اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدشعاع المقياس للبيون والأصفار في شكل العامل
Scalar radius of the pion and zeros in the form factor
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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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