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F. A. Chishtie

Publications and source records attributed to F. A. Chishtie.

54 records · Page 3Linked to original sources
arXiv2002

Renormalization-Mass Scale Dependence in QCD Contributions to Semileptonic $b \to u$ Decay

QCD contributions to the $b \to u \ell^- \barν_\ell$ decay rate, which are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient dependence on the renormalization mass $μ$ to compromise phenomenological predictions for inclusive semileptonic $B \to X_u$ processes. Such scale dependence is ameliorated by the renormalization-group (RG) extraction and summation of all leading and RG-accessible subleading logarithms occurring subsequent to two-loop order in the perturbative series. This optimal RG-improvement of the known portion of the perturbative series virtually eliminates $μ$-dependence as a source of theoretical uncertainty in the predicted semileptonic $B \to X_u$ inclusive rate.

hep-ph↗
arXiv2002

Three Loop Estimate of the Inclusive Semileptonic $b\to c$ Decay Rate

The renormalization-scale ($μ$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\barν_\ell$ decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MS-bar scheme. Three-loop contributions to the decay rate are estimated by developing Pade approximant techniques particularly suited to perturbative calculations in the pole mass scheme. An optimized Pade estimate of the three-loop contributions is obtained by comparison of the Pade estimates with the three-loop terms determined by renormalization-group invariance. The resulting three-loop estimate in the pole-mass scheme exhibits minimal sensitivity to the renormalization scale near $μ=1.0 GeV$, leading to an estimated decay rate of $192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)=992\pm 217 GeV^5$ inclusive of theoretical uncertainties and non-perturbative effects.

hep-ph↗
arXiv2002

Closed-Form Summation of RG-Accessible Logarithmic Contributions to Semileptonic B-Decays and Other Perturbative Processes

For any perturbative series that is known to $k$-subleading orders of perturbation theory, we utilise the process-appropriate renormalization-group (RG) equation in order to obtain all-orders summation of series terms proportional to $α^n \log^{n-k}(μ^2)$ with $k = {0,1,2,3}$, corresponding to the summation to all orders of the leading and subsequent-three-subleading logarithmic contributions to the full perturbative series. These methods are applied to the perturbative series for semileptonic $b$-decays in both MS-bar and pole-mass schemes, and they result in RG-summed series for the decay rates which exhibit greatly reduced sensitivity to the renormalization scale $μ$. Such summation via RG-methods of all logarithms accessible from known series terms is also applied to perturbative QCD series for vector- and scalar-current correlation functions, the perturbative static potential function, the (single-doublet standard-model) Higgs decay amplitude into two gluons, as well as the Higgs-mediated high-energy cross-section for $W^+W^-\to ZZ$ scattering. The resulting RG-summed expressions are also found to be much less sensitive to the renormalization scale than the original series for these processes.

hep-ph↗
arXiv2002

Constraints on Higher-Order Perturbative Corrections in $b\to u$ Semileptonic Decays from Residual Renormalization-Scale Dependence

The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group invariant quantities. This technique is applied to the inclusive semileptonic process $b\to u \barν_\ell\ell^-$ (explicitly known to two-loop order) to obtain bounds on the three- and four-loop perturbative coefficients that are not accessible via the renormalization group. Using the principle of minimal sensitivity, an estimate is obtained for the perturbative contributions to $Γ(b\to u \barν_\ell\ell^-)$ that incorporates theoretical uncertainty from as-yet-undetermined higher order QCD corrections.

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arXiv2001

A study of the gravitational wave form from pulsars II

We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, taking into account the rotation and orbital motion of the Earth. We also briefly discuss the Zak-Gelfand Integral Transform. The Zak-Gelfand Integral Transform that arises in our analytic approach has also been useful for Schrodinger operators in periodic potentials in condensed matter physics (Bloch wave functions).

astro-ph↗
arXiv2001

RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the \bar{MS} series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic Padé-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Padé-predictions. The predicted value for the third RG-accessible coefficient is found to be within 7% relative |error| of its true value for n_f leq 6, and is shown to be in exact agreement with its true value in the n_f \to \infty limit. Asymptotic Padé estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. Comparison is also made with recent estimates of the three-loop contribution to the configuration-space static-potential function.

hep-ph↗
arXiv2001

Pade Estimate of QCD's Infrared Boundary

A mass scale $μ_c$ representing the boundary between effective theories of strong interactions and perturbative QCD (infrared and ultraviolet regimes) exists when the $β$-function is characterized by a simple pole. This behaviour, which is known to occur in N=1 supersymmetric Yang-Mills theories, leads to an infrared attractor in the evolution of the coupling constant, with the mass scale $μ_c$ of the attractor providing a natural boundary between the infrared and ultraviolet regimes. It is demonstrated that [2|2], [3|1] and [1|3] Pade-approximant versions of the three-flavour QCD $β$-function each contain a simple pole corresponding to such an infrared attractor. All three approximants, separately considered, are seen to lead to nearly equivalent estimates for the mass scale $μ_c$.

hep-ph↗
arXiv2001

Estimate of the Three-Loop MS bar Contribution to sigma(W_L^+ W_L^- --> Z_L Z_L)

The three-loop contribution to the MS bar single-Higgs-doublet standard-model cross-section $σ(W_L^+ W_L^- \to Z_L Z_L)$ at s = (5M_H)^2 is estimated via least-squares matching of the asymptotic Pade-approximant prediction of the next order term, a procedure that has been previously applied to QCD corrections to correlation functions and decay amplitudes. In contrast to these prior applications, the expansion parameter for the W_L^+ W_L^- \to Z_L Z_L process is the non-asymptotically-free quartic scalar-field coupling of the standard model, suggesting that the least-squares matching be performed over the "infrared" mu^2 <= s region of the scale parameter. All three coefficients of logarithms within the three-loop term obtained by such matching are found to be within 6.6% relative error of their true values, as determined via renormalization-group methods. Surprisingly, almost identical results are obtained by performing the least squares matching over the mu^2 >= s region.

hep-ph↗
arXiv2000

Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Known perturbative expressions for the decay rates of 115 GeV Higgs particle into either two gluons or a $b\bar{b}$ pair are shown to exhibit renormalization-scale-($μ$)-dependence that is largely removed via renormalization-group/Pade-approximant estimates of these rates' next order contributions. The extrema in $μ$ characterizing both rates, as determined from fully-known orders of perturbation theory, are very nearly equal to corresponding $μ$-insensitive rates obtained via estimation of their next order contributions, consistent with "minimal-sensitivity" expectations.

hep-ph↗
arXiv2000

A study of the gravitational wave form from pulsars

We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar,taking into account the rotation of the Earth for a one day observation period.

astro-ph↗
arXiv2000

Probing the Infrared Structure of Gauge Theories: A Pade-Approximant Approach

Pade-approximant treatments of the known terms of the QCD $β$-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop $β$-function contribution. Below this flavour threshold, Pade approximants based upon the QCD $β$-function manifest the same infrared attractor structure as that which characterizes the exact NSVZ $β$-function of supersymmetric gluodynamics. Such infrared attractor structure is also seen to characterize Pade-approximant treatments of vector SU(N) gauge theory in the large $N$ limit, suggesting common infrared dynamics for the strong and weak phases of this theory.

hep-ph↗
arXiv2000

Reducing the Theoretical Uncertainty in Extracting |V_{ub}| from the Inclusive Semileptonic b to u Decay Rate

Utilizing asymptotic Pade-approximant methods, we estimate the three-loop order MS-bar coefficients of alpha_s^3[\log(μ^2/m^2_b(μ)]^k terms [k = {0,1,2,3}] within the $b \to u\ell^-\barν_\ell$ decay rate. Except for the coefficient of the k = 0 term, all other coefficients may also be obtained via renormalization-group (RG) methods. The relative errors in asymptotic Pade-approximant estimates of the k = {1,2,3} terms are found to be 5.1% or less, thereby providing an estimate of the theoretical uncertainty in the asymptotic Pade-approximant estimate of the RG-inaccessible k = 0 term. By a judicious choice in the renormalization scale parameter, we are able to extract |V_{ub}| from the inclusive decay rate to within 7% theoretical uncertainty.

hep-ph↗
arXiv2000

Next-Order Estimate of Higgs to Two-Gluon Rate

Using asymptotic Pade approximant methods, we have calculated the O(alpha_s^5) contribution to the Standard-Model H to gg decay rate. This process is of particular interest because of the slow convergence evident from the known terms of its QCD series. The O(alpha_s^5) term is expressed as a 3rd degree polynomial in $L= log (\frac{μ^2}{m_t^2(μ)})$. We find that the asymptotic Pade predictions for the renormalization-group accessible coefficients of L, L^2 and L^3 are within 1%, 2% and 7% of their respective values. The inclusion of the O(alpha_s^5) contribution renders the full decay rate virtually scale independent over the entire 0.3 M_H < mu < M_t range of the renormalization scale mu.

hep-ph↗
arXiv2000

Pade-Summation Approach to QCD Beta-Function Infrared Properties

We address whether Padé-summations of the $\bar{MS}$ QCD $β$-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and Shifman for the case of supersymmetric gluodynamics. Below an approximant-dependent flavour threshold $(6 \leq n_f \leq 8)$, we find that Padé-summation $β$-functions incorporating $[2|1], [1|2], [2|2], [1|3]$, and $[3|1]$ approximants always exhibit a positive pole prior to the occurrence of their first positive zero, precluding any identification of this first positive zero as an infrared-stable fixed point of the $β$- function. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop $β$-function contribution. Moreover, the pole in question suggests the occurrence of dynamics in which both a strong and an asymptotically-free phase share a common infrared attractor. We briefly discuss the possible relevance of infrared-attractor dynamics to the success of recent calculations of the glueball mass spectra in QCD with $N_c \to \infty$ via supergravity. As $n_f$ increases above an approximant-dependent flavour threshold, Padé-summation $β$-functions incorporating $[2|2], [1|3]$, and $[3|1]$ approximants exhibit dynamics controlled by an infrared-stable fixed point over a widening domain of the five-loop $\bar{MS}$ $β$-function parameter $(β_4/β_0)$. Above this threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number.

hep-ph↗
arXiv2000

Pade-Improved Estimates of Hadronic Higgs Decay Rates

Asymptotic Pade-approximant methods are utilized to estimate the order $α_s^5$ contribution to the $H\to gg$ rate and the order $α_s^4$ contribution to the $H \to b \bar{b}$ rate. The former process is of particular interest because of the slow convergence evident from the three known terms of its QCD series, which begins with an order $α_s^2$ leading-order term. The order $α_s^5$ contribution to the $H \to gg$ rate is expressed as a degree-3 polynomial in $L \equiv ln (μ^2 / m_t^2 (μ))$. We find that asymptotic Pade-approximant predictions for the coefficients of $L$, $L^2$, and $L^3$ are respectively within 1%, 2%, and 7% of true values extracted via renormalization-group methods. Upon including the full set of next-order coefficients, the $H \to gg$ rate is found to be virtually scale-independent over the 0.3 $M_{H} < μ< M_t$ range of the renormalization scale-parameter $μ$. We conclude by discussing the small order $α_s^4$ contribution to the $H \to b \bar{b}$ rate, which is obtained from a prior asymptotic Pade-approximant estimate of the order $α_s^4$ contribution to the quark-antiquark scalar-current correlation function.

hep-ph↗
arXiv2000

Estimate of the Three-Loop Perturbative Contribution to Inclusive Semileptonic b to u Decays

We utilize asymptotic Pade-approximant methods to estimate the three-loop order MS bar-scheme coefficients within the inclusive semileptonic b to u decay rate for four and five active quark flavours. The estimates we obtain for the three renormalization-group-accessible coefficients within the three-loop contribution are all found to be within 5.1% of their true values, using a least-squares procedure in conjunction with an asymptotic Pade-approximant estimate of the three-loop term over the entire $μ\ge m_b$ domain. Given the input values $α_s(M_Z) = 0.118 \pm 0.004$ and $m_b(m_b) =4.17 \pm 0.05 GeV$, the three-loop expression for the purely-perturbative contribution to the decay rate is minimally sensitive to renormalization scale at $μ= 1.775 GeV$, at which scale the three-loop contribution is estimated to be only 1.4% of the leading tree-order contribution. We estimate the full perturbative decay rate to be $192π^3Γ(b\to u\barν_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2070 {\rm GeV^5} \pm 16%$, inclusive of theoretical uncertainties from series truncation, the input parameters, and the estimation procedure.

hep-ph↗
arXiv1999

Pade-Improvement of CP-odd Higgs Decay Rate into Two Gluons

We present an asymptotic Pade-approximant estimate for the four-loop coefficients within the linear combination of correlators entering the recently calculated decay rate of a CP-odd Higgs boson, with an assumed mass $m_A = 100 GeV$, into two gluons. All but one of these coefficients are shown to be determined for arbitrary $m_A$ from the known 3-loop-order rate by renormalization group methods. Asymptotic Pade-approximant estimates for these coefficients are all seen to be within 12% of their correct values. The four-loop term in the decay rate for $m_A = 100 GeV$ is estimated to be only 4.3% of its leading one-loop contribution.

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