First direct lattice calculation of the chiral perturbation theory low-energy constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mo>ℓ</mml:mo><mml:mn>7</mml:mn></mml:msub></mml:math>
نویسندگان
چکیده
We evaluate by means of lattice QCD calculations the low-energy constant $\ell_{7}$ which parametrizes strong isospin effects at NLO in $\rm{SU}(2)$ chiral perturbation theory. Among all constants NLO, is one known less precisely, and its uncertainty currently larger than $50\%$. Our strategy based on RM123 approach path-integral expanded powers breaking parameter $\Delta m= (m_{d}-m_{u})/2$. In order to relevant correlators we make use recently proposed rotated twisted-mass (RTM) scheme. Within approach, it possible cleanly extract value from either pion mass splitting $M_{\pi^{+}}-M_{\pi^{0}}$ induced $\mathcal{O}\left((\Delta m)^{2}\right)$ (mass method), or coupling neutral $\pi^{0}$ isoscalar operator $\left(\bar{u}\gamma_{5}u + \bar{d}\gamma_{5} d\right)/\sqrt{2}$ $\mathcal{O}(\Delta m)$ (matrix element method). this pilot study limit analysis a single ensemble generated Extended Twisted Mass Collaboration (ETMC) with $N_{f}=2+1+1$ dynamical quark flavours, corresponds spacing $a\simeq 0.095~{\rm fm}$ $M_{\pi}\simeq 260~{\rm MeV}$. find that matrix method outperforms terms resulting statistical accuracy. determination, $\ell_{7} = 2.5(1.4)\times 10^{-3}$, agreement improves previous calculations.
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ژورنال
عنوان ژورنال: Physical review
سال: 2021
ISSN: ['0556-2813', '1538-4497', '1089-490X']
DOI: https://doi.org/10.1103/physrevd.104.074513