FERMILAB-PUB-12-541-E

The D0 Collaboration111with visitors from aAugustana College, Sioux Falls, SD,
USA, bThe University of Liverpool, Liverpool, UK, cUPIITA-IPN, Mexico City,
Mexico, dDESY, Hamburg, Germany, eSLAC, Menlo Park, CA, USA, fUniversity
College London, London, UK, gCentro de Investigacion en Computacion - IPN,
Mexico City, Mexico, hECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico
and iUniversidade Estadual Paulista, São Paulo, Brazil.

# Measurement of the $\bm{p\bar{p}\to W+b+X}$ production cross section at
$\bm{\sqrt{s}=1.96}$ TeV

V.M. Abazov  Joint Institute for Nuclear Research, Dubna, Russia  B. Abbott
University of Oklahoma, Norman, Oklahoma 73019, USA  B.S. Acharya  Tata
Institute of Fundamental Research, Mumbai, India  M. Adams  University of
Illinois at Chicago, Chicago, Illinois 60607, USA  T. Adams  Florida State
University, Tallahassee, Florida 32306, USA  G.D. Alexeev  Joint Institute for
Nuclear Research, Dubna, Russia  G. Alkhazov  Petersburg Nuclear Physics
Institute, St. Petersburg, Russia  A. Altona University of Michigan, Ann
Arbor, Michigan 48109, USA  A. Askew  Florida State University, Tallahassee,
Florida 32306, USA  S. Atkins  Louisiana Tech University, Ruston, Louisiana
71272, USA  K. Augsten  Czech Technical University in Prague, Prague, Czech
Republic  C. Avila  Universidad de los Andes, Bogotá, Colombia  F. Badaud
LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France  L. Bagby  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  B. Baldin
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  D.V.
Bandurin  Florida State University, Tallahassee, Florida 32306, USA  S.
Banerjee  Tata Institute of Fundamental Research, Mumbai, India  E. Barberis
Northeastern University, Boston, Massachusetts 02115, USA  P. Baringer
University of Kansas, Lawrence, Kansas 66045, USA  J.F. Bartlett  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  U. Bassler
CEA, Irfu, SPP, Saclay, France  V. Bazterra  University of Illinois at
Chicago, Chicago, Illinois 60607, USA  A. Bean  University of Kansas,
Lawrence, Kansas 66045, USA  M. Begalli  Universidade do Estado do Rio de
Janeiro, Rio de Janeiro, Brazil  L. Bellantoni  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  S.B. Beri  Panjab University,
Chandigarh, India  G. Bernardi  LPNHE, Universités Paris VI and VII,
CNRS/IN2P3, Paris, France  R. Bernhard  Physikalisches Institut, Universität
Freiburg, Freiburg, Germany  I. Bertram  Lancaster University, Lancaster LA1
4YB, United Kingdom  M. Besançon  CEA, Irfu, SPP, Saclay, France  R.
Beuselinck  Imperial College London, London SW7 2AZ, United Kingdom  P.C. Bhat
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Bhatia
University of Mississippi, University, Mississippi 38677, USA  V. Bhatnagar
Panjab University, Chandigarh, India  G. Blazey  Northern Illinois University,
DeKalb, Illinois 60115, USA  S. Blessing  Florida State University,
Tallahassee, Florida 32306, USA  K. Bloom  University of Nebraska, Lincoln,
Nebraska 68588, USA  A. Boehnlein  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  D. Boline  State University of New York, Stony
Brook, New York 11794, USA  E.E. Boos  Moscow State University, Moscow, Russia
G. Borissov  Lancaster University, Lancaster LA1 4YB, United Kingdom  A.
Brandt  University of Texas, Arlington, Texas 76019, USA  O. Brandt  II.
Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen,
Germany  R. Brock  Michigan State University, East Lansing, Michigan 48824,
USA  A. Bross  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  D. Brown  LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France
J. Brown  LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France  X.B.
Bu  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  M.
Buehler  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
V. Buescher  Institut für Physik, Universität Mainz, Mainz, Germany  V.
Bunichev  Moscow State University, Moscow, Russia  S. Burdinb Lancaster
University, Lancaster LA1 4YB, United Kingdom  C.P. Buszello  Uppsala
University, Uppsala, Sweden  E. Camacho-Pérez  CINVESTAV, Mexico City, Mexico
B.C.K. Casey  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  H. Castilla-Valdez  CINVESTAV, Mexico City, Mexico  S. Caughron  Michigan
State University, East Lansing, Michigan 48824, USA  S. Chakrabarti  State
University of New York, Stony Brook, New York 11794, USA  D. Chakraborty
Northern Illinois University, DeKalb, Illinois 60115, USA  K.M. Chan
University of Notre Dame, Notre Dame, Indiana 46556, USA  A. Chandra  Rice
University, Houston, Texas 77005, USA  E. Chapon  CEA, Irfu, SPP, Saclay,
France  G. Chen  University of Kansas, Lawrence, Kansas 66045, USA  S.
Chevalier-Théry  CEA, Irfu, SPP, Saclay, France  S.W. Cho  Korea Detector
Laboratory, Korea University, Seoul, Korea  S. Choi  Korea Detector
Laboratory, Korea University, Seoul, Korea  B. Choudhary  Delhi University,
Delhi, India  S. Cihangir  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  D. Claes  University of Nebraska, Lincoln, Nebraska
68588, USA  J. Clutter  University of Kansas, Lawrence, Kansas 66045, USA  M.
Cooke  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
W.E. Cooper  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  M. Corcoran  Rice University, Houston, Texas 77005, USA  F. Couderc  CEA,
Irfu, SPP, Saclay, France  M.-C. Cousinou  CPPM, Aix-Marseille Université,
CNRS/IN2P3, Marseille, France  A. Croc  CEA, Irfu, SPP, Saclay, France  D.
Cutts  Brown University, Providence, Rhode Island 02912, USA  A. Das
University of Arizona, Tucson, Arizona 85721, USA  G. Davies  Imperial College
London, London SW7 2AZ, United Kingdom  S.J. de Jong  Nikhef, Science Park,
Amsterdam, the Netherlands  Radboud University Nijmegen, Nijmegen, the
Netherlands  E. De La Cruz-Burelo  CINVESTAV, Mexico City, Mexico  F. Déliot
CEA, Irfu, SPP, Saclay, France  R. Demina  University of Rochester, Rochester,
New York 14627, USA  D. Denisov  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  S.P. Denisov  Institute for High Energy Physics,
Protvino, Russia  S. Desai  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  C. Deterre  CEA, Irfu, SPP, Saclay, France  K. DeVaughan
University of Nebraska, Lincoln, Nebraska 68588, USA  H.T. Diehl  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Diesburg
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  P.F. Ding
The University of Manchester, Manchester M13 9PL, United Kingdom  A. Dominguez
University of Nebraska, Lincoln, Nebraska 68588, USA  A. Dubey  Delhi
University, Delhi, India  L.V. Dudko  Moscow State University, Moscow, Russia
D. Duggan  Rutgers University, Piscataway, New Jersey 08855, USA  A. Duperrin
CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France  S. Dutt  Panjab
University, Chandigarh, India  A. Dyshkant  Northern Illinois University,
DeKalb, Illinois 60115, USA  M. Eads  University of Nebraska, Lincoln,
Nebraska 68588, USA  D. Edmunds  Michigan State University, East Lansing,
Michigan 48824, USA  J. Ellison  University of California Riverside,
Riverside, California 92521, USA  V.D. Elvira  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  Y. Enari  LPNHE, Universités Paris
VI and VII, CNRS/IN2P3, Paris, France  H. Evans  Indiana University,
Bloomington, Indiana 47405, USA  A. Evdokimov  Brookhaven National Laboratory,
Upton, New York 11973, USA  V.N. Evdokimov  Institute for High Energy Physics,
Protvino, Russia  G. Facini  Northeastern University, Boston, Massachusetts
02115, USA  L. Feng  Northern Illinois University, DeKalb, Illinois 60115, USA
T. Ferbel  University of Rochester, Rochester, New York 14627, USA  F. Fiedler
Institut für Physik, Universität Mainz, Mainz, Germany  F. Filthaut  Nikhef,
Science Park, Amsterdam, the Netherlands  Radboud University Nijmegen,
Nijmegen, the Netherlands  W. Fisher  Michigan State University, East Lansing,
Michigan 48824, USA  H.E. Fisk  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  M. Fortner  Northern Illinois University,
DeKalb, Illinois 60115, USA  H. Fox  Lancaster University, Lancaster LA1 4YB,
United Kingdom  S. Fuess  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  A. Garcia-Bellido  University of Rochester, Rochester,
New York 14627, USA  J.A. García-González  CINVESTAV, Mexico City, Mexico
G.A. García-Guerrac CINVESTAV, Mexico City, Mexico  V. Gavrilov  Institute for
Theoretical and Experimental Physics, Moscow, Russia  P. Gay  LPC, Université
Blaise Pascal, CNRS/IN2P3, Clermont, France  W. Geng  CPPM, Aix-Marseille
Université, CNRS/IN2P3, Marseille, France  Michigan State University, East
Lansing, Michigan 48824, USA  D. Gerbaudo  Princeton University, Princeton,
New Jersey 08544, USA  C.E. Gerber  University of Illinois at Chicago,
Chicago, Illinois 60607, USA  Y. Gershtein  Rutgers University, Piscataway,
New Jersey 08855, USA  G. Ginther  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  University of Rochester, Rochester, New York
14627, USA  G. Golovanov  Joint Institute for Nuclear Research, Dubna, Russia
A. Goussiou  University of Washington, Seattle, Washington 98195, USA  P.D.
Grannis  State University of New York, Stony Brook, New York 11794, USA  S.
Greder  IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France  H.
Greenlee  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
G. Grenier  IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and
Université de Lyon, Lyon, France  Ph. Gris  LPC, Université Blaise Pascal,
CNRS/IN2P3, Clermont, France  J.-F. Grivaz  LAL, Université Paris-Sud,
CNRS/IN2P3, Orsay, France  A. Grohsjeand CEA, Irfu, SPP, Saclay, France  S.
Grünendahl  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  M.W. Grünewald  University College Dublin, Dublin, Ireland  T. Guillemin
LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France  G. Gutierrez  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  P. Gutierrez
University of Oklahoma, Norman, Oklahoma 73019, USA  J. Haley  Northeastern
University, Boston, Massachusetts 02115, USA  L. Han  University of Science
and Technology of China, Hefei, People’s Republic of China  K. Harder  The
University of Manchester, Manchester M13 9PL, United Kingdom  A. Harel
University of Rochester, Rochester, New York 14627, USA  J.M. Hauptman  Iowa
State University, Ames, Iowa 50011, USA  J. Hays  Imperial College London,
London SW7 2AZ, United Kingdom  T. Head  The University of Manchester,
Manchester M13 9PL, United Kingdom  T. Hebbeker  III. Physikalisches Institut
A, RWTH Aachen University, Aachen, Germany  D. Hedin  Northern Illinois
University, DeKalb, Illinois 60115, USA  H. Hegab  Oklahoma State University,
Stillwater, Oklahoma 74078, USA  A.P. Heinson  University of California
Riverside, Riverside, California 92521, USA  U. Heintz  Brown University,
Providence, Rhode Island 02912, USA  C. Hensel  II. Physikalisches Institut,
Georg-August-Universität Göttingen, Göttingen, Germany  I. Heredia-De La Cruz
CINVESTAV, Mexico City, Mexico  K. Herner  University of Michigan, Ann Arbor,
Michigan 48109, USA  G. Heskethf The University of Manchester, Manchester M13
9PL, United Kingdom  M.D. Hildreth  University of Notre Dame, Notre Dame,
Indiana 46556, USA  R. Hirosky  University of Virginia, Charlottesville,
Virginia 22904, USA  T. Hoang  Florida State University, Tallahassee, Florida
32306, USA  J.D. Hobbs  State University of New York, Stony Brook, New York
11794, USA  B. Hoeneisen  Universidad San Francisco de Quito, Quito, Ecuador
J. Hogan  Rice University, Houston, Texas 77005, USA  M. Hohlfeld  Institut
für Physik, Universität Mainz, Mainz, Germany  I. Howley  University of Texas,
Arlington, Texas 76019, USA  Z. Hubacek  Czech Technical University in Prague,
Prague, Czech Republic  CEA, Irfu, SPP, Saclay, France  V. Hynek  Czech
Technical University in Prague, Prague, Czech Republic  I. Iashvili  State
University of New York, Buffalo, New York 14260, USA  Y. Ilchenko  Southern
Methodist University, Dallas, Texas 75275, USA  R. Illingworth  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  A.S. Ito  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Jabeen  Brown
University, Providence, Rhode Island 02912, USA  M. Jaffré  LAL, Université
Paris-Sud, CNRS/IN2P3, Orsay, France  A. Jayasinghe  University of Oklahoma,
Norman, Oklahoma 73019, USA  M.S. Jeong  Korea Detector Laboratory, Korea
University, Seoul, Korea  R. Jesik  Imperial College London, London SW7 2AZ,
United Kingdom  P. Jiang  University of Science and Technology of China,
Hefei, People’s Republic of China  K. Johns  University of Arizona, Tucson,
Arizona 85721, USA  E. Johnson  Michigan State University, East Lansing,
Michigan 48824, USA  M. Johnson  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  A. Jonckheere  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  P. Jonsson  Imperial College London,
London SW7 2AZ, United Kingdom  J. Joshi  University of California Riverside,
Riverside, California 92521, USA  A.W. Jung  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  A. Juste  Institució Catalana de
Recerca i Estudis Avançats (ICREA) and Institut de Física d’Altes Energies
(IFAE), Barcelona, Spain  E. Kajfasz  CPPM, Aix-Marseille Université,
CNRS/IN2P3, Marseille, France  D. Karmanov  Moscow State University, Moscow,
Russia  P.A. Kasper  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  I. Katsanos  University of Nebraska, Lincoln, Nebraska 68588, USA
R. Kehoe  Southern Methodist University, Dallas, Texas 75275, USA  S. Kermiche
CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France  N. Khalatyan
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Khanov
Oklahoma State University, Stillwater, Oklahoma 74078, USA  A. Kharchilava
State University of New York, Buffalo, New York 14260, USA  Y.N. Kharzheev
Joint Institute for Nuclear Research, Dubna, Russia  I. Kiselevich  Institute
for Theoretical and Experimental Physics, Moscow, Russia  J.M. Kohli  Panjab
University, Chandigarh, India  A.V. Kozelov  Institute for High Energy
Physics, Protvino, Russia  J. Kraus  University of Mississippi, University,
Mississippi 38677, USA  A. Kumar  State University of New York, Buffalo, New
York 14260, USA  A. Kupco  Center for Particle Physics, Institute of Physics,
Academy of Sciences of the Czech Republic, Prague, Czech Republic  T. Kurča
IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de
Lyon, Lyon, France  V.A. Kuzmin  Moscow State University, Moscow, Russia  S.
Lammers  Indiana University, Bloomington, Indiana 47405, USA  G. Landsberg
Brown University, Providence, Rhode Island 02912, USA  P. Lebrun  IPNL,
Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon,
Lyon, France  H.S. Lee  Korea Detector Laboratory, Korea University, Seoul,
Korea  S.W. Lee  Iowa State University, Ames, Iowa 50011, USA  W.M. Lee  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  X. Lei
University of Arizona, Tucson, Arizona 85721, USA  J. Lellouch  LPNHE,
Universités Paris VI and VII, CNRS/IN2P3, Paris, France  D. Li  LPNHE,
Universités Paris VI and VII, CNRS/IN2P3, Paris, France  H. Li  LPSC,
Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National
Polytechnique de Grenoble, Grenoble, France  L. Li  University of California
Riverside, Riverside, California 92521, USA  Q.Z. Li  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  J.K. Lim  Korea Detector
Laboratory, Korea University, Seoul, Korea  D. Lincoln  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  J. Linnemann  Michigan
State University, East Lansing, Michigan 48824, USA  V.V. Lipaev  Institute
for High Energy Physics, Protvino, Russia  R. Lipton  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  H. Liu  Southern
Methodist University, Dallas, Texas 75275, USA  Y. Liu  University of Science
and Technology of China, Hefei, People’s Republic of China  A. Lobodenko
Petersburg Nuclear Physics Institute, St. Petersburg, Russia  M. Lokajicek
Center for Particle Physics, Institute of Physics, Academy of Sciences of the
Czech Republic, Prague, Czech Republic  R. Lopes de Sa  State University of
New York, Stony Brook, New York 11794, USA  H.J. Lubatti  University of
Washington, Seattle, Washington 98195, USA  R. Luna-Garciag CINVESTAV, Mexico
City, Mexico  A.L. Lyon  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  A.K.A. Maciel  LAFEX, Centro Brasileiro de Pesquisas
Físicas, Rio de Janeiro, Brazil  R. Madar  Physikalisches Institut,
Universität Freiburg, Freiburg, Germany  R. Magaña-Villalba  CINVESTAV, Mexico
City, Mexico  S. Malik  University of Nebraska, Lincoln, Nebraska 68588, USA
V.L. Malyshev  Joint Institute for Nuclear Research, Dubna, Russia  Y. Maravin
Kansas State University, Manhattan, Kansas 66506, USA  J. Martínez-Ortega
CINVESTAV, Mexico City, Mexico  R. McCarthy  State University of New York,
Stony Brook, New York 11794, USA  C.L. McGivern  The University of Manchester,
Manchester M13 9PL, United Kingdom  M.M. Meijer  Nikhef, Science Park,
Amsterdam, the Netherlands  Radboud University Nijmegen, Nijmegen, the
Netherlands  A. Melnitchouk  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  D. Menezes  Northern Illinois University, DeKalb,
Illinois 60115, USA  P.G. Mercadante  Universidade Federal do ABC, Santo
André, Brazil  M. Merkin  Moscow State University, Moscow, Russia  A. Meyer
III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany  J.
Meyer  II. Physikalisches Institut, Georg-August-Universität Göttingen,
Göttingen, Germany  F. Miconi  IPHC, Université de Strasbourg, CNRS/IN2P3,
Strasbourg, France  N.K. Mondal  Tata Institute of Fundamental Research,
Mumbai, India  M. Mulhearn  University of Virginia, Charlottesville, Virginia
22904, USA  E. Nagy  CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille,
France  M. Naimuddin  Delhi University, Delhi, India  M. Narain  Brown
University, Providence, Rhode Island 02912, USA  R. Nayyar  University of
Arizona, Tucson, Arizona 85721, USA  H.A. Neal  University of Michigan, Ann
Arbor, Michigan 48109, USA  J.P. Negret  Universidad de los Andes, Bogotá,
Colombia  P. Neustroev  Petersburg Nuclear Physics Institute, St. Petersburg,
Russia  H.T. Nguyen  University of Virginia, Charlottesville, Virginia 22904,
USA  T. Nunnemann  Ludwig-Maximilians-Universität München, München, Germany
J. Orduna  Rice University, Houston, Texas 77005, USA  N. Osman  CPPM, Aix-
Marseille Université, CNRS/IN2P3, Marseille, France  J. Osta  University of
Notre Dame, Notre Dame, Indiana 46556, USA  M. Padilla  University of
California Riverside, Riverside, California 92521, USA  A. Pal  University of
Texas, Arlington, Texas 76019, USA  N. Parashar  Purdue University Calumet,
Hammond, Indiana 46323, USA  V. Parihar  Brown University, Providence, Rhode
Island 02912, USA  S.K. Park  Korea Detector Laboratory, Korea University,
Seoul, Korea  R. Partridgee Brown University, Providence, Rhode Island 02912,
USA  N. Parua  Indiana University, Bloomington, Indiana 47405, USA  A. Patwa
Brookhaven National Laboratory, Upton, New York 11973, USA  B. Penning  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Perfilov
Moscow State University, Moscow, Russia  Y. Peters  II. Physikalisches
Institut, Georg-August-Universität Göttingen, Göttingen, Germany  K. Petridis
The University of Manchester, Manchester M13 9PL, United Kingdom  G. Petrillo
University of Rochester, Rochester, New York 14627, USA  P. Pétroff  LAL,
Université Paris-Sud, CNRS/IN2P3, Orsay, France  M.-A. Pleier  Brookhaven
National Laboratory, Upton, New York 11973, USA  P.L.M. Podesta-Lermah
CINVESTAV, Mexico City, Mexico  V.M. Podstavkov  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  A.V. Popov  Institute for High
Energy Physics, Protvino, Russia  M. Prewitt  Rice University, Houston, Texas
77005, USA  D. Price  Indiana University, Bloomington, Indiana 47405, USA  N.
Prokopenko  Institute for High Energy Physics, Protvino, Russia  J. Qian
University of Michigan, Ann Arbor, Michigan 48109, USA  A. Quadt  II.
Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen,
Germany  B. Quinn  University of Mississippi, University, Mississippi 38677,
USA  M.S. Rangel  LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de
Janeiro, Brazil  K. Ranjan  Delhi University, Delhi, India  P.N. Ratoff
Lancaster University, Lancaster LA1 4YB, United Kingdom  I. Razumov  Institute
for High Energy Physics, Protvino, Russia  P. Renkel  Southern Methodist
University, Dallas, Texas 75275, USA  I. Ripp-Baudot  IPHC, Université de
Strasbourg, CNRS/IN2P3, Strasbourg, France  F. Rizatdinova  Oklahoma State
University, Stillwater, Oklahoma 74078, USA  M. Rominsky  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Ross  Lancaster
University, Lancaster LA1 4YB, United Kingdom  C. Royon  CEA, Irfu, SPP,
Saclay, France  P. Rubinov  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  R. Ruchti  University of Notre Dame, Notre Dame, Indiana
46556, USA  G. Sajot  LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3,
Institut National Polytechnique de Grenoble, Grenoble, France  P. Salcido
Northern Illinois University, DeKalb, Illinois 60115, USA  A. Sánchez-
Hernández  CINVESTAV, Mexico City, Mexico  M.P. Sanders  Ludwig-Maximilians-
Universität München, München, Germany  A.S. Santosi LAFEX, Centro Brasileiro
de Pesquisas Físicas, Rio de Janeiro, Brazil  G. Savage  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  L. Sawyer  Louisiana
Tech University, Ruston, Louisiana 71272, USA  T. Scanlon  Imperial College
London, London SW7 2AZ, United Kingdom  R.D. Schamberger  State University of
New York, Stony Brook, New York 11794, USA  Y. Scheglov  Petersburg Nuclear
Physics Institute, St. Petersburg, Russia  H. Schellman  Northwestern
University, Evanston, Illinois 60208, USA  C. Schwanenberger  The University
of Manchester, Manchester M13 9PL, United Kingdom  R. Schwienhorst  Michigan
State University, East Lansing, Michigan 48824, USA  J. Sekaric  University of
Kansas, Lawrence, Kansas 66045, USA  H. Severini  University of Oklahoma,
Norman, Oklahoma 73019, USA  E. Shabalina  II. Physikalisches Institut, Georg-
August-Universität Göttingen, Göttingen, Germany  V. Shary  CEA, Irfu, SPP,
Saclay, France  S. Shaw  Michigan State University, East Lansing, Michigan
48824, USA  A.A. Shchukin  Institute for High Energy Physics, Protvino, Russia
R.K. Shivpuri  Delhi University, Delhi, India  V. Simak  Czech Technical
University in Prague, Prague, Czech Republic  P. Skubic  University of
Oklahoma, Norman, Oklahoma 73019, USA  P. Slattery  University of Rochester,
Rochester, New York 14627, USA  D. Smirnov  University of Notre Dame, Notre
Dame, Indiana 46556, USA  K.J. Smith  State University of New York, Buffalo,
New York 14260, USA  G.R. Snow  University of Nebraska, Lincoln, Nebraska
68588, USA  J. Snow  Langston University, Langston, Oklahoma 73050, USA  S.
Snyder  Brookhaven National Laboratory, Upton, New York 11973, USA  S.
Söldner-Rembold  The University of Manchester, Manchester M13 9PL, United
Kingdom  L. Sonnenschein  III. Physikalisches Institut A, RWTH Aachen
University, Aachen, Germany  K. Soustruznik  Charles University, Faculty of
Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic
J. Stark  LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut
National Polytechnique de Grenoble, Grenoble, France  D.A. Stoyanova
Institute for High Energy Physics, Protvino, Russia  M. Strauss  University of
Oklahoma, Norman, Oklahoma 73019, USA  L. Suter  The University of Manchester,
Manchester M13 9PL, United Kingdom  P. Svoisky  University of Oklahoma,
Norman, Oklahoma 73019, USA  M. Titov  CEA, Irfu, SPP, Saclay, France  V.V.
Tokmenin  Joint Institute for Nuclear Research, Dubna, Russia  Y.-T. Tsai
University of Rochester, Rochester, New York 14627, USA  K. Tschann-Grimm
State University of New York, Stony Brook, New York 11794, USA  D. Tsybychev
State University of New York, Stony Brook, New York 11794, USA  B. Tuchming
CEA, Irfu, SPP, Saclay, France  C. Tully  Princeton University, Princeton, New
Jersey 08544, USA  L. Uvarov  Petersburg Nuclear Physics Institute, St.
Petersburg, Russia  S. Uvarov  Petersburg Nuclear Physics Institute, St.
Petersburg, Russia  S. Uzunyan  Northern Illinois University, DeKalb, Illinois
60115, USA  R. Van Kooten  Indiana University, Bloomington, Indiana 47405, USA
W.M. van Leeuwen  Nikhef, Science Park, Amsterdam, the Netherlands  N. Varelas
University of Illinois at Chicago, Chicago, Illinois 60607, USA  E.W. Varnes
University of Arizona, Tucson, Arizona 85721, USA  I.A. Vasilyev  Institute
for High Energy Physics, Protvino, Russia  P. Verdier  IPNL, Université Lyon
1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France  A.Y.
Verkheev  Joint Institute for Nuclear Research, Dubna, Russia  L.S.
Vertogradov  Joint Institute for Nuclear Research, Dubna, Russia  M. Verzocchi
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  M.
Vesterinen  The University of Manchester, Manchester M13 9PL, United Kingdom
D. Vilanova  CEA, Irfu, SPP, Saclay, France  P. Vokac  Czech Technical
University in Prague, Prague, Czech Republic  H.D. Wahl  Florida State
University, Tallahassee, Florida 32306, USA  M.H.L.S. Wang  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  J. Warchol  University
of Notre Dame, Notre Dame, Indiana 46556, USA  G. Watts  University of
Washington, Seattle, Washington 98195, USA  M. Wayne  University of Notre
Dame, Notre Dame, Indiana 46556, USA  J. Weichert  Institut für Physik,
Universität Mainz, Mainz, Germany  L. Welty-Rieger  Northwestern University,
Evanston, Illinois 60208, USA  A. White  University of Texas, Arlington, Texas
76019, USA  D. Wicke  Fachbereich Physik, Bergische Universität Wuppertal,
Wuppertal, Germany  M.R.J. Williams  Lancaster University, Lancaster LA1 4YB,
United Kingdom  G.W. Wilson  University of Kansas, Lawrence, Kansas 66045, USA
M. Wobisch  Louisiana Tech University, Ruston, Louisiana 71272, USA  D.R. Wood
Northeastern University, Boston, Massachusetts 02115, USA  T.R. Wyatt  The
University of Manchester, Manchester M13 9PL, United Kingdom  Y. Xie  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  R. Yamada
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Yang
University of Science and Technology of China, Hefei, People’s Republic of
China  T. Yasuda  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  Y.A. Yatsunenko  Joint Institute for Nuclear Research, Dubna,
Russia  W. Ye  State University of New York, Stony Brook, New York 11794, USA
Z. Ye  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  H.
Yin  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  K.
Yip  Brookhaven National Laboratory, Upton, New York 11973, USA  S.W. Youn
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  J.M. Yu
University of Michigan, Ann Arbor, Michigan 48109, USA  J. Zennamo  State
University of New York, Buffalo, New York 14260, USA  T. Zhao  University of
Washington, Seattle, Washington 98195, USA  T.G. Zhao  The University of
Manchester, Manchester M13 9PL, United Kingdom  B. Zhou  University of
Michigan, Ann Arbor, Michigan 48109, USA  J. Zhu  University of Michigan, Ann
Arbor, Michigan 48109, USA  M. Zielinski  University of Rochester, Rochester,
New York 14627, USA  D. Zieminska  Indiana University, Bloomington, Indiana
47405, USA  L. Zivkovic  Brown University, Providence, Rhode Island 02912, USA

###### Abstract

We present a measurement of the cross section for $W$ boson production in
association with at least one $b$-quark jet in proton-antiproton collisions.
The measurement is made using data corresponding to an integrated luminosity
of $6.1$ fb-1 recorded with the D0 detector at the Fermilab Tevatron
$p\bar{p}$ Collider at $\sqrt{s}=1.96$ TeV. We measure an inclusive cross
section of $\sigma(W~{}(\to\mu\nu)+b+X)=1.04~{}\pm~{}0.05\thinspace$(stat.)
$\pm~{}0.12\thinspace$(syst.) pb and $\sigma(W(\to e\nu)+b+X)=1.00$
$\pm~{}0.04\thinspace$(stat.) $\pm~{}0.12\thinspace$(syst.) pb in the phase
space defined by $p_{T}^{\nu}>25$ GeV, $p_{T}^{\text{$b$-jet}}>20$ GeV,
$|\eta^{\text{$b$-jet}}|<1.1$, and a muon (electron) with $p_{T}^{\ell}>20$
GeV and $|\eta^{\mu}|<1.7$ ($|\eta^{e}|<1.1$ or $1.5<|\eta^{e}|<2.5$). The
combined result per lepton family is $\sigma(W(\to\ell\nu)+b+X)=1.05$
$\pm~{}0.12\thinspace$(stat.+syst.) for $|\eta^{\ell}|<1.7$. The results are
in agreement with predictions from next-to-leading order QCD calculations
using mcfm, $\sigma(W+b)\cdot{\cal
B}(W\to\ell\nu)=1.34~{}^{+0.41}_{-0.34}\thinspace(\textrm{syst.})$, and also
with predictions from the sherpa and madgraph Monte Carlo event generators.

###### pacs:

12.38.Qk, 13.85.Qk, 14.65.Fy, 14.70.Fm

The measurement of the production cross section of a $W$ boson in association
with a $b$-quark jet provides a stringent test of quantum chromodynamics
(QCD). Processes involving $W/Z$ bosons in association with $b$ quarks are
also the largest backgrounds in studies of the standard model (SM) Higgs boson
decaying to two $b$ quarks, in measurements of top quark properties in both
single and pair production, and in numerous searches for physics beyond the
SM. The cross section for the process $p\bar{p}\to W+b+X$ has been calculated
with next-to-leading order (NLO) precision assoc_wb1 ; assoc_wb . Subprocesses
at NLO include $q\bar{q}~{}\to~{}Wb\bar{b},~{}q\bar{q}~{}\to~{}Wb\bar{b}g$,
and $qg~{}\to~{}Wb\bar{b}q^{\prime}$. An additional small contribution comes
from sea $b$ quarks in the incoming proton or antiproton, $bq\to
Wbq^{\prime}$.

In this letter we describe a measurement of the cross section for $W$ boson
production in association with $b$-quark jets in $p\bar{p}$ interactions,
where a $W$ boson is identified via its electronic or muonic decay modes. A
measurement of $W+b$ production cross section with up to two jets at
$\sqrt{s}=1.96$ TeV has been published by the CDF Collaboration wbb_cdf  and
an inclusive measurement has been published by the ATLAS Collaboration
wbb_atlas  at $\sqrt{s}=7$ TeV. The measured production cross section reported
by CDF is $\sigma\cdot{\cal B}(W\to\ell\nu)=2.74\pm
0.27\thinspace(\text{stat.})\pm 0.42\thinspace(\text{syst.})$ pb
($\ell=e,~{}\nu$), while the theoretical expectation for this quantity based
on NLO calculations is $1.22\pm 0.14\thinspace\text{(syst.)}$ pb wbb_cdf .
With the CDF measurement of $W+b$ production exceeding significantly the NLO
prediction, while the ATLAS result is in agreement with the expectation, an
independent measurement is important to understand the production of $W$
bosons in association with $b$ jets at hadron colliders.

The data used in this analysis were collected between July 2006 and December
2010 using the D0 detector at the Fermilab Tevatron Collider at
$\sqrt{s}~{}=~{}1.96$ TeV, and correspond to an integrated luminosity of 6.1
$\mathrm{fb}^{-1}$. We first briefly describe the main components of the D0
Run II detector run2det  relevant to this analysis. The D0 detector has a
central tracking system consisting of a silicon microstrip tracker (SMT)
layer0  and a central fiber tracker (CFT), both located within a 2 T
superconducting solenoidal magnet, with designs optimized for tracking and
vertexing at pseudorapidities $|\eta|<3$ and $|\eta|<2.5$, respectively coord
. A liquid argon and uranium calorimeter has a central section (CC) covering
pseudorapidities $|\eta|\lesssim 1.1$, and two end calorimeters (EC) that
extend coverage to $|\eta|\approx 4.2$, with all three housed in separate
cryostats calopaper . An outer muon system, at $|\eta|<2$, consists of a layer
of tracking detectors and scintillation trigger counters in front of 1.8 T
toroids, followed by two similar layers after the toroids. Luminosity is
measured using plastic scintillator arrays located in front of the EC
cryostats. The trigger and data acquisition systems are designed to
accommodate the high instantaneous luminosities of Run II.

The $W+b$ candidates are selected by triggering on single lepton or lepton-
plus-jet signatures with a three-level trigger system. The trigger
efficiencies are approximately $70\%$ for the muon channel and $95\%$ for the
electron channel.

$W$ boson candidates are identified in the $\mu+\nu$ and $e+\nu$ decay
channels whereas a small fraction of selected events arises from leptonical
decaying tau leptons. Offline event selection requires a reconstructed primary
$p\bar{p}$ interaction primary vertex (PV) that has at least three associated
tracks and is located within $60$ cm of the center of the detector along the
beam direction. The vertex selection for $W+b$ events is about $97\%$
efficient as measured in simulations.

Electrons are identified using calorimeter and tracking information. The
selection requires exactly one electron with transverse momentum
$p_{T}^{e}>20$ GeV identified by an electromagnetic (EM) shower in the central
($|\eta^{e}|<1.1$) or endcap ($1.5<|\eta^{e}|<2.5$) calorimeter by comparing
the longitudinal and transverse shower profiles to those of simulated
electrons. The showers must be spatially isolated from other energetic
particles, deposit most of their energy in the EM part of the calorimeter, and
pass a likelihood criterion that includes a spatial track match. In the
central detector region, an $E/p$ requirement is applied, where $E$ is the
energy of the calorimeter cluster and $p$ is the momentum of the track. The
transverse momentum measurement of electrons is based on calorimeter energy
information.

The muon selection requires the candidate to be reconstructed from hits in the
muon system and matched to a reconstructed track in the central tracker. The
transverse momentum of the muon must exceed $p_{T}^{\mu}>20$ GeV, with
$|\eta^{\mu}|<1.7$. Muons are required to be spatially isolated from other
energetic particles using information from the central tracking detectors and
calorimeter diboson_prd . Muons from cosmic rays are rejected by applying a
timing criterion on the hits in the scintillator layers and by applying
restrictions on the displacement of the muon track with respect to the
selected PV.

Candidate $W+\textrm{jets}$ events are then selected by requiring at least one
reconstructed jet with $|\eta^{\text{jet}}|<1.1$ and $p_{T}^{\text{jet}}>20$
GeV. Jets are reconstructed from energy deposits in the calorimeter using the
iterative midpoint cone algorithm jet_algo  and a cone of radius $\Delta
R=0.5$ in $y$-$\varphi$ space coord . The energies of jets are corrected for
detector response, the presence of noise and multiple $p\bar{p}$ interactions,
and for energy deposited outside of the jet reconstruction cone. To enrich the
sample with $W$ bosons, events are required to have missing transverse energy
$\mbox{$E\kern-6.00006pt/$ }_{T}\\!$ $>25$ GeV due to the neutrino escaping
detection.

Background processes for this analysis are electroweak
$W+\textrm{jets}/\gamma$ production, $Z/\gamma^{*}$ production, $t{\bar{t}}$
and single top quark production, diboson production, and multijet events with
jets misidentified as leptons. The $W+b$ signal and SM background processes
are simulated using a combination of pythia v6.409 pythia  and alpgen v2.3
alpgen  with pythia providing parton showering and hadronization. We use
pythia Tune A with CTEQ6L1 pdf_cteq6M  parton distribution functions (PDFs)
and perform a detailed geant-based geant  simulation of the D0 detector. The
$V{\rm+jets}$ ($V=W/Z$) processes are normalized to the inclusive $W$ and
$Z$-boson cross sections calculated at NNLO hamberg . The $Z$-boson $p_{T}$
distribution is modeled to match the distribution observed in data zpt_xsec ,
taking into account the dependence on the number of reconstructed jets. To
reproduce the $W$-boson $p_{T}$ distribution in simulated events, the product
of the measured $Z$-boson $p_{T}$ spectrum and the ratio of $W$ to $Z$-boson
$p_{T}$ distributions at NLO is used as correction. NLO+NNLL (next-to-next-to-
leading log) calculations are used to normalize $t{\bar{t}}~{}$ production
mochuwer , while single top quark production is normalized to NNLO single_top
. The NLO $WW$, $WZ$, and $ZZ$ production cross section values are obtained
with mcfm program mcfm . For the $W$+heavy-flavor jet ($b$ or $c$ quark)
events, the ratio of the alpgen prediction to the NLO prediction for
$W+b\bar{b}$ and $W+c\bar{c}$ is obtained from mcfm mcfm  and applied as a
correction factor. The simulation is also corrected for the trigger
efficiencies measured in data.

Instrumental backgrounds and those from semileptonic decays of hadrons,
referred to as “multijet” background, are estimated from data. The
instrumental background is important for the electron channel, where a jet
with a high electromagnetic fraction can pass electron identification
criteria, or a photon can be misidentified as an electron. In the muon
channel, the multijet background is less significant and arises mainly from
the semileptonic decay of heavy quarks in which the muon satisfies the
isolation requirements. We require that the $W$ boson candidates have a
transverse mass $M_{T}$ mtw  satisfying
$40~{}\text{GeV}+~{}\frac{1}{2}\mbox{$\mbox{$E\kern-6.00006pt/$ }_{T}\\!$
}<M_{T}<120$ GeV to suppress multijet background and mis-reconstructed events.
The average efficiency determined in simulation for a $W+b$ signal to pass
these requirements is about $82\%$.

Identification of $b$ jets is crucial for this measurement. Once the inclusive
$W+{\rm jets}$ sample is defined, the jets considered for $b$ tagging are
subject to a requirement called taggability. This requirement is imposed to
decouple the performance of the $b$-jet identification from detector effects.
For a jet to be taggable, it must contain at least two tracks with at least
one hit in the SMT, $p_{T}>1$ GeV for the highest-$p_{T}$ track and
$p_{T}>0.5$ GeV for the next-to-highest $p_{T}$ track. The efficiency for a
jet to be taggable is about $90\%$ in the selected phase space.

The D0 $b$-tagging algorithm for identifying heavy flavor jets is based on a
combination of variables sensitive to the presence secondary vertices (SV) or
tracks displaced from the PV. This analysis uses an updated $b$ tagger
utilizing a multivariate analysis (MVA) tmva ; gamma_b  that provides improved
performance over the previous neural network based algorithm bid_nim . The
most sensitive input variables to the MVA are the number of reconstructed
secondary vertices in the jet, the invariant mass of charged particles
associated with the SV ($M_{\text{SV}}$), the number of tracks used to
reconstruct the SV, the two-dimensional decay length significance of the SV in
the plane transverse to the beam, a weighted combination of the tracks’
transverse impact parameter significances, and the probability that the tracks
from the jet originate from the PV, which is referred to as the jet lifetime
probability (JLIP). The MVA provides a continuous output value that tends
towards one for $b$ jets and zero for non-$b$ jets. Events are considered in
which at least one jet passes a tight MVA requirement corresponding to an
efficiency of $\approx 50\%$ for $b$ jets. The likelihood for a light jet
($u$, $d$, $s$ quarks and gluons) to be misidentified for the corresponding
MVA selection is about $0.5$%. Simulated events are corrected to have the same
efficiencies for taggability and $b$-tagging requirements as found in data.
These corrections are derived in a flavor dependent manner bid_nim , using
independent $QCD$ enriched data samples and simulated events with enriched
light and heavy jet contributions. Jets containing $b$ quarks have a different
energy response and receive an additional energy correction of about $6\%$ as
determined from simulation. Figure 1 shows the transverse mass of the
candidate events before and after applying $b$-jet identification.

In addition to the MVA output, we perform further selections using
$M_{\text{SV}}$ and JLIP variables. $M_{\text{SV}}$ provides good
discrimination between $b$, $c$, and light quark jets due to their different
masses gamma_b . The two variables together take into account the kinematics
of the event and, in order to further improve the separation power, they are
combined in a single variable ${\cal
D}_{\text{MJL}}~{}=\frac{1}{2}~{}\left(M_{\text{SV}}/(5~{}\text{GeV})-\ln(\text{JLIP})/20\right)$
zbzlf .A loose criterion for an event to pass at least ${\cal
D}_{\text{MJL}}>0.1$ is applied to remove poorly reconstructed events. The
efficiency for signal events to pass this selection is about $97\%$.

The numbers of expected and observed events before and after applying the
$b$-jet identification in data and simulation are listed in Table 1. The
$b$-tagging column includes the selection requirement on ${\cal
D}_{\text{MJL}}$.

Process | No $b$-tag |  $b$-tag
---|---|---
$V+$heavy flavor | 41093 | $\pm$ | 8924 | 5068 | $\pm$ | 1124
$V+$light flavor | 516661 | $\pm$ | 56734 | 5718 | $\pm$ | 678
Diboson | 4728 | $\pm$ | 519 | 222 | $\pm$ | 26
Top | 5431 | $\pm$ | 536 | 1602 | $\pm$ | 181
Multijet | 20527 | $\pm$ | 4458 | 794 | $\pm$ | 180
Expected events | 588440 | $\pm$ | 57610 | 13405 | $\pm$ | 1338
Data | 586289 | 12793
Table 1: Numbers of events for data and contributing processes before and
after applying $b$-jet identification. Uncertainties include statistical and
systematic contributions. The contribution of $Z+\textrm{jets}$ events to the
$V+\textrm{jets}$ samples is $\approx 5\%$ for heavy and light flavor jets
before and after $b$-tagging.

Figure 1: [color online] Transverse mass of the $\ell\nu$ system (a) before
and (b) after $b$-jet identification. The data are shown by black markers,
simulated background processes are shown by filled histograms. The data
uncertainties are statistical only. An estimate of the systematic uncertainty
on the simulated background processes is shown by the shaded bands

We measure the fraction of $W+b+X$ events in the final selected sample by
performing a binned maximum likelihood fit to the observed data distribution
of the ${\cal D}_{\text{MJL}}$ discriminant in our sample shown in Fig. 2. The
templates for $W$+light flavor, $W+b$, and $W+c$ jets shown in Fig. 2 are
taken from the efficiency-corrected simulation. Expected contributions from
$Z$+jets, single top quark, $t\bar{t}$, diboson, and multijet production are
subtracted from the data. After performing the fits, we obtain the number of
events with different jet flavors listed in Table 2.

The measured cross sections are presented at the particle level by correcting
for detector acceptance, selection-efficiencies, and $b$-jet identification.
We quote our result as a cross section in a restricted phase space: at least
one $b$-jet with $p_{T}^{\text{$b$-jet}}>20$ GeV,
$|\eta^{\text{$b$-jet}}|<1.1$ and a muon with $p_{T}^{\mu}~{}>~{}20$ GeV and
$|\eta^{\mu}|<1.7$ or an electron with $p_{T}^{e}>20$ GeV and $|\eta^{e}|<1.1$
or $1.5<|\eta^{e}|<2.5$. For the neutrino momentum we require $p_{T}^{\nu}>25$
GeV.

| $W\to\mu\nu$ | $W\to e\nu$
---|---|---
Processxxxx | Events | Fraction | Events | Fraction
$W+b$ | $1306\pm 166$ | $0.3\pm 0.04$ | $1676\pm 212$ | $0.27\pm 0.03$
$W+c$ | $664\pm 97$ | $0.1\pm 0.02$ | $1096\pm 159$ | $0.18\pm 0.03$
$W+\textrm{l.f.}$ | $2152\pm 265$ | $0.5\pm 0.07$ | $3479\pm 425$ | $0.56\pm 0.07$
Data$-$Bkgd | $4127\pm 150$ |  | $6255\pm 168$ |
Table 2: Estimated numbers of $W+\text{jet}$ events from fitting the flavor-
specific processes, along with the expected background of $W$ boson processes
and the data after subtracting $Z$+jets, single top quark, $t\bar{t}$, and
diboson background processes. $l.f.$ stands for light flavor jets.
Uncertainties include statistical and systematic contributions.

Systematic uncertainties are determined by varying experimental parameters and
efficiency/acceptance corrections by one standard deviation and propagating
the effect on ${\cal D}_{\text{MJL}}$. The systematic uncertainties are
dominated by effects related to the measurement of jets. The contributions
from jet energy resolution, jet modeling, and detector effects are about
$2.5\%,~{}3\%$, and $4\%$, respectively. Uncertainties on $b$-jet
identification are determined in data and simulations by using $b$-jet-
enriched samples and are about $2\%-5\%$ per jet. The uncertainties due to
lepton identification are about $2\%$. The integrated luminosity is known to a
precision of $6.1\%$ lumi . The uncertainty of the template fit is estimated
by varying the normalization and shape from the data corrections of the $W$
boson processes and the fit parameters (about $6\%$). By summing the
uncertainties in quadrature we obtain a final total systematic uncertainty on
the cross section measurements of approximately $12\%$.

The cross section times branching fraction is calculated by dividing the
number of signal events measured by integrated luminosity ($\mathcal{L}$),
acceptance ($\mathcal{A}$), and efficiencies ($\epsilon$) of the selection
requirements:

Figure 2: [color online] Contributions of the various jet flavors normalized
to the measured cross section obtained from a fit in the $W\to\mu\nu$ channel
on both (a) linear and (b) logarithmic scales. The various $W+\textrm{jets}$
processes are shown as filled histograms and data, after the subtraction of
contributions from Drell-Yan, diboson, and top quark production, are
represented with black markers. The uncertainties include both statistical and
systematic contributions.

$\sigma(W+b)\cdot{\cal B}(W\to\ell\nu)=\frac{N_{W+b}}{{\cal L}\cdot{\cal
A}\cdot\epsilon},$ (1)

where $\epsilon$ is given by the product of the trigger, object
reconstruction, and selection efficiencies.

We first present results separately for the muon channel and electron channel
because they are performed in slightly different requirements on the phase
space of the lepton and then combine using a common phase space. We measure
from the cross section in the muon channel where $W\to\mu\nu$ in a visible
phase space defined by $p_{T}^{\mu}>20$ GeV, $|\eta^{\mu}|<1.7$ with at least
one $b$-jet limited to $p_{T}^{\text{$b$-jet}}>20$ GeV and
$|\eta^{\text{$b$-jet}}|<1.1$ as,

$\begin{split}\sigma(W+b)\cdot{\cal B}(W\to\mu\nu)=\phantom{xxxxxx}\\\ 1.04\pm
0.05\thinspace\textrm{(stat.)}\pm
0.12\thinspace\textrm{(syst.)~{}pb.}\end{split}$ (2)

We perform an NLO QCD prediction using mcfm v6.1, based on CTEQ6M PDF
pdf_cteq6M  and a central scale of $M_{W}+2m_{b}$, where $m_{b}=4.7$ GeV is
the mass of the $b$ quark. Uncertainties are estimated by varying
renormalization and factorization scales by a factor of two in each direction,
varying $m_{b}$ between $4.2$ and $5$ GeV, and by using an alternative PDF
set. The mcfm calculation predicts $\sigma(W+b)\cdot{\cal
B}(W\to\mu\nu)=1.34~{}^{+0.40}_{-0.33}~{}(\textrm{scale})\pm
0.06~{}(\textrm{PDF})~{}^{+0.09}_{-0.05}~{}(m_{b})$ pb. Predictions obtained
using sherpa v1.4 and CTEQ6.6 PDFs pdf_cteq6M  lead to a value $1.21\pm
0.03\thinspace(\textrm{stat.})$ pb. Using madgraph5 mg5  with CTEQ6L1 PDFs, we
obtain $1.52\pm 0.02\thinspace(\textrm{stat.})$ pb. Uncertainties for scale
variations, PDFs, and the $b$-quark mass are on the order of about 30%.

In the electron channel, we measure the cross section times branching fraction
by selecting $p_{T}^{e}>20$ GeV, $|\eta^{e}|<1.1$ or $1.5<|\eta^{e}|<2.5$, at
least one $b$-jet as above and obtain

$\begin{split}\sigma(W+b)\cdot{\cal B}(W\to e\nu)=\phantom{xxxxxx}\\\ 1.00\pm
0.04\thinspace\textrm{(stat.)}\pm
0.12\thinspace\textrm{(syst.)~{}pb.}\end{split}$ (3)

The mcfm calculated cross section for this channel is $\sigma(W+b)\cdot{\cal
B}(W\to e\nu)=1.28~{}^{+0.40}_{-0.33}~{}(\textrm{scale})\pm
0.06~{}(\textrm{PDF})~{}^{+0.09}_{-0.05}~{}(m_{b})$ pb. The sherpa prediction
is $1.08\pm 0.03\thinspace(\textrm{stat.})$ pb, while the madgraph5 prediction
is $1.44\pm 0.02\thinspace(\textrm{stat.})$ pb. The combined systematic effect
scale, PDF and $m_{b}$ variations is also around 30%.

Using the mcfm prediction we extrapolate the measurement in the electron final
state to the same selection requirements as the muon final state to allow for
a consistent combination. Combining the results in $W\to\mu\nu$ and $W\to
e\nu$ decays we obtain

$\begin{split}\sigma(W+b)\cdot{\cal B}(W\to\ell\nu)=\phantom{xxxxxx}\\\
1.05\pm 0.03\thinspace\textrm{(stat.)}\pm
0.12\thinspace\textrm{(syst.)~{}pb.}\end{split}$ (4)

The small experimental uncertainty should allow to further constrain
theoretical predictions. In summary, we have performed a measurement of the
inclusive cross section for $W$ boson production in association with at least
one $b$-jet at $\sqrt{s}=1.96$ TeV, considering final states with $W\to\mu\nu$
($W\to e\nu$) events in a restricted phase space of $p_{T}^{\ell}>20$ GeV,
$|\eta^{\mu}|<1.7$ ($|\eta^{e}|<1.1$ or $1.5<|\eta^{e}|<2.5$), with $b$ jets
limited to $p_{T}^{\text{$b$-jet}}>20$ GeV and $|\eta^{\text{$b$-jet}}|<1.1$.
The measured cross sections agree within uncertainties with NLO QCD
calculations and predictions obtained using the sherpa and madgraph
generators.

We thank the staffs at Fermilab and collaborating institutions, and
acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France);
MON, NRC KI and RFBR (Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil);
DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); NRF (Korea);
FOM (The Netherlands); STFC and the Royal Society (United Kingdom); MSMT and
GACR (Czech Republic); BMBF and DFG (Germany); SFI (Ireland); The Swedish
Research Council (Sweden); and CAS and CNSF (China). Special thanks as well to
John Campbell for his support with mcfm and Patrick Fox with madgraph.

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# SIMD-SIZE AWARE WEIGHT REGULARIZATION
FOR FAST NEURAL VOCODING ON CPU

###### Abstract

This paper proposes weight regularization for a faster neural vocoder. Pruning
time-consuming DNN modules is a promising way to realize a real-time vocoder
on a CPU (e.g. WaveRNN, LPCNet). Regularization that encourages sparsity is
also effective in avoiding the quality degradation created by pruning.
However, the orders of weight matrices must be contiguous in SIMD size for
fast vocoding. To ensure this order, we propose explicit SIMD size aware
regularization. Our proposed method reshapes a weight matrix into a tensor so
that the weights are aligned by group size in advance, and then computes the
group Lasso-like regularization loss. Experiments on 70% sparse subband
WaveRNN show that pruning in conventional Lasso and column-wise group Lasso
degrades the synthetic speech’s naturalness. The vocoder with proposed
regularization 1) achieves comparable naturalness to that without pruning and
2) performs meaningfully faster than other conventional vocoders using
regularization.

Index Terms—  speech synthesis, neural vocoder, regularization, SIMD, group
pruning

##  1 Introduction

The neural vocoder represented by WaveNet [1] has dramatically improved the
quality of text-to-speech (TTS) synthesis. While WaveNet can generate high-
quality speech waveforms directly from conditioning features via a large
causal convolution-based autoregressive model, its huge computational cost and
autoregressive (AR) architecture prevent fast vocoding. To allow easier
parallel computation, many neural vocoders based on non-autoregressive
structures have been proposed [2, 3, 4, 5, 6, 7]. These schemes offer high
processing speeds if the device is specialized for parallel computing, such as
GPUs. On the other hand, to achieve fast neural vocoding on CPUs, the
computational complexity must be reduced drastically. WaveRNN achieves real-
time vocoding by replacing huge causal convolutions of WaveNet with a simple
GRU, and pruning its weights [8]. LPCNet also introduces signal processing
insights into the speech generation process and reduces the number of DNN
parameters from that of WaveRNN [9]. Other approaches to reduce the number of
DNN inferencing iterations, with multi-sample generation in a single forward
propagation step [10, 11] and prediction of shortened subband signals instead
of waveforms [12, 13].

Quantization and low-rank approximation are promising alternatives to pruning
for paring the DNN module’s computational complexity. [13] roughly quadrupled
speeds by quantizing neural vocoder weights to 8-bit integers, but it requires
quantization error-aware training and an appropriate intrinsic implementation
for integers, resulting in high implementation cost and hardware dependency.
Although the low-rank approximation shrinks the model size, its speed-up
contribution is limited due to the increased number of matrices that must be
computed, which requires more matrix-vector product instructions (e.g. “gemv”)
to be called [14]. Pruning [15, 16] used in WaveRNN and LPCNet substitutes the
elements of the weight matrix with zeros in the training process. During
inference, the calculation of zero weights can be skipped, and hardware
dependency is also small because the weights can be treated as floating-point
without modification. While excessive pruning leads to quality degradation,
regularization is an effective solution. Lasso regularization promotes a
sparse model, thus allowing for a smaller gap in the model with and without
pruning [17]. However, the order of non-zero weight elements becomes non-
contiguous when using Lasso for regularization. To exploit fully the fast
single instruction multiple data (SIMD) operations intrinsic to CPUs, the non-
zero elements must be contiguous, so Lasso is not optimal for SIMD. The use of
group Lasso (gLasso) [18] allows for a sequence of non-zero elements, but the
model’s expressiveness is sacrificed due to row- or column-wise weight
sparsity.

To ensure both speed and quality, we propose a gLasso-like regularization
approach that explicitly sparsifies weights with the group pruning size. The
proposed method aligns the weights in both the non-zero and zero regions with
enough size to fully occupy the SIMD registers at once. Thus, group pruning
across the boundary between regions can be avoided, and computational
efficiency can be improved while maintaining model expressiveness. In our
experiments, we used multi-sample subband WaveRNN [19] with 70% sparsity.
While pruning degraded the naturalness of the synthetic speech of the vocoder
without regularization and the one with the use of Lasso and gLasso
regularization, regularization with the proposed method and pruning maintained
the same naturalness as that achieved before pruning. We also found that our
vocoder was faster than the conventional alternatives.

##  2 Multi-sample subband WaveRNN

###  2.1 Model architecture and its training

Fig. 1: Overview of multi-sample subband WaveRNN via multivariate Gaussian
[19]. This vocoder predicts $M$ subband signals simultaneously in single
forward propagation step ($M$=2 is used in this figure).

Subband WaveRNN [13] reduces sequence length from $T$ to $T/B$ by predicting
$B$-band subband signals instead of a speech waveform. [19] extended it to
multi-sample generation for even faster vocoding; Fig. 1 shows an overview.
The model consists of an encoder and a decoder, which are responsible for
frame rate and sample rate, respectively. Encoders upsample frame-level
acoustic features to corresponding samples. The decoder generates predictions
of the next time $t+\tau\forall_{m}\in[1,M-1]$ from the output of the encoder
and the previous $M$ subband signals, where $m$ is the index of the number of
subband signals to be generated simultaneously. To generate multiple samples
in single forward propagation, linear layer FC3s are provided for subband
signals of $t+\tau\forall_{m}\in[1,M-1]$. This module jointly predicts the
associations among subband signals because PQMF has band overlaps. Assuming a
multivariate Gaussian as FC3’s target, this vocoder minimizes the negative
log-likelihood given by:

$\displaystyle{\cal L}_{{\rm
NLL}}\left(\theta\right)=-\sum\limits_{t=1}^{T/B}{\sum\limits_{m=1}^{M}{\ln{\cal
N}\left({{\bm{x}}_{t+m};{\bm{\mu}}\left({{\bm{z}}_{t+\tau\forall_{m}},\theta}\right),{\bm{\Sigma}}\left({{\bm{z}}_{t+\tau\forall_{m}},\theta}\right)}\right)}},$
(1)

where $\theta$, ${\bm{z}}_{t}$, ${\bm{x}}_{t}\in{\mathbb{R}}^{B}$,
${\bm{\mu}}\in{\mathbb{R}}^{B}$ and ${\bm{\Sigma}}\in{\mathbb{R}}^{B\times B}$
are the DNN model parameters, FC2’s output, subband signals, the mean vector
and covariance matrix of the multivariate Gaussian, respectively. To guarantee
spectral reproducibility, STFT loss ${\cal L}_{{\rm STFT}}\left(\theta\right)$
[20] is calculated by generating subband signals from the multivariate
Gaussian via a reparameterization trick. This is added to Eq. (1) without
scaling to optimize the vocoder.

###  2.2 Weight pruning

For fast vocoding, pruning is performed during training. We performed pruning
by gradually increasing sparsity [16] in the same manner as WaveRNN using:

$\displaystyle
d_{s}=d\left[{1-\left\\{{1-\left({s-s_{0}}\right)/S}\right\\}^{3}}\right],$
(2)

where $s$, $s_{0}$, and $S$ are the current-, start-, and total- pruning step,
respectively. $d$ is the target density, thus the sparsity is defined as
$1-d$. To fully utilize vector algebra with SIMD, we apply group pruning [15].
The group size of FC1, GRU, and FC2 for pruning was set to 16. Taking Intel’s
AVX2 intrinsic instruction set as SIMD, the dot product can be calculated for
16 elements in two SIMD operations. This is done by putting eight 32-bit float
elements on a register and calculating the dot product, which is then applied
to and added to the other eight neighboring elements.

###  2.3 Weight regularization

In order to avoid a degradation in model expressiveness due to pruning,
regularization is an efficient approach to sparsify the model in advance. A
well-known Lasso regularization term is computed as follows:

$\displaystyle{\cal L}_{{\rm
Reg}}^{\textsc{Lasso}}\left(\theta\right)=\sum\limits_{r}{\sum\limits_{i=1}^{I_{r}}{\sum\limits_{j=1}^{J_{r}}{\left|{W_{r}\left({i,j}\right)}\right|}}},$
(3)

where $r$, ${\bm{W}}_{r}\in{\mathbb{R}}^{I_{r}\times J_{r}}$ are the DNN
module’s index and the weight matrix to be regularized, respectively. $i$ and
$j$ denote the row and column indices.

The regularization term of column-wise group Lasso is given by:

$\displaystyle{\cal L}_{{\rm
Reg}}^{\textsc{gLasso}}\left(\theta\right)=\sum\limits_{r}{\sum\limits_{j=1}^{J_{r}}{\left\|{{\bm{w}}_{r}^{i}},\right\|}}$
(4)

where ${{\bm{w}}_{r}^{i}}$ and $\left\|\cdot\right\|$ are the ${\bm{W}}_{r}$’s
$i$-th column vector and the L2 norm operator, respectively. The final
objective function with regularization is reformulated as:

$\displaystyle{\cal L}\left(\theta\right)={\cal L}_{{\rm
NLL}}\left(\theta\right)+{\cal L}_{{\rm STFT}}\left(\theta\right)+\lambda{\cal
L}_{{\rm Reg}}\left(\theta\right),$ (5)

where $\lambda$ is the scale for the regularization term ${\cal L}_{{\rm
Reg}}\left(\theta\right)$.

##  3 Proposed SIMD-size aware weight reguralizaton

The Lasso and gLasso regularizations described in Section 2.3 could suffer
from group pruning of sparse weights across the zero/non-zero boundary,
resulting in quality degradation. To overcome this problem, we propose a
regularization that assumes group pruning at the SIMD size. The weight matrix
${\bm{W}}_{r}$ is reshaped in advance into a third-order tensor ${\mathbfcal
W}_{r}\in{\mathbb{R}}^{I_{r}\times J_{r}/G\times G}$ to make the sparse
weight’s block size equal to group pruning size $G$. Then, the proposed
regularization term for this tensor is formulated as follows:

$\displaystyle{\cal L}_{{\rm
Reg}}^{\textsc{Proposed}}\left(\theta\right)=\sum\limits_{r}{\sum\limits_{i=1}^{I_{r}}{\sum\limits_{j=1}^{J_{r}}{\sqrt{\sum\limits_{g=1}^{G}{{\cal
W}_{r}\left({i,j,g}\right)^{2}}}}}}.$ (6)

Fig. 2: Comparison between Lasso, gLasso, and our regularization proposal
applied to a single weight matrix. The white and gray regions denote non-zero
and zero components, respectively.

Figure 2 compares regularized weights when Lasso, gLasso, and our proposed
method (Proposed) are applied. The white and gray regions of the matrices in
this figure are the non-zero and zero components, respectively. This prior
matrix-to-tensor conversion and computing Eq. (6) contribute to SIMD size
group-wise sparsification. Therefore, group-wise sparsified weights can be
preferentially pruned, reducing the probability of pruning portions contain
non-zero elements. Since weights are continuous in SIMD size, weights can
always be assigned to aligned memory, which is advantageous in terms of
computing efficiency.

##  4 Experiments

###  4.1 Setup

We used speech data uttered by a Japanese professional female speaker. The
sampling frequency was 22.05 kHz. 200 utterances were extracted as evaluation
data (18.3 minutes), and the remainder were used for training and validation
(30.6 hours).

Eighty-dimensional logarithmic mel-spectrograms were used as the conditioning
feature of the neural vocoder. The analysis frame shift was 5 ms111Although we
also investigated the commonly used frame shift of 12.5 ms in our preliminary
experiments, we chose to set it to 5 ms because it better reproduced the pitch
of synthetic speech. If a faster inference speed is preferred, the frame shift
can be set to 12.5 ms like other studies for lower encoder computational
complexity.. The ResNet of the encoder has ten residual blocks, each
consisting of 1D-convolution with 128 units, batch normalization, and
activation. ReLU was used for all activations, and the simultaneous generation
sample was set to two likewise [19]. This multi-sample vocoder occasionally
failed to predict accurate variance parameters which yielded clicking sounds.
To avoid this problem, we 1) eliminated variance outliers and 2) clipped
sampled results in a similar way to [10]. The number of training steps was
5000k, and parameters for pruning steps in Eq. (2) were set to $S_{0}=2000$k
and $S=2500$k. We used $d=0.3$ and $\lambda$ in Eq. (5) to $1.0\times 10^{-4}$
for all regularization methods. This guarantees that the model sparsity is at
least 70%. If the number of zero elements increases due to regularization, the
sparsity could be higher than this. The vocoder’s optimization was performed
using RAdam [21], with $\alpha=1.0\times 10^{-4}$, $\beta=\left({0.9,{\kern
1.0pt}0.999}\right)$, and $\varepsilon=1.0\times 10^{-8}$.

###  4.2 Weight heatmap comparison

Fig. 3: FC1’s weight heatmap comparison. From top to bottom: w/o Reg, Lasso,
gLasso, and Proposed. The right and left heatmaps show without and with
pruning, respectively. The left-side of the heatmaps receive the recurrent
multiple subband signals (e.g. “Detail 1”). Other right-side of ones accept
the encoder’s conditioned output (e.g. “Detail 2”). The comparison of “Detail
1” and “2” between w/o and w/ Prune, demonstrated that Proposed kept the
minimum difference among them.

Figure 3 shows FC1 (described in Fig. 1) weight heatmaps before and after
pruning for each method. The horizontal and vertical axes are the input and
output dimensions, respectively. Comparing w/o Reg (w/o Prune) and w/o Reg (w/
Prune), we can see that the elements have been replaced with zero leaving
large components. As described in Fig. 1, the recurrent multiple subband
signals are fed to FC1, so these weights are particularly large on the left-
side of the heatmap as if to focus on their signals (e.g. “Detail 1” in Fig.
3). Other right-side weight components are responsible for receiving encoder’s
ouputs (e.g. “Detail 2”). These results revealed that w/o Reg (w/ Prune)
disregarded or neglected the encoder’s conditioned outputs. Although Lasso
(w/o Prune) was not overly dependent on the most recent sample, its weights
had discontinuous order. The gLasso (w/o Prune) yield poor sparsification,
because under the constraint of sparsifying entire columns, it was difficult
to find compact representations. These regularizations, like w/o Reg (w/o
Prune), are prone to degrade the synthesized speech’s quality because group
pruning is applied across the boundaries between zero and non-zero. On the
other hand, the proposed method Proposed (w/o Prune) was sparse and its
weights were continuously aligned in group pruning size $G=16$ in the column
direction before pruning. Since there is no drastic difference in the heatmaps
between with and without pruning, we found that pruning can be done without
sacrificing the model’s expressiveness.

###  4.3 Subjective evaluations

We subjectively evaluated the naturalness of synthetic speech by using mean
opinion score (MOS) on a five-point scale ranging from 5: very natural to 1:
very unnatural. Sixty listeners participated in the test via crowdsourcing.
They evaluated ten sentences for each method, randomly selected from all 200
evaluation data, for a total of sixty sentences. These participants were
different evaluators for analytic resynthesis and TTS.

####  4.3.1 Vocoding for extracted acoustic features from natural speech

Fig. 4: Mean opinion scores of naturalness. Acoustic features for vocoding
were extracted from natural speech. Fig. 5: Mean opinion scores in terms of
naturalness. Acoustic features for vocoding were predicted by the TTS model.

Figure 4 shows the subjective evaluation results of vocoding with acoustic
features extracted from natural speech. w/o Reg (w/o Prune) yielded lower
performance than Ground truth, but still obtained high naturalness. w/o Reg
(w/ Prune) degraded significantly more than w/o Reg (w/o Prune). This is due
to 1) neglecting the conditioning spectral information in pruning, and 2)
excessive reliance on recurrent samples led to quality degradation due to
mismatches with the training time; as described in Section 4.2. The
performance of gLasso (w/ Prune) also falls for the same reason, just not as
much as w/o Reg (w/ Prune). On the other hand, Lasso (w/ Prune) showed no more
significant degradation from w/o Reg, even with pruning. This is due to the
fact that model does not rely excessively on recent samples, but focuses more
on the conditioning spectral information. Proposed (w/ Prune) outperforms
these pruned models and achieves naturalness comparable to that of w/o Reg
(w/o Prune).

####  4.3.2 Vocoding for acoustic features predicted by TTS

To investigate robustness against degraded acoustic features, FastSpeech2 [22]
as the TTS model was also trained with the same data as the neural vocoders.
We fed 380 kinds of symbols including phoneme and prosodic information to
FastSpeech2. It was optimized via a minimum mean absolute error criterion with
2000k steps by Adam [23] with $\beta=\left({0.9,{\kern 1.0pt}0.98}\right)$,
and $\varepsilon=1.0\times 10^{-9}$. We followed the same learning rate
schedule in [24].

Figure 5 shows the subjective evaluation results. The overall difference in
scores between ground truth and synthetic speech was greater when using
features extracted from natural speech since acoustic features predicted by
TTS were degraded from the original one. The Proposed (w/ Prune) matched the
naturalness of w/o Reg (w/o Prune). This result confirms that the
regularization proposal is robust to acoustic features degraded by TTS.

###  4.4 Vocoding speed comparison

The real-time factors (RTFs) were calculated to measure the inference speeds
for all methods. RTF is defined by:

$\displaystyle{\rm RTF}:=T_{{\rm inference}}/T_{{\rm data}},$ (7)

where $T_{{\rm data}}$ and $T_{{\rm inference}}$ are speech length and single-
thread inference time measured on an Intel Core i7-8750H CPU 2.20 GHz,
respectively.

Fig. 6: Average RTFs obtained from all evaluation data.

Figure 6 shows averaged RTFs from all evaluation data. w/o Reg (w/ Prune)
yielded a significant speed improvement over w/o Reg (w/o Prune) owing to
pruning. Lasso (w/ Prune) showed no speed improvement from w/o Reg (w/ Prune).
As discussed in Section 4.2, this was attributed to Lasso regularization
promoting non-contiguous sparse matrices, which fails to yield a SIMD-friendly
contiguous sparse matrix. On the other hand, gLasso (w/ Prune) slightly
improved the RTF. The reason is the 70% sparsity by pruning, further increased
column-wise contiguous zeroed regions via regularization. The proposed method
achieved better RTFs than gLasso (w/ Prune), since it achieved a group-wise
sparser matrix than gLasso, as mentioned in Section 4.2. Our RTF=0.080 is
nearly comparable to the one of the recent non-AR HiFi-GAN (v3) [7], which
works fast on CPUs (RTF=0.075). Since they used a higher clock CPU (Intel Core
i7 CPU 2.6 GHz) than ours, our proposed method might outperform their speed if
on the same CPU. Furthermore, the combination of the other faster approach for
WaveRNN (e.g. [25]) and the proposed regularization would be able to provide a
significant speed-up compared to HiFi-GAN.

##  5 Conclusion

In this work, we proposed SIMD-size aware group-wise regularization to avoid
the quality degradation associated with neural vocoder pruning. We
incorporated the regularization proposal into a subband WaveRNN-based vocoder
and showed that the regularized weights have group-wise continuous orders
suitable for SIMD computation. No major differences in our vocoder’s weight
layout were observed via heatmaps of before and after pruning. Subjective
evaluations regarding naturalness demonstrated that the proposed pruned
vocoder outperformed that with no regularization, Lasso, and group Lasso. In
particular, our vocoder achieved comparable naturalness to that achieved
without pruning. A speed evaluation also revealed that our vocoder performed
significantly faster than the existing alternatives.

Our method can also increase contiguous zeroed region more efficiently than
Lasso and gLasso even if regularized to fit processors with smaller SIMD
sizes, e.g. Intel SSE4 and Arm NEON. So we expect to run significantly faster
than them without any loss of quality. Our first future work will apply the
proposed method for Arm NEON and confirm its efficiency on embedded
processors. Our second second future work will compare and combine our
regularization with AlignReg [26], which has similar concepts proposed for
natural language processing. Since the proposed regularization is not limited
to neural vocoders, we will also plan to apply it to other computationally
expensive models (e.g. RNN-T [27] and BERT [28]).

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