Measurement of the Hadronic Form Factor in D0 --> K- e+ nue Decays
BABAR-PUB-07/015
SLAC-PUB-12417
Measurement of the Hadronic Form Factor in D0 → K−e+νe Decays.
B. Aubert, M. Bona, D. Boutigny, Y. Karyotakis, J. P. Lees, V. Poireau, X. Prudent, V. Tisserand, and A. Zghiche
Laboratoire de Physique des Particules, IN2P3/CNRS et Université de Savoie, F-74941 Annecy-Le-Vieux, France
J. Garra Tico and E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
L. Lopez and A. Palano
Università di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
G. Eigen, B. Stugu, and L. Sun
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
G. S. Abrams, M. Battaglia, D. N. Brown, J. Button-Shafer, R. N. Cahn, Y. Groysman,
R. G. Jacobsen, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, D. Lopes Pegna,
G. Lynch, L. M. Mir, T. J. Orimoto, M. T. Ronan,∗ K. Tackmann, and W. A. Wenzel
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
P. del Amo Sanchez, C. M. Hawkes, and A. T. Watson
University of Birmingham, Birmingham, B15 2TT, United Kingdom
T. Held, H. Koch, B. Lewandowski, M. Pelizaeus, T. Schroeder, and M. Steinke
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
D. Walker
University of Bristol, Bristol BS8 1TL, United Kingdom
D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom,
C. Hearty, N. S. Knecht, T. S. Mattison, and J. A. McKenna
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
A. Khan, M. Saleem, and L. Teodorescu
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
V. E. Blinov, A. D. Bukin, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin,
S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, and K. Yu Todyshev
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
M. Bondioli, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, and D. P. Stoker
University of California at Irvine, Irvine, California 92697, USA
S. Abachi and C. Buchanan
University of California at Los Angeles, Los Angeles, California 90024, USA
S. D. Foulkes, J. W. Gary, F. Liu, O. Long, B. C. Shen, and L. Zhang
University of California at Riverside, Riverside, California 92521, USA
H. P. Paar, S. Rahatlou, and V. Sharma
University of California at San Diego, La Jolla, California 92093, USA
J. W. Berryhill, C. Campagnari, A. Cunha, B. Dahmes, T. M. Hong, D. Kovalskyi, and J. D. Richman
University of California at Santa Barbara, Santa Barbara, California 93106, USA
http://arxiv.org/abs/0704.0020v1
T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman,
T. Schalk, B. A. Schumm, A. Seiden, D. C. Williams, M. G. Wilson, and L. O. Winstrom
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
E. Chen, C. H. Cheng, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, and F. C. Porter
California Institute of Technology, Pasadena, California 91125, USA
G. Mancinelli, B. T. Meadows, K. Mishra, and M. D. Sokoloff
University of Cincinnati, Cincinnati, Ohio 45221, USA
F. Blanc, P. C. Bloom, S. Chen, W. T. Ford, J. F. Hirschauer, A. Kreisel, M. Nagel,
U. Nauenberg, A. Olivas, J. G. Smith, K. A. Ulmer, S. R. Wagner, and J. Zhang
University of Colorado, Boulder, Colorado 80309, USA
A. M. Gabareen, A. Soffer, W. H. Toki, R. J. Wilson, F. Winklmeier, and Q. Zeng
Colorado State University, Fort Collins, Colorado 80523, USA
D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, J. Merkel, A. Petzold, B. Spaan, and K. Wacker
Universität Dortmund, Institut für Physik, D-44221 Dortmund, Germany
T. Brandt, V. Klose, M. J. Kobel, H. M. Lacker, W. F. Mader, R. Nogowski,
J. Schubert, K. R. Schubert, R. Schwierz, J. E. Sundermann, and A. Volk
Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany
D. Bernard, G. R. Bonneaud, E. Latour, V. Lombardo, Ch. Thiebaux, and M. Verderi
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
P. J. Clark, W. Gradl, F. Muheim, S. Playfer, A. I. Robertson, and Y. Xie
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, A. Cecchi, G. Cibinetto, P. Franchini,
E. Luppi, M. Negrini, A. Petrella, L. Piemontese, E. Prencipe, and V. Santoro
Università di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
F. Anulli, R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Pacetti, P. Patteri, I. M. Peruzzi,† M. Piccolo, M. Rama, and A. Zallo
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
A. Buzzo, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge,
S. Passaggio, C. Patrignani, E. Robutti, A. Santroni, and S. Tosi
Università di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
K. S. Chaisanguanthum, M. Morii, and J. Wu
Harvard University, Cambridge, Massachusetts 02138, USA
R. S. Dubitzky, J. Marks, S. Schenk, and U. Uwer
Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
D. J. Bard, P. D. Dauncey, R. L. Flack, J. A. Nash, M. B. Nikolich, and W. Panduro Vazquez
Imperial College London, London, SW7 2AZ, United Kingdom
P. K. Behera, X. Chai, M. J. Charles, U. Mallik, N. T. Meyer, and V. Ziegler
University of Iowa, Iowa City, Iowa 52242, USA
J. Cochran, H. B. Crawley, L. Dong, V. Eyges, W. T. Meyer, S. Prell, E. I. Rosenberg, and A. E. Rubin
Iowa State University, Ames, Iowa 50011-3160, USA
A. V. Gritsan, Z. J. Guo, and C. K. Lae
Johns Hopkins University, Baltimore, Maryland 21218, USA
A. G. Denig, M. Fritsch, and G. Schott
Universität Karlsruhe, Institut für Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
N. Arnaud, J. Béquilleux, M. Davier, G. Grosdidier, A. Höcker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot,
S. Rodier, P. Roudeau, M. H. Schune, J. Serrano, V. Sordini, A. Stocchi, W. F. Wang, and G. Wormser
Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
C. A. Chavez, I. J. Forster, J. R. Fry, E. Gabathuler, R. Gamet,
D. E. Hutchcroft, D. J. Payne, K. C. Schofield, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, K. A. George, F. Di Lodovico, W. Menges, and R. Sacco
Queen Mary, University of London, E1 4NS, United Kingdom
G. Cowan, H. U. Flaecher, D. A. Hopkins, P. S. Jackson, T. R. McMahon, F. Salvatore, and A. C. Wren
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
D. N. Brown and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
J. Allison, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, T. J. West, and J. I. Yi
University of Manchester, Manchester M13 9PL, United Kingdom
J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, and J. M. Tuggle
University of Maryland, College Park, Maryland 20742, USA
G. Blaylock, C. Dallapiccola, S. S. Hertzbach, X. Li, T. B. Moore, E. Salvati, and S. Saremi
University of Massachusetts, Amherst, Massachusetts 01003, USA
R. Cowan, P. H. Fisher, G. Sciolla, S. J. Sekula, M. Spitznagel, F. Taylor, and R. K. Yamamoto
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
S. E. Mclachlin, P. M. Patel, and S. H. Robertson
McGill University, Montréal, Québec, Canada H3A 2T8
A. Lazzaro and F. Palombo
Università di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, R. Kroeger, D. A. Sanders, D. J. Summers, and H. W. Zhao
University of Mississippi, University, Mississippi 38677, USA
S. Brunet, D. Côté, M. Simard, P. Taras, and F. B. Viaud
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
H. Nicholson
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
G. De Nardo, F. Fabozzi,‡ L. Lista, D. Monorchio, and C. Sciacca
Università di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
M. A. Baak, G. Raven, and H. L. Snoek
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
G. Benelli, L. A. Corwin, K. K. Gan, K. Honscheid, D. Hufnagel, H. Kagan, R. Kass,
J. P. Morris, A. M. Rahimi, J. J. Regensburger, R. Ter-Antonyan, and Q. K. Wong
Ohio State University, Columbus, Ohio 43210, USA
N. L. Blount, J. Brau, R. Frey, O. Igonkina, J. A. Kolb, M. Lu,
R. Rahmat, N. B. Sinev, D. Strom, J. Strube, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
N. Gagliardi, A. Gaz, M. Margoni, M. Morandin, A. Pompili,
M. Posocco, M. Rotondo, F. Simonetto, R. Stroili, and C. Voci
Università di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
E. Ben-Haim, H. Briand, G. Calderini, J. Chauveau, P. David, L. Del Buono,
Ch. de la Vaissière, O. Hamon, Ph. Leruste, J. Malclès, J. Ocariz, and A. Perez
Laboratoire de Physique Nucléaire et de Hautes Energies,
IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,
Université Denis Diderot-Paris7, F-75252 Paris, France
L. Gladney
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
M. Biasini, R. Covarelli, and E. Manoni
Università di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
C. Angelini, G. Batignani, S. Bettarini, M. Carpinelli, R. Cenci, A. Cervelli, F. Forti, M. A. Giorgi,
A. Lusiani, G. Marchiori, M. A. Mazur, M. Morganti, N. Neri, E. Paoloni, G. Rizzo, and J. J. Walsh
Università di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
M. Haire
Prairie View A&M University, Prairie View, Texas 77446, USA
J. Biesiada, P. Elmer, Y. P. Lau, C. Lu, J. Olsen, A. J. S. Smith, and A. V. Telnov
Princeton University, Princeton, New Jersey 08544, USA
E. Baracchini, F. Bellini, G. Cavoto, A. D’Orazio, D. del Re, E. Di Marco, R. Faccini, F. Ferrarotto, F. Ferroni,
M. Gaspero, P. D. Jackson, L. Li Gioi, M. A. Mazzoni, S. Morganti, G. Piredda, F. Polci, F. Renga, and C. Voena
Università di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
M. Ebert, H. Schröder, and R. Waldi
Universität Rostock, D-18051 Rostock, Germany
T. Adye, G. Castelli, B. Franek, E. O. Olaiya, S. Ricciardi, W. Roethel, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
R. Aleksan, S. Emery, M. Escalier, A. Gaidot, S. F. Ganzhur, G. Hamel de Monchenault,
W. Kozanecki, M. Legendre, G. Vasseur, Ch. Yèche, and M. Zito
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
X. R. Chen, H. Liu, W. Park, M. V. Purohit, and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, USA
M. T. Allen, D. Aston, R. Bartoldus, P. Bechtle, N. Berger, R. Claus, J. P. Coleman, M. R. Convery,
J. C. Dingfelder, J. Dorfan, G. P. Dubois-Felsmann, D. Dujmic, W. Dunwoodie, R. C. Field, T. Glanzman,
S. J. Gowdy, M. T. Graham, P. Grenier, C. Hast, T. Hryn’ova, W. R. Innes, J. Kaminski, M. H. Kelsey,
H. Kim, P. Kim, M. L. Kocian, D. W. G. S. Leith, S. Li, S. Luitz, V. Luth, H. L. Lynch, D. B. MacFarlane,
H. Marsiske, R. Messner, D. R. Muller, C. P. O’Grady, I. Ofte, A. Perazzo, M. Perl, T. Pulliam,
B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyder, J. Stelzer, D. Su,
M. K. Sullivan, K. Suzuki, S. K. Swain, J. M. Thompson, J. Va’vra, N. van Bakel, A. P. Wagner,
M. Weaver, W. J. Wisniewski, M. Wittgen, D. H. Wright, A. K. Yarritu, K. Yi, and C. C. Young
Stanford Linear Accelerator Center, Stanford, California 94309, USA
P. R. Burchat, A. J. Edwards, S. A. Majewski, B. A. Petersen, and L. Wilden
Stanford University, Stanford, California 94305-4060, USA
S. Ahmed, M. S. Alam, R. Bula, J. A. Ernst, V. Jain, B. Pan, M. A. Saeed, F. R. Wappler, and S. B. Zain
State University of New York, Albany, New York 12222, USA
W. Bugg, M. Krishnamurthy, and S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, and R. F. Schwitters
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen, X. C. Lou, and S. Ye
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi, F. Gallo, D. Gamba, and M. Pelliccioni
Università di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
M. Bomben, L. Bosisio, C. Cartaro, F. Cossutti, G. Della Ricca, L. Lanceri, and L. Vitale
Università di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
V. Azzolini, N. Lopez-March, F. Martinez-Vidal, D. A. Milanes, and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. Albert, Sw. Banerjee, B. Bhuyan, K. Hamano, R. Kowalewski, I. M. Nugent, J. M. Roney, and R. J. Sobie
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
J. J. Back, P. F. Harrison, T. E. Latham, G. B. Mohanty, and M. Pappagallo§
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
H. R. Band, X. Chen, S. Dasu, K. T. Flood, J. J. Hollar,
P. E. Kutter, Y. Pan, M. Pierini, R. Prepost, S. L. Wu, and Z. Yu
University of Wisconsin, Madison, Wisconsin 53706, USA
H. Neal
Yale University, New Haven, Connecticut 06511, USA
(Dated: October 25, 2018)
The shape of the hadronic form factor f+(q
2) in the decay D0 → K−e+νe has been measured
in a model independent analysis and compared with theoretical calculations. We use 75 fb−1 of
data recorded by the BABAR detector at the PEPII electron-positron collider. The corresponding
decay branching fraction, relative to the decay D0 → K−π+, has also been measured to be RD =
BR(D0 → K−e+νe)/BR(D
→ K−π+) = 0.927± 0.007± 0.012. From these results, and using the
present world average value for BR(D0 → K−π+), the normalization of the form factor at q2 = 0
is determined to be f+(0) = 0.727 ± 0.007 ± 0.005 ± 0.007 where the uncertainties are statistical,
systematic, and from external inputs, respectively.
PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er
∗Deceased †Also with Università di Perugia, Dipartimento di Fisica, Perugia,
I. INTRODUCTION
Measurements of exclusive semileptonic D decays pro-
vide an accurate determination of the hadronic form fac-
tors entering in these decays. Assuming that the CKM
matrix is unitary, the elements |Vcs| and |Vcd| can be de-
termined:
|Vcs| = |Vud| −
|Vcb|2
+O(λ6) = 0.9729± 0.0003, (1)
using the measured values [1] of |Vud| and |Vcb|, and the
sine of the Cabibbo angle λ = sin(θc) ≃ 0.227. Theo-
retical predictions give estimates of the form factors in
exclusive semileptonic B and D meson decays. Precise
measurements of the hadronic form factors in D decays
can help to validate predictions from QCD calculations in
both D and B decays. Better understanding of the form
factors in B decays is necessary to improve the precision
on the determination of |Vcb| and |Vub|.
In D0 → K−e+νe decays [2], with a pseudoscalar
hadron emitted in the final state, and neglecting the elec-
tron mass, the differential decay rate depends only on one
form factor f+(q
|Vcs|2
∣~pK(q
∣f+(q
, (2)
where GF is the Fermi constant, q
2 is the invariant mass
squared of the two leptons, e+ and νe, and ~pK(q
2) is
the kaon three-momentum in the D0 rest frame [3]. In
this paper we present measurements of the q2 variation
and absolute value of the hadronic form factor at q2 = 0
for the decay D0 → K−e+νe(γ). The data consist of
D mesons produced in e+e− → cc̄ continuum events at
a center of mass energy near the Υ (4S) mass, and were
recorded by the BABAR detector at the Stanford Linear
Accelerator Center’s PEP-II collider. A semi-inclusive
reconstruction technique is used to select charm semilep-
tonic decays with high efficiency. As a result of this ap-
proach, events with a photon radiated during the D0 de-
cay are included in the signal. The systematic uncertain-
ties are kept as low as possible by using control samples
extracted from data where possible.
Measurements of D → Kℓ̄νℓ, based on smaller signal
events samples, have been published by the CLEO [4],
FOCUS [5] and Belle [6] collaborations.
This paper is organized as follows. A general descrip-
tion of the hadronic form factor, f+(q
2), is given in Sec-
tion II, where the different parameterizations considered
Italy
‡Also with Università della Basilicata, Potenza, Italy
§Also with IPPP, Physics Department, Durham University,
Durham DH1 3LE, United Kingdom
in this analysis are explained. In Section III a short de-
scription of the detector components that are important
to this measurement is given. The selection of signal
events and the rejection of background are considered in
Section IV. In Section V, the measured q2 variation of
the hadronic form factor is discussed and compared with
previous measurements. In Section VI the measured de-
cay rate is given and in Section VII these measurements
are combined to obtain the value of f+(0).
II. THE F+(Q
2) HADRONIC FORM FACTOR
The amplitude for the decay D0 → K−ℓ+νℓ depends
on two hadronic form factors:
< K(p′)|Vµ|D(p) > =
pµ + p
µ − qµ
m2D −m2K
m2D −m2K
qµf0(q
2) (3)
where Vµ = s̄γµc. The constraint f+(0) = f0(0) en-
sures that there is no singularity at q2 = 0. When the
charged lepton is an electron, the contribution from f0
is proportional to m2e and can be neglected in decay rate
measurements.
The parameterizations of f+(q
2) which have been com-
pared with present measurements and a few examples of
theoretical approaches, proposed to determine the val-
ues of corresponding parameters, are considered in the
following.
A. Form factor parameterizations
The most general expressions of the form factor f+(q
are analytic functions satisfying the dispersion relation:
Res(f+)q2=m2
ℑf+(t)
t− q2 − iǫ
. (4)
The only singularities in the complex t ≡ q2 plane orig-
inate from the interaction of the charm and the strange
quarks in vector states. They are a pole, situated at the
D∗s mass squared and a cut, along the positive real axis,
starting at threshold (t+ = (mD+mK)
2) for D0K− pro-
duction.
1. Taylor expansion
This cut t-plane can be mapped onto the open unit
disk with center at t = t0 using the variable:
z(t, t0) =
t+ − t−
t+ − t0√
t+ − t+
t+ − t0
. (5)
In this variable, the physical region for the semileptonic
decay (0 < t < t− = q
max = (mD−mK)2) corresponds to
a real segment extending between ±zmax = ±0.051. This
value of zmax is obtained for t0 = t+
1− t−/t+
The z expansion of f+ is thus expected to converge
quickly. The most general parameterization [7], consis-
tent with constraints from QCD,
f+(t) =
P (t)Φ(t, t0)
ak(t0) z
k(t, t0), (6)
is based on earlier considerations [8]. The function
P (t) = z(t,m2D∗
) has a zero at the D∗s pole mass and
|P | = 1 along the unit circle; Φ is given by:
Φ(t, t0) =
24πχV
t+ − t
t+ − t0
t+ − t+
t+ − t+
t+ − t0
t+ − t+
t+ − t−
(t+ − t)
where χV can be obtained from dispersion relations using
perturbative QCD and depends on u = ms/mc [9]. At
leading order, with u = 0 [10],
32π2m2c
. (8)
The choice of P and Φ is such that:
a2k(t0) ≤ 1. (9)
Having measured the first coefficients of this expansion,
Eq. (9) can constrain the others. This constraint, which
depends on χV , may have to be abandoned in the case of
charm decays as the charm-quark mass may not be large
enough to prevent the previous evaluation of χV from
receiving large 1/mc and QCD corrections. However the
parameterization given in Eq. (6) remains valid and it
has been compared [7] with available measurements. The
first two terms in the expansion were sufficient to describe
the data.
2. Model-dependent parameterizations
A less general approach assumes that the q2 variation
of f+(q
2) is governed mainly by the D∗s pole and that
the other contributions can be accounted for by adding
another effective pole at a higher mass [11]:
f+(0)
1− αpole
1− q2
αpole
1− q2
γpolem
= f+(0)
1− δpole q
1− q2
1− βpole q
) (10)
with δpole = (1/γpole − αpole)/(1 − αpole) and βpole =
1/γpole.
If in addition, the form factors f+ and f0 must obey a
relation, valid at large recoil and in the heavy quark limit,
then αpole = 1/γpole [11] (βpole = αpole and δpole = 0 in
this case). Equation (10) becomes:
f+(0)
1− q2
1− αpole q
) , (11)
known as the modified pole ansatz. Initially an even
simpler expression, the simple pole ansatz, was proposed
which considered only the contribution from the D∗s pole.
In the following, the pole mass entering in
f+(0)
1− q2
is fitted. Note that such an effective pole mass value has
no clear physical interpretation and that the proposed q2
variation does not comply with constraints from QCD.
The obtained value may nonetheless be useful for com-
parison with results from different experiments.
B. Quantitative expectations
Values of the parameters that determine f+(q
2) were
obtained initially from constituent quark models and
from QCD sum rules. These two approaches have an in-
trinsically limited accuracy. In this respect, results from
lattice QCD computations are more promising because
their accuracy is mainly limited by available computing
resources.
1. Quark Models
Quark model calculations estimate meson wave func-
tions and use them to compute the matrix elements that
appear in the hadronic current. There are a large variety
of theoretical calculations [12]. Among these models we
have selected the ISGW model [13], simply because it is
widely used to simulate heavy hadron semileptonic de-
cays. This model was expected to be valid in the vicinity
of q2max, a region of maximum overlap between the ini-
tial and final meson wave functions. In ISGW2 [14] the
exponential q2 dependence of the form factor has been
replaced by another parameterization, with a dipole be-
havior, expected to be valid over a larger q2 range:
f ISGW2+ (q
(1 + αI(q2max − q2))
, αI =
r2. (13)
The predicted values of the parameters are f+(q
max) =
1.23 and r = 1.12 GeV−1 [14].
TABLE I: Parameterizations of f+(q
modeling parameters expected values
z expansion[8] a0, rk = ak/a0 no prediction
general 2-poles [11] f+(0), βpole, δpole no prediction
modified pole [11] f+(0), αpole δpole = 0
simple pole f+(0), mpole mpole = mD∗
ISGW2[14] f+(t−), αI f+(t−) = 1.23
αI = 0.104 GeV
2. QCD sum rules
QCD sum rules [15] and their extension on the light
cone [16], are expected to be valid at low q2. Using a
value of 150 MeV for the strange quark mass, one obtains
[16]:
f+(0) = 0.78± 0.11 and αpole = −0.07+0.15−0.07, (14)
using the modified pole ansatz. The uncertainty of f+(0)
is estimated to be of order 15%, and the q2 dependence
is expected to be dominated by a single pole at the D∗s
mass because the value of αpole is compatible with zero.
3. Lattice QCD
Lattice QCD computation is the only approach able
to compute f+(q
2) from first principles. Current results
must be extrapolated to physical values of light quark
masses and corrected for finite lattice size and discriti-
zation effects. There have been several evaluations of
2) for different values of the momentum transfer in
the quenched approximation [17, 18]. These results have
been combined [17], giving f+(0) = 0.73 ± 0.07. The
first unquenched calculation has been published recently
[19]: f+(0) = 0.73± 0.03± 0.07 and αpole = 0.50± 0.04,
using the modified pole ansatz to parameterized the q2
dependence of the form factor.
C. Analyzed parameterizations
The different parameterizations of f+(q
2) considered in
this analysis are summarized in Table I, along with their
corresponding parameters and expected values, where
available.
III. THE BABAR DETECTOR AND DATASET
A detailed description of the BABAR detector and of the
algorithms used for charged and neutral particle recon-
struction and identification is provided elsewhere [20, 21].
Charged particles are reconstructed by matching hits
in the 5-layer double-sided silicon vertex tracker (SVT)
with track elements in the 40-layer drift chamber (DCH),
which is filled with a gas mixture of helium and isobu-
tane. Slow particles which do not leave enough hits in the
DCH due to the bending in the 1.5-T magnetic field, are
reconstructed in the SVT. Charged hadron identification
is performed combining the measurements of the energy
deposition in the SVT and in the DCH with the informa-
tion from the Cherenkov detector (DIRC). Photons are
detected and measured in the CsI(Tl) electro-magnetic
calorimeter (EMC). Electrons are identified by the ra-
tio of the track momentum to the associated energy de-
posited in the EMC, the transverse profile of the shower,
the energy loss in the DCH, and the Cherenkov angle in
the DIRC. Muons are identified in the instrumented flux
return, composed of resistive plate chambers interleaved
with layers of steel and brass.
The results presented here are obtained using a to-
tal integrated luminosity of 75 fb−1 registered by the
BABAR detector during the years 2000-2002. Monte Carlo
(MC) simulation samples of Υ (4S) decays, charm and
other light quark pairs from continuum equivalent, re-
spectively, to 2.8, 1.2 and 0.7 times the data statistics,
respectively, have been generated using GEANT4 [22].
These are used mainly to evaluate background compo-
nents. Quark fragmentation, in continuum events, is de-
scribed using the JETSET package [23]. The MC distri-
butions have been rescaled to the data sample luminosity,
using the expected cross sections of the different compo-
nents (1.3nb for cc, 0.525 nb for B+B− and B0B̄0, 2.09nb
for light uū, dd̄ and ss̄ quark events). Dedicated sam-
ples of pure signal events, equivalent to seven times the
data statistics, are used to correct measurements for effi-
ciency and finite resolution effects. They have been gen-
erated using the modified pole parameterization ansatz
for f+(q
2) with αpole = 0.50. Radiative decays (D
K−e+νeγ) are modeled by PHOTOS [24]. To account for
one of the most important sources of background, a spe-
cial event sample with, in each event, at least one cascade
decay D∗+ → D0π+, D0 → K−π0e+νe (or its charge
conjugate) has been generated with a parameterization
of the form factors in agreement with measurements from
the FOCUS collaboration [25]. Events with a D∗+ and
a D0 decaying into K−π+ or K−π+π0 have been recon-
structed in data and simulation. These control samples
have been used to adjust the c-quark fragmentation dis-
tribution and the kinematic characteristics of particles
accompanying the D meson in order to better match the
data. They have been used also to measure the recon-
struction accuracy on the missing neutrino momentum.
IV. SIGNAL RECONSTRUCTION
We reconstruct D0 → K−e+νe(γ) decays in e+e− →
cc̄ events where theD0 originates from theD∗+ → D0π+.
The main sources of background arise from events with
a kaon and electron candidate. Such events come from
Υ (4S) decays and the continuum production of charmed
hadrons. Their contribution is reduced using variables
sensitive to the particle production characteristics that
are different for signal and background events.
A. Signal selection
Charged and neutral particles are boosted to the cen-
ter of mass system (c.m.) and the event thrust axis is
determined. The direction of this axis is required to be
in the interval | cos(θthrust)| < 0.6 to minimize the loss of
particles in regions close to the beam axis. A plane per-
pendicular to the thrust axis is used to define two hemi-
spheres, equivalent to the two jets produced by quark
fragmentation. In each hemisphere, we search for pairs
of oppositely charged leptons and kaons. For the charged
lepton candidates we consider only electrons or positrons
with c.m. momentum greater than 0.5 GeV/c.
Since the νe momentum is unmeasured, a kinematic
fit is performed, constraining the invariant mass of the
candidate e+K−νe system to the D
0 mass. In this fit,
theD0 momentum and the neutrino energy are estimated
from the other particles measured in the event. The D0
direction is taken as the direction opposite to the sum of
the momenta of all reconstructed particles in the event,
except for the kaon and the positron associated with the
signal candidate. The energy of the jet is determined
from the total c.m. energy and from the measured masses
of the two jets. The neutrino energy is estimated as the
difference between the total energy of the jet and the
sum of the energies of all reconstructed particles in the
hemisphere. A correction, which depends on the value
of the missing energy measured in the opposite jet, is
applied to account for the presence of missing energy due
to particles escaping detection, even in the absence of a
neutrino from the D0 decay.
The D0 candidate is retained if the χ2 probability of
the kinematic fit exceeds 10−3. Detector performance for
the reconstruction of the D0 direction and for the missing
energy are measured using events in which the D0 decays
into K−π+. Corrections are applied to account for ob-
served differences between data and simulation. Each
D0 candidate is combined with a charged pion, with the
same charge as the lepton, and situated in the same hemi-
sphere. The mass difference δ(m) = m(D0π+)−m(D0)
is evaluated and is shown in Fig. 1. This distribution con-
tains events which in addition pass the requirements on
the Fisher discriminant FBB̄ suppressingBB̄ background
and also give a satisfactory kinematic fit constraining the
invariant mass . This last requirement is the reason of
the slow decrease of the δ(m) distribution. At large δ(m)
values, a small excess of background is measured in data
and the simulation is rescaled accordingly. Only events
with δ(m) < 0.16 GeV/c2 are used in the analysis.
10000
15000
20000
0.15 0.2 0.25 0.3
Signal
Peaking cc bkg
Non-peaking cc bkg
0.15 0.2 0.25 0.3
δ(m) (GeV/c2)
FIG. 1: Comparison of the δ(m) distributions from data and
simulated events. MC events have been normalized to the
sample luminosity according to the different cross sections.
An excess of background events of the order of 5% is observed
for large values of δ(m). The arrow indicates the additional
selection applied for the q2 distribution measurement.
B. Background rejection
Background events arise from Υ (4S) decays and
hadronic events from the continuum. Three variables
are used to reduce the contribution from BB̄ events:
R2 (the ratio between the second and zeroth order Fox-
Wolfram moments [26]), the total charged and neutral
multiplicity and the momentum of the soft pion (πs) from
the D∗+. These variables exploit the topological differ-
ences between events with B decays and events with cc̄
fragmentation. The particle distribution in Υ (4S) decay
events tends to be isotropic as the B mesons are pro-
duced near threshold, while the distribution in cc̄ events
is jet-like as the c.m. energy is well above the charm
threshold. This also results in a softer D∗+ momentum
spectrum in Υ (4S) decays compared to cc̄ events.
Corresponding distributions of these variables for sig-
nal and background events are given in Fig. 2. These
variables have been combined linearly in a Fisher dis-
criminant. The requirement FBB̄ > 0.5 retains 65% of
signal and 6% of BB̄-background events.
0 0.5 1
B events
c events
Charged + neutral multiplicity
0 0.25 0.5
pπs (GeV/c)
-5 0 5
FIG. 2: MC simulations of distributions of the variables used
in the Fisher discriminant analysis to reduce the BB̄ event
background: a) the normalized second Fox-Wolfram moment
(R2), b) the event particle multiplicity, c) the slow-pion mo-
mentum distribution, in the c.m. frame, d) the Fisher variable
for BB̄ and for charm signal events.
Background events from the continuum arise mainly
from charm particles as requiring an electron and a kaon
reduces the contribution from light-quark flavors to a low
level. Because charm hadrons take a large fraction of the
charm quark energy charm decay products have higher
average energies and different angular distributions (rel-
ative to the thrust axis or to the D direction) compared
with other particles in the hemisphere emitted from the
hadronization of the c and c quarks. These other parti-
cles are referred to as “spectator” in the following; the
“leading” particle is the one with the largest momentum.
To reduce background from cc̄ events, the following vari-
ables are used:
• the D0 momentum;
• the spectator system mass, msp., which has lower
values for signal events;
• the direction of the spectator system momentum
relative to the thrust axis cos θsp.−thrust;
• the momentum of the leading spectator track;
• the direction of the leading spectator track relative
to the D0 direction;
0 2.5 5
0 2.5
msp. (GeV/c
c bkg.
signal
cosθsp.-thrust
-1 0 1
cosθe
FIG. 3: MC simulations of some of the variables used in
the Fisher discriminant analysis to reduce the cc̄-event back-
ground: a) the D0 momentum after the kinematic fit, b) the
mass of the spectator system (peaks, at low mass values cor-
respond to events with a single charged pion or photon recon-
structed in the spectator system), c) the cosine of the angle
between the spectator system momentum and the thrust di-
rection, d) the cosine of the angle of the positron direction,
relative to the kaon direction, in the eνe c.m. frame.
• the direction of the leading spectator track relative
to the thrust axis;
• the direction of the lepton relative to the kaon di-
rection, in the dilepton rest frame, cos θe;
• the charged lepton momentum, pe, in the c.m.
frame.
The first six variables depend on the properties of c-quark
hadronization whereas the last two are related to de-
cay characteristics of the signal. Distributions for four
of the most discriminating variables are given in Fig. 3.
D0 → K−π+ events have been used to tune the simu-
lation parameters so that distributions of the variables
used to reject background agree with those measured
with data events. These eight variables have been com-
bined linearly into a Fisher discriminant variable (Fcc)
and events have been kept for values above 0. This selec-
tion retains 77% of signal events that were kept by the
previous selection requirement and rejecting 66% of the
background (Fig. 4).
The remaining background from cc̄-events can be di-
vided into peaking (60%) and non-peaking (40%) candi-
-1 0 1 2 3
signal
c bkg.
B+ bkg.
B0 bkg.
uds bkg.
-1 0 1 2 3
FIG. 4: Distribution of the values of the Fisher variable in
the signal region (δ(m) < 0.16 GeV/c2 in a), and for masses
above the signal region (δ(m) > 0.16 GeV/c2 in b).
dates. Peaking events are those background events whose
distribution is peaked around the signal region. These
are mainly events with a real D∗+ in which the slow π+
is included in the candidate track combination. Back-
grounds from e+e− annihilations into light uū, dd̄, ss̄
quarks and BB̄ events are non-peaking. These compo-
nents, from simulation, are displayed in Fig. 1.
C. q2 measurement
To improve the accuracy of the reconstructed D0 mo-
mentum, the nominal D∗+ mass is added as a constraint
in the previous fit and only events with a χ2 probabil-
ity higher than 1% are kept (Fig. 1 is obtained requiring
only that the fit has converged). The measured q2r distri-
bution, where q2r = (pD − pK)
, is given in Fig. 5. There
are 85260 selectedD0 candidates containing an estimated
number of 11280 background events. The non-peaking
component comprises 54% of the background.
To obtain the true q2 distribution, the measured one
has to be corrected for selection efficiency and detector
resolution effects. This is done using an unfolding algo-
rithm based on MC simulation of these effects.
The variation of the selection efficiency as a func-
tion of q2 is given in Fig. 6. The resolution of the
q2 measurement for signal events is obtained from MC
10000
15000
0 0.5 1 1.5 2
Signal
Background
q2r (GeV
FIG. 5: The measured q2r distribution (data points) compared
to the sum of the estimated background and of the fitted
signal components.
simulation. The resolution function can fitted by the
sum of two Gaussian functions, with standard deviations
σ1 = 0.066 GeV
2 and σ2 = 0.219 GeV
2, respectively.
The narrow component corresponds to 40% of the events.
To obtain the unfolded q2 distribution for signal events,
corrected for resolution and acceptance effects, the Singu-
lar Value Decomposition (SVD) [27] of the resolution ma-
trix has been used. This method uses a two-dimensional
matrix which relates the generated q2 distribution to the
detected distribution, q2r , as input. After subtracting the
estimated background contribution, the measured binned
q2r distribution is linearly transformed into the unfolded
q2 distribution. This approach provides the full covari-
ance matrix for the bin contents of the unfolded distri-
bution. Singular values (SV) are ordered by decreasing
values. These values contain the information needed to
transform the measured distribution into the unfolded
spectrum, along with statistical uncertainties from fluc-
tuations. Not all SV are relevant; non-significant values
have zero mean and standard deviation equal to unity
[27]. Using toy simulations, we find that seven SV have
to be kept with events distributed over ten bins. Because
the measurement of the form-factor parameters relies on
the measured q2r distribution, it does not require unfold-
ing, and is independent of this particular choice.
0 0.5 1 1.5 2
 (GeV
FIG. 6: The efficiency as a function of q2, measured with
simulated signal events, after all selection criteria applied.
V. RESULTS ON THE Q2 DEPENDENCE OF
THE HADRONIC FORM FACTOR
The unfolded q2 distribution, normalized to unity, is
presented in Fig. 7 and in Table II. Also given in this
table are the statistical and total uncertainties and the
correlations of the data in the ten bins. Figure 7 shows
the result of fits to the data for two parameterizations of
the form factor with a single free parameter, the simple
pole and the modified pole ansatz. Both fitted distribu-
tions agree well with the data.
A summary of these and other form factor parame-
terizations is given in Table III. These results will be
discussed in detail in Section VB.
The fit to a model is done by comparing the number
of events measured in a given bin of q2 with the expecta-
tion from the exact analytic integration of the expression
∣~pK(q
∣f+(q
over the bin range, with the overall
normalization left free. The result of the fit correspond-
ing to the parameterization of the form factor using two
parameters (see Eq. 10) is given in Fig. 8.
A. Systematic Uncertainties
Systematic uncertainties of the form factor parame-
ters are likely to originate from imperfect simulation of
c-quark fragmentation and the detector response, from
uncertainties in the background composition and the in-
dividual contributions for the selected signal sample, the
0 0.5 1 1.5 2
Data unfolded
2 ) Pole mass
Modif. pole mass
-0.01
0 0.5 1 1.5 2
 (GeV
FIG. 7: Comparison between the normalized unfolded q2 dis-
tribution obtained from this analysis, and those corresponding
to two fitted models. Lower plot gives the difference between
measured and fitted distributions. The error bars represent
statistical errors only.
0 0.5 1 1.5
βpole
FIG. 8: Contours at 70% and 90% CL resulting from the fit of
the parameterization of the form factor q2 dependence with
two parameters as given in Eq. (10). The value δpole = 0
corresponds to the modified pole ansatz.
uncertainty in the modeling of the signal decay and the
TABLE II: Statistical and total uncertainty matrices for the normalized decay distribution (corrected for acceptance and finite
resolution effects) in ten bins of q2 from 0 to 2 GeV2, and for the ratio RD (see Section VI). The total decay distribution
has been normalized to unity for q2 varying over ten 0.2 GeV2 intervals. The uncertainty matrices are provided for both the
statistical (upper half) and total (lower half) uncertainties. The uncertainty on each measured value is given along the diagonal.
Off-diagonal terms correspond to the correlation coefficients.
q2 bin (GeV2) [0, 0.2] [0.2, 0.4] [0.4, 0.6] [0.6, 0.8] [0.8, 1.0] [1.0, 1.2] [1.2, 1.4] [1.4, 1.6] [1.6, 1.8] [1.8, 2.0]
RD and 0.9269
fractions 0.2008 0.1840 0.1632 0.1402 0.1122 0.0874 0.0602 0.0367 0.0146 0.0007
statistical 0.0072 0.166 0.122 0.111 0.107 0.107 0.102 0.101 0.116 0.081 0.060
uncertainties 0.0031 -0.451 -0.155 0.117 0.005 0.023 0.002 0.002 -0.002 -0.002
and 0.0037 -0.225 -0.304 0.095 0.041 -0.025 -0.005 0.005 -0.005
correlations 0.0033 -0.155 -0.345 0.079 0.058 -0.018 -0.010 -0.006
0.0029 -0.113 0.352 0.058 0.066 -0.013 -0.024
0.0025 0.073 -0.345 0.018 0.075 0.067
0.0020 -0.029 -0.329 -0.004 0.060
0.0016 0.110 -0.339 -0.347
0.0011 0.217 0.012
0.00075 0.965
0.000057
total 0.0139 -0.154 0.072 0.034 0.093 0.046 0.084 0.231 0.278 0.210 0.184
uncertainties 0.0041 -0.462 -0.257 0.022 0.099 0.089 -0.232 -0.092 -0.056 -0.048
and 0.0040 -0.102 -0.247 0.005 0.020 0.015 -0.035 -0.055 -0.048
correlations 0.0035 -0.122 -0.377 0.050 0.074 -0.043 -0.033 -0.027
0.0030 -0.127 0.320 0.092 0.056 -0.038 -0.048
0.0026 0.041 -0.331 0.033 0.089 0.079
0.0022 0.084 -0.264 0.010 0.057
0.0018 0.159 -0.235 -0.254
0.0012 0.369 0.194
0.0009 0.973
0.000065
TABLE III: Fitted values of the parameters corresponding to different parameterizations of f+(q
2). The last column gives the
χ2/NDF of the fit when using the value expected for the parameter.
Theoretical Unit Parameters χ2/NDF Expectations
ansatz [χ2/NDF]
z expansion r1 = −2.5± 0.2 ± 0.2 5.9/7
r2 = 0.6± 6.± 5.
Modified pole αpole = 0.377 ± 0.023 ± 0.029 6.0/8
Simple pole GeV/c2 mpole = 1.884 ± 0.012 ± 0.015 7.4/8 2.112 [243/9]
ISGW2 GeV−2 αI = 0.226 ± 0.005 ± 0.006 6.4/8 0.104 [800/9]
measurement of the q2 distribution. We study the origin
and size of various systematic effects, correct the MC sim-
ulation, if possible, assess the impact of the uncertainty
of the size of correction on the fit results, and adopt the
observed change as a contribution to the systematic un-
certainty on the fitted parameters for the different param-
eterizations under study. Some of these studies make use
of standard BABAR evaluations of detection efficiencies,
others rely on special data control samples, for instance
hadronic decays D0 → K−π+ or K−π+π0.
1. c-quark hadronization tuning
The signal selection is based on variables related to
c-quark fragmentation and decay properties of signal
events. Simulated events have been weighted to agree
with the distributions observed in data. Weights have
been obtained using events with a reconstructed D0 de-
caying into K−π+. After applying these corrections,
the distribution of the Fisher discriminant that contains
these variables is compared for data and simulation. The
remaining difference is used to evaluate the correspond-
ing systematic uncertainty. It corresponds to the varia-
tions on fitted quantities obtained by correcting or not
for this difference, which is below 5% over the range of
this variable.
2. Reconstruction algorithm
It is important to verify that the q2 variation of the
selection efficiency is well described by the simulation.
This is done by analyzing D0 → K−π+π0 as if they were
K−e+νe events. The two photons from the π
0 are re-
moved and events are reconstructed using the algorithm
applied to the semileptonic D0 decay. The “missing” π0
and the charged pion play, respectively, the roles of the
neutrino and the electron. To preserve the correct kine-
matic limits, it is necessary to take into account that
the “fake” neutrino has the π0 mass and that the “fake”
electron has the π+ mass.
Data and simulated events, which satisfy the same
analysis selection criteria as for Keνe, have been com-
pared. For this test, the cos(θe) and pe are removed from
the Fisher discriminant, because distributions for these
two variables are different from the signal events.
The ratio of efficiencies measured in data and simula-
tion is fit with a linear expression in q2. The correspond-
ing slope, (0.71±0.68)%, indicates that there is no signif-
icant bias when the event selection criteria are applied.
The measured slope is used to define a correction and to
estimate the corresponding systematic uncertainty.
3. Resolution on q2
To measure possible differences between data and
simulation on the q2 reconstruction accuracy, D0 →
K−π+π0 events are used again. Distributions of the dif-
ference q2r − q2, obtained by selecting events in a given
bin of q2 are compared. These distributions are system-
atically slightly narrower for simulated events and the
fraction of events in the distant tails are higher for data
(see Fig. 9).
With the D0 → K−π+ sample we study, in data and
simulation, the accuracy of the D0 direction and missing
energy reconstruction for the D0 → K−e+νe analysis.
This information is used in the mass-constrained fits and
thus influences the q2 reconstruction. Once the simula-
tion is tuned to reproduce the results obtained on data
for these parameters, the q2 resolution distributions agree
very well, as shown in Fig. 9. One half of the measured
variation on the fitted parameters from these corrections
has been taken as a systematic uncertainty.
4. Particle identification
Effects from a momentum-dependent difference be-
tween data and simulated events on the charged lepton
and on the kaon identification have been evaluated. Such
-0.4 -0.2 0 0.2 0.4
-0.4 -0.2 0 0.2 0.4
q2r-q
2 (GeV2)
-0.4 -0.2 0 0.2 0.4
-0.4 -0.2 0 0.2 0.4
q2r-q
2 (GeV2)
FIG. 9: Distribution of the difference between the true and
the reconstructed value of q2. D0 → K−π+π0 data events
correspond to dark squares and open circles are used for
simulated ones. Ratio (Data/MC) of the two distributions
are displayed. The distributions in a) compare data and
simulated events before applying corrections measured with
D0 → K−π+ events, whereas these corrections have been ap-
plied for plots in b).
differences, which are typically below 2%, have been mea-
sured for selected, high purity samples of electrons and
kaons. These corrections have been applied and the ob-
served variation has been taken as the estimate of the
systematic uncertainty.
5. Background estimate
The background under the D∗+ signal has two compo-
nents that have, respectively, non-peaking and peaking
behavior.
The non-peaking background originates from non-cc
events and from continuum charm events in which the
πs candidate does not come from a cascading D
∗+. By
comparing data and simulated event rates for δ(m) >
0.18 GeV/c2 (see Fig. 1), a correction of 1.05 is deter-
mined from simulation for the non-peaking background.
This correction is applied and an uncertainty of ±0.05 is
used as the corresponding systematic uncertainty.
Events which include a slow pion originating from D∗+
decay contribute in several ways to the peaking back-
ground. The production rate of D∗+ mesons in the sim-
ulation is in agreement with expectations based on mea-
surements from CLEO [28]. The uncertainty of ±0.06 on
this comparison is dominated by the systematic uncer-
tainty from the CLEO result.
To study the remaining effects, the peaking back-
ground components have been divided according to the
process from which they originate and have been ordered
by decreasing level of importance:
• the K− and the electron originate from a D0 de-
cay (54%). The main source comes from D0 →
K−π0e+νe. We have corrected the decay branch-
ing fraction used for this channel in the MC (2.02%)
using recent measurements (2.17± 0.16% [1]). The
uncertainty on this value has been used to evaluate
the corresponding systematic uncertainty.
• the electron comes from a converted photon or a
Dalitz decay (24%). It has been assumed that the
simulation correctly accounts for this component;
• the K− does not originate from a charm hadron
(14%). This happens usually when there is another
negative charged kaon accompanying the D∗+. We
have studied the production of charged kaon accom-
panying a D∗+ using D0 → K−π+ events and mea-
sure a correction factor of 0.87±0.02 and 0.53±0.02,
respectively, for same sign and opposite sign K-
D∗ pairs. The simulation is modified accordingly
and the remaining systematic uncertainty from this
source becomes negligible;
• fake kaon candidate (mainly pions) (6%) or fake
electrons (1%). Differences between data and MC
on the evaluation of fake rates have been studied
in BABAR. As this affects small components of the
total peaking background rate, the effect of these
differences has been neglected.
6. Fitting procedure and radiative events
To fit form factor parameters we compare the num-
ber of expected events in each bin with the measured
one after all corrections. In this approach it is always
assumed that the q2 variation of f+(q
2) is given ex-
actly by the form factor parameterization. This hy-
pothesis is not correct, a priori, for radiative decays as
q2 = (pD − pK)2 = (pe+ pν + pγ)2 is not (perhaps) equal
to the variable that enters in f+ for such decays. PHO-
TOS is used to generate decays with additional photons
and the modified pole ansatz is taken to parameterize
the hadronic form factor in signal events. To quantify
possible distortion of the fit we compare the fitted value
of a form factor parameter with the one obtained from a
fit to the generated q2 distribution (see Table IV).
TABLE IV: Measured differences between the nominal and
fitted values of parameters. Quoted uncertainties correspond
to MC statistics. The last column gives the impact of the
radiative effects on the form factor measurements as predicted
by PHOTOS.
Parameter Measured difference Bias from
(true-fitted) radiation
δ(r1) (×0.01) 1.2± 13.0 −0.4± 2.7
δ(r2) +1.7± 3.6 +1.9± 0.7
δ(αpole) (×0.01) −1.2± 1.4 −1.1± 0.3
δ(mpole) (MeV/c
2) +4.5± 6.3 +4.6± 1.4
δ(αI) (×0.001GeV
−2) −2.7± 3.1 −2.4± 0.7
Corresponding corrections, given in the second column
of Table IV, have been applied and quoted uncertainties
enter in the systematic uncertainty evaluation.
To evaluate the importance of corrections induced by
radiative effects, we have compared also the fitted value
of a parameter on q2 distributions generated with and
without using PHOTOS. Measured differences are given
in the last column of Table IV. They have not been
applied to the values quoted in Table III for the different
parameters. We measure also that radiative effects affect
mainly the fraction of the decay spectrum in the first bin
in Table II which has to be increased by 0.0012 to correct
for this effect.
7. Control of the statistical accuracy in the SVD approach
Once the number of SV is fixed, one must verify that
the statistical precision obtained for each binned un-
folded value is correct and if biases generated by remov-
ing information are under control. These studies are done
with toy simulations. One observes that the uncertainty
TABLE V: Summary of systematic uncertainties on the fitted parameters.
Source δ (mpole) δαpole δ (αI) δ (r1) δ (r2)
(MeV/c2) (×0.01) (×0.001 GeV−2) (×0.01)
c-hadronization tuning 3.0 0.6 1.1 6.7 1.4
Reconstruction algorithm 7.8 1.6 3.1 6.5 0.2
Resolution on q2 3.4 0.7 1.4 3.0 2.1
Particle ID 5.5 1.1 2.3 3.8 0.4
Background estimate 7.7 1.4 3.0 12.7 2.0
Fitting procedure 6.3 1.4 3.1 13.0 3.6
Total 15.0 2.9 6.0 21.0 4.9
obtained from a fit of the unfolded distribution is un-
derestimated by a factor which depends on the statistics
of simulated events and is ∼ 1.06 in the present anal-
ysis. Pull distributions indicate also that the unfolded
values, in each bin, have biases which are below 10% of
the statistical uncertainty. Similar studies are done for
the determination of form factor parameters.
8. Summary of systematic errors
The systematic uncertainties for determining form fac-
tor parameters are summarized in Table V.
The systematic error matrix for the ten unfolded val-
ues is computed by considering, in turn, each source of
uncertainty and by measuring the variation, δi, of the cor-
responding unfolded value in each bin (i). The elements
of the uncertainty matrix are the sum, over all sources
of systematic uncertainty, of the quantities δi · δj . The
total error matrix is evaluated as the sum of the matrices
corresponding, respectively, to statistical and systematic
uncertainties.
B. Comparison with expectations and with other
measurements
The summary of the fits to the normalized q2 distri-
butions are presented in Table III. As long as we allow
the form factor parameters to be free in the fit, the fit-
ted distributions agree well with the data and it is not
possible to reject any of the parameterizations.
However, if the form factor parameters are constrained
to specific predicted values, the agreement is not good.
For the ISGW2 model, the predicted dependence of the
form factor on q2 disagrees with the data and the fit-
ted value of the parameter αI differs from the predicted
value, αI = 0.104 GeV
−2 by more than a factor two.
As observed by previous experiments, the simple pole
model ansatz, with mpole = mD∗
= 2.112 GeV/c2 does
not reproduce the measurements. This means that the
contribution from the continuum DK interaction can-
not be neglected. If one introduces a second parame-
ter δpole to account for contributions from an effective
pole at higher mass (see Eq. 10) the two parameters are
fully correlated and there is no unique solution, as illus-
trated in Fig. 8. The modified pole ansatz corresponds
to δpole = 0.
In Table VI the fitted parameters for the simple pole
ansatz and the modified pole [11] ansatz are compared
for different experiments. The fitted pole masses are all
well below the mass of the D∗s meson. The results pre-
sented here are consistent within the stated uncertainties
with earlier measurements. Except for the BELLE mea-
surement, all other measurements appear to favor a value
of αpole that is lower than the value predicted by lattice
QCD, namely αpole = 0.50± 0.04.
TABLE VI: Fitted values for the parameters corresponding
respectively to a pole mass and a modified pole mass model
for the form factor.
Experiment mpole (GeV/c
2) αpole
CLEO [4] 1.89 ± 0.05+0.04−0.03 0.36 ± 0.10
+0.03
−0.07
FOCUS [5] 1.93 ± 0.05 ± 0.03 0.28 ± 0.08 ± 0.07
BELLE [6] 1.82 ± 0.04 ± 0.03 0.52 ± 0.08 ± 0.06
This analysis 1.884 ± 0.012 ± 0.015 0.38 ± 0.02 ± 0.03
In Fig. 10, the dependence of the form factor on q2 is
presented. The data are compared to earlier measure-
ments by the FOCUS experiment, as well as with pre-
dictions from lattice QCD calculations [19]. As stated
above, the data favor a somewhat lower value for αpole.
The data have also been mapped into the variable z.
Figure 11 shows the product P ×Φ× f+ as a function of
z. By convention, this quantity is constrained to unity
at z = zmax, which corresponds to q
2 = 0. We perform a
fit to a polynomial, P × Φ × f+ ∼ 1 + r1z + r2z2. The
data are compatible with a linear dependence, which is
fully consistent with the modified pole ansatz for f+(q
as illustrated in Fig. 11.
VI. BRANCHING FRACTION MEASUREMENT
The D0 → K−e+νe branching fraction is measured
relative to the reference decay channel, D0 → K−π+.
0 0.5 1 1.5 2
q2(GeV2)
BABAR
FOCUS
Lattice-QCD (αpole = 0.50(4))
FIG. 10: Comparison of the measured variation of
2)/f+(0) obtained in the present analysis and in the FO-
CUS experiment [5]. The band corresponds to lattice QCD
[19] with the estimated uncertainty.
Specifically, we compare the ratio of rates for the decay
chains D∗+ → D0π+, D0 → K−e+νe, and D0 → K−π+
in data and simulated events, this way, many systematic
uncertainties cancel,
BR(D0 → K−e+νe)data
BR(D0 → K−π+)data
BR(D0 → K−e+νe)MC
BR(D0 → K−π+)MC
N(cc̄)Keν
N(cc̄)Kπ
L(data)Kπ
L(data)Keν
N(D0 → K−e+νe)data
N(D0 → K−e+νe)MC
N(D0 → K−π+)MC
N(D0 → K−π+)data
ǫ(D0 → K−e+νe)MC
ǫ(D0 → K−e+νe)data
ǫ(D0 → K−π+)data
ǫ(D0 → K−π+)MC
The first line in this expression is the ratio of the
branching fraction for the two channels used in the sim-
ulation:
BR(D0 → K−e+νe)MC
BR(D0 → K−π+)MC
0.0364
0.0383
. (16)
The second line is the ratio of the number of cc̄ simu-
lated events and the integrated luminosities for the two
channels:
N(cc̄)Keν
N(cc̄)Kπ
L(data)Kπ
L(data)Keν
117.0× 106
117.3× 106 ×
73.43 fb−1
74.27 fb−1
-0.05 -0.025 0 0.025 0.05
)   Modif. pole fit
BaBar
FIG. 11: Measured values for P×Φ×f+ are plotted versus−z
and requiring that P ×Φ× f+ = 1 for z = zmax. The straight
lines represent the result for the modified pole ansatz, the fit
in the center and the statistical and total uncertainty.
The third line corresponds to the ratios of measured
numbers of signal events in data and in simulation, and
the last line gives the ratios of the efficiencies to data and
simulation.
A. Selection of candidate signal events
The selection ofD0 → K−e+νe candidates is explained
in section IVA. For the rate measurement, the con-
straint on the D∗+ mass is not applied and also the
momentum of the soft pion candidate is not included
in the Fisher discriminant variable designed to suppress
BB̄-background. Since generic simulated signal events
used in this measurement have been generated with the
ISGW2 model, they have been weighted so that their q2
distribution agrees with the measurement presented in
this paper. Furthermore, we require for the Fisher dis-
criminant FBB̄ > 0 and restrict δ(m) < 0.16 GeV/c
After background subtraction, there remain 76283± 323
and 95302 ± 309 events in data and simulation, respec-
tively. This gives:
N(D0 → K−e+νe)data
N(D0 → K−e+νe)MC
= 0.8004± 0.0043. (18)
To select D0 → K−π+ candidates, the same data sam-
ples are used and particles, in each event, are selected in
the same way. The same selection criteria on the Fisher
1.75 1.8 1.85 1.9 1.95
D0→K-π+
D0→K-π+γ
D0→K-K+
D0→π-π+
Other
m(Kπ) (GeV/c2)
0.14 0.1425 0.145 0.1475 0.15
D0→K-π+
D0→K-π+γ
Other bkg
m(D0π)-m(D0) (GeV/c2)
0.14 0.16 0.18 0.2
MC bkg
m(D0π)-m(D0) (GeV/c2)
0.14 0.1425 0.145 0.1475 0.15
m(D0π)-m(D0) (GeV/c2)
FIG. 12: Events selected for the reference channel D∗+ → D0π+, D0 → K−π+. a) Kπ mass distribution for events selected
in the range δ(m) ∈ [0.143, 0.148] GeV/c2. b) δ(m) distribution for events selected in the range m(Kπ) ∈ [1.83, 1.89] GeV/c2.
c) same distribution as in b), displayed on a larger mass range with the non-peaking background indicated (shaded area). d)
δ(m) distribution after non-peaking background subtraction, data (points with statistical errors) and simulated events (shaded
histogram).
discriminant to suppress BB̄-events, on the thrust axis
direction and on other common variables are applied.
Events are also analyzed in the same way, with two hemi-
spheres defined from the thrust axis. In each hemisphere
a D0 candidate is reconstructed by combining a charged
K with a pion of opposite sign. These tracks have to
form a vertex and the Kπ mass must be within the range
[1.77, 1.95] GeV/c2. Another charged pion of appropri-
ate sign is added to form a D∗+ candidate.
In addition, the following selection criteria are used:
• the fraction of the beam momentum, in the c.m.
frame, taken by the D∗ candidate must exceed 0.48
to remove contributions from BB̄ events;
• the measured D0 mass must be in the range be-
tween 1.83 and 1.89 GeV/c2. This requirement
eliminates possible contributions from remaining
D0 → K−K+ or π+π− decays (see Fig. 12-a);
• the vertex fit for the D0 and D∗ have to converge.
The δ(m) distribution for candidate events is shown in
Fig. 12-c. The following components contribute to the
D∗+ signal (see Fig. 12-b):
• D0 → K−π+ with no extra photon;
• D0 → K−π+ with at least one extra photon;
• D0 → K−π+(γ) where the π+, mainly from the
D∗+, decays into a muon.
The δ(m) distribution corresponding to other event
categories does not show a peaking component in the
D∗+ signal region. The total background level, is nor-
malized to data using events in the δ(m) interval between
0.165 and 0.200 GeV/c2 (see Fig. 12-c). This global scal-
ing factor is equal to 1.069±0.011. After background sub-
traction, the δ(m) distributions obtained in data and sim-
ulation can be compared in Fig. 12-d. Since the D∗+ sig-
nal is narrower in the simulation, we use a mass window
such that this difference has a small effect on the mea-
sured number of D∗+ events in data and in the simula-
tion. There are 166960±409 and 134537±374 candidates
selected in the interval δ(m) ∈ [0.142, 0.149] GeV/c2 for
simulated and data events respectively. This means:
N(D0 → K−π+)MC
N(D0 → K−π+)data
= 1.230± 0.0046. (19)
B. Efficiency corrections
The impact of the selection requirement on the recon-
structed Kπ mass, has been studied. The Kπ mass dis-
tribution signal for simulated events (not including radia-
tive photons) is compared with the corresponding distri-
bution obtained with data after background subtraction.
The background contributions are taken from the simula-
tion. The fraction of D0 candidates in the selected mass
range (between 1.83 and 1.89 GeV/c2) is (97.64±0.25)%
in MC and (97.13± 0.29)% in data events. The ratio of
efficiencies is equal to:
ǫ(D0 → K−π+)data
ǫ(D0 → K−π+)MC
= 0.9947± 0.0039. (20)
Since D0 → K−e+νe events have been selected using
a selection requirement on δ(m), we need to confirm that
the distribution of this variable is similar in data and
simulation. This is checked by comparing the distribu-
tions obtained with D0 → K−π+π0 events analyzed as
if they were semileptonic decays. The δ(m) distributions
are compared in Fig. 13. Below 0.16 GeV/c2, there are
0.93552±0.00066 of the D∗+ candidates in the simulation
and 0.93219± 0.00078 for data. The corresponding ratio
of efficiencies (MC/data) is equal to 1.0036± 0.0010.
Using D0 → K−π+π0 events, we also measure the dif-
ference between the fraction of events retained after the
mass-constrained fits. Namely, it is 0.98038± 0.00037 in
the simulation compared to 0.97438 ± 0.00049 in data.
The relative efficiency (MC/data) for this selection is
1.0062 ± 0.0006. Based on these two measured correc-
tions the ratio of efficiencies are:
ǫ(D0 → K−e+νe)MC
ǫ(D0 → K−e+νe)data
= 1.0098± 0.0011. (21)
The quoted uncertainties, in this section, are of statistical
origin and will be included in the statistical uncertainty
on RD. Other differences between the two analyzed chan-
nels are considered in the following section and contribute
to systematic uncertainties.
0.15 0.2 0.25 0.3
0.15 0.2 0.25 0.3
δ(m) (GeV/c2)
FIG. 13: δ(m) distribution for D0 → K−π+π0 events ana-
lyzed as if they were semileptonic decays. Distributions have
been normalized to unity; note that the bin size is not uni-
form. The bottom plot shows the ratio of the two distribu-
tions above.
C. Systematic uncertainties on RD
A summary of the systematic uncertainties on RD are
given in Table VII. They originate from selection criteria
which are different for the two channels. Some of these
uncertainties are the same as those already considered
for the determination of the q2 variation of f+.
1. Correlated systematic uncertainties
Systematic uncertainties on the decay rate coming
from effects that contribute in the measurement of the
q2 dependence of f+(q
2) are evaluated in Section VA
and the full covariance matrix for the measurements of
the number of D0 → K−e+νe signal events and the frac-
tion of the decay spectrum fitted in each of the ten bins
is determined. Among the sources of systematic uncer-
tainties, listed in Table V, those corresponding to:
• the reconstruction algorithm,
• the tuning of the resolution on q2,
• the corrections applied on electron identification,
• the background normalization
are taken as common sources. Corresponding relative
uncertainties on RD are given in Table VII.
Other systematic uncertainties contributing to the
form factor measurement also affect the reference chan-
nel and so their effects on RD cancel. They are related to
the c-hadronization tuning and to the corrections applied
on the kaon identification.
2. Selection requirement on the Fisher discriminant
The stability of the fraction of D0 → K−e+νe events
selected in data and in simulation as a function of the
Fisher discriminant, Fcc, designed to suppress cc̄ back-
ground has been examined. This is done by comparing
the distributions of this variable measured in data and in
simulation as given in Fig. 4 for two selected intervals in
δ(m).
The value corresponding to Fcc > 0 and for events se-
lected in the range δ(m) < 0.16 GeV/c2 is used as the
central result and half the difference between the mea-
surements corresponding to Fcc greater than−0.25 and +
0.25 is taken as systematic uncertainty. This range cor-
responds to a relative change of 40% of the efficiency for
signal events, and gives an uncertainty of ±0.0061 on the
ratio of data and simulated signal candidates.
3. D∗+ counting in D0 → K−π+
D∗+ candidates are selected in the range δ(m) ∈
[0.142, 0.149] GeV/c2. From the simulation it is ex-
pected that the fraction of signal events outside this
interval is equal to 1.4%. Even though the D∗+ sig-
nal is slightly narrower in the simulation, there is not
a large discrepancy in the tails. The fraction of signal
events measured in the sidebands δ(m) ∈ [0.140, 0.142]⊕
[0.149, 0.150] GeV/c2 is 0.4% and 0.5%, respectively, for
simulation and data. An uncertainty of ±0.004, cor-
responding to 30% uncertainty on the total fraction of
events outside the selected δ(m) interval is assumed.
TABLE VII: Summary of systematic uncertainties on the
relative decay rate measurement.
Source Relative variation
Reconstruction algorithm ±0.42%
Resolution on q2 ∼ 0
Electron ID ±0.56%
Background subtraction ±0.63%
Cut on Fisher variable ±0.76%
D∗+ counting (D0 → K−π+) ±0.40%
Total ±1.27%
D. Decay rate measurement
Combining all measured fractions in Eq. (15), the mea-
sured relative decay rate is:
RD = 0.9269± 0.0072± 0.0119. (22)
Using the world average for the branching fraction
BR(D0 → K−π+) = (3.80± 0.07)% [1], gives BR(D0 →
K−e+νe(γ)) = (3.522 ± 0.027 ± 0.045± 0.065)%, where
the last quoted uncertainty corresponds to the accuracy
on BR(D0 → K−π+).
VII. SUMMARY
The decay rate distribution for the channel D0 →
K−e+νe(γ) has been measured in ten bins in Table II.
Several theoretical expectations for the variation of this
form factor with q2 have been considered and values for
the corresponding parameters have been obtained (see
Table III). The q2 variation of the form factor can be
parameterized with a single parameter using different ex-
pressions. The ISGW2 model with expected values for
the parameters is excluded, as is the pole mass parame-
terization with mpole = mD∗
The value of the decay branching fraction has been also
measured independent of a model.
Combining these measurements, the value of the
hadronic form factor is obtained:
f+(0) =
|Vcs|
, (23)
where BR is the measured D0 → K−e+νe branching
fraction, τD0 = (410.1± 1.5)× 10−15 s [1] is the D0 life-
time and I =
∣~pK(q
∣f+(q
2)/f+(0)
dq2. To
account for the variation of the form factor within one
bin, and in particular to extrapolate the result at q2 = 0,
the pole mass and the modified pole ansatze have been
used; the corresponding values obtained for f+(0) differ
by 0.002. Taking the average between these two values
and including their difference in the systematic uncer-
tainty, this gives
f+(0) = 0.727± 0.007± 0.005± 0.007, (24)
where the last quoted uncertainty corresponds to the ac-
curacy on BR(D0 → K−π+), τD0 and |Vcs|. It agrees
with expectations and in particular with LQCD compu-
tations [19]. Using the z expansion of Eq. (6), we find
a0 = (2.98± 0.01± 0.03± 0.03)× 10−2.
The high accuracy of the present measurement will be
a reference test for improved lattice determinations of the
q2 variation of f+.
VIII. ACKNOWLEDGMENTS
The authors wish to thank R. J. Hill, D. Becirevic, C.
Bernard, Ph. Boucaud, S. Descotes-Genon, L. Lellouch,
J.-P. Leroy, A. Le Yaouanc and O. Pène for their help
with the theoretical interpretation of these results.
We are grateful for the extraordinary contributions of
our PEP-II colleagues in achieving the excellent luminos-
ity and machine conditions that have made this work pos-
sible. The success of this project also relies critically on
the expertise and dedication of the computing organiza-
tions that support BABAR. The collaborating institutions
wish to thank SLAC for its support and the kind hospital-
ity extended to them. This work is supported by the US
Department of Energy and National Science Foundation,
the Natural Sciences and Engineering Research Coun-
cil (Canada), Institute of High Energy Physics (China),
the Commissariat à l’Energie Atomique and Institut Na-
tional de Physique Nucléaire et de Physique des Partic-
ules (France), the Bundesministerium für Bildung und
Forschung and Deutsche Forschungsgemeinschaft (Ger-
many), the Istituto Nazionale di Fisica Nucleare (Italy),
the Foundation for Fundamental Research on Matter
(The Netherlands), the Research Council of Norway, the
Ministry of Science and Technology of the Russian Fed-
eration, Ministerio de Educación y Ciencia (Spain), and
the Particle Physics and Astronomy Research Council
(United Kingdom). Individuals have received support
from the Marie-Curie IEF program (European Union)
and the A. P. Sloan Foundation.
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http://arxiv.org/abs/hep-ph/0606023
	Introduction
	The f+(q2) hadronic form factor
	Form factor parameterizations
	Taylor expansion
	Model-dependent parameterizations
	Quantitative expectations
	Quark Models
	QCD sum rules
	Lattice QCD
	Analyzed parameterizations
	The BABAR Detector and Dataset
	Signal reconstruction
	Signal selection
	Background rejection
	q2 measurement
	Results on the q2 dependence of the hadronic form factor 
	Systematic Uncertainties
	c-quark hadronization tuning
	Reconstruction algorithm
	Resolution on q2
	Particle identification
	Background estimate
	Fitting procedure and radiative events
	Control of the statistical accuracy in the SVD approach
	Summary of systematic errors
	Comparison with expectations and with other measurements
	Branching fraction measurement
	Selection of candidate signal events
	Efficiency corrections
	Systematic uncertainties on RD
	Correlated systematic uncertainties
	Selection requirement on the Fisher discriminant
	D*+ counting in D0K- +
	Decay rate measurement
	Summary
	Acknowledgments
	References
