RDIS

    Planned data cover range Q2 = 1.5 – 5.0 GeV2, with data for both H and D at Q2 = 2 GeV2

    Have no idea at all how R will behave at large pT

    Planned data cover range in PT up to ~ 1 GeV. The coverage in f is excellent (o.k.) up to PT = 0.2 (0.4) GeV.


    Transverse Momentum Dependence of Semi-Inclusive Pion Production

    • Not much is known about the orbital motion of partons

    • Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks

    Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt.

    Pt= pt +zkt+ O(kt2/Q2)

    z = Ep/n

    pT ~ L < 0.5 GeV optimal for studies as theoretical framework for Semi-Inclusive Deep Inelastic Scattering has been well developed at small transverse momentum [A. Bacchetta et al., JHEP 0702 (2007) 093].


    m Production

    p

    X

    TMD

    Transverse momentum dependence of SIDIS

    Linked to framework of Transverse Momentum Dependent Parton Distributions

    s

    Unpolarized target

    Longitudinally pol. target

    TMDq(x,kT)

    Transversely pol. target

    Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions q and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width  Emerging new area of study

    I. Integrated over pT and f

    Hall C: PRL 98:022001 (2007)

    Hall B: arXiv:0809.1153

    II. PT and f dependence

    Possibility to constrain kT dependence of up and down quarks separately by combination of p+ and p- final states, proton and deuteron targets

    Hall B: arXiv:0809.1153

    Hall C: PL B665 (2008) 20

    III. Transverse polarized target: E06-010 transversity experiment in Hall A


    Transverse momentum dependence of SIDIS Production

    General formalism for (e,e’h) coincidence reaction w. polarized beam:

    [A. Bacchetta et al., JHEP 0702 (2007) 093]

    (Y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

    Azimuthal fh dependence crucial to separate out kinematic effects (Cahn effect) from twist-2 correlations and higher twist effects.

    data fit on EMC (1987) and Fermilab (1993) data assuming Cahn effect→ <m02> = 0.25 GeV2

    (assuming m0,u =m0,d)


    Transverse momentum dependence of SIDIS Production

    General formalism for (e,e’h) coincidence reaction:

    Factorized formalism for SIDIS (e,e’h):

    In general, A and B are functions of (x,Q2,z,pT,f).

    e.g., “Cahn effect”:


    PR12-09-017: P ProductionT coverage

    Can do meaningful measurements at low pT (down to 0.05 GeV) due to excellent momentum and angle resolutions!

    f= 90o

    • Excellent f coverage

    • up to pT = 0.2 GeV

    • Sufficient f coverage

    • up to pT = 0.4 GeV

    • (compared to the E00-108

    • case below, now also good

    • coverage at f ~ 0o)

    • Limited f coverage

    • up to pT = 0.5 GeV

    pT = 0.6

    pT = 0.4

    f= 0o

    f= 180o

    E00-108

    f= 270o

    PT ~ 0.5 GeV: use f dependencies measured in CLAS12 experiments (E12-06-112, LOI12-09-005)


    Model P ProductionT dependence of SIDIS

    Gaussian distributions for PT dependence, no sea quarks, and leading order in (kT/q)

    Inverse of total width for each combination of quark flavor and fragmentation function given by:

    And take Cahn effect into account, with e.g. (similar for c2, c3, and c4):


    Unpolarized SIDIS – JLab data (cont.) Production

    Constrain kT dependence of up and down quarks separately

    1) Probe p+ and p- final states

    2) Use both proton and neutron (d) targets

    3) Combination allows, in principle, separation of quark width from fragmentation widths

    (if sea quark contributions small)

    Example

    1st example: Hall C, PL B665 (2008) 20

    Simple model, host of assumptions (factorization valid, fragmentation functions do not depend on quark flavor, transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature, sea quarks are negligible, assume Cahn effect, etc.) 


    Unpolarized SIDIS – JLab data (cont.) Production

    Constrain kT dependence of up and down quarks separately

    1) Probe p+ and p- final states

    2) Use both proton and neutron (d) targets

    3) Combination allows, in principle, separation of quark width from fragmentation widths

    (if sea quark contributions small)

    Example

    1st example: Hall C, PL B665 (2008) 20

    x = 0.32

    z = 0.55

    Numbers are close to expectations! But, far too early to claim success: simple model only, not a complete f coverage, uncertainties in exclusive event & diffractive r contributions, SIDIS partonic framework valid?

    Example

    <pt2> (favored)

    <kt2> (up)


    PR12-09-017 Projected Results - I Production

    III

    IV

    II

    VI

    I

    V


    Kaon Identification Production

    • Particle identification in SHMS:

    • 0) TOF at low momentum (~1.5 GeV)

    • Heavy (C4F8O) Gas Cherenkov

    • to select p+ (> 3 GeV)

    • 60 cm of empty space could be

    • used for two aerogel detectors:

    • - n = 1.015 to select p+ (> 1 GeV)

    • select K+ (> 3 GeV)

    • - n = 1.055 to select K+ (>1.5 GeV)

    Heavy Gas Cherenkov and 60 cm of empty space


    Spin-off: study x-z Factorization for kaons Production

    P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000)

    At large z-values easier to separate current and target fragmentation region  for fast hadrons factorization (Berger Criterion) “works” at lower energies

    If same arguments as validated for p apply to K:

    At W = 2.5 GeV: z > 0.6

    (but, z < 0.65 limit may not apply for kaons!)


    PR12-09-017 Projected Results - Kaons Production

    III

    IV

    II

    VI

    I

    V


    Summary Production

    • Access to the parton model through semi-inclusive DIS data was established with 6-GeV data

    • Still many questions about the exact interpretation of SIDIS experiments and the validity of such access in cross section measurements

    • In ratios (or similar, asymmetries) life seems to become simpler, and access seems verified

    • Many outstanding questions remain:

      • Is R in SIDIS the same as R in DIS, as anticipated from the high-energy factorized Ansatz?

      • To what extent is factorization truly valid? (especially at high pT, at small pT it should be valid at tree-level)

      • Experimentally, where does it work for kaons?

      • Does fragmentation depend on quark flavor?

      • What are the transverse momentum distributions of the various quark and fragmentation functions?


    Choice of Kinematics Production(here for PR12-09-017)

    HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering

    11 GeV phase space

    6 GeV phase space

    E00-108

    PR12-09-017

    Scan in (x,z,pT)

    + scan in Q2

    at fixed x

    For semi-inclusive, less Q2 phase space at fixed x due to:

    i) MX2 > 2.5 GeV2; and ii) need to measure at both sides of Qg


    S Productioneq2q(x) Dqp(z)

    Kinematic Factorization

    (after integration over pT and f)

    Both Current and Target Fragmentation Processes Possible. At Leading Order:

    Berger Criterion

    Dh > 2 Rapidity gap for

    factorization

    Separates Current and Target Fragmentation Region in Rapidity


    Low-Energy x-z Factorization Production

    Seq2q(x) Dqp(z)

    (after integration over pT and f)

    P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000)

    At large z-values easier to separate current and target fragmentation region  for fast hadrons factorization (Berger Criterion) “works” at lower energies

    p

    At W = 2.5 GeV: z > 0.4 At W = 5 GeV: z > 0.2

    (Typical JLab-6 GeV) (Typical HERMES)


    Non-trivial contributions to (e,e’ Productionp) Cross Section

    Radiation contributions, including from exclusive

    Contributions from r

    Further data from CLAS12 (r) and Hall C (Fp-12, pCT-12) will constrain!


    Estimate of Contribution of Productionr to R = sL/sT

    High e

    Low e

    • Conclusion: If r contribution is as simulated and

    • known to 10%  5% relative error in R (worst case)

    • (CLAS12 data important to constrain r contributions!)

    • Above uncertainty assumed RSIDIS = RDIS (small!)

    • Essentially same uncertainty at Q2 = 2.0 and 4.0 GeV2


    SIDIS Formalism Production

    General formalism for (e,e’h) coincidence reaction w. polarized beam:

    [A. Bacchetta et al., JHEP 0702 (2007) 093]

    (Y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

    Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions fq and (one or more) fragmentation functions Dqh, each with own characteristic (Gaussian) width.


    Transverse momentum dependence of SIDIS Production

    E00-108

    Pt dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller?

    Pt dependence very similar for proton and deuterium targets


    Transverse Momentum Dependence: E00-108 Summary Production

    • E00-108 results can only be considered suggestive at best:

    • limited kinematic coverage

      • - assume (PT,f) dependency ~ Cahn effect

  • very simple model assumptions

  • but PT dependence off D seems shallower than H

  • and intriguing explanation in terms of flavor/kT deconvolution

    • Many limitations could be removed with 12 GeV:

    • wider range in Q2

    • improved/full coverage in f (at low pT)

    • larger range in PT

    • wider range in x and z (to separate quark from fragmentation widths)

    • possibility to check various model assumptions

      • Power of (1-z) for D-/D+

      • quantitative contribution of Cahn term

      • Dup+ = Ddp-

      • Higher-twist contributions

      • consistency of various kinematics (global fit vs. single-point fits)


    PR12-09-017 Projected Results - II Production

    Simulated data use (mu)2 = (md)2 = 0.2, and then fit using statistical errors.

    Step 1: Kinematics I-VI fitted separately, (pT,f) dependency ~ Cahn

    Step 2: Add eight parameters to mimic possible HT, but assume Cahn

     uncertainties grow with about factor of two

    Step 3: Simulate with and without Cahn term

     results remain similar as in step 2


    PR12-09-017 Projected Results - II Production

    Simulated data use (mu)2 = (md)2 = 0.2, and then fit using statistical errors.

    Step 1: Kinematics I-VI fitted separately, (pT,f) dependency ~ Cahn

    (if all six fitted together, diameter < 0.01 GeV2)

    Step 2: Add eight parameters to mimic possible HT, but assume Cahn

     uncertainties grow with about factor of two

    (if all six fitted together, diameter remains < 0.01 GeV2)

    Step 3: Simulate with and without Cahn term

     results remain similar as in step 2

    (if all six fitted together, diameter grows to < 0.02 GeV2)

    Step 1: Kinematics I-VI fitted separately, (pT,f) dependency ~ Cahn

    Step 2: Add eight parameters to mimic possible HT, but assume Cahn

     uncertainties grow with about factor of two

    Step 3: Simulate with and without Cahn term

     results remain similar as in step 2


    Non-trivial contributions to (e,e’ Productionp) Cross Section

    Radiative Corrections - Typical corrections are <10% for z < 0.7.

    - Checked with SIMC and POLRAD 2.0.

    - Good agreement between both methods.

    Exclusive Pions - Interpolated low-W2, low-Q2 of MAID

    with high-W2, high-Q2 of Brauel/Bebek.

    - Introduces large uncertainty at low z,

    but contributions there are small.

    - Tail agreed to 10-15% with “HARPRAD”.

    - Further constraints with Fp-12 and pCT-12.

    Pions from Diffractive r - Used PYTHIA with modifications as

    implemented by HERMES (Liebing,Tytgat).

    - Used this to guide r cross section in SIMC.

    - simulated results agree to 10-15% with

    CLAS data (Harut Avagian).

    - In all cases, quote results with/without

    diffractive r subtraction.


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