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Register a new userScalar radius of the pion and zeros in the form factor
شعاع المقياس للبيون والأصفار في شكل العامل
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شعاع البيون المربع، لا ر ^ 2 را ^ بي_س، يلعب دورا مهما لتحديدات الدقيقة الحالية لإطارات البيون. في الأخير، يحصل يندوراين على لا ر ^ 2 را ^ بي_س = 0.75 بم 0.07 فم ^ 2 باستخدام تمثيل أومنيس للعامل الشكلي البيون الغير متشابه للإسوبين الصفر (أيه). هذه القيمة أكبر من القيمة المحسوبة عن طريق حل المعادلات المسخليشويلي-أومنيس، لا ر ^ 2 را ^ بي_س = 0.61 بم 0.04 فم ^ 2. وبالتالي يحدث فرق كبير بين كلا القيم، بالنسبة للدقة. نحن نجدد طريقة يندوراين ونظهر أنه عند تطبيق الاستمرارية للعامل الشكلي البيون الغير متشابه للإسوبين الصفر تحت التغييرات الصغيرة في إطارات البيون المدخلة، يتطلب ذلك صفرا في العامل الشكلي لبعض تطبيقات الطاقة المنخفضة الصف الصفر I = 0. وبمجرد الحساب لذلك، يصبح النتيجة لا ر ^ 2 را ^ بي_س = 0.65 بم 0.05 فم ^ 2. المصدر الرئيسي لخطأ في تحديدنا هو الأخطاء التجريبية الحالية في إطارات البيون الصف الصفر I = 0 المنخفضة. وتساهم أخرى مهمة في خطأنا هي السلوك التطبيقي الغير محدد بعد الآن لمطابقة الشكل البيون الغير متشابه للإسوبين الصفر من QCD.
The quadratic pion scalar radius, la r^2ra^pi_s, plays an important role for present precise determinations of pipi scattering. Recently, Yndurain, using an Omn`es representation of the null isospin(I) non-strange pion scalar form factor, obtains la r^2ra^pi_s=0.75pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omn`es equations, la r^2ra^pi_s=0.61pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Yndurains method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input pipi phase shifts, a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is la r^2ra_s^pi=0.65pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0 pipi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.
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We report on a program to compute the electromagnetic form factors of mesons. We discuss the techniques used to compute the pion form factor and present results computed with domain wall valence fermions on MILC asqtad lattices, as well as with Wilson fermions on quenched lattices. The methods can easily be extended to rho-to-gamma-pi transition form factors.
We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the rho to pions is largely independent of the quark mass while the quark mass dependence of the rho--mass is given by recent lattice data. By employing the Omnes representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the rho-pi-pi coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely <r^4> = 0.73 +- 0.09 fm^4 or equivalently c_V=4.00pm 0.50 GeV^{-4}.
The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive rho-meson is used to calculate the scalar radius of the pion at next to leading (one loop) order in perturbation theory. Due to renormalizability, this determination involves no free parameters. The result is $<r^2_pi>_s = 0.40 {fm}^2$. This value gives for $bar{ell}_4$, the low energy constant of chiral perturbation theory, $bar{ell}_4 = 3.4$, and $F_pi/F = 1.05$, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the $rhopipi$ coupling, the only sizable uncertainty in this result is due to the (uncalculated) NNLO contribution.
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J. P. B. C. de Melo
, R^omulo Moreira Moita
, Kazuo Tsushiman (Laboratorio de Fisica Teorica e Computacional
2016
The pion electromagnetic form factor is calculated at lower and higher momentum transfer in order to explore constituent quark models and the differences among those models. In particular, the light-front constituent quark model is utilized here to calculate the pion electromagnetic form factor at lower and higher energies. The matrix elements of the electromagnetic current, are calculated with both plus and minus components of the electromagnetic current in the light-front. Further, the electromagnetic form factor is compared with other models in the literature and experimental data.
We consider the pion structure in the region of low and moderately high momentum transfers: at low $Q^2$, the pion is treated as a composite system of constituent quarks; at moderately high momentum transfers, $Q^2=10div25;GeV^2$, the pion ff is calculated within perturbative QCD taking into account one--gluon hard exchange. Using the data on pion ff at $Q^2<3;GeV^2$ and pion axial--vector decay constant, we reconstruct the pion wf in the soft and intermediate regions. This very wave function combined with one--gluon hard scattering amplitude allows a calculation of the pion ff in the hard region $Q^2=10div25;GeV^2$. A specific feature of the reconstructed pion wf is a quasi--zone character of the $qbar q$--excitations. On the basis of the obtained pion wf and the data on deep inelastic scattering off the pion, the valence quark distribution in a constituent quark is determined.
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