arXiv subjects

York-Peng Yao

Publications and source records attributed to York-Peng Yao.

At least 19 recordsLinked to original sources

arXiv2016

The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes

The integrations leading to the Cachazo-He-Yuan (CHY) double-color $n$-point massless scalar amplitude are carried out one integral at a time. Möbius invariance dictates the final amplitude to be independent of the three Möbius constants $σ_r, σ_s, σ_t$, but their choice affects integrations and the intermediate results. The effect of the Möbius constants, the two colors, and the scattering functions on each integration is investigated. A systematic way to carry out the $n-3$ integrations is explained, each exposing one of the $n-3$ propagators of the Feynman diagrams. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude.

hep-th↗

arXiv2016

Evaluation of the CHY Gauge Amplitude

The Cachazo-He-Yuan (CHY) formula for $n$-gluon scattering is known to give the same amplitude as the one obtained from Feynman diagrams, though the former contains neither vertices nor propagators explicitly. The equivalence was shown by indirect means, not by a direct evaluation of the $(n\! - \!3)$-dimensional integral in the CHY formula. The purpose of this paper is to discuss how such a direct evaluation can be carried out. There are two basic difficulties in the calculation: how to handle the large number of terms in the reduced Pfaffian, and how to carry out the integrations in the presence of a $σ$-dependence much more complicated than the Parke-Taylor form found in a CHY double-color scalar amplitude. We have solved both of these problems, and have formulated a method that can be applied to any $n$. Many examples are provided to illustrate these calculations.

hep-th↗

arXiv2016

Off-Shell CHY Amplitudes

The Cachazo-He-Yuan (CHY) formula for on-shell scattering amplitudes are extended off-shell. The off-shell amplitudes are Möbius invariant, and have the same momentum poles as the on-shell amplitudes. The same technique is also used to obtain off-shell massive scalar and vector boson amplitudes.

hep-th↗

arXiv2014

Color kinematic symmetric (BCJ) numerators in a light-like gauge

Color-ordered tree level scattering amplitudes in Yang-Mills theories can be written as a sum over terms which display the various propagator poles of Feynman diagrams. The numerators in these expressions which are obtained by straightforward application of Feynman rules are not satisfying any particular relations, typically. However, by reshuffling terms, it is known that one can arrive at a set of numerators which satisfy the same Jacobi identity as the corresponding color factors. By extending previous work by us we show how this can be systematically accomplished within a Lagrangian framework. We construct an effective Lagrangian which yields tree-level color-kinematic symmetric numerators in Yang-Mills theories in a light-like gauge at five-points. The five-point effective Lagrangian is non-local and it is zero by Jacobi identity. The numerators obtained from it respect the original pole structure of the color-ordered amplitude. We discuss how this procedure can be systematically extended to higher order.

hep-th↗

arXiv2010

Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes

Writing the fully color dressed and graviton amplitudes, respectively, as ${\bf A}= = $ and ${\bf A}_{gr}= <\tilde N|M|N> $, where $|A> $ is a set of Kleiss-Kuijf color-ordered basis, $|N>, $|\tilde N> $ and $|C>$ are the similarly ordered numerators and color coefficients, we show that the propagator matrix $M$ has $(n-3)(n-3)!$ independent eigenvectors $|λ^0_j>$ with zero eigenvalue, for $n$-particle processes. The resulting equations $<λ^0_j|A> = 0$ are relations among the color ordered amplitudes. The freedom to shift $|N> \to |N> +\sum_j f_j|λ^0_j>$ and similarly for $|\tilde N>$, where $f_j$ are $(n-3)(n-3)!$ arbitrary functions, encodes generalized gauge transformations. They yield both BCJ amplitude and KLT relations, when such freedom is accounted for. Furthermore, $f_j$ can be promoted to the role of effective Lagrangian vertices in the field operator space.

hep-th↗

arXiv2008

Analytic Scattering Amplitudes for QCD

By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time equation and gauge invariance requirement, this approach leads to recursion relations, which greatly simplify the construction of multi-gluon scattering amplitudes. The setting for this discussion is in the space-cone gauge.

hep-th↗

arXiv2008

The Space-Cone Gauge, Lorentz Invariance and On-Shell Recursion for One-Loop Yang-Mills amplitudes

Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$ amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. Of great importance is the power of gauge Lorentz invariance, which is enough to determine the soft factors in the latter cases.

hep-th↗

arXiv2005

QCD recursion relations from the largest time equation

We show how by reassembling the tree level gluon Feynman diagrams in a convenient gauge, space-cone, we can explicitly derive the BCFW recursion relations. Moreover, the proof of the gluon recursion relations hinges on an identity in momentum space which we show to be nothing but the Fourier transform of the largest time equation. Our approach lends itself to natural generalizations to include massive scalars and even fermions.

hep-th↗

arXiv2004

Momentum Representation of Coulomb Wave Functions and Level Shifts in Bottomonium due to Charm Effects

Since effective potentials derived from Feynman diagrams are naturally given in momentum space, we formulate the non-relativistic Coulomb problem entirely in momentum representation. We give momentum wave functions for all quantum numbers in one-dimensional integrals, even though they can be evaluated. Angular momentum decomposed Green's functions are then compactly represented. We apply this formalism to investigate the next to next leading order charm effects on 1S bottomonium level shift. Our one insertion results are given completely in analytic form and numerically agree with previous results. Our two insertion results are also in agreement. The net effect of finite charm mass is to decrease the bottom mass by 33 MeV, as determined through the measured 1S energy.

hep-ph↗

arXiv2000

Exact non-factorizable O(alpha_s g^2) two-loop contribution to Z -> b bbar

For Z -> b bbar, we calculate all the two-loop top dependent Feynman graphs, which have mixed QCD and electroweak contributions that are not factorizable. For evaluating the graphs, without resorting to a mass expansion, we apply a two-loop extension of the one-loop Passarino-Veltman reduction. This is an analytic-numerical method, which first converts all diagrams into a set of ten standard scalar functions, and then integrates them numerically over the remaining Feynman parameters, with rapid convergence and high accuracy. We discuss the treatment of infrared singularities within our methods. We do not resort to unitarity cuts of two-point functionsfor calculating decay rates; these are useful only to obtain an inclusive rate. For this reason, experimental cuts and the experimental infrared energy resolution can be implemented in our calculation, once the corresponding one-loop gluon Bremsstrahlung process is added to this calculation.

hep-ph↗

arXiv2000

Exact O(g^2 alpha_s) top decay width from general massive two-loop integrals

We calculate the b-dependent self-energy of the top quark at O(g^2 α_s) by using a general massive two-loop algorithm proposed in a previous article. From this we derive by unitarity the O(α_s) radiative corrections to the decay width of the top quark, where all effects associated with the $b$ quark mass are included without resorting to a mass expansion. Our results agree with the analytical results available for the O(α_s) correction to the top quark width.

hep-ph↗

arXiv1998

Backgound Gluon Effects on B -> X_s gamma gamma

We consider non-perturbative QCD effects on the energy spectrum of either one of the photons in B -> X_s gamma gamma. These are due to the subprocesses in which a charm quark loop interacts with a self-consistently produced background static QCD field. The magnitude is estimated to be a few percents in B -> X_s gamma gamma, but can be quite substantial in B_s -> gamma gamma. An extension of the Euler-Heisenberg Lagrangian is given.

hep-ph↗

arXiv1997

QCD Corrections to $b\to sγγ$ and Exclusive $B_s\to γγ$ Decay

The short distance QCD corrections to $b\to sγγ$ are calculated in the leading logarithmic approximation. The equivalence of operator basis reduction for S-matrix elements by using the equations of motion or by proving a low energy theorem is discussed. We apply the above results to the exclusive $B_s\to γγ$ decay. The branching ratio of this decay is found to be $5\times 10^{-7}$ in the Standard Model. We also found that QCD corrections modify considerably the ratio between CP-even and CP-odd two-photon amplitudes.

hep-ph↗

arXiv1995

A Finite Group Analysis of the Quark Mass Matrices and Flavor Dynamics

We perform a finite group analysis on the quark mass matrices. We argue that the dominant terms should be proportional to class operators of the group and that symmetry breaking to split the mass spectrum and simultaneous diagonalizability to suppress flavor changing neutral currents can be accomplished at this point. The natural setting is a multi-scalar model and the scalar doublets can have masses of the weak scale without any parameter tuning. When we specialize to $S_3$ as the group of choice, we arrive at the results that the dominant mass terms are $\lhook $democratic$\rhook $ and that the ratios of light masses and the Cabbibo angle $\cong ({m_d\over m_s})^{1\over 2}$ are all given by group parameters in the breaking of $S_3$ to $S_2$. A large mass expansion is then performed and a generalized Wolfenstein parameterization is given. Further breaking by way of introducing heavy-light transitions in the down-type mass matrix is here related to the heavy-light Cabbibo-Kobayashi-Maskawa elements.

hep-ph↗

arXiv1994

${1\over m_b}$ and ${1\over m_t}$ Expansion of the Weak Mixing Matrix

We perform a $1/m_b$ and $1/m_t$ expansion of the Cabibbo-Kobayashi- Maskawa mixing matrix. Data suggest that the dominant parts of the Yukawa couplings are factorizable into sets of numbers $\vert r>$, $\vert s>$, and $\vert s'>$, associated, respectively, with the left-handed doublets, the right-handed up singlets, and the right- handed down singlets. The first order expansion is consistent with Wolfenstein parameterization, which is an expansion in $sin θ_c$ to third order. The mixing matrix elements in the present approach are partitioned into factors determined by the relative orientations of $\vert r>$, $\vert s>$, and $\vert s'>$ and the dynamics provided by the subdominant mass matrices. A short discussion is given of some experimental support and a generalized Fritzsch model is used to contrast our approach.

hep-ph↗

arXiv1994

Renormalization of four-quark operators, effective theory, and the role of evanescent operators

We present, in the context of dimensional regularization, a prescription to renormalize Feynman diagrams with an arbitrary number of external fermions. This prescription, which is based on the original t'Hooft-Veltman proposal to keep external particles in four dimensions, is particularly useful to define the 'renormalization' (in the context of effective Lagrangian) of physical four-quark operators without introducing any evanescent operator. The results obtained for $b\rightarrow s$ processes agree with those from the so-called naive prescription, but disagree with the ones with the introduction of evanescent operators in a renormalization group analysis. We also present an explicit two loop calculation of the mixing of the evanescent operators with the physical dimension five operators for the same processes. Particular attention is paid to the unboundedness nature of such mixing and how a formal finite transformation is effected to decouple. The inevitable mass dependence of one of these schemes in the literature is pointed out as the cause for the difference mentioned.

hep-ph↗

arXiv1993

Exact $α_s$ Calculation of $b\rightarrow s + γ$, \ $b\rightarrow s + g$

We present an exact $α_s$ calculation of the Wilson coefficients associated with the dipole moment operators. We also give an estimate of the branching ratio for $b\rightarrow s γ$. We find that higher dimensional effects are under control within $9\%$ for $BR(b\rightarrow s γ)=(4.3\pm 0.37 )\times 10^{-4}$.

hep-ph↗

arXiv1993

Effective Lagrangian for $b \rightarrow s$ Processes with QCD-Corrections

We present a complete calculation of the effective lagrangian for $b \rightarrow s$ processes with $QCD$ corrections, in the leading logarithm approximation, for the cases $m_t=m_w$ and $m_t \gg m_w$. The effective lagrangian is then applied to estimate the $b \rightarrow s γ$ decay rate. We find that it is enhanced by a factor of 6 for the case $m_t=m_w$, and a factor of about 2 for $m_t \gg m_w$. Our results differ from those found in the literature, but are not very different numerically for $m_t=m_w$.

hep-ph↗