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Title: Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order

Abstract

The authors calculate the complete next-to-next-to-leading order QCD corrections to the charm contribution of the rare decay K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}. They encounter several new features, which were absent in lower orders. They discuss them in detail and present the results for the two-loop matching conditions of the Wilson coefficients, the three-loop anomalous dimensions, and the two-loop matrix elements of the relevant operators that enter the next-to-next-to-leading order renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the next-to-next-to-leading order QCD corrections leads to a significant reduction of the theoretical uncertainty from {+-} 9.8% down to {+-} 2.4% in the relevant parameter P{sub c}(X), implying the leftover scale uncertainties in {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) and in the determination of |V{sub td}|, sin 2{beta}, and {gamma} from the K {yields} {pi}{nu}{bar {nu}} system to be {+-} 1.3%, {+-} 1.0%, {+-} 0.006, and {+-} 1.2{sup o}, respectively. For the charm quark {ovr MS} mass m{sub c}(m{sub c}) = (1.30 {+-} 0.05) GeV and |V{sub us}| = 0.2248 the next-to-leading order value P{sub c}(X) = 0.37 {+-} 0.06 is modified to P{sub c}(X) = 0.38 {+-} 0.04 at the next-to-next-to-leading order level with themore » latter error fully dominated by the uncertainty in m{sub c}(m{sub c}). They present tables for P{sub c}(X) as a function of m{sub c}(m{sub c}) and {alpha}{sub s}(M{sub z}) and a very accurate analytic formula that summarizes these two dependences as well as the dominant theoretical uncertainties. Adding the recently calculated long-distance contributions they find {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) = (8.0 {+-} 1.1) x 10{sup -11} with the present uncertainties in m{sub c}(m{sub c}) and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. They also emphasize that improved calculations of the long-distance contributions to K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}} and of the isospin breaking corrections in the evaluation of the weak current matrix elements from K{sup +} {yields} {pi}{sup 0}e{sup +}{nu} would be valuable in order to increase the potential of the two golden K {yields} {pi}{nu}{bar {nu}} decays in the search for new physics.« less

Authors:
; ; ; ; ; ; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
897292
Report Number(s):
FERMILAB-PUB-05-512-T
arXiv eprint number hep-ph/0603079; TRN: US0701382
DOE Contract Number:
AC02-07CH11359
Resource Type:
Journal Article
Resource Relation:
Journal Name: JHEP 0611:002,2006; Journal Volume: 11
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANOMALOUS DIMENSION; DECAY; EVALUATION; ISOSPIN; MATRIX ELEMENTS; PHYSICS; QUANTUM CHROMODYNAMICS; QUARKS; RENORMALIZATION; Phenomenology-HEP

Citation Formats

Buras, Andrzej J., /Munich, Tech. U., Gorbahn, Martin, /Durham U., IPPP /Karlsruhe U., TTP, Haisch, Ulrich, /Fermilab /Zurich U., Nierste, Ulrich, and /Karlsruhe U., TTP /Fermilab. Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order. United States: N. p., 2006. Web. doi:10.1088/1126-6708/2006/11/002.
Buras, Andrzej J., /Munich, Tech. U., Gorbahn, Martin, /Durham U., IPPP /Karlsruhe U., TTP, Haisch, Ulrich, /Fermilab /Zurich U., Nierste, Ulrich, & /Karlsruhe U., TTP /Fermilab. Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order. United States. doi:10.1088/1126-6708/2006/11/002.
Buras, Andrzej J., /Munich, Tech. U., Gorbahn, Martin, /Durham U., IPPP /Karlsruhe U., TTP, Haisch, Ulrich, /Fermilab /Zurich U., Nierste, Ulrich, and /Karlsruhe U., TTP /Fermilab. Wed . "Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order". United States. doi:10.1088/1126-6708/2006/11/002. https://www.osti.gov/servlets/purl/897292.
@article{osti_897292,
title = {Charm quark contribution to K+ ---> pi+ nu anti-nu at next-to-next-to-leading order},
author = {Buras, Andrzej J. and /Munich, Tech. U. and Gorbahn, Martin and /Durham U., IPPP /Karlsruhe U., TTP and Haisch, Ulrich and /Fermilab /Zurich U. and Nierste, Ulrich and /Karlsruhe U., TTP /Fermilab},
abstractNote = {The authors calculate the complete next-to-next-to-leading order QCD corrections to the charm contribution of the rare decay K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}. They encounter several new features, which were absent in lower orders. They discuss them in detail and present the results for the two-loop matching conditions of the Wilson coefficients, the three-loop anomalous dimensions, and the two-loop matrix elements of the relevant operators that enter the next-to-next-to-leading order renormalization group analysis of the Z-penguin and the electroweak box contribution. The inclusion of the next-to-next-to-leading order QCD corrections leads to a significant reduction of the theoretical uncertainty from {+-} 9.8% down to {+-} 2.4% in the relevant parameter P{sub c}(X), implying the leftover scale uncertainties in {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) and in the determination of |V{sub td}|, sin 2{beta}, and {gamma} from the K {yields} {pi}{nu}{bar {nu}} system to be {+-} 1.3%, {+-} 1.0%, {+-} 0.006, and {+-} 1.2{sup o}, respectively. For the charm quark {ovr MS} mass m{sub c}(m{sub c}) = (1.30 {+-} 0.05) GeV and |V{sub us}| = 0.2248 the next-to-leading order value P{sub c}(X) = 0.37 {+-} 0.06 is modified to P{sub c}(X) = 0.38 {+-} 0.04 at the next-to-next-to-leading order level with the latter error fully dominated by the uncertainty in m{sub c}(m{sub c}). They present tables for P{sub c}(X) as a function of m{sub c}(m{sub c}) and {alpha}{sub s}(M{sub z}) and a very accurate analytic formula that summarizes these two dependences as well as the dominant theoretical uncertainties. Adding the recently calculated long-distance contributions they find {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) = (8.0 {+-} 1.1) x 10{sup -11} with the present uncertainties in m{sub c}(m{sub c}) and the Cabibbo-Kobayashi-Maskawa elements being the dominant individual sources in the quoted error. They also emphasize that improved calculations of the long-distance contributions to K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}} and of the isospin breaking corrections in the evaluation of the weak current matrix elements from K{sup +} {yields} {pi}{sup 0}e{sup +}{nu} would be valuable in order to increase the potential of the two golden K {yields} {pi}{nu}{bar {nu}} decays in the search for new physics.},
doi = {10.1088/1126-6708/2006/11/002},
journal = {JHEP 0611:002,2006},
number = ,
volume = 11,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2006},
month = {Wed Mar 01 00:00:00 EST 2006}
}
  • The authors calculate the complete next-to-next-to-leading order QCD correction of the charm quark contribution to the branching ratio for the rare decay K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}} in the standard model. The inclusion of these {Omicron}({alpha}{sub s}) contributions leads to a significant reduction of the theoretical uncertainty from {+-} 10.1% down to {+-} 2.4% in the relevant parameter P{sub c}, implying the left over scale uncertainties in {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) and in the determination of |V{sub td}|, sin 2{beta} and {gamma} from the K {yields} {pi}{nu}{bar {nu}} system to be {+-} 1.3%, {+-} 1.0%, {+-} 0.006more » and {+-} 1.2{sup o}, respectively. for the charm quark {ovr MS} mass m{sub c}(m{sub c}) = (1.30 {+-} 0.05) GeV and |V{sub us}| = 0.2248 the next-to-leading order value P{sub c} = 0.37 {+-} 0.06 is modified to P{sub c} = 0.37 {+-} 0.04 at the next-to-next-to-leading order level with the latter error fully dominated by the uncertainty in m{sub c}(m{sub c}). Adding the recently calculated long-distance contributions we find {Beta}(K{sup +} {yields} {pi}{sup +}{nu}{bar {nu}}) = (8.0 {+-} 1.1) x 10{sup -11} with the quoted error almost entirely due to the present uncertainties in m{sub c}(m{sub c}) and the Cabibbo-Kobayashi-Maskawa elements.« less
  • We calculate the charm-quark contribution to the decay K{sub L}{yields}{mu}{sup +}{mu}{sup -} in next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P{sub c} from {+-}22% down to {+-}7%, corresponding to scale uncertainties of {+-}3% and {+-}6% in the short-distance part of the branching ratio and the determination of the Wolfenstein parameter {rho} from K{sub L}{yields}{mu}{sup +}{mu}{sup -}. The error in P{sub c}=0.115{+-}0.018 is now in equal shares due to the combined scale uncertainties and the current uncertainty in the charm-quark mass. We find B(K{sub L}{yields}{mu}{sup +}{mu}{sup -}){sub SD}=(0.79{+-}0.12)x10{sup -9}, with the present uncertaintymore » in the Cabibbo-Kobayashi-Maskawa element V{sub td} being the dominant individual source in the quoted error.« less
  • We perform a next-to-next-to-leading order QCD analysis of the charm-top-quark contribution {eta}{sub ct} to the effective |{Delta}S|=2 Hamiltonian in the standard model. {eta}{sub ct} represents an important part of the short distance contribution to the parameter {epsilon}{sub K}. We calculate the three-loop anomalous dimension of the leading operator Q-tilde{sub S2}, the three-loop mixing of the current-current and penguin operators into Q-tilde{sub S2}, and the corresponding two-loop matching conditions at the electroweak, the bottom-quark, and the charm-quark scale. As our final numerical result we obtain {eta}{sub ct}=0.496{+-}0.047, which is roughly 7% larger than the next-to-leading-order (NLO) value {eta}{sub ct}{sup NLO}=0.457{+-}0.073. Thismore » results in a prediction for |{epsilon}{sub K}|=(1.90{+-}0.26)x10{sup -3}, which corresponds to an enhancement of approximately 3% with respect to the value obtained using {eta}{sub ct}{sup NLO}.« less
  • We calculate the charm quark contribution to the rare decay K{sup +}{yields}{pi}{sup +}{nu}{nu} in the next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P{sub c} from {+-}10.1% down to {+-}2.4%, corresponding to scale uncertainties of {+-}1.3%, {+-}1.0%, {+-}0.006, and {+-}1.2 deg. in B(K{sup +}{yields}{pi}{sup +}{nu}{nu}) and in |V{sub td}|, sin2{beta}, and {gamma} extracted from the K{yields}{pi}{nu}{nu} system. The error in P{sub c}=0.37{+-}0.04 is now fully dominated by the current uncertainty of {+-}3.8% in the charm quark mass m{sub c}. We find B(K{sup +}{yields}{pi}{sup +}{nu}{nu})=(8.0{+-}1.1)x10{sup -11}, where the quoted error stems almost entirely frommore » the present uncertainties in m{sub c} and the Cabibbo-Kobayashi-Maskawa elements.« less
  • We compute the leading-log QED, the next-to-leading-log QED-QCD, and the electroweak corrections to the charm quark contribution relevant for the rare decay K{sup +}{yields}{pi}{sup +}{nu}{nu}. The corresponding parameter P{sub c}(X) is increased by up to 2% with respect to the pure QCD estimate to P{sub c}(X)=0.372{+-}0.015 for m{sub c}(m{sub c})=(1.286{+-}0.013)GeV, {alpha}{sub s}(M{sub Z})=0.1176{+-}0.0020, and |V{sub us}|=0.2255. For the branching ratio we find B(K{sup +}{yields}{pi}{sup +}{nu}{nu})=(8.5{+-}0.7)x10{sup -11}, where the quoted uncertainty is dominated by the Cabibbo-Kobayashi-Maskawa elements.