<i>Current Algebras and Application to Particle Physics</i> and <i>Current Algebras and Their Applications</i>

Adler, Stephen L.; Renner, B.; Bernstein, Jeremy

doi:10.1063/1.3034556

Cited by 24 publications

(45 citation statements)

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“…This symmetry has been accepted as a fundamental concept in the hadron physics due to the successes of the various low energy theorems [10] and the chiral perturbation theory in the threshold region [11,12]. These studies are based on spontaneous broken chiral symmetry, where the pions are considered as the Nambu-Goldstone bosons realized by this symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

Δ(1232)inπN→ππNreaction

Kammano

Masaki

2004

Phys. Rev. C

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The contribution of ∆(1232) to the πN → ππN reaction is examined by making use of the chiral reduction formula developed by Yamagishi and Zahed. The influence of the π∆∆ and ρN ∆ interactions on this reaction, which has not been regarded as important so far, is considered for all channels with the initial π ± p states. The total cross sections are calculated to tree level for the energy up to T π = 400 MeV. Although the π∆∆ and ρN ∆ interactions give a small effect on the π + p → π + π + n, π − p → π + π − n, and π − p → π 0 π 0 n channels, the π ± p → π ± π 0 p channels are found to be sensitive to these interactions.

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Section: Introductionmentioning

confidence: 99%

Δ(1232)inπN→ππNreaction

Kammano

Masaki

2004

Phys. Rev. C

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“…impose all those symmetries of the 1-φ-R Tmatrix that are not symmetries of the 1-φ-I Green's functions (6) nor of the complete effective Lagrangian (7). 8 In particular the ν D SM G tbτ ντ -analogue of the Adler selfconsistency conditions [38,39] (see for example [33] p. 37), derived in Appendix A, of which the Goldstone Theorem is a special case, ensures the infra-red finiteness of the theory for exactly zero pseudoscalar masses, m 2 π = 0.…”

Section: ) Spontaneously Brokenmentioning

confidence: 99%

“…Infra-red finiteness, Goldstone theorem, and automatic tadpole renormalization "Whether you like it or not, you have to include in the Lagrangian all possible terms consistent with locality and power counting, unless otherwise constrained by Ward identities." Kurt Symanzik, in a 1970 private letter to Raymond Stora [46] In Appendix A we extend Adler's self-consistency condition [38,39] (originally written for the SU (2) L × SU (2) R Gell-Mann-Lévy model [17]), to the case of the ν D SM G tbτ ντ Lagrangian (1)…”

Section: 4mentioning

confidence: 99%

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Global SU(3)C×SU(2)L
Lynn¹,
Starkman²
2017
Phys. Rev. D
1
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3
0
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This work is dedicated to the memory of Raymond Stora . In the SU (2)L × SU (2)R Linear Sigma Model with PCAC, a tower of Ward-Takahashi Identities (WTI) have long been known to give relations among 1-Scalar-Particle-Irreducible (1-φ-I) Green's functions, and among I-Scalar-Particle-Reducible (1-φ-R) T-Matrix elements for external scalars (i.e. the Brout-Englert-Higgs (BEH) scalar H, and 3 pseudoscalars π). In this paper, we extend these WTI and the resulting relations to the SU (3)C × SU (2)L × U (1)Y Linear Sigma Model including the heaviest generation of Standard Model (SM) fermions -the ungauged (i.e. global) Standard Model SM G tbτ ντ -supplemented with the minimum necessary neutrino content -right-handed neutrinos and Yukawa-coupling-induced Dirac neutrino mass, to obtain the CP -conserving νDSM G tbτ ντ , and extract powerful constraints on the effective Lagrangian: e.g. showing that they make separate tadpole renormalization unnecessary, and guarrantee infra-red finiteness. The crucial observation is that ultra-violet quadratic divergences (UVQD), and all other relevant operators, contribute only to m 2 π , a pseudo-Nambu-Goldstone boson (NGB) mass-squared, which appears in intermediate steps of calculations. A WTI between Transition-Matrix elements (or, in this global theory equivalently the Goldstone Theorem) then enforces m 2 π = 0 exactly for the true NGB in the spontaneous symmetry breaking (SSB) mode of the theory. The Goldstone Theorem thus causes all relevant operator contributions, originating to all-loop-orders from virtual scalars H, π, quarks q c L ; t c R ; b c R and leptons lL; ντ R ; τR with (c = r, w, b), to vanish identically! We show that our regularization-scheme-independent, WTI-driven results are unchanged by the addition of certain SU (3)C ×SU ( W eak . Specifically, we prove that these heavy degrees of freedom decouple completely from the low-energy νDSM G tbτ ντ effective Lagrangian, contributing only irrelevant operators after quarticcoupling renormalization.

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“…Finally, let us consider a problem in current algebra 117 ), the soft-meson theorems for n + 3n decay. We shall see that it is essential that the analysis be carried out in terms of short-distance expansions.…”

Section: N + 3n Decaymentioning

confidence: 99%

Asymptotic Behaviour in Quantum Field Theory

Crewther¹

1976

Weak and Electromagnetic Interactions at High Energies

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Convergence is tested by applying power-counting arguments 10 • 11 ). Imagine that a subset S = {p~, ... , p~} of the loop momenta {p 1 , ••• , p£} is scaled to infinity [all p~ = O(n) with n ~ 00 ] with all other momenta held fixed*). The exponent c(r) for its asymptotic behaviour as p 1 , ••• , p£ become large is reduced by at least 1, while no increase occurs in the other c(S). Therefore, if a/aq.1.is applied a sufficient number of times tor, the result is completely convergent.Since rd. (the divergent part of r) is annihilated by these differentiations, it lV must be a polynomial of degree~ d(r) in q 1 , ••• , qL-l. In diagrammatic language ( Fig. 1), this means that rd. is a local vertex produced by shrinking the blob r lV to a point.An £-loop divergence of this type is easily cancelled by including a counterterm ~ff£ in the Lagrangian ;t with bare vertex equal to -rdiv' However, many lPI graphs do not possess this property of being "primitively divergent"~<*). An arbitrary £-loop lPI graph may contain divergent £ 1 -loop lPI subgraphs (£ 1 < £) which must first be made convergent by including suitable counterterms ~ff£' in ff; i.e., it will be necessary to include internal counterterm vertices in the blob in Fig. 1. So we try the following prescription 10 • 12 ): *) **)More precisely, write pj = nrj and let n tend to 00 , keeping all rj, Pi ('any pj), and qi fixed and not allowing any partial sum L' r of the rj to vanish.Tfle latter condition ensures that a p 1 -dependent propagator (which carries momentum n l' r + ~p1p' p + f 1 q) has the expected asymptotic dependence on n. The special directions l r = 0 are covered by looking at appropriate su b sets s' of s .A primitively divergent graph becomes convergent if any internal line is cut.-3 -i) Start with !t 0 , a Lagrangian from which propagators and vertices can be constructed.ii) Construct counterterms 62? 1 which remove all divergences in 1-loop lPI graphs generated by 21 0 • iii) Use a new Lagrangian 'l! 1 = :t + 6 'l! to generate 2-loop graphs and construct , a , 16 '/! 2 to get rid of the resulting lPI divergences, and so on, to any finite number of loops and vertices 13 ):J,1 = ii-I + ~£1.Obviously, we obtain finite results for diagrams in which, for each pair of divergent lPI subgraphs, one subgraph is entirely contained within the other ("nested" divergences) or the two subgraphs are disjoint. The difficult step in the proof 12 )of convergence is to disentangle overlapping divergences (sets of divergent lPI graphs which are neither disjoint nor nested). The result, valid for all polynomial interactions (renormalizable or otherwise), is that the above procedure renders all subintegrations convergent by power-counting*). In other words, the Given the constraint (1.6), the rule for renormalization counterterms ~Q generated by lPI diagrams with a single Q-insertion is simply dim(Q) (1. 8) For example, consider = I 2. d);i., 2m1(1. 9)as a trial Lagrangian. Only the two-and four-legged lPI amplitudes r( 2 ),r ( 4 ) are superficially divergent. Accor...

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Current Algebras and Application to Particle Physics and Current Algebras and Their Applications

Cited by 24 publications

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Δ(1232)inπN→ππNreaction

Δ(1232)inπN→ππNreaction

Global SU(3)C×SU(2)L
Lynn¹,
Starkman²
2017
Phys. Rev. D
1
0
3
0
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Asymptotic Behaviour in Quantum Field Theory

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Current Algebras and Application to Particle Physics and Current Algebras and Their Applications

Cited by 24 publications

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Δ(1232)inπN→ππNreaction

Δ(1232)inπN→ππNreaction

Global SU(3)C×SU(2)LLynn1, Starkman2 2017Phys. Rev. D1030View full textAdd to dashboardCite

Asymptotic Behaviour in Quantum Field Theory

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Global SU(3)C×SU(2)L
Lynn¹,
Starkman²
2017
Phys. Rev. D
1
0
3
0
View full text Add to dashboard Cite