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

Journal Article · Thu Mar 03 00:00:00 EST 2022 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.105.054502· OSTI ID:1847174

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

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

;

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.

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

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

Contributing Organization:: ETM Collaboration

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

OSTI ID:: 1847174

Alternate ID(s):: OSTI ID: 1902150

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 105 Journal Issue: 5; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (87)

Renormalization constants of local operators for Wilson type improved fermions Alexandrou, C.; Constantinou, M.; Korzec, T. Physical Review D, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevD.86.014505	journal	July 2012
A measurement of the pion charge radius Amendolia, S. R.; Badelek, B.; Batignani, G. Physics Letters B, Vol. 146, Issue 1-2 https://doi.org/10.1016/0370-2693(84)90655-5	journal	October 1984
Renormalization constants for 2-twist operators in twisted mass QCD Alexandrou, C.; Constantinou, M.; Korzec, T. Physical Review D, Vol. 83, Issue 1 https://doi.org/10.1103/PhysRevD.83.014503	journal	January 2011
Electromagnetic Charge Radius of the Pion at High Precision Ananthanarayan, B.; Caprini, Irinel; Das, Diganta Physical Review Letters, Vol. 119, Issue 13 https://doi.org/10.1103/PhysRevLett.119.132002	journal	September 2017
Direct Measurement of the $π^{-}$ Form Factor Dally, E. B.; Drickey, D. J.; Hauptman, J. M. Physical Review Letters, Vol. 39, Issue 19 https://doi.org/10.1103/PhysRevLett.39.1176	journal	November 1977
Scalar pion form factor in two-flavor lattice QCD Gülpers, Vera; von Hippel, Georg; Wittig, Hartmut Physical Review D, Vol. 89, Issue 9 https://doi.org/10.1103/PhysRevD.89.094503	journal	May 2014
Non-perturbative renormalization of quark bilinear operators with N f = 2 (tmQCD) Wilson fermions and the tree-level improved gauge action Constantinou, M.; Dimopoulos, P.; Frezzotti, R. Journal of High Energy Physics, Vol. 2010, Issue 8 https://doi.org/10.1007/JHEP08(2010)068	journal	August 2010
Breakup of hadron masses and the energy-momentum tensor of QCD Ji, Xiangdong Physical Review D, Vol. 52, Issue 1 https://doi.org/10.1103/PhysRevD.52.271	journal	July 1995
High-statistics study of the $τ^{-} \to π^{-} π^{0} ν_{τ}$ decay Fujikawa, M.; Hayashii, H.; Eidelman, S. Physical Review D, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevD.78.072006	journal	October 2008
Pion scalar form factor and another confirmation of the existence of the $f_{0} (500)$ meson Dubnička, S.; Dubničková, A. Z.; Liptaj, A. Physical Review D, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevD.90.114003	journal	December 2014
First measurement of the reaction π−e → π−π0e Amendolia, S. R.; Arik, M.; Badelek, B. Physics Letters B, Vol. 155, Issue 5-6 https://doi.org/10.1016/0370-2693(85)91603-X	journal	June 1985
Hadron structure from lattice quantum chromodynamics Hägler, Ph. Physics Reports, Vol. 490, Issue 3-5 https://doi.org/10.1016/j.physrep.2009.12.008	journal	May 2010
The pion's electromagnetic form factor at small momentum transfer in full lattice QCD collaborations, RBC and UKQCD; Boyle, P. A.; Flynn, J. M. Journal of High Energy Physics, Vol. 2008, Issue 07 https://doi.org/10.1088/1126-6708/2008/07/112	journal	July 2008
Lattice calculation of pion form factors with overlap fermions Wang, Gen; Liang, Jian; Draper, Terrence Physical Review D, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevD.104.074502	journal	October 2021
QCD Analysis of the Mass Structure of the Nucleon Ji, Xiangdong Physical Review Letters, Vol. 74, Issue 7 https://doi.org/10.1103/PhysRevLett.74.1071	journal	February 1995
Separated kaon electroproduction cross section and the kaon form factor from 6 GeV JLab data Carmignotto, M.; Ali, S.; Aniol, K. Physical Review C, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevC.97.025204	journal	February 2018
Light meson form factors in $N_f=2+1$ QCD with dynamical overlap quarks Kaneko, Takashi Proceedings of The XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010) https://doi.org/10.22323/1.105.0146	conference	June 2011
The 4-loop quark mass anomalous dimension and the invariant quark mass Vermaseren, J. A. M.; Larin, S. A.; van Ritbergen, T. Physics Letters B, Vol. 405, Issue 3-4 https://doi.org/10.1016/S0370-2693(97)00660-6	journal	July 1997
𝒪( a ² ) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons Constantinou, M.; Lubicz, V.; Panagopoulos, H. Journal of High Energy Physics, Vol. 2009, Issue 10 https://doi.org/10.1088/1126-6708/2009/10/064	journal	October 2009
Scaling study of the pion electroproduction cross sections Horn, T.; Qian, X.; Arrington, J. Physical Review C, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevC.78.058201	journal	November 2008
Rho-omega mixing and the pion electromagnetic form-factor O'Connell, H. B.; Pearce, B. C.; Thomas, A. W. Physics Letters B, Vol. 354, Issue 1-2 https://doi.org/10.1016/0370-2693(95)00642-X	journal	July 1995
Erratum: Nucleon Matrix Elements of the Antisymmetric Quark Tensor [Phys. Rev. Lett. 122 , 122001 (2019)] Hoferichter, Martin; Kubis, Bastian; Ruiz de Elvira, Jacobo Physical Review Letters, Vol. 124, Issue 19 https://doi.org/10.1103/PhysRevLett.124.199901	journal	May 2020
Mellin moments $⟨ x ⟩$ and $⟨ x^{2} ⟩$ for the pion and kaon from lattice QCD Alexandrou, Constantia; Bacchio, Simone; Cloët, Ian Physical Review D, Vol. 103, Issue 1 https://doi.org/10.1103/PhysRevD.103.014508	journal	January 2021
Pion and kaon $⟨ x^{3} ⟩$ from lattice QCD and PDF reconstruction from Mellin moments Alexandrou, Constantia; Bacchio, Simone; Cloët, Ian Physical Review D, Vol. 104, Issue 5 https://doi.org/10.1103/PhysRevD.104.054504	journal	September 2021
Nonperturbative renormalization of quark bilinear operators and $B_{K}$ using domain wall fermions Aoki, Y.; Boyle, P. A.; Christ, N. H. Physical Review D, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevD.78.054510	journal	September 2008
Non-perturbative renormalisation of composite operators in lattice QCD Göckeler a., M.; Horsley, R.; Oelrich, H. Nuclear Physics B, Vol. 544, Issue 3 https://doi.org/10.1016/S0550-3213(99)00036-X	journal	April 1999
Generalized parton distributions in impact parameter space Diehl, M. The European Physical Journal C, Vol. 25, Issue 2 https://doi.org/10.1007/s10052-002-1016-9	journal	September 2002
Impact parameter dependent parton distributions and off-forward parton distributions for ζ→0 Burkardt, Matthias Physical Review D, Vol. 62, Issue 7 https://doi.org/10.1103/PhysRevD.62.071503	journal	September 2000
Determination of the Pion Charge Form Factor at $Q^{2} = 1.60$ and $2.45 (GeV / c)^{2}$ Horn, T.; Aniol, K.; Arrington, J. Physical Review Letters, Vol. 97, Issue 19 https://doi.org/10.1103/PhysRevLett.97.192001	journal	November 2006
The decay of a light Higgs boson Donoghue, John F.; Gasser, J.; Leutwyler, H. Nuclear Physics B, Vol. 343, Issue 2 https://doi.org/10.1016/0550-3213(90)90474-R	journal	October 1990
A measurement of the space-like pion electromagnetic form factor Amendolia, S. R.; Arik, M.; Badelek, B. Nuclear Physics B, Vol. 277 https://doi.org/10.1016/0550-3213(86)90437-2	journal	January 1986
The vector and scalar form factors of the pion to two loops Bijnens, Johan; Colangelo, Gilberto; Talavera, Pere Journal of High Energy Physics, Vol. 1998, Issue 05 https://doi.org/10.1088/1126-6708/1998/05/014	journal	May 1998
Chiral expansion of pion form factors beyond one loop Gasser, J.; Meiβner, Ulf-G. Nuclear Physics B, Vol. 357, Issue 1 https://doi.org/10.1016/0550-3213(91)90460-F	journal	June 1991
The static approximation of heavy-light quark systems. A detailed lattice study Alexandrou, C.; Güsken, S.; Jegerlehner, F. Nuclear Physics B, Vol. 414, Issue 3 https://doi.org/10.1016/0550-3213(94)90262-3	journal	February 1994
Three loop anomalous dimension of non-singlet quark currents in the RI′ scheme Gracey, J. A. Nuclear Physics B, Vol. 662, Issue 1-2 https://doi.org/10.1016/S0550-3213(03)00335-3	journal	July 2003
Determination of the pion charge form factor for $Q^{2} =$ 0.60–1.60 GeV $^{2}$ Tadevosyan, V.; Blok, H. P.; Huber, G. M. Physical Review C, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevC.75.055205	journal	May 2007
Spacelike pion form factor from analytic continuation and the onset of perturbative QCD Ananthanarayan, B.; Caprini, Irinel; Imsong, I. Sentitemsu Physical Review D, Vol. 85, Issue 9 https://doi.org/10.1103/PhysRevD.85.096006	journal	May 2012
Pion Electromagnetic Form Factor at Spacelike Momenta Chang, L.; Cloët, I. C.; Roberts, C. D. Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.141802	journal	October 2013
Pion form factors from two-flavor lattice QCD with exact chiral symmetry Aoki, S.; Chiu, T. W.; Fukaya, H. Physical Review D, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRevD.80.034508	journal	August 2009
Two-pion contribution to hadronic vacuum polarization Colangelo, Gilberto; Hoferichter, Martin; Stoffer, Peter Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)006	journal	February 2019
Further measurements of forward-charged-pion electroproduction at large $k^{2}$ Bebek, C. J.; Brown, C. N.; Herzlinger, M. Physical Review D, Vol. 9, Issue 5 https://doi.org/10.1103/PhysRevD.9.1229	journal	March 1974
Spin Structure of the Pion Brömmel, D.; Diehl, M.; Göckeler, M. Physical Review Letters, Vol. 101, Issue 12 https://doi.org/10.1103/PhysRevLett.101.122001	journal	September 2008
Theory of Dynamical Symmetry Breaking Higashijima, Kiyoshi Progress of Theoretical Physics Supplement, Vol. 104 https://doi.org/10.1143/PTPS.104.1	journal	January 1991
A general method for non-perturbative renormalization of lattice operators Martinelli, G.; Pittori, C.; Sachrajda, C. T. Nuclear Physics B, Vol. 445, Issue 1 https://doi.org/10.1016/0550-3213(95)00126-D	journal	July 1995
A study of smearing techniques for hadron correlation functions Güsken, Stephan Nuclear Physics B - Proceedings Supplements, Vol. 17 https://doi.org/10.1016/0920-5632(90)90273-W	journal	September 1990
Pion structure from lattice QCD Javadi-Motaghi, Narjes; Bali, Gunnar; Collins, Sara Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013) https://doi.org/10.22323/1.187.0447	conference	April 2014
Measurement of the Charged Pion Electromagnetic Form Factor Volmer, J.; Abbott, D.; Anklin, H. Physical Review Letters, Vol. 86, Issue 9 https://doi.org/10.1103/PhysRevLett.86.1713	journal	February 2001
Renormalization functions for $N_{f} = 2$ and $N_{f} = 4$ twisted mass fermions Alexandrou, Constantia; Constantinou, Martha; Panagopoulos, Haralambos Physical Review D, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevD.95.034505	journal	February 2017
Pion vector and scalar form factors with dynamical overlap quarks Kaneko, Takashi Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008) https://doi.org/10.22323/1.066.0158	conference	June 2009
Simulating twisted mass fermions at physical light, strange, and charm quark masses Alexandrou, Constantia; Bacchio, Simone; Charalambous, Panagiotis Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevD.98.054518	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)] Burkardt, Matthias Physical Review D, Vol. 66, Issue 11 https://doi.org/10.1103/PhysRevD.66.119903	journal	December 2002
Transverse deformation of parton distributions and transversity decomposition of angular momentum Burkardt, Matthias Physical Review D, Vol. 72, Issue 9 https://doi.org/10.1103/PhysRevD.72.094020	journal	November 2005
Measurement of the $π^{-}$ form factor Dally, E. B.; Drickey, D. J.; Hauptman, J. M. Physical Review D, Vol. 24, Issue 7 https://doi.org/10.1103/PhysRevD.24.1718	journal	October 1981
Renormalization of local quark-bilinear operators for $N_{f} = 3$ flavors of stout link nonperturbative clover fermions Constantinou, M.; Horsley, R.; Panagopoulos, H. Physical Review D, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevD.91.014502	journal	January 2015
Quark mass anomalous dimension to O (αs4) Chetyrkin, K. G. Physics Letters B, Vol. 404, Issue 1-2 https://doi.org/10.1016/S0370-2693(97)00535-2	journal	July 1997
Review of Particle Physics Zyla, P. A.; Barnett, R. M.; Beringer, J. Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 8 https://doi.org/10.1093/ptep/ptaa104	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 Amendolia, S. R.; Badelek, B.; Batignani, G. Physics Letters B, Vol. 138, Issue 5-6 https://doi.org/10.1016/0370-2693(84)91938-5	journal	April 1984
Direct Measurement of the Negative-Kaon Form Factor Dally, E. B.; Hauptman, J. M.; Kubic, J. Physical Review Letters, Vol. 45, Issue 4 https://doi.org/10.1103/PhysRevLett.45.232	journal	July 1980
The pion form factor from lattice QCD with two dynamical flavours Brömmel, D.; Diehl, M.; Göckeler, M. The European Physical Journal C, Vol. 51, Issue 2 https://doi.org/10.1140/epjc/s10052-007-0295-6	journal	May 2007
Perturbatively improving regularization-invariant momentum scheme renormalization constants Constantinou, M.; Costa, M.; Göckeler, M. Physical Review D, Vol. 87, Issue 9 https://doi.org/10.1103/PhysRevD.87.096019	journal	May 2013
Electroproduction of ?+ n, ?- p andK + ?,K + 2211; 0 final states above the resonance region Brauel, P.; Canzler, T.; Cords, D. Zeitschrift f�r Physik C Particles and Fields, Vol. 3, Issue 2 https://doi.org/10.1007/BF01443698	journal	June 1979
Nucleon axial, tensor, and scalar charges and $σ$ -terms in lattice QCD Alexandrou, C.; Bacchio, S.; Constantinou, M. Physical Review D, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevD.102.054517	journal	September 2020
Determination of the pion form factor up to $Q^{2} = 4$ ${GeV}^{2}$ from single-charged-pion electroproduction Bebek, C. J.; Brown, C. N.; Herzlinger, M. Physical Review D, Vol. 13, Issue 1 https://doi.org/10.1103/PhysRevD.13.25	journal	January 1976
Measurement of the Σ− charge radius by Σ−–electron elastic scattering Eschrich, I.; Krüger, H.; Simon, J. Physics Letters B, Vol. 522, Issue 3-4 https://doi.org/10.1016/S0370-2693(01)01285-0	journal	December 2001
Electroproduction of single pions at low $ε$ and a measurement of the pion form factor up to $Q^{2} = 10$ ${GeV}^{2}$ Bebek, C. J.; Brown, C. N.; Holmes, S. D. Physical Review D, Vol. 17, Issue 7 https://doi.org/10.1103/PhysRevD.17.1693	journal	April 1978
Elastic-Scattering Measurement of the Negative-Pion Radius Dally, E. B.; Hauptman, J. M.; Kubic, J. Physical Review Letters, Vol. 48, Issue 6 https://doi.org/10.1103/PhysRevLett.48.375	journal	February 1982
Nucleon Matrix Elements of the Antisymmetric Quark Tensor Hoferichter, Martin; Kubis, Bastian; Ruiz de Elvira, Jacobo Physical Review Letters, Vol. 122, Issue 12 https://doi.org/10.1103/PhysRevLett.122.122001	journal	March 2019
Electromagnetic pion form factor in the timelike region Barkov, L. M.; Chilingarov, A. G.; Eidelman, S. I. Nuclear Physics B, Vol. 256 https://doi.org/10.1016/0550-3213(85)90399-2	journal	January 1985
Charge symmetry breaking effects in pion and kaon structure Hutauruk, Parada T. P.; Bentz, Wolfgang; Cloët, Ian C. Physical Review C, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevC.97.055210	journal	May 2018
Pion form factor and charge radius from lattice QCD at the physical point Gao, Xiang; Karthik, Nikhil; Mukherjee, Swagato Physical Review D, Vol. 104, Issue 11 https://doi.org/10.1103/PhysRevD.104.114515	journal	December 2021
A measurement of the kaon charge radius Amendolia, S. R.; Batignani, G.; Beck, G. A. Physics Letters B, Vol. 178, Issue 4 https://doi.org/10.1016/0370-2693(86)91407-3	journal	October 1986
Generalized parton distributions in impact parameter space Diehl, M. The European Physical Journal C, Vol. 31, Issue 2 https://doi.org/10.1140/epjc/s2003-01356-4	journal	November 2003
Effective field theory description of the pion form factor Guerrero, Francisco; Pich, Antonio Physics Letters B, Vol. 412, Issue 3-4 https://doi.org/10.1016/S0370-2693(97)01070-8	journal	October 1997
Pion Structure as Observed in the Reaction π − N → μ + μ − X at 80 GeV/ c Palestini, S.; Biino, C.; Greenhalgh, J. F. Physical Review Letters, Vol. 55, Issue 24 https://doi.org/10.1103/PhysRevLett.55.2649	journal	December 1985
Three loop tensor current anomalous dimension in QCD Gracey, J. A. Physics Letters B, Vol. 488, Issue 2 https://doi.org/10.1016/S0370-2693(00)00859-5	journal	August 2000
Spin densities in the transverse plane and generalized transversity distributions Diehl, M.; Hägler, Ph. The European Physical Journal C, Vol. 44, Issue 1 https://doi.org/10.1140/epjc/s2005-02342-6	journal	September 2005
Flavor dependence of the pion and kaon form factors and parton distribution functions Hutauruk, Parada T. P.; Cloët, Ian C.; Thomas, Anthony W. Physical Review C, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevC.94.035201	journal	September 2016
Computation of the electromagnetic pion form factor from lattice QCD in the ε regime Fukaya, H.; Aoki, S.; Hashimoto, S. Physical Review D, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevD.90.034506	journal	August 2014
Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action Becirevic, D.; Gimenez, V.; Lubicz, V. Journal of High Energy Physics, Vol. 2004, Issue 08 https://doi.org/10.1088/1126-6708/2004/08/022	journal	August 2004
Revealing the structure of light pseudoscalar mesons at the electron–ion collider Arrington, J.; Gayoso, C. Ayerbe; Barry, P. C. Journal of Physics G: Nuclear and Particle Physics, Vol. 48, Issue 7 https://doi.org/10.1088/1361-6471/abf5c3	journal	May 2021
Coincidence Electroproduction of Charged Pions and the Pion Form Factor Brown, C. N.; Canizares, C. R.; Cooper, W. E. Physical Review D, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevD.8.92	journal	July 1973
Charged pion form factor between $Q^{2} = 0.60$ and 2.45 ${GeV}^{2}$ . I. Measurements of the cross section for the $^{1} H (e, e^{'} π^{+}) n$ reaction Blok, H. P.; Horn, T.; Huber, G. M. Physical Review C, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevC.78.045202	journal	October 2008
Dispersive and chiral symmetry constraints on the light meson form factors Caprini, I. The European Physical Journal C, Vol. 13, Issue 3 https://doi.org/10.1007/s100520000308	journal	April 2000
Charged pion form factor between $Q^{2} = 0.60$ and $2.45 GeV^{2}$ . II. Determination of, and results for, the pion form factor Huber, G. M.; Blok, H. P.; Horn, T. Physical Review C, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevC.78.045203	journal	October 2008
Determination of the longitudinal and the transverse part in π+ electroproduction Ackermann, H.; Azemoon, T.; Gabriel, W. Nuclear Physics B, Vol. 137, Issue 3 https://doi.org/10.1016/0550-3213(78)90523-0	journal	May 1978
$N_f$ dependence of the quark condensate from a chiral sum rule Moussallam, B. The European Physical Journal C, Vol. 14, Issue 1 https://doi.org/10.1007/s100520000303	journal	May 2000
Quark masses using twisted-mass fermion gauge ensembles Alexandrou, C.; Bacchio, S.; Bergner, G. Physical Review D, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevD.104.074515	journal	October 2021

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