<i>π</i>-<i>π</i>scattering and chiral Lagrangians

Donoghue, John F.; Ramírez, Carlos A.; Valencia, G.

doi:10.1103/physrevd.38.2195

Cited by 67 publications

(58 citation statements)

References 21 publications

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“…As such, π − π reactions provide a direct link between the theoretical formalism of chiral symmetry and experiment. This is exemplified in the many existing studies of π − π scattering using chiral Lagrangians [1][2][3][4][5][6][7] that endeavour to calculate scattering amplitudes and scattering lengths. References [1][2][3] introduce [1] and use [2,3] chiral perturbation theory (ChPT), while [4][5][6] calculate scattering lengths in the Nambu-Jona-Lasinio (NJL) model [8,9].…”

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confidence: 99%

“…Both s and p wave scattering lengths are well reproduced in these models. Essentially, the Weinberg limit [10] can be recovered in all cases, and corrections to it, due to processes such as pion rescattering are accounted for, for example in [2].…”

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confidence: 99%

“…This is so for several reasons. In particular, this scattering involves only the lightest pseudoscalar modes of the theory, that occupy a special role as being the Goldstone particles associated with the almost exact SU L (2) × SU R (2) symmetry that is observed in the particle spectrum. As such, π − π reactions provide a direct link between the theoretical formalism of chiral symmetry and experiment.…”

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π-π scattering lengths at finite temperature

et al. 1995

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The s-wave π − π scattering lengths a I (T ) at finite temperature T and isospin I = 0, 2 are calculated within the SU(2) Nambu-Jona-Lasinio model. a 2 (T ) displays a singularity at the Mott temperature T M , defined as m π (T M ) = 2m q (T M ), while a 0 (T ) is singular in addition at the lower temperature T d , where, m σ and m π being the masses of the σ and π mesons, respectively. Numerically we find T d = 198MeV and T M = 215MeV. We speculate on possible experimental consequences.. *

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π-π scattering lengths at finite temperature

et al. 1995

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“…Early work describing the one loop chiral calculation of γγ → π 0 π 0 yielded results which, while valid for small enough pion mass, receive significant corrections even at the physical threshold. These corrections have been seen in a two loop chiral calculation [5] and in dispersive studies [4], [11], and are also needed experimentally. Since the chiral results for this particular reaction are modified at such a low energy, one needs to use other methods in order to work at higher energies.…”

Section: γγ → ππ and A Model For γγ → W W Zzmentioning

confidence: 99%

The reactions γγ → WL+WL− and γγ → ZLZL in SU(N) strongly interacting theories

Donoghue¹,

Torma²

1994

Nuclear Physics B

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“…Also in the SU (2) X SU (2) case we may quote values [ 5 ] extracted from experiment; renormalized at 0.5 GeV they read ot~ x°t = -0.010, ot~ xvt =0.0075. This may be compared to 19/I = -0.0032, ot2= 0.0063 for the case…”

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confidence: 99%

A nonlocal model of chiral dynamics

1989

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We consider a noniocal generalization of the nonlinear a model. Our chirally symmetric model couples quarks with self-energy Z(p) to Goldstone bosons (GBs). By integrating out the quarks we obtain a chiral lagrangian, the parameters of which are finite integrals of Z'(p). We find that chiral symmetry is not sufficient to derive the well-known Pagels-Stokar formula for the GB decay constant. We reproduce the Wess-Zumino term and we illustrate the dependence of other four derivative coefficients on ,Y(p).We wish to consider a simple model of quarks with a nonlocal and nonlinear coupling to a Goldstone boson (GB) field. We hope to capture more of the physics of chiral symmetry breaking in gauge theories than does a standard nonlinear sigma model with the following GB-quark coupling:(1) Our model consists of N flavors of quarks each with Arc "colors" interacting with a GB field via a bilocal coupling: ZP~,(x, y) =@(x)6(x-y)~g(y) + ~(x)Y,,~(x, y)~(y) .( 2) S~ is a nonlinear function, to be determined, of the GB field n(x) -ZaAana(X) [2a are generators of SU(N), Tr ~.a,~b= ½t~ab]. ~n is a nontrivial matrix only in the SU(N)L× SU(N)R flavor space. We shall require that n(x) transforms under chiral transformations in the standard nonlinear manner, and that Z~ transforms in such a way that SU (N)L × SU (N)R is a global symmetry. The model also has a vector U (Arc) "color" symmetry, but we leave this ungauged. We will work in euclidean space.We are considering a bilocal coupling since for vanishing n we shall require that Z,,(x, y)~Z(x-y)di~ (i,j= 1, .... N). S(x-y) is the Fourier transform of the quark self-energy Z(p), a function ofp 2. In a gauge theory with zero bare mass quarks the dynamical self-energy S(p) is the order parameter of chiral symmetry breaking. The appearance of Z(x-y) in our model allows us to input a realistic self-energy as would be determined for example by some approximation to the gap equation in a gauge theory. In contrast, a local sigma model with fermions has S(x-y)ocd(x-y) and Z(p)=constant; this is not representative of a dynamical mass in a gauge theory. Since we use Z(x-y) to represent an order parameter, it is then natural that the Goldstone fields appear as fluctuations in the orientation of Z(x-y) in SU(N)L× SU(N)R.The statement that GBs should appear as "fluctuations of the order parameter" will define our model. It is equivalent to insisting that @(x)Z,~(x, y)g(y) should reduce to ( 1 ) in the special case that Z(x-y) = rod (x-y). This is a nontrivial restriction since various derivative couplings are also allowed in a local nonlinear sigma model; we intentionally omit the nonlocal generalizations of all such terms.The GB kinetic terms and self-couplings will be generated dynamically. In fact we will integrate out the quark fields and show that a derivative expansion yields a local chiral lagrangian for the GBs:

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π-πscattering and chiral Lagrangians

Cited by 67 publications

References 21 publications

π-π scattering lengths at finite temperature

π-π scattering lengths at finite temperature

The reactions γγ → WL+WL− and γγ → ZLZL in SU(N) strongly interacting theories

A nonlocal model of chiral dynamics

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