# Matrix elements of the electromagnetic operator between kaon and pion states

## Abstract

We compute the matrix elements of the electromagnetic operator sF{sub {mu}{nu}}{sigma}{sup {mu}{nu}}d between kaon and pion states, using lattice QCD with maximally twisted-mass fermions and two flavors of dynamical quarks (N{sub f}=2). The operator is renormalized nonperturbatively in the RI'/MOM scheme and our simulations cover pion masses as light as 270 MeV and three values of the lattice spacing from {approx_equal}0.07 up to {approx_equal}0.1 fm. At the physical point our result for the corresponding tensor form factor at zero-momentum transfer is f{sub T}{sup K{pi}}(0)=0.417(14{sub stat})(5{sub syst}), where the systematic error does not include the effect of quenching the strange and charm quarks. Our result differs significantly from the old quenched result f{sub T}{sup K{pi}}(0)=0.78(6) obtained by the SPQ{sub cd}R Collaboration with pion masses above 500 MeV. We investigate the source of this difference and conclude that it is mainly related to the chiral extrapolation. We also study the tensor charge of the pion and obtain the value f{sub T}{sup {pi}{pi}}(0)=0.195(8{sub stat})(6{sub syst}) in good agreement with, but more accurate than the result f{sub T}{sup {pi}{pi}}(0)=0.216(34) obtained by the QCDSF Collaboration using higher pion masses.

- Authors:

- Dip. di Fisica, Universita di Roma ''La Sapienza'', P.le A. Moro 5, I-00185 Roma (Italy)
- Dip. di Fisica, Universita Roma Tre, Via della Vasca Navale 84, I-00146 Roma (Italy)
- (Italy)
- SISSA, Via Bonomea 265, I-34136 Trieste (Italy)
- INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Roma (Italy)

- Publication Date:

- OSTI Identifier:
- 21607798

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.84.074503; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRALITY; EXTRAPOLATION; FLAVOR MODEL; FORM FACTORS; KAONS; MASS; MATRIX ELEMENTS; MEV RANGE 100-1000; MOMENTUM TRANSFER; PIONS; QUANTUM CHROMODYNAMICS; QUARKS; QUENCHING; SIMULATION; BOSONS; COMPOSITE MODELS; DIMENSIONLESS NUMBERS; ELEMENTARY PARTICLES; ENERGY RANGE; FERMIONS; FIELD THEORIES; HADRONS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; MESONS; MEV RANGE; NUMERICAL SOLUTION; PARTICLE MODELS; PARTICLE PROPERTIES; PSEUDOSCALAR MESONS; QUANTUM FIELD THEORY; QUARK MODEL; STRANGE MESONS; STRANGE PARTICLES

### Citation Formats

```
Baum, I., Lubicz, V., INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Martinelli, G., Orifici, L., and Simula, S.
```*Matrix elements of the electromagnetic operator between kaon and pion states*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.84.074503.

```
Baum, I., Lubicz, V., INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Martinelli, G., Orifici, L., & Simula, S.
```*Matrix elements of the electromagnetic operator between kaon and pion states*. United States. doi:10.1103/PHYSREVD.84.074503.

```
Baum, I., Lubicz, V., INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Martinelli, G., Orifici, L., and Simula, S. Sat .
"Matrix elements of the electromagnetic operator between kaon and pion states". United States. doi:10.1103/PHYSREVD.84.074503.
```

```
@article{osti_21607798,
```

title = {Matrix elements of the electromagnetic operator between kaon and pion states},

author = {Baum, I. and Lubicz, V. and INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Roma and Martinelli, G. and Orifici, L. and Simula, S.},

abstractNote = {We compute the matrix elements of the electromagnetic operator sF{sub {mu}{nu}}{sigma}{sup {mu}{nu}}d between kaon and pion states, using lattice QCD with maximally twisted-mass fermions and two flavors of dynamical quarks (N{sub f}=2). The operator is renormalized nonperturbatively in the RI'/MOM scheme and our simulations cover pion masses as light as 270 MeV and three values of the lattice spacing from {approx_equal}0.07 up to {approx_equal}0.1 fm. At the physical point our result for the corresponding tensor form factor at zero-momentum transfer is f{sub T}{sup K{pi}}(0)=0.417(14{sub stat})(5{sub syst}), where the systematic error does not include the effect of quenching the strange and charm quarks. Our result differs significantly from the old quenched result f{sub T}{sup K{pi}}(0)=0.78(6) obtained by the SPQ{sub cd}R Collaboration with pion masses above 500 MeV. We investigate the source of this difference and conclude that it is mainly related to the chiral extrapolation. We also study the tensor charge of the pion and obtain the value f{sub T}{sup {pi}{pi}}(0)=0.195(8{sub stat})(6{sub syst}) in good agreement with, but more accurate than the result f{sub T}{sup {pi}{pi}}(0)=0.216(34) obtained by the QCDSF Collaboration using higher pion masses.},

doi = {10.1103/PHYSREVD.84.074503},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 7,

volume = 84,

place = {United States},

year = {2011},

month = {10}

}