اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThermal Behaviour of $pi-pi$ Scattering Lengths in the Nambu--Jona-Lasinio model
101
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We calculate the thermal evolution of $pi-pi$ scattering lengths, in the frame of the Nambu--Jona-Lasinio model. The thermal corrections were calculated at the one loop level using Thermofield Dynamics. We present also results for the pion thermal mass. Our procedure implies the modeling of a propagating scalar meson as a resumation of chains of quark bubbles, which is presented explicitly. We compare our results with previous analysis of this problem in the frame of different theoretical approaches.
قيم البحث
اقرأ أيضاً
Using the Nambu--Jona-Lasinio model with the $U(2)times U(2)$ chiral symmetric effective four-quark interactions, we derive the amplitude of the radiative decay $f_1(1285) topi^+pi^-gamma$, find the decay width $Gamma (f_1topi^+pi^-gamma)=346,mbox{ke
V}$ and obtain the spectral di-pion effective mass distribution. It is shown that in contrast to the majority of theoretical estimates (which consider the $a_1(1260)$ meson exchange as the dominant one), the most relevant contribution to this process comes out from the $rho^0$-resonance exchange related with the triangle $f_1rho^0gamma$ anomaly. The spectral function is obtained to be confronted with the future empirical data.
Within the framework of the extended Nambu -- Jona-Lasinio model, we calculate the matrix element of the $tau to f_1(1285) pi^{-} u_{tau}$ decay, obtain the invariant mass distribution of the $f_1pi$ -system and estimate the branching ratio Br$(tau
to f_1 pi^{-} u_{tau})=4.0times 10^{-4}$. The two types of contributions are considered: the contact interaction, and the axial-vector $I^G(J^{PC})=1^-(1^{++})$ resonance exchange. The latter includes the ground $a_1(1260)$ state, and its first radially excited state, $a_1(1640)$. The corrections caused by the $pi -a_1$ transitions are taken into account. Our estimate is in a good agreement with the latest empirical result Br$(tau to f_1 pi^{-} u_{tau})=(3.9pm 0.5)times 10^{-4}$. The distribution function obtained for the decay $tau to f_1(1285) pi^{-} u_{tau}$ shows a clear signal of $a_1(1640)$ resonance which should be compared with future experimental data including our estimate of the decay width $Gamma (a_1(1640) to f_1 pi )=14.1,mbox{MeV}$.
The anomalous decays $f_1(1285)torho^0pi^+pi^-$ and $a_1(1260)toomegapi^+pi^-$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu -- Jona-Lasinio model. We consider the Lagrangian with $U(2)_Ltimes U(2)_R
$ chiral symmetric four quark interactions. The theory is bosonized and corresponding effective meson vertices are obtained in the leading order of $1/N_c$ and derivative expansions. The uncertainties related with the surface terms of anomalous quark triangle diagrams are fixed by the corresponding symmetry requirements. We make a numerical estimate of the decay widths $Gamma (f_1(1285)torho^0pi^+pi^-)=2.78, mbox{MeV}$ and $Gamma (a_1(1260)toomegapi^+pi^-)=87, mbox{keV}$. Our result on the $f_1(1285)torho^0pi^+pi^-$ decay rate is in a good agreement with experiment. It is shown that a strong suppression of the $a_1(1260)toomega pipi$ decay is a direct consequence of destructive interference between box and triangle anomalies.
Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure Nambu-Jona-Lasinio mod
el is not renormalizable, presence of the gauge interaction makes it possible that the theory is renormalized as an interacting continuum theory at the critical line in the ladder approximation. Extra higher dimensional operators (``counter terms) are not needed for the theory to be renormalized. By virtue of the effective potential approach, the renormalization (``symmetric renormalization) is performed in a phase-independent manner both for the symmetric and the spontaneously broken phases of the chiral symmetry. We explicitly obtain $beta$ function having a nontrivial ultraviolet fixed line for the renormalized coupling as well as the bare one. In both phases the anomalous dimension is very large ($ ge 1$) without discontinuity across the fixed line. Operator product expansion is explicitly constructed, which is consistent with the large anomalous dimension owing to the appearance of the nontrivial extra power behavior in the Wilson coefficient for the unit operator. The symmetric renormalization breaks down at the critical gauge coupling, which is cured by the generalized renormalization scheme (``$tM$-dependent renormalization). Also emphasized is the formal resemblance to the four-fermion theory in less than four dimensions which is renormalizable in $1/N$ expansion.
We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-
Jona-Lasinio model with all the parameters properly fixed by the QCD Lagrangian and the determination of the mass gap of the gluon sector.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
