Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD

Alexandrou, Constantia; Bacchio, Simone; Cloët, Ian; Constantinou, Martha; Delmar, Joseph; Hadjiyiannakou, Kyriakos; Koutsou, Giannis; Lauer, Colin; Vaquero, Alejandro

doi:10.1103/PhysRevD.105.054502

Title: Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD

Abstract

We present a calculation of the scalar, vector and tensor form factors for the pion and kaon in lattice QCD. We use an ensemble of two degenerate light, a strange and a charm quark (N_f = 2 + 1 + 1) of maximally twisted mass fermions with clover improvement. The corresponding pion and kaon masses are about 265 MeV and 530 MeV, respectively. The calculation is done in both rest and boosted frames obtaining data for four-vector momentum transfer squared up to –q² = 2.5 GeV² for the pion and 3 GeV² for the kaon. The excited-states effects are studied by analyzing six values of the source-sink time separation for the rest frame (1.12 – 2.23 fm) and for four values for the boosted frame (1.12 – 1.67 fm). The lattice data are renormalized non-perturbatively and the results for the scheme- and scale-dependent scalar and tensor form factors are presented in the $$\overline{MS}$$ scheme at a scale of 2 GeV. We apply different parametrizations to describe q²-dependence of the form factors to extract the scalar, vector and tensor radii, as well as the tensor anomalous magnetic moment. We compare the pion and kaon form factors to study SU(3) flavor symmetry breaking effects. By combining the data for the vector and tensor form factors we also obtain the lowest moment of the densities of transversely polarized quarks in the impact parameter space. Finally, we give an estimate for the average transverse shift in the y direction for polarized quarks in the x direction.

Authors:

Alexandrou, Constantia; Bacchio, Simone; Cloët, Ian;

; Delmar, Joseph; Hadjiyiannakou, Kyriakos; Koutsou, Giannis;

;

; ETM Collaboration

Publication Date:: Thu Mar 03 00:00:00 EST 2022

Research Org.:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF); European Union (EU)

Contributing Org.:: ETM Collaboration

OSTI Identifier:: 1847174

Alternate Identifier(s):: OSTI ID: 1902150

Grant/Contract Number:: SC0020405; AC02-06CH11357; POST-DOC/0718/0100; CULTURE/AWARDYR/0220; 951732; 82376; PHY17-19626; PHY20-13064; 765048

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 105 Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Alexandrou, Constantia, Bacchio, Simone, Cloët, Ian, Constantinou, Martha, Delmar, Joseph, Hadjiyiannakou, Kyriakos, Koutsou, Giannis, Lauer, Colin, Vaquero, Alejandro, and ETM Collaboration. Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD.  United States: N. p., 2022. 
Web.  doi:10.1103/PhysRevD.105.054502.

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                    Alexandrou, Constantia, Bacchio, Simone, Cloët, Ian, Constantinou, Martha, Delmar, Joseph, Hadjiyiannakou, Kyriakos, Koutsou, Giannis, Lauer, Colin, Vaquero, Alejandro, & ETM Collaboration. Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD.  United States.  https://doi.org/10.1103/PhysRevD.105.054502

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                    Alexandrou, Constantia, Bacchio, Simone, Cloët, Ian, Constantinou, Martha, Delmar, Joseph, Hadjiyiannakou, Kyriakos, Koutsou, Giannis, Lauer, Colin, Vaquero, Alejandro, and ETM Collaboration. Thu .  
"Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD".  United States.  https://doi.org/10.1103/PhysRevD.105.054502.

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@article{osti_1847174,

  title        = {Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD},

  author       = {Alexandrou, Constantia and Bacchio, Simone and Cloët, Ian and Constantinou, Martha and Delmar, Joseph and Hadjiyiannakou, Kyriakos and Koutsou, Giannis and Lauer, Colin and Vaquero, Alejandro and ETM Collaboration},

  abstractNote = {We present a calculation of the scalar, vector and tensor form factors for the pion and kaon in lattice QCD. We use an ensemble of two degenerate light, a strange and a charm quark (Nf = 2 + 1 + 1) of maximally twisted mass fermions with clover improvement. The corresponding pion and kaon masses are about 265 MeV and 530 MeV, respectively. The calculation is done in both rest and boosted frames obtaining data for four-vector momentum transfer squared up to –q2 = 2.5 GeV2 for the pion and 3 GeV2 for the kaon. The excited-states effects are studied by analyzing six values of the source-sink time separation for the rest frame (1.12 – 2.23 fm) and for four values for the boosted frame (1.12 – 1.67 fm). The lattice data are renormalized non-perturbatively and the results for the scheme- and scale-dependent scalar and tensor form factors are presented in the $\overline{MS}$ scheme at a scale of 2 GeV. We apply different parametrizations to describe q2-dependence of the form factors to extract the scalar, vector and tensor radii, as well as the tensor anomalous magnetic moment. We compare the pion and kaon form factors to study SU(3) flavor symmetry breaking effects. By combining the data for the vector and tensor form factors we also obtain the lowest moment of the densities of transversely polarized quarks in the impact parameter space. Finally, we give an estimate for the average transverse shift in the y direction for polarized quarks in the x direction.},

  doi          = {10.1103/PhysRevD.105.054502},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 105,

  place        = {United States},

  year         = {Thu Mar 03 00:00:00 EST 2022},

  month        = {Thu Mar 03 00:00:00 EST 2022}

}

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The European Physical Journal C, Vol. 14, Issue 1
DOI: 10.1007/s100520000303

Quark masses using twisted-mass fermion gauge ensembles
journal, October 2021

Alexandrou, C.; Bacchio, S.; Bergner, G.
Physical Review D, Vol. 104, Issue 7
DOI: 10.1103/PhysRevD.104.074515

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Title: Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD

Abstract

Citation Formats

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journal, May 2014

Non-perturbative renormalization of quark bilinear operators with N f = 2 (tmQCD) Wilson fermions and the tree-level improved gauge action
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journal, October 2008

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journal, December 2014

First measurement of the reaction π−e → π−π0e
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conference, June 2011

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journal, November 2008

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journal, July 1995

Erratum: Nucleon Matrix Elements of the Antisymmetric Quark Tensor [Phys. Rev. Lett. 122 , 122001 (2019)]
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journal, January 2021

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journal, September 2000

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journal, November 2006

The decay of a light Higgs boson
journal, October 1990

A measurement of the space-like pion electromagnetic form factor
journal, January 1986

The vector and scalar form factors of the pion to two loops
journal, May 1998

Chiral expansion of pion form factors beyond one loop
journal, June 1991

The static approximation of heavy-light quark systems. A detailed lattice study
journal, February 1994

Three loop anomalous dimension of non-singlet quark currents in the RI′ scheme
journal, July 2003

Determination of the pion charge form factor for $Q^{2} =$ 0.60–1.60 GeV $^{2}$
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journal, May 2012

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journal, October 2013

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journal, September 2008

Theory of Dynamical Symmetry Breaking
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conference, April 2014

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Simulating twisted mass fermions at physical light, strange, and charm quark masses
journal, September 2018

Erratum: Impact parameter dependent parton distributions and off-forward parton distributions for $\vec{ζ} 0$ [Phys. Rev. D 62 , 071503(R) (2000)]
journal, December 2002

Transverse deformation of parton distributions and transversity decomposition of angular momentum
journal, November 2005

Measurement of the $π^{-}$ form factor
journal, October 1981

Renormalization of local quark-bilinear operators for $N_{f} = 3$ flavors of stout link nonperturbative clover fermions
journal, January 2015

Quark mass anomalous dimension to O (αs4)
journal, July 1997

Review of Particle Physics
journal, August 2020

Measurement of the pion form factor in the time-like region for q2 values between 0.1 (GeV/c)2 and 0.18 (GeV/c)2
journal, April 1984

Direct Measurement of the Negative-Kaon Form Factor
journal, July 1980

The pion form factor from lattice QCD with two dynamical flavours
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Perturbatively improving regularization-invariant momentum scheme renormalization constants
journal, May 2013

Electroproduction of ?+ n, ?- p andK + ?,K + 2211; 0 final states above the resonance region
journal, June 1979

Nucleon axial, tensor, and scalar charges and $σ$ -terms in lattice QCD
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journal, January 1976

Measurement of the Σ− charge radius by Σ−–electron elastic scattering
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Electroproduction of single pions at low $ε$ and a measurement of the pion form factor up to $Q^{2} = 10$ ${GeV}^{2}$
journal, April 1978

Elastic-Scattering Measurement of the Negative-Pion Radius
journal, February 1982

Nucleon Matrix Elements of the Antisymmetric Quark Tensor
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Electromagnetic pion form factor in the timelike region
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Charge symmetry breaking effects in pion and kaon structure
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Pion form factor and charge radius from lattice QCD at the physical point
journal, December 2021

A measurement of the kaon charge radius
journal, October 1986

Generalized parton distributions in impact parameter space
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Effective field theory description of the pion form factor
journal, October 1997

Pion Structure as Observed in the Reaction π − N → μ + μ − X at 80 GeV/ c
journal, December 1985

Three loop tensor current anomalous dimension in QCD
journal, August 2000

Spin densities in the transverse plane and generalized transversity distributions
journal, September 2005

Flavor dependence of the pion and kaon form factors and parton distribution functions
journal, September 2016

Computation of the electromagnetic pion form factor from lattice QCD in the ε regime
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