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Title: Estimate of B(B{yields}X{sub s}{gamma}) at O({alpha}{sub s}{sup 2})

Abstract

Combining our results for various O({alpha}{sub s}{sup 2}) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find B(B{yields}X{sub s}{gamma})=(3.15{+-}0.23)x10{sup -4} for E{sub {gamma}}>1.6 GeV in the B-meson rest frame. The four types of uncertainties: nonperturbative (5%), parametric (3%), higher-order (3%), and m{sub c}-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.

Authors:
 [1];  [2]; ; ;  [3]; ; ;  [4];  [5]; ;  [6];  [7];  [8]; ;  [9];  [10];  [11];  [12];  [13]
  1. Institute of Theoretical Physics, Warsaw University, PL-00-681 Warsaw (Poland)
  2. (Switzerland)
  3. Yerevan Physics Institute, 375036 Yerevan (Armenia)
  4. Institut fuer Theoretische Physik, Universitaet Bern, CH-3012 Bern (Switzerland)
  5. Institut fuer Theoretische Physik und Astrophysik, Universitaet Wuerzburg, D-97074 Wuerzburg (Germany)
  6. Department of Physics, University of Alberta, AB T6G 2J1 Edmonton (Canada)
  7. Physikalisches Institut, Albert-Ludwigs-Universtitaet, D-79104 Freiburg (Germany)
  8. INFN, Torino and Dipartimento di Fisica Teorica, Universita di Torino, I-10125 Torino (Italy)
  9. Institut fuer Theoretische Teilchenphysik, Universitaet Karlsruhe (Thailand), D-76128 Karlsruhe (Germany)
  10. Institut fuer Theoretische Physik, Universitaet Zuerich, CH-8057 Zuerich (Switzerland)
  11. Theoretical Physics Division, CERN, CH-1211 Geneva 23 (Switzerland)
  12. (United States)
  13. Deutsches Elektronen-Synchrotron DESY, D-15738 Zeuthen (Germany)
Publication Date:
OSTI Identifier:
20861593
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevLett.98.022002; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; B MESONS; BRANCHING RATIO; CORRECTIONS; ERRORS; GEV RANGE 01-10; INTERPOLATION; PARTICLE DECAY; QUADRATURES; QUANTUM CHROMODYNAMICS

Citation Formats

Misiak, M., Theoretical Physics Division, CERN, CH-1211 Geneva 23, Asatrian, H. M., Hovhannisyan, A., Poghosyan, V., Bieri, K., Ewerth, T., Greub, C., Czakon, M., Czarnecki, A., Slusarczyk, M., Ferroglia, A., Gambino, P., Gorbahn, M., Steinhauser, M., Haisch, U., Hurth, T., SLAC, Stanford University, Stanford, California 94309, and Mitov, A. Estimate of B(B{yields}X{sub s}{gamma}) at O({alpha}{sub s}{sup 2}). United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.022002.
Misiak, M., Theoretical Physics Division, CERN, CH-1211 Geneva 23, Asatrian, H. M., Hovhannisyan, A., Poghosyan, V., Bieri, K., Ewerth, T., Greub, C., Czakon, M., Czarnecki, A., Slusarczyk, M., Ferroglia, A., Gambino, P., Gorbahn, M., Steinhauser, M., Haisch, U., Hurth, T., SLAC, Stanford University, Stanford, California 94309, & Mitov, A. Estimate of B(B{yields}X{sub s}{gamma}) at O({alpha}{sub s}{sup 2}). United States. doi:10.1103/PHYSREVLETT.98.022002.
Misiak, M., Theoretical Physics Division, CERN, CH-1211 Geneva 23, Asatrian, H. M., Hovhannisyan, A., Poghosyan, V., Bieri, K., Ewerth, T., Greub, C., Czakon, M., Czarnecki, A., Slusarczyk, M., Ferroglia, A., Gambino, P., Gorbahn, M., Steinhauser, M., Haisch, U., Hurth, T., SLAC, Stanford University, Stanford, California 94309, and Mitov, A. Fri . "Estimate of B(B{yields}X{sub s}{gamma}) at O({alpha}{sub s}{sup 2})". United States. doi:10.1103/PHYSREVLETT.98.022002.
@article{osti_20861593,
title = {Estimate of B(B{yields}X{sub s}{gamma}) at O({alpha}{sub s}{sup 2})},
author = {Misiak, M. and Theoretical Physics Division, CERN, CH-1211 Geneva 23 and Asatrian, H. M. and Hovhannisyan, A. and Poghosyan, V. and Bieri, K. and Ewerth, T. and Greub, C. and Czakon, M. and Czarnecki, A. and Slusarczyk, M. and Ferroglia, A. and Gambino, P. and Gorbahn, M. and Steinhauser, M. and Haisch, U. and Hurth, T. and SLAC, Stanford University, Stanford, California 94309 and Mitov, A.},
abstractNote = {Combining our results for various O({alpha}{sub s}{sup 2}) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find B(B{yields}X{sub s}{gamma})=(3.15{+-}0.23)x10{sup -4} for E{sub {gamma}}>1.6 GeV in the B-meson rest frame. The four types of uncertainties: nonperturbative (5%), parametric (3%), higher-order (3%), and m{sub c}-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.},
doi = {10.1103/PHYSREVLETT.98.022002},
journal = {Physical Review Letters},
number = 2,
volume = 98,
place = {United States},
year = {Fri Jan 12 00:00:00 EST 2007},
month = {Fri Jan 12 00:00:00 EST 2007}
}
  • We calculate the set of O({alpha}{sub s}{sup 2}) corrections to the branching ratio and to the photon energy spectrum of the decay process B{yields}X{sub s{gamma}} originating from the interference of diagrams involving the electromagnetic dipole operator O{sub 7} with diagrams involving the chromomagnetic dipole operator O{sub 8}. The corrections evaluated here are one of the elements needed to complete the calculations of the B{yields}X{sub s{gamma}} branching ratio at next-to-next-to-leading order in QCD. We conclude that this set of corrections does not change the central value of the standard model prediction for Br(B{yields}X{sub s{gamma}}) by more than 1%.
  • We calculate the fermionic corrections to the photon-energy spectrum of {bar B}{yields}X{sub s}{gamma} which arise from the self-interference of the chromomagnetic dipole operator Q{sub 8} at next-to-next-to-leading order by applying naive non-Abelianization. The resulting O({beta}{sub 0}{alpha}{sub s}{sup 2}) correction to the {bar B}{yields}X{sub s}{gamma} branching ratio amounts to a relative shift of +0.12% (+0.27%) for a photon-energy cut of 1.6 GeV (1.0 GeV). We also comment on the potential size of resummation and nonperturbative effects related to Q{sub 8}.
  • The flavor-changing electromagnetic dipole operator O{sub 7} gives the dominant contribution to the B{yields}X{sub s}{gamma} decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung contributions. The optical theorem is applied, and the relevant imaginary parts of three-loop diagrams are computed following the lines of our recent t{yields}X{sub b}W calculation. The complete result allows us to test the validity of the naive non-Abelianization (NNA) approximation that has been previously applied to estimate the next-to-next-to-leading order QCD correction to {gamma}(B{yields}X{sub s}{gamma})/{gamma}(B{yields}X{sub u}e{nu}). When both decay widths are normalized to m{sub b,R}{sup 5} in the samemore » renormalization scheme R, the calculated O({alpha}{sub s}{sup 2}) correction is sizable ({approx}6%), and the NNA estimate is about 1/3 too large. On the other hand, when the ratio of the decay widths is written as Sxm{sub b,MS}{sup 2}(m{sub b})/m{sub b,pole}{sup 2}, the calculated O({alpha}{sub s}{sup 2}) correction to S is at the level of 1% for both the complete and the NNA results.« less
  • We examine the anomalous dimension matrix appropriate for the phase space restricted B{yields}X{sub u}l{nu} and B{yields}X{sub s}{gamma} decay spectra to subleading nonperturbative order. The time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the nonlocal operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shapemore » functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of V{sub ub}.« less