DVCS systematic studies and model calculations

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Introduction

The goal of this page is to document the latest strategies and codes which were used to calculate systematic uncertainties for the DVCS analyses. This includes stand-alone codes which provide GPD model calculations. For more details, the reader is referred to the release reports. Everybody in the DVCS group is highly welcome to contribute! (This page does not write itself)

DVCS systematic studies

In this section, the systematic studies and corrections are described which are commonly used in the DVCS analyses. Further reading:

• Summary on systematic uncertainties in DVCS-TTSA, Eduard Avetisyan, March 2008

Beam- and target-polarization scale uncertainty

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NEEDTEXT

Background Corrections

Important note: This page has not yet been reviewed by Aram! Use the information below with caution. Other pages that have not been reviewed yet can be found in the category FORREVIEW.

The 'exclusive' data sample selected by applying a squared missing-mass, Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle \left.M_{X}^{2}\right.} cut, contains contaminations from several background processes (see also DVCS Monte-Carlo Page), unless information from the Recoil Detector is included. These are

• Associated BH, where an 'excited' proton resonance (e.g. $\left.\Delta ^{+}\right.$) occupies the final state accounts for $\left.\sim 13\%\right.$. Without the Recoil detector, no correction can be applied to account for this background signal.
• Semi-Inclusive DIS, where a neutral meson (e.g. Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\pi^{0}\right.} ) occupies the final state accounts for Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\sim 3\%\right.} . The detected photon cluster is either due to one of the meson decay photons where the other is out with detector acceptance, or from both decay photons if they are too close together for the detector to resolve.
• Exclusive Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\pi^{0}\right.} which has been shown by Arne to contribute less than Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.0.7\%\right.} . This can be investigated further with the Recoil Detector.

The extracted azimuthal asymmetries can be corrected for contributions from the last two background processes in each kinematic bin by :

Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle A_{corr.}={\frac {A_{measured}-f_{sidis}A_{sidis}-f_{excl.}A_{excl.}}{(1-f_{sidis}-f_{excl.})}}}

where Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. f_{sidis} \right.} (Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. f_{excl.} \right.} ) is the fractional contribution from the semi-inclusive DIS (exclusive Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\pi^{0}\right.} ) process and Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. A_{sidis} \right.} ($\left.A_{excl.}\right.$) is the corresponding asymmetry.

• Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. A_{sidis} \right.} can be extracted from data by performing a 2-photon analysis. Using the same burst-level and DIS event selection as the DVCS analysis except 2 trackless 'photon' clusters are required in the calorimeter. The floowing criteria must be met:
  • energy deposits of Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.5 GeV\right.} for the leading photon
  • Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.1 GeV\right.} for the non-leading.
  • The ratio of the pion and virtual photon energies Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle z \stackrel{lab}{=} (E_{1}+E_{2})/\nu } is required to be greater than Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle \left.0.8\right.}
  • the squared invariant mass of the 2-photon system Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle M_{\gamma\gamma}^{2} \stackrel{lab}{=} 2E_{1}E_{2}(1-\cos\theta_{\gamma\gamma}) } should meet the criteria Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle 0.10 GeV < M_{\gamma\gamma}^{2} < 0.17 GeV }
• Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.A_{excl.}\right.} cannot be extracted from data due to limited statistics so is assigned a value of Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. 0 \pm 1\right.}
• The fractional contributions $\left.f_{sidis}\right.$ and Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. f_{excl.} \right.} in each kinematic bin are extracted from Monte Carlo (DISng resp. gmc_excl).

The systematic uncertainty arising from this correction is obtained by propagating the statistical uncertainties from Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. A_{sidis} \right.} , Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. A_{excl.} \right.} , Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left. f_{sidis} \right.} and Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle \left.f_{excl.}\right.} in the asymmetry correction equation above and adding each in quadrature. Half of this correction uncertainty is added along with half of the actual correction as the systematic uncertainty.

Calorimeter miscalibration and shift of missing mass peak

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NEEDTEXT

Data correction + sys. uncertainty

We could not identify an instrumental effect for the observed missing mass shift between different data sets and therefore applied a systematic uncertainty covering the effect of this shift. As each of the data sets could be shifted the 'true' Mx value is an equal distribution with a width corresponding to the relative shifts of these data sets. The error of an equal distribution is 1/sqrt(12), approximately 1/4. Therefore we chose 1/4 of the effect as systematic uncertainty.

Detector inefficiencies

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NEEDTEXT

e.g. H0 ineff. if tr21 cut is applied.

"4-in-1": smearing, bin width, acceptance, misalignment

Important note: This page has not yet been reviewed by Maru! Use the information below with caution. Other pages that have not been reviewed yet can be found in the category FORREVIEW.

• To estimate the combined effect of detector smearing, finite bin width (see Zhenyu's mail), the Hermes acceptance and the misalignment of the detector with respect to the lepton beam onto the measured amplitudes, the generated amplitudes are compared to the amplitudes reconstructed from gmcDVCS or gmcDual ( see below in the section Model Calculations). The difference between the amplitudes obtained in this way is assigned as systematic uncertainty Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\delta=A_{\mathrm{generated}}-A_{\mathrm{reconstructed}}\right.} . If Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.N\right.} models are available, the quadratically added sum of the individual uncertainties Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\delta_i\right.} is used to obtain the total systematic uncertainty due to the 4-in-1, Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \left.\delta_{\mathrm{tot}}\right.} (RMS difference):

Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle \delta _{\mathrm {tot} }={\sqrt {{\frac {1}{N}}\sum _{i}^{N}\delta _{i}^{2}}}}

An example is given on the right hand side; the blue curves correspond to the reconstructed amplitudes, the red dashed ones to the generated amplitudes.

• See also the Misalignment page.

DVCS model calculations

VGG type

Important note: This page has not yet been reviewed by Morgan! Use the information below with caution. Other pages that have not been reviewed yet can be found in the category FORREVIEW.

VGG = Vanderhaeghen, Guichon, Guidal (1999)

VGG models

References: [DVCS-theo-003] and [DVCS-theo-004]

• Based on double distributions.
• Includes a D-term to restore full polynomiality.
  • Mail thread May 2010 in communication with Michel Guidal
• Includes a factorized and a Regge-inspired t-ansatz.
• Skewness depends on free parameters b_val and b_sea. NEEDEXPERT In the table below, which b parameter is this? Both?
• Includes twist-3 contributions.
• The model variants: NEEDEXPERT. One could e.g. copy (or modify) the corresponding sections from the deuterium draft DC39. CR 6.4.2009
  • VGG Regge. It is obviously none of the fast models 1-5?
  • VGG Factorized
  • with/without D-term
  • connection to models A-E of fast VGG type?

The VGG model has been shown to be rather naive, but it is the best that is available. We have more or less decided to use the models with the Regge-inspired t-dependence with and without a D-term, which should exist from a mathematical perspective but is not necessarily borne out by our data.

The standard selection is to include the WW-approximation for the inclusion of twist-3 terms, and use the MRST paramterisation of PDFs in order to provide the restriction of the GPD model in the kinematic limit t->0, ξ->0. We calculate with four combinations of the b-parameter set, b_val={1,9},b_sea={1,9}. These four values of the b-parameters are used to provide a theory band in the published plots.

Fast VVG-type models

• Reference: [DVCS-theo-006] , page 4. There the letters A-E are used, at Hermes we usually call the models 1-5.

Variant	t-ansatz	Skewness	b-parameter	D-term	Remarks
1 (A)	factorized	none	b=9	none
2 (B)	factorized	included (double-distribution formalism)	b=1	none
3 (C)	factorized	included (double-distribution formalism)	b=3	none	as B except for b-param
4 (D)	factorized	included (double-distribution formalism)	b=1	included	as B except for D-term
5 (E)	factorized	included (double-distribution formalism)	b=3	included	as B except for b-param and D-term

• b=9 means in practice Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle b\rightarrow\infty} (skewedness-independent parameterization)
• For the unpolarized hydrogen release in 2008, only models 1,3,5 were included in the determination of the 4-in-1 systematic uncertainty. 2 and 4 are only variants of 3 and 5, respectively.

DVCS moments from VVG

At present (2008/2009), three different frameworks are used in the Hermes DVCS group to calculate VGG-type DVCS moments:

1. VGG stand-alone code (Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \rightarrow} normal VGG)

• The VGG-standalone code is used to calculate the model curves of the DVCS amplitudes (see the example on the right hand side). The bands surrounding the actual curves arise from the variation of the b-parameters b_val and b_sea (which determine the contributions of valence and sea quarks in the nucleon to the asymmetries) between unity and infinity. The variation of b_sea has the strongest effect.
• It is rather CPU-intensive.
• There are two versions available:
  • The Zhenyu/Dietmar version (older), originally provided by Vanderhaeghen VGG01 (2001).
    • VGG from Vanderhaeghen The standalone VGG code originally received from Vanderhaeghen. Used for the TTSA paper (DC68) and the proton release in April 2008 (DC69).
  • The Glasgow version (later, more developed, e.g. also VM), originally provided by Guidal VGG05 (2005)
    • VGG from Guidal 10.9.2007 in the wiki docu area
      • Reference: PRD 72, 054013 (2005) arXiv:0410251/hep-ph
      • Technical remark: for the calculation of the BCA, minimum 50 integration points should be used, see Guidal's mail April 2010
      • Inti's mail of 13.9.2007
    • Used for the deuterium model curves (DC39 and DC81, in the latter case also taking properly into account Htilde), the polarized hydrogen publication (DC80) and the 2006/2007 DVCS release of Feb. 2010.
• Maru sees differences between the results of the two codes at high -t.
  • The problem is evident for BSAs but can also be seen in other asymmetries - this indicates that the difference arises in the treatment of the GPD 'H'.
  • Morgan's initial investigations show that the Guidal code (as opposed to the older Vanderhaeghen code) has some differences in the flexibility of its treatment of the H-tilde GPD and possibly its treatment of E, but no obvious indication of a difference in its treatment of H. However, the major differences in the results of the code seem to occur at higher t which directly corresponds to the different hypotheses for the Dirac and Pauli form factors. The Guidal code, unsurprisingly, includes his work to take account of two-photon corrections to the form factors.
• Mail thread about the two "VGG flavors", March 2010

2. qplot (Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \rightarrow} fast VGG)

• The program qplot is used to calculate the generated amplitudes for the '4-in-1' systematic uncertainty (see example plot there).
• qplot is a Fortran-code with the 5 fast VGG-type models implemented ('stand-alone gmcDVCS'). qplot does not contain twist-3.
• Available example versions:
  • qplot for unpolarized deuterium in the wiki docu area, courtesy of Maru
  • qplot for polarized deuterium in the wiki docu area, courtesy of Aram
  • qplot for unpolarized proton qplot version used for the proton release in April 2008, courtesy of Dietmar

3. gmcDVCS

• gmcDVCS is used to extract the reconstructed amplitudes in the Hermes acceptance for the '4-in-1' systematic uncertainty, including smearing and misalignment.
• gmcDVCS is a Monte Carlo generator with the full Hermes MC glory and the 5 fast VGG-type models implemented.
• Find more information on gmcDVCS on the MC generator page

Remarks

• The results from the VGG-standalone code are less than 20% away from any of the 3 used model variants in the determination of the '4-in-1' systematic uncertainty.
• Frameworks 1. (VGG stand-alone) and 3. (gmcDVCS) have been checked by Maru to be compatible with each other. Until an example plot from Maru is available (status: Dec.2008), compare the model curves on the released plots with the generated amplitudes in the deuterium release report.
• See also Dietmar's docu-mail from 11.12.2008.

Data-model comparisons

• In general, moments of the Beam Spin Asymmetry (BSA) compare worse than the other moments to the VGG-type models.
• Latest publications with data-model comparisons: [DVCS-procs-001] and [DVCS-talks-002]

Guzey's Dual model

• Guzey-Teckentrup 2006 (Dual-GT)
• Publications containing the description of the minimal dual parameterization model: [DVCS-theo-007] and [DVCS-theo-008]
• Models GPDs H and E, no H-tilde and E-tilde
• Based on infinite sum of t-channel resonances
• Model variants: 2 different t-dependences
  • Regge inspired ansatz
  • Factorized t-ansatz (exponential t-dependence)
• Leading Order in the strong coupling constant; only leading twist (twist-2)
• Latest publications with data-model comparisons: [DVCS-theo-009]
• gmc_Dual Monte-Carlo Generator
• The stand-alone Dual code is available here (for BSA and BCA)

Dieter Mueller

• See DVCS-theo-012 (predictions for BCA, BSA, LTSA)

Links

Links to codes and scripts

Please see corresponding sections in this page.

Further Reading

• Hermes DVCS release reports
• Roger Barlow, Systematic Errors: facts and fictions. hep-ex/0207026

Related Pages

• DVCS Analysis Page
• DVCS Monte-Carlo Page
• MC Generators