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We compute the non-perturbative contribution of semileptonic tensor operators $$ \left(\overline{q}{\sigma}^{\mu \nu }q\right)\left(\overline{\ell}{\sigma}_{\mu \nu}\ell \right) $$ q ¯ σ μ ν q ℓ ¯ σ μ ν ℓ to the purely leptonic process μ → eγ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to μ → e processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, ΛBSM ≳ 450 TeV. We briefly discuss how the same method applies to dark-matter interactions.

We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q \sigma^{\mu \nu} q)(\bar \ell \sigma_{\mu \nu} \ell)$ to the purely leptonic process $\mu \to e \gamma$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $\mu \to e $ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $\Lambda_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions., Comment: 21 pages, 1 figure; version published in JHEP

We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. The use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.

We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q ��^{����} q)(\bar \ell ��_{����} \ell)$ to the purely leptonic process $��\to e ��$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $��\to e $ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $��_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions., 21 pages, 1 figure; version published in JHEP

Effective field theories of electroweak symmetry breaking are discussed from a geometric point of view. Deviations of longitudinal gauge boson and scalar scattering amplitudes from their standard model values are given by the curvature of the scalar manifold, which is positive in G/H sigma models. The distinction between linear and non-linear transformations of the scalar fields is explained.

An exactly solvable large $N$ model is constructed which reduces at low energies to the Standard Model plus the dimension six Higgs-gauge operators $g_1^2 H^\dagger H B_{\mu \nu} B^{\mu \nu}$, $g_2^2 H^\dagger H W^a_{\mu \nu} W^{a\mu \nu}$, $g_1 g_2 H^\dagger \tau^a H W^a_{\mu \nu} B^{\mu \nu}$, and $\epsilon^{abc} W^a_{\mu}{}^\nu W^b_{\nu}{}^\rho W^c_{\rho}{}^\mu$. All other dimension six operators are suppressed by powers of $1/N$. The Higgs-gauge operators lead to deviations from the Standard Model $h \to \gamma\gamma$ and $h \to \gamma Z$ rates. A simple variant of the model can be used to also generate the Higgs-gluon operator $g_3^2 H^\dagger H G^A_{\mu \nu} G^{A\mu \nu}$ which contributes to the Higgs production rate via gluon fusion.

We give a general decomposition of the h -> VF amplitude where V={W,Z} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=l^+l^-, l nu (l =e, mu) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracted from a global fit to Higgs signal strengths. We also demonstrate how rare h -> VP decays, where P is a single hadron, with SM rates in the 10^{-5} range, can be used to provide complementary information on the couplings of the newly discovered Higgs-like scalar and are an interesting probe of the vacuum structure of the theory. We give a general decomposition of the h→VF amplitude where V={W±,Z0} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=ℓ+ℓ− , ℓν¯(ℓ=e,μ) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracted from a global fit to Higgs signal strengths. We also demonstrate how rare h→VP decays, where P is a pseudo-scalar meson, with SM rates in the 10−5 range, can be used to provide complementary information on the couplings of the newly discovered Higgs-like scalar and are an interesting probe of the vacuum structure of the theory. We give a general decomposition of the h -> VF amplitude where V={W,Z} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=l^+l^-, l nu (l =e, mu) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracted from a global fit to Higgs signal strengths. We also demonstrate how rare h -> VP decays, where P is a single hadron, with SM rates in the 10^{-5} range, can be used to provide complementary information on the couplings of the newly discovered Higgs-like scalar and are an interesting probe of the vacuum structure of the theory.

We compute the renormalization of dimension six Higgs-gauge boson operators that can modify \Gamma(h -> \gamma \gamma) at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consistent with renormalization group evolution. We study the implications of our results for Higgs phenomenology and for new physics models which attempt to explain a deviation in \Gamma(h -> \gamma \gamma). We derive a new relation between the S parameter and the \Gamma(h -> \gamma \gamma) and \Gamma(h ->Z \gamma) decay rates., Comment: 20 pp. 2 fig

We compute the renormalization of dimension six Higgs-gauge boson operators that can modify ��(h -> ����) at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consistent with renormalization group evolution. We study the implications of our results for Higgs phenomenology and for new physics models which attempt to explain a deviation in ��(h -> ����). We derive a new relation between the S parameter and the ��(h -> ����) and ��(h ->Z ��) decay rates., 20 pp. 2 fig

We give a general decomposition of the h -> VF amplitude where V={W,Z} and F is a generic leptonic or hadronic final state, in the standard model (SM), and in the context of a general effective field theory. The differential distributions for F=l^+l^-, l nu (l =e, mu) are reported, and we show how such distributions can be used to determine modified Higgs couplings that cannot be directly extracted from a global fit to Higgs signal strengths. We also demonstrate how rare h -> VP decays, where P is a single hadron, with SM rates in the 10^{-5} range, can be used to provide complementary information on the couplings of the newly discovered Higgs-like scalar and are an interesting probe of the vacuum structure of the theory., 5 pages, 4 figures [v3: numerics updated, refs added, accepted PLB version]

We derive a factorization formula for the double Drell-Yan cross section in terms of double parton distribution functions (dPDFs). Diparton flavor, spin and color correlations and parton-exchange interference terms contribute, even for unpolarized beams. Soft radiation effects are nontrivial for the color correlation and interference contributions, and are described by non-perturbative soft functions. We provide a field-theoretic definition of the quark dPDFs and study some of their basic properties, including discrete symmetries and their interpretation in a non-relativistic quark model. We calculate the renormalization group evolution of the quark dPDFs and of the soft functions. The evolution receives contributions from both ultraviolet and rapidity divergences. We find that color correlation and interference effects are Sudakov suppressed, greatly reducing the number of dPDFs needed to describe double parton scattering at high energy experiments., 24 pages, 15 figures, v2: added WW cross section, additional spin structures, finite terms of one-loop soft function, journal version

We extend an effective theory framework developped in Refs. [1,2] to sum electroweak Sudakov logarithms in high energy processes to also include massive gauge bosons in the final state. The calculations require an additional regulator on top of dimensional regularization to tame the collinear singularities. We propose to use the Delta regulator, which respects soft-collinear factorization., 7 pages, reference added

We present expressions for shape variables of B decay distributions in several different mass schemes, to order $\alpha_s^2\beta_0$ and (Lambda_{QCD}/mb)^3. Such observables are sensitive to the b quark mass and matrix elements in the heavy quark effective theory, and recent measurements allow precision determinations of some of these parameters. We perform a combined fit to recent experimental results from CLEO, BABAR, and DELPHI, and discuss the theoretical uncertainties due to nonperturbative and perturbative effects. We discuss the possible discrepancy between the OPE prediction, recent BABAR results and the measured branching fraction to D and D* states. We find |Vcb| = (40.8 +- 0.9) x 10^{-3} and mb^{1S} = 4.74 +- 0.10 GeV, where the errors are dominated by experimental uncertainties., Comment: 23 pages, 3 figures, Version to appear in PRD

The 1/k contribution to the heavy quark potential is first generated at one loop order in QCD. We compute the two loop anomalous dimension for this potential, and find that the renormalization group running is significant. The next-to-leading-log coefficient for the heavy quark production current near threshold is determined. The velocity renormalization group result includes the alpha_s^3 ln^2(alpha_s) ``non-renormalization group logarithms'' of Kniehl and Penin., 30 pages, journal version

The one-loop QCD heavy quark potential is computed to order v^2 in the color singlet and octet channels. Several errors in the previous literature are corrected. To be consistent with the velocity power counting, the full dependence on |p' + p|/|p' - p| is kept. The matching conditions for the NRQCD one-loop potential are computed by comparing the QCD calculation with that in the effective theory. The graphs in the effective theory are also compared to terms from the hard, soft, potential, and ultrasoft regimes in the threshold expansion. The issue of off-shell versus on-shell matching and gauge dependence is discussed in detail for the 1/(m k) term in the potential. Matching on-shell gives a 1/(m k) potential that is gauge independent and does not vanish for QED., 28 pages, References added and minor changes to section III, results unchanged

We show how to compute loop graphs in heavy baryon chiral perturbation theory including the full functional dependence on the ratio of the Delta--nucleon mass difference to the pion mass, while at the same time automatically incorporating the 1/N cancellations that follow from the large-N spin-flavor symmetry of baryons in QCD. The one-loop renormalization of the baryon axial vector current is studied to demonstrate the procedure. A new cancellation is identified in the one-loop contribution to the baryon axial vector current. We show that loop corrections to the axial vector currents are exceptionally sensitive to deviations of the ratios of baryon-pion axial couplings from SU(6) values.

The photon energy spectrum in inclusive weak radiative B -> X_s gamma decay is computed to order alpha_s^2 beta_0. This result is used to extract a value for the HQET parameter $\bar\Lambda$ from the average , and a value of the parameter $\lambda_1$ from . An accurate measurement of can determine the size of the nonperturbative contributions to the Upsilon(1S) mass which cannot be absorbed into the b quark pole mass., Comment: 16 pages, RevTeX

The photon energy spectrum in inclusive weak radiative B -> X_s gamma decay is computed to order alpha_s^2 beta_0. This result is used to extract a value for the HQET parameter $\bar��$ from the average , and a value of the parameter $��_1$ from . An accurate measurement of can determine the size of the nonperturbative contributions to the Upsilon(1S) mass which cannot be absorbed into the b quark pole mass., 16 pages, RevTeX

1. Introduction 2. The Gross-Neveu Model 3. QCD 3.1 N-Counting Rules for Diagrams 3.1.1 U(1) Ghosts 3.2 The 't Hooft Model 3.3 $N$-Counting Rules for Correlation Functions 3.4 The Master Field 4. Meson Phenomenology 4.1 Zweig's Rule 4.2 Exotics 4.3 Chiral Perturbation Theory 4.4 Non-leptonic K Decay 4.5 $K-\bar K$ mixing 4.6 Axial U(1) and the eta' Mass 4.7 Resonances and 1/N 5 Baryons 5.1 N-Counting Rules for Baryons 5.2 The Non-Relativistic Quark Model 6 Spin-Flavor Symmetry for Baryons 6.1 Consistency Conditions 6.2 1/N Corrections 6.3 Solution of Consistency Conditions 7 Masses with SU(3) Breaking 8 Other Results for Baryons 9 Large N and Chiral Perturbation Theory, Comment: 1997 Les Houches Lectures. 82 pages, 47 figures

1. Introduction 2. The Gross-Neveu Model 3. QCD 3.1 N-Counting Rules for Diagrams 3.1.1 U(1) Ghosts 3.2 The 't Hooft Model 3.3 $N$-Counting Rules for Correlation Functions 3.4 The Master Field 4. Meson Phenomenology 4.1 Zweig's Rule 4.2 Exotics 4.3 Chiral Perturbation Theory 4.4 Non-leptonic K Decay 4.5 $K-\bar K$ mixing 4.6 Axial U(1) and the eta' Mass 4.7 Resonances and 1/N 5 Baryons 5.1 N-Counting Rules for Baryons 5.2 The Non-Relativistic Quark Model 6 Spin-Flavor Symmetry for Baryons 6.1 Consistency Conditions 6.2 1/N Corrections 6.3 Solution of Consistency Conditions 7 Masses with SU(3) Breaking 8 Other Results for Baryons 9 Large N and Chiral Perturbation Theory, 1997 Les Houches Lectures. 82 pages, 47 figures

Theoretical predictions for inclusive semileptonic B decay rates are rewritten in terms of the Upsilon(1S) meson mass instead of the b quark mass, using a modified perturbation expansion. This method gives theoretically consistent and phenomenologically useful results. Perturbation theory is well behaved, and the largest theoretical error in the predictions coming from the uncertainty in the quark mass is eliminated. The results are applied to the determination of $|V_{cb}|$, $|V_{ub}|$, and $\lambda_1$., Comment: 8 pages revtex

The operator mixing matrix for the dimension six operators in the heavy quark effective theory Lagrangian is computed at one loop. The results are shown to be consistent with constraints from the equations of motion, and from reparametrization invariance., 8 pages, revtex

The 1/N expansion of QCD can be used to calculate properties of nucleons and Delta baryons, such as masses, magnetic moments, and pion couplings. The predictions of the 1/N expansion are in excellent agreement with the experimental data. The 1/N expansion also provides an understanding of the relation between the quark model, the Skyrme model, and QCD. This talk reviews some of the recent developments., Comment: 14 pages, 4 eps figures. (Plenary Talk at PANIC 96)

These lectures introduce some of the basic ideas of effective field theories. The topics discussed include: relevant and irrelevant operators and scaling, renormalization in effective field theories, decoupling of heavy particles, power counting, and naive dimensional analysis. Effective Lagrangians are used to study the $\Delta S=2$ weak interactions and chiral perturbation theory., Comment: 52 pages, 20 figures. Uses temuphys.cmm (available from xxx.lanl.gov) One lecture of introductory material added to hep-ph/9508245 (1996 Schladming Winter School Lectures)

We predict differential decay distributions for phi->rho gamma gamma and phi -> omega gamma gamma using chiral perturbation theory. We also consider the isospin violating decay phi -> omega pi^0. Experimental information on these decays can be used to determine couplings in the heavy vector meson chiral Lagrangian., Comment: It was shown by P. Ko et al., hep-ph/9510205 (Phys. Lett. B366 (1996) 287), that there is a etaprime pole contribution that dominates over what we calculated

The breaking of flavor SU(3) symmetry in the axial couplings and magnetic moments of baryons is analyzed in the $1/N_c$ expansion. A simple meson loop graph which is known to be of order $\sqrt{m_s}$ and leading order in $1/N_c$ correctly predicts the pattern of symmetry breaking in the magnetic moments. It is, however, not possible to use this graph to predict the magnitude of the breaking. The situation with the axial couplings is less clear. In this case the breakings are relatively small and do not appear to follow an obvious pattern. Nevertheless there is a clear indication that, with symmetry breaking taken into account, the F/D ratio (defined in the presence of SU(3) breaking) is considerably less than the SU(6) value of 2/3. With sizeable uncertainty, we find F/D \approx 0.44. The quantity 3F-D which is relevant for the analysis of spin-dependent deep inelastic scattering is considerably smaller than the SU(6) value of unity. The new value, 3F-D=0.27+-0.09, is consistent with vanishing strange-quark spin in the nucleon., 13 pages, 4 epsf figures, uses revtex

The inclusive and exclusive semileptonic decay distributions for b -> c decay are computed in the Shifman-Voloshin limit. The inclusive decay distributions (computed using an operator product expansion) depend on quark masses, and the exclusive decay distributions depend on hadron masses. Nevertheless, we show explicitly how the first two terms in the 1/m expansion match between the inclusive and exclusive decays. Agreement between the inclusive and exclusive decay rates requires a minimum smearing region of size Lambda_QCD before local duality holds in QCD. The alpha_s corrections to the inclusive and exclusive decay rates are also shown to agree to order (log m)/m^2. The alpha_s/m^2 corrections are used to obtain the alpha_s correction to Bjorken's inequality on the slope of the Isgur-Wise function., 22 pages, 3 eps figures, uses revtex (Revision: a discussion of radiative corrections to the bound K>0 of Section 7.B has been added; some typos, including labels in fig 2)

We predict differential decay distributions for phi->rho gamma gamma and phi -> omega gamma gamma using chiral perturbation theory. We also consider the isospin violating decay phi -> omega pi^0. Experimental information on these decays can be used to determine couplings in the heavy vector meson chiral Lagrangian., It was shown by P. Ko et al., hep-ph/9510205 (Phys. Lett. B366 (1996) 287), that there is a etaprime pole contribution that dominates over what we calculated

The spin-flavor structure of large N baryons is described in the 1/N expansion of QCD using quark operators. The complete set of quark operator identities is obtained, and used to derive an operator reduction rule which simplifies the 1/N expansion. The operator reduction rule is applied to the axial currents, masses, magnetic moments and hyperon non-leptonic decay amplitudes in the $SU(3)$ limit, to first order in $SU(3)$ breaking, and without assuming $SU(3)$ symmetry. The connection between the Skyrme and quark representations is discussed. An explicit formula is given for the quark model operators in terms of the Skyrme model operators to all orders in $1/\N$ for the two flavor case., 36 pages, 2 eps figures, uses revtex

For high energy processes ($M\gg \Lambda_{QCD}$) there are infrared safe hadronic shape variables that have a calculable perturbative expansion in $\alpha_s(M^2)$. However, nonperturbative power suppressed corrections to these variables are not well understood. We use the behavior of large orders of the perturbation expansion to gain insight into the nonperturbative corrections. Our results suggest that certain shape variables have nonperturbative corrections suppressed by fractional powers of $\Lambda_{QCD}^2/M^2$., Comment: (12 pages, 2 figures, uses harvmac and uufiles), UCSD/PTH 94-11

The properties of baryons can be computed in a systematic expansion in $1/N_c$, where $N_c$ is the number of colors. Recent results on the axial couplings and masses of baryons (for the case of three flavors) are presented. The results give insight into the structure of flavor $SU(3)$ breaking for baryons. ---------------------------------------------------------------------------- Talks presented at the Symposium on Internal Spin Structure of the Nucleon (Yale University, Jan 94) and at the Workshop on Continuous Advances in QCD (Theoretical Physics Institute, University of Minnesota, Feb 94)., (12 pages, 3 figures. Uses harvmac and uufiles), UCSD/PTH 94-01

A systematic expansion in 1/N is constructed for baryons in QCD. Predictions of the 1/N expansion at leading and subleading order for baryon axial current coupling constant ratios such as F/D, baryon masses and magnetic moments are derived. The baryon sector of QCD has a light quark spin-flavor symmetry at leading order in 1/N. The formalism of induced representations for contracted Lie algebras is introduced to explain the consequences of this symmetry. Relations are first derived for the simplest case of two light flavors of quarks. The generalization of the large N expansion to N_f = 3 flavors is subtle and is treated using several complementary methods. The 1/N expansion severely restricts the form of SU(3) breaking in the baryon sector. Extrapolation of the large N results to N=3 permits quantitative comparison with experimental data. Deviations of the measured quantities from exact spin-flavor symmetry predictions are accurately described by the subleading 1/N corrections. Implications of the 1/N expansion for baryon chiral perturbation theory are discussed., (71 pgs in l format, 9 figs, uses harvmac and uufiles), UCSD/PTH 93-21

We prove that the 1/N corrections to the baryon axial current matrix elements are proportional to their lowest order values. This implies that the first correction to axial current coupling constant ratios vanishes, and that the $SU(2N_f)$ spin-flavor symmetry relations are only violated at second order in 1/N., (6 pages, 2 figs, uses harvmac and uufiles), UCSD/PTH 93-18

The basic ideas and power counting rules of chiral perturbation theory are discussed. The formalism of velocity dependent fields for baryons, and for hadrons containing a heavy quark, is explained. (Invited Talk, 1993 QCD Rencontres de Moriond), (uses harvmac, 9 pages, 1 figure), UCSD/PTH 93-12

The differential decay spectrum $d\Gamma/dE_e dq^2$ for the semileptonic decay of an unpolarized hadron containing a b-quark, and the decay spectrum $d\Gamma/dE_e dq^2 d\!\cos\theta$ for polarized $\Lambda_b$ decay are computed to second order in the $1/m_b$ expansion. Most of the $1/m_b^2$ corrections have a simple physical interpretation, which is discussed in detail. The implications of the results for the determination of $V_{ub}$ are discussed. The decay spectra for semileptonic decay of hadrons containing a c-quark are also given. There is a subtlety in the use of the equations of motion at order $1/m_b^2$ in the heavy quark expansion which is explained., Comment: (46 pages, 8 figs, uses harvmac and uufiles), UCSD/PTH 93-14, CALT-68-1883 (REVISED VERSION: Some typos corrected, and one incorrect paragraph deleted)

QCD contains stable four-quark $QQ \overline{qq}$ hadronic states in the limit where the heavy quark mass goes to infinity. (Here $Q$ denotes a heavy quark, $\overline{q}$ a light antiquark and the stability refers only to the strong interactions.) The long-range binding potential is due to one-pion exchange between ground state $Q \overline{q}$ mesons, and is computed using chiral perturbation theory. For the $Q = b$, this long-range potential may be sufficiently attractive to produce a weakly bound two-meson state.

The main focus of these lectures is on those aspects of deep inelastic scattering that can be derived directly from QCD using quantum field theory, without recourse to phenomenological models. The emphasis is on spin dependent scattering, but the theory of spin averaged scattering is also discussed. A detailed analysis is given for the case of spin 1/2 targets, with a brief discussion of higher spin targets at the end. The QCD derivation of the Callan-Gross relation, the longitudinal structure function $F_L$, and the Bjorken and Ellis-Jaffe sum rules is presented. I also discuss the Wilczek-Wandzura contribution to $g_2$, and why the Gottfried sum rule does not hold in QCD., Comment: 48 Pages, 8 Figures; 7th Lake Louise Winter Institute, eds. Campbell et al. (Lectures presented at the Lake Louise Winter Institute, February, 1992)

We show that QCD contains stable four-quark QQ\qbar\qbar hadronic states in the limit where the heavy quark mass goes to infinity. (Here Q denotes a heavy quark, \qbar a light antiquark and the stability refers only to the strong interactions.) The long range binding potential is due to one pion exchange between ground state Q\qbar mesons, and is computed using chiral perturbation theory. For the Q=b, this long range potential may be sufficiently attractive to produce a weakly bound two meson state., Comment: (21 pages, 1 figure; uses harvmac.tex, tables.tex and uufiles), CERN-TH.6744/92, CALT-68-1869