Dimension-Six Terms in the Standard Model Lagrangian

When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmueller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in Ref.[3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 4 new operators arise in the four-fermion sector.Comment: 16 pages, no figures, v3: Redundant B-violating operator remove

Anomalous Neutrino Reactions at HERA

We study the sensitivity of HERA to new physics using the helicity suppressed reaction $e_R p \rightarrow \nu X$, where the final neutrino can be a standard model one or a heavy neutrino. The approach is model independent and is based on an effective lagrangian parametrization. It is shown that HERA will put significant bounds on the scale of new physics, though, in general, these are more modest than previously thought. If deviations from the standard model are observed in the above processes, future colliders such as the SSC and LHC will be able to directly probe the physics responsible for these discrepancies}Comment: 11 Pages + 2 figures is TOPDRAWER (included at the end or available by mail). Report UCRHEP-T113 (requires the macropackage PHYZZX). A line in the TeX file requesting an input file has been removed, it caused problem

Testing the Higgs boson gluonic couplings at LHC

We study Higgs + jet production at hadron colliders in order to look for new physics residual effects possibly described by the $dim=6$ operators {\O}_{GG} and {\widetilde\O}_{GG} which induce anomalous $Hgg$ and $Hggg$ couplings. Two ways for constraining these operators at LHC may be ~useful. The first is based on the total Higgs boson production rate induced by gluon-gluon fusion, in which the main cause of limitations are due to theoretical uncertainties leading to sensitivities of $|d_G|\simeq 3.\times 10^{-4}$ and $|\widetilde{d}_G|\simeq 1.4\times 10^{-3}$ for the corresponding anomalous couplings, in the mass range 100 GeV \lsim \mh \lsim 2~00 GeV. These results imply sensitivity to new physics scales of 51 and 24 TeV respectively. The second way investigated here concerns the shape of the Higgs transverse momentum; for which the theoretical uncertainties are less severe and the limitations are mainly induced by statistics. A simple analysis, based on the ratio of the number of events at large and low $p_T$ at LHC, leads to similar sensitivities, if only the $H\to \gamma \gamma$ decay mode is used. But the sensitivities can now be improved by a factor 2 to 10, depending on the Higgs mass, if the Higgs decay modes to $WW^*$, $ZZ^*$, $WW$, $ZZ$ are also used.Comment: 23 pages and 7 figures, version to appear in Phys.ReV.D. e-mail: [email protected]

Field Transformations and the Classical Equation of Motion in Chiral Perturbation Theory

The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory. The use of the 'classical equation of motion' is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations not only eliminates structures, or, what is equivalent, expresses certain structures in terms of already known different structures, but also leads to a modification of coefficients of higher--order terms. This will become relevant, once one considers effective interaction terms beyond next--to--leading order, i.e., beyond $O(p^4)$.Comment: TRIUMF preprint TRI-PP-94-64, 10 pages in LaTex using RevTex macr

A Perturbative Calculation of the Electromagnetic Form Factors of the Deuteron

Making use of the effective field theory expansion recently developed by the authors, we compute the electromagnetic form factors of the deuteron analytically to next-to-leading order (NLO). The computation is rather simple, and involves calculating several Feynman diagrams, using dimensional regularization. The results agree well with data and indicate that the expansion is converging. They do not suffer from any ambiguities arising from off-shell versus on-shell amplitudes.Comment: 22 pages, 8 figures. Discussion of effective range theory added, typos correcte

Higgs-Boson Mass Limits and Precise Measurements beyond the Standard Model

The triviality and vacuum stability bounds on the Higgs-boson mass (\mh) were revisited in presence of weakly-coupled new interactions parameterized in a model-independent way by effective operators of dimension 6. The constraints from precision tests of the Standard Model were taken into account. It was shown that for the scale of new physics in the region \Lambda \simeq 2 \div 50 \tev the Standard Model triviality upper bound remains unmodified whereas it is natural to expect that the lower bound derived from the requirement of vacuum stability is substantially modified depending on the scale \La and strength of coefficients of effective operators. A natural generalization of the standard triviality condition leads also to a substantial reduction of the allowed region in the (\Lambda,\mh) space.Comment: 18 pages 3 eps figures. The discussion in the appendix was modified slightly and some typographical errors were correcte

Bounds on the Higgs-Boson Mass in the Presence of Non-Standard Interactions

The triviality and vacuum stability bounds on the Higgs-boson mass are revisited in the presence of new interactions parameterized in a model-independent way by an effective lagrangian. When the scale of new physics is below 50 TeV the triviality bound is unchanged but the stability lower bound is increased by 40-60 GeV. Should the Higgs-boson mass be close to its current lower experimental limit, this leads to the possibility of new physics at the scale of a few TeV, even for modest values of the effective lagrangian parameters.Comment: 5 pages, 2 figures, RevTex, submitted to PR

Virtual Compton scattering off the nucleon at low energies

We investigate the low-energy behavior of the four-point Green's function $\Gamma^{\mu\nu}$ describing virtual Compton scattering off the nucleon. Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive the leading terms of an expansion of the operator in the four-momenta $q$ and $q'$ of the initial and final photon, respectively. The model-independent result is expressed in terms of the electromagnetic form factors of the free nucleon, i.e., on-shell information which one obtains from electron-nucleon scattering experiments. Model-dependent terms appear in the operator at $O(q_\alpha q'_\beta)$, whereas the orders $O(q_\alpha q_\beta)$ and $O(q'_\alpha q'_\beta)$ are contained in the low-energy theorem for $\Gamma^{\mu\nu}$, i.e., no new parameters appear. We discuss the leading terms of the matrix element and comment on the use of on-shell equivalent electromagnetic vertices in the calculation of ``Born terms'' for virtual Compton scattering.Comment: 26 pages, RevTex, to appear in Phys. Rev.

Extension of the Chiral Perturbation Theory Meson Lagrangian to Order P6P^6

We have derived the most general chirally invariant Lagrangian ${\cal L}_6$ for the meson sector at order $p^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\cal L}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion' terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating $p^6$ contributions to simple processes.Comment: 59 pages in LaTex, using RevTex macro, TRIUMF preprint TRI-PP-94-6

Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO

We consider the Standard Model as an effective theory at the weak scale $v$ of a generic new strong interaction that dynamically breaks electroweak symmetry at the energy scale $\Lambda\sim$ (few) TeV. Assuming only the minimal field content with the Standard Model fermions and gauge bosons, but without a light Higgs particle, we construct the complete Lagrangian through next-to-leading order, that is, including terms of order $v^2/\Lambda^2$. The systematics behind this expansion is clarified. Although similar to chiral perturbation theory, it is not governed by the dimension of operators alone, but depends in an essential way on the loop expansion. Power-counting formulas are derived that indicate the classes of operators required at the next-to-leading order. The complete set of operators at leading and next-to-leading order is then listed, based on the restrictions implied by the Standard-Model gauge symmetries. We recover the well-known operators discussed in the literature in connection with the electroweak chiral Lagrangian and in similar contexts, but we collect a complete and systematic list of all terms through order $v^2/\Lambda^2$. This includes some operators not discussed in explicit terms before. We also show that a few of the previously considered operators can be eliminated via the equations of motion. As another important result we confirm the known list of dimension-6 operators in the Standard Model with an elementary Higgs doublet, essentially as a special case of our scenario.Comment: 35 pages, 1 figure; references adde