We propose that the non-perturbative part of the fragmentation function describing the transition from a heavy quark to a heavy meson is proportional to the square of the produced meson wave function at the origin, taking into account hyperfine interactions. We analyze the effects of this proposal on the number of pseudoscalar mesons compared to the number of vector mesons produced and find a good agreement with experimental data. Finally, we discuss further experimental checks for our hypothesis.Facultad de Ciencias Exacta

Cornet, Fernando

García Canal, Carlos Alberto

Physics Letters B

English

Servicio de Difusión de la Creación Intelectual

Physics Letters B 662 (2008) 341–343www.elsevier.com/locate/physletbSpin dependence of heavy quark fragmentationFernando Cornet a,∗, Carlos A. García Canal ba Departamento de Física Teórica y del Cosmos and Centro Anadaluz de Física de Partículas, Universidad de Granada, E-18071 Granada, Spainb Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata (1900), ArgentinaReceived 15 October 2007; received in revised form 7 March 2008; accepted 10 March 2008Available online 14 March 2008Editor: A. RingwaldAbstractWe propose that the non-perturbative part of the fragmentation function describing the transition from a heavy quark to a heavy meson isproportional to the square of the produced meson wave function at the origin, taking into account hyperfine interactions. We analyze the effectsof this proposal on the number of pseudoscalar mesons compared to the number of vector mesons produced and find a good agreement withexperimental data. Finally, we discuss further experimental checks for our hypothesis.© 2008 Elsevier B.V. Open access under CC BY license.Heavy quark production in high energy collisions, eithere+e−, ep, pp or pp¯, provides a good laboratory to test QCDin both, its perturbative and non-perturbative sectors. In all theexperiments both sectors contribute. In processes with a hadronin the initial state one has to consider the quark and gluon dis-tribution functions in the initial hadron and the heavy quarkfragmentation function describing the transition of the heavyquark into the measured final state hadronic system. In e+e−processes only this last non-perturbative piece contributes. Theexperimental situation on charm and bottom production in dif-ferent collision events has been reviewed in [1]. It is clear thatin order to get the maximum theoretical information from theincreasingly precise experimental data on heavy quark produc-tion one must have a good description of all the pieces involvedin the calculation, in particular of the fragmentation functions.The heavy quark fragmentation function is obtained by theconvolution of two contributions: a perturbative and a non-perturbative one. The perturbative part describes the productionof a heavy quark surrounded by a cloud of soft gluons andeventual hard radiation processes. The non-perturbative partdescribes the hadronization of this quark with the given mo-mentum fraction into a meson. Usually, a purely phenomeno-logical parametrization is used for the non-perturbative part.* Corresponding author.E-mail address: cornet@ugr.es (F. Cornet).0370-2693 © 2008 Elsevier B.V.doi:10.1016/j.physletb.2008.03.021Open access under CC BY license.The most commonly used [2] are the ones by: Kartvelishviliet al. [3], Bowler [4], Peterson et al. [5], Collins and Spiller [6],Colangelo and Nason [7] and Braaten et al. [8]. Among theseparametrizations only the last one [8] distinguishes among thespin of the produced meson. Here we will discuss an alternativeway of making this distinction.All these parametrizations provide different realizations ofthe original Bjorken [9] and Suzuki [10] proposal that the heavyquark fragmentation function, contrary to what happens withlight quarks, should be very hard, i.e., the heavy quark shouldretain most of its momentum in the hadronization process. Theexact shape of the dependence of the fragmentation function onthe heavy quark momentum is controlled, in the parametriza-tions cited above, by some free parameters (the number of freeparameters depends on the parametrization) that have to be fit-ted to the experimental data. In general these parameters haveno absolute physical meaning (see for example [2] for a discus-sion).In addition to the dependence of the fragmentation functionswith the heavy quark momentum, the different experimentshave also measured the relative number of charmed and bot-tom mesons produced in the pseudoscalar state (D and B) andin the vector state (D?, B?). More specifically, they have mea-sured the quantity PV defined by(1)PV = VP + V ,342 F. Cornet, C.A. García Canal / Physics Letters B 662 (2008) 341–343where V and P stand for the number of vector and pseudoscalarstates produced, respectively. The present experimental valuesfor charmed mesons are:PDV = 0.566 ± 0.025+0.007+0.022−0.022−0.023, ZEUS (γp) [11],PDV = 0.590 ± 0.037+0.022−0.018, ZEUS (DIS) [12],PDV = 0.693 ± 0.045 ± 0.004 ± 0.009, H1 [13],PDV = 0.614 ± 0.023, e+e− average [14].These values provide a world average(2)P¯ DV = 0.611 ± 0.016.For B mesons there is only one measurement available [1](3)PBV = 0.75 ± 0.04+0.023−0.025.The values for the charmed mesons are clearly smaller thanthe widely used naive spin counting prediction PV = 0.75, butthis is not the case for the bottom mesons. So, whatever mech-anism in the fragmentation process is claimed to be responsiblefor the decrease of PV with respect to the naive predictionshould, in a natural way, produce a much smaller effect formesons containing a b quark than for mesons containing ac quark.In this Letter we propose that the fragmentation function ofa heavy quark, Q, into a heavy meson M should be propor-tional to the square of the meson M hyperfine-corrected wavefunction at the origin. It is important to notice that in the analy-sis of semileptonic meson decays a sensible improvement ofthe theoretical results when compared with experimental data,was obtained by breaking heavy quark symmetry and takinghyperfine interactions into account [15]. We, thus, propose toexplicitly include in the naive PV expression (1) the hyperfinecorrections via different wave functions at the origin for scalarand vector states. Consequently, we consider instead(4)PV =µPV+ 1¶−1=µ13|ψP (0)|2|ψV (0)|2 + 1¶−1.Notice that if the wave functions at the origin are known, ourexpression (4) does not include new unknown parameters be-cause we only modify the normalization of the fragmentationfunctions leaving their dependence on the heavy quark momen-tum unchanged.Even if at lowest order in Heavy Quark Effective Theorythe wave functions at the origin for the pseudoscalar and vec-tor states are the same, and this would reproduce the naive spincounting result, they differ at O(1/mQ) and, obviously, the ef-fects on the PV predictions will be larger for mesons containinga c quark than for mesons containing a b quark.In the update [15] of the Isgur–Scora–Grinstein–Wise model[16] one finds approximate variational wave functions that con-sider separately each spin state. The distinction between spinstates is mandatory in order to get agreement with the experi-mental data for the decays. The wave functions for the lowestlying pseudoscalar and vector states are taken to be of the form(5)ψ1S = β3/2S3/4 expµ−1β2Sr2¶,π 2Table 1Values of the parameter βS entering in the wave functions of the mesons, seeEq. (5) and predictions for heavy meson production ratesMeson Mass (MeV) βS (GeV) PVD 1864.1 0.45 0.64D∗ 2006.7 0.38Ds 1969.0 0.56 0.59D∗s 2112.0 0.44B 5279.3 0.43 0.71B∗ 5325.0 0.40Bs 5369.6 0.54 0.69B∗s 5412.8 0.49where the parameter βS is fixed in [15] minimizing the ener-gies, including hyperfine interactions, to properly describe theobserved meson spectra. It is important to notice that the val-ues obtained in this way for the different meson states providea good description of all semileptonic c and b decays. The val-ues obtained in Ref. [15] are shown in Table 1. Since the wavefunction is an intrinsic property of the meson, one can use theseresults for the production process. This is done, for instance,in J/Ψ production in e+e− where the cross section is writ-ten in terms of the decay width Γ (J/Ψ → e+e−) which isproportional to the J/Ψ wave function at the origin. Also, inthe calculation of the J/Ψ fragmentation function, the wavefunction at the origin is fixed from the data on the J/Ψ decaywidth [17].The results we obtain plugging the hyperfine-corrected wavefunctions at the origin from Eq. (5) into our Eq. (4) are shownin the last column of Table 1. We obtain a sensible reductionin the value of PDV with respect to the naive spin countingprediction and our result is in good agreement with the experi-mental data. For PBV the obtained reduction is much smaller andthe result is within one standard deviation of the experimentaldata, Eq. (3). We should stress here once more that these valuesof PV only depend on one tunable parameter for each meson,βS . For these parameters we have taken the values obtained inRef. [15] in a completely independent analysis, as discussedabove.We have also calculated our predictions for the relative num-ber of Ds and D?s as well as Bs and B?s and shown the resultsin the last column of in Table 1. The reduction with respect tothe naive prediction is larger in the mesons containing a heavyand a strange quark than in the mesons containing a heavy anda u or d quark. This is a prediction of our assumption that canbe experimentally checked. In particular, the low value of PDsVlooks promising for such a test.The expression in Eq. (4) is only valid if both the pseudosca-lar and vector mesons entering have the same quark content.If only one of them contains a strange quark (in addition tothe heavy quark) one has to take into account also the strangesuppression factor that is usually defined as the ratio of thenumber of charmed strange mesons with respect to the num-ber of charmed non-strange mesons produced. However, un-der our hypothesis one should be careful because these ratiosdepend now on the hyperfine-corrected wave functions at theF. Cornet, C.A. García Canal / Physics Letters B 662 (2008) 341–343 343origin. One would expect, however, that the strange suppres-sion factor would only contain information about the relativeprobability of producing an ss¯ from the vacuum compared tothe probability of producing a pair of light quarks. This means,one would expect the strange suppression factor to be indepen-dent of the spin of the produced mesons. So, in order to definesuch a spin independent strange suppression factor one has touse:(6)γSI = |ψD(0)|2|ψDs (0)|2γP = |ψD∗(0)|2|ψD∗s (0)|2γV ,where γP = Ds/D and γV = D?s /D? are the suppression fac-tors measured in the pseudoscalar and vector channels, respec-tively. Using the βS parameters listed in Table 1, it is clear thatγSI = 0.52γP = 0.64γV .Final remarksThe naive spin counting prediction for the ratio PV does notfit the experimental data, in particular in the case of charmedD mesons. We propose that the fragmentation functions shouldbe proportional to the square of the produced meson hyperfine-corrected wave function at the origin. This amounts to changethe normalization factors of the available non-perturbative frag-mentation functions keeping their dependence on the heavy-meson energy fraction unchanged. We have analyzed the effectsof this proposal on the values of PV for charmed and bottommesons and found very good agreement with the experimentaldata using values for the wave functions at the origin fixed frommeson decays. As a way to check our proposal we estimate thevalues of PV for charmed-strange and bottom-strange mesonsfor which no experimental data are yet available. Further checkscan be performed measuring our proposed spin dependence ofthe strange suppression factor.AcknowledgementsWe thank F. del Aguila, L. Labarga and M. Zambrana foruseful discussions. F.C. acknowledges financial support fromJunta de Andalucia (FQM-330) and Ministerio Español deEducación y Ciencia (FPA2006-05294). C.A.G.C. warmly ac-knowledges the hospitality of Departamento de Física Teóricay del Cosmos of the Universidad de Granada that made possi-ble this collaboration and to the Junta de Andalucia for financialsupport during his visit to Granada.References[1] L.K. Gladilin, in: M. Kuze, K. Nagano, K. Tokushuku (Eds.), Proceed-ings of the 14th International Workshop on Deep Inelastic Scattering, DIS2006, Tsukuba, Japan, 20–24 April 2006, World Scientific, 2007, p. 569,hep-ex/0607036.[2] The Review of Particle Physics, W.-M. Yao, et al., J. Phys. G 33 (2006) 1.[3] V.G. Kartvelishvili, A.K. Likhoded, V.A. Petrov, Phys. Lett. B 78 (1978)615.[4] M.G. Bowler, Z. Phys. C 11 (1981) 169.[5] C. Peterson, D. Schlatter, I. Schmitt, P.M. Zerwas, Phys. Rev. D 27 (1983)105.[6] P.D.B. Collins, T.P. Spiller, J. Phys. G 11 (1985) 1289.[7] G. Colangelo, P. Nason, Phys. Lett. B 285 (1992) 167.[8] E. Braaten, K. Cheung, S. Fleming, T.C. Yuan, Phys. Rev. D 51 (1995)4819.[9] J.D. Bjorken, Phys. Rev. D 17 (1978) 171.[10] M. Suzuki, Phys. Lett. B 71 (1977) 139.[11] ZEUS Collaboration, S. Chekanov, et al., Eur. Phys. J. C 44 (2005) 351.[12] ZEUS Collaboration, Contributed paper to the XXXIII International Con-ference on High Energy Physics, August 2006, preprint number ZEUS-prel-05-007-plus.[13] H1 Collaboration, A. Aktas, et al., Eur. Phys. J. C 38 (2005) 447.[14] L. Gladilin, hep-ex/9912064.[15] D. Scora, N. Isgur, Phys. Rev. D 52 (1995) 2783.[16] N. Isgur, D. Scora, B. Grinstein, M.B. Wise, Phys. Rev. D 39 (1989) 799.[17] K. Hagiwara, W. Qi, C.F. Qiao, J.X. Wang, arXiv: 0705.0803 [hep-ph].

Spin dependence of heavy quark fragmentation

SEDICI - Repositorio de la UNLP

Physics Letters B 662 (2008) 341–343
www.elsevier.com/locate/physletb
Spin dependence of heavy quark fragmentation
Fernando Cornet a,∗, Carlos A. García Canal b
a Departamento de Física Teórica y del Cosmos and Centro Anadaluz de Física de Partículas, Universidad de Granada, E-18071 Granada, Spain
b Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata (1900), Argentina
Received 15 October 2007; received in revised form 7 March 2008; accepted 10 March 2008
Available online 14 March 2008
Editor: A. Ringwald
Abstract
We propose that the non-perturbative part of the fragmentation function describing the transition from a heavy quark to a heavy meson is
proportional to the square of the produced meson wave function at the origin, taking into account hyperfine interactions. We analyze the effects
of this proposal on the number of pseudoscalar mesons compared to the number of vector mesons produced and find a good agreement with
experimental data. Finally, we discuss further experimental checks for our hypothesis.
© 2008 Elsevier B.V. Open access under CC BY license.Heavy quark production in high energy collisions, either
e+e−, ep, pp or pp¯, provides a good laboratory to test QCD
in both, its perturbative and non-perturbative sectors. In all the
experiments both sectors contribute. In processes with a hadron
in the initial state one has to consider the quark and gluon dis-
tribution functions in the initial hadron and the heavy quark
fragmentation function describing the transition of the heavy
quark into the measured final state hadronic system. In e+e−
processes only this last non-perturbative piece contributes. The
experimental situation on charm and bottom production in dif-
ferent collision events has been reviewed in [1]. It is clear that
in order to get the maximum theoretical information from the
increasingly precise experimental data on heavy quark produc-
tion one must have a good description of all the pieces involved
in the calculation, in particular of the fragmentation functions.
The heavy quark fragmentation function is obtained by the
convolution of two contributions: a perturbative and a non-
perturbative one. The perturbative part describes the production
of a heavy quark surrounded by a cloud of soft gluons and
eventual hard radiation processes. The non-perturbative part
describes the hadronization of this quark with the given mo-
mentum fraction into a meson. Usually, a purely phenomeno-
logical parametrization is used for the non-perturbative part.
* Corresponding author.
E-mail address: cornet@ugr.es (F. Cornet).0370-2693 © 2008 Elsevier B.V.
doi:10.1016/j.physletb.2008.03.021
Open access under CC BY license.The most commonly used [2] are the ones by: Kartvelishvili
et al. [3], Bowler [4], Peterson et al. [5], Collins and Spiller [6],
Colangelo and Nason [7] and Braaten et al. [8]. Among these
parametrizations only the last one [8] distinguishes among the
spin of the produced meson. Here we will discuss an alternative
way of making this distinction.
All these parametrizations provide different realizations of
the original Bjorken [9] and Suzuki [10] proposal that the heavy
quark fragmentation function, contrary to what happens with
light quarks, should be very hard, i.e., the heavy quark should
retain most of its momentum in the hadronization process. The
exact shape of the dependence of the fragmentation function on
the heavy quark momentum is controlled, in the parametriza-
tions cited above, by some free parameters (the number of free
parameters depends on the parametrization) that have to be fit-
ted to the experimental data. In general these parameters have
no absolute physical meaning (see for example [2] for a discus-
sion).
In addition to the dependence of the fragmentation functions
with the heavy quark momentum, the different experiments
have also measured the relative number of charmed and bot-
tom mesons produced in the pseudoscalar state (D and B) and
in the vector state (D?, B?). More specifically, they have mea-
sured the quantity PV defined by
(1)PV = V
P + V ,
342 F. Cornet, C.A. García Canal / Physics Letters B 662 (2008) 341–343where V and P stand for the number of vector and pseudoscalar
states produced, respectively. The present experimental values
for charmed mesons are:
PDV = 0.566 ± 0.025+0.007+0.022−0.022−0.023, ZEUS (γp) [11],
PDV = 0.590 ± 0.037+0.022−0.018, ZEUS (DIS) [12],
PDV = 0.693 ± 0.045 ± 0.004 ± 0.009, H1 [13],
PDV = 0.614 ± 0.023, e+e− average [14].
These values provide a world average
(2)P¯ DV = 0.611 ± 0.016.
For B mesons there is only one measurement available [1]
(3)PBV = 0.75 ± 0.04+0.023−0.025.
The values for the charmed mesons are clearly smaller than
the widely used naive spin counting prediction PV = 0.75, but
this is not the case for the bottom mesons. So, whatever mech-
anism in the fragmentation process is claimed to be responsible
for the decrease of PV with respect to the naive prediction
should, in a natural way, produce a much smaller effect for
mesons containing a b quark than for mesons containing a
c quark.
In this Letter we propose that the fragmentation function of
a heavy quark, Q, into a heavy meson M should be propor-
tional to the square of the meson M hyperfine-corrected wave
function at the origin. It is important to notice that in the analy-
sis of semileptonic meson decays a sensible improvement of
the theoretical results when compared with experimental data,
was obtained by breaking heavy quark symmetry and taking
hyperfine interactions into account [15]. We, thus, propose to
explicitly include in the naive PV expression (1) the hyperfine
corrections via different wave functions at the origin for scalar
and vector states. Consequently, we consider instead
(4)PV =
µ
P
V
+ 1
¶−1
=
µ
1
3
|ψP (0)|2
|ψV (0)|2 + 1
¶−1
.
Notice that if the wave functions at the origin are known, our
expression (4) does not include new unknown parameters be-
cause we only modify the normalization of the fragmentation
functions leaving their dependence on the heavy quark momen-
tum unchanged.
Even if at lowest order in Heavy Quark Effective Theory
the wave functions at the origin for the pseudoscalar and vec-
tor states are the same, and this would reproduce the naive spin
counting result, they differ at O(1/mQ) and, obviously, the ef-
fects on the PV predictions will be larger for mesons containing
a c quark than for mesons containing a b quark.
In the update [15] of the Isgur–Scora–Grinstein–Wise model
[16] one finds approximate variational wave functions that con-
sider separately each spin state. The distinction between spin
states is mandatory in order to get agreement with the experi-
mental data for the decays. The wave functions for the lowest
lying pseudoscalar and vector states are taken to be of the form
(5)ψ1S = β
3/2
S
3/4 exp
µ
−1β2Sr2
¶
,π 2Table 1
Values of the parameter βS entering in the wave functions of the mesons, see
Eq. (5) and predictions for heavy meson production rates
Meson Mass (MeV) βS (GeV) PV
D 1864.1 0.45 0.64
D∗ 2006.7 0.38
Ds 1969.0 0.56 0.59
D∗s 2112.0 0.44
B 5279.3 0.43 0.71
B∗ 5325.0 0.40
Bs 5369.6 0.54 0.69
B∗s 5412.8 0.49
where the parameter βS is fixed in [15] minimizing the ener-
gies, including hyperfine interactions, to properly describe the
observed meson spectra. It is important to notice that the val-
ues obtained in this way for the different meson states provide
a good description of all semileptonic c and b decays. The val-
ues obtained in Ref. [15] are shown in Table 1. Since the wave
function is an intrinsic property of the meson, one can use these
results for the production process. This is done, for instance,
in J/Ψ production in e+e− where the cross section is writ-
ten in terms of the decay width Γ (J/Ψ → e+e−) which is
proportional to the J/Ψ wave function at the origin. Also, in
the calculation of the J/Ψ fragmentation function, the wave
function at the origin is fixed from the data on the J/Ψ decay
width [17].
The results we obtain plugging the hyperfine-corrected wave
functions at the origin from Eq. (5) into our Eq. (4) are shown
in the last column of Table 1. We obtain a sensible reduction
in the value of PDV with respect to the naive spin counting
prediction and our result is in good agreement with the experi-
mental data. For PBV the obtained reduction is much smaller and
the result is within one standard deviation of the experimental
data, Eq. (3). We should stress here once more that these values
of PV only depend on one tunable parameter for each meson,
βS . For these parameters we have taken the values obtained in
Ref. [15] in a completely independent analysis, as discussed
above.
We have also calculated our predictions for the relative num-
ber of Ds and D?s as well as Bs and B?s and shown the results
in the last column of in Table 1. The reduction with respect to
the naive prediction is larger in the mesons containing a heavy
and a strange quark than in the mesons containing a heavy and
a u or d quark. This is a prediction of our assumption that can
be experimentally checked. In particular, the low value of PDsV
looks promising for such a test.
The expression in Eq. (4) is only valid if both the pseudosca-
lar and vector mesons entering have the same quark content.
If only one of them contains a strange quark (in addition to
the heavy quark) one has to take into account also the strange
suppression factor that is usually defined as the ratio of the
number of charmed strange mesons with respect to the num-
ber of charmed non-strange mesons produced. However, un-
der our hypothesis one should be careful because these ratios
depend now on the hyperfine-corrected wave functions at the
F. Cornet, C.A. García Canal / Physics Letters B 662 (2008) 341–343 343origin. One would expect, however, that the strange suppres-
sion factor would only contain information about the relative
probability of producing an ss¯ from the vacuum compared to
the probability of producing a pair of light quarks. This means,
one would expect the strange suppression factor to be indepen-
dent of the spin of the produced mesons. So, in order to define
such a spin independent strange suppression factor one has to
use:
(6)γSI = |ψD(0)|
2
|ψDs (0)|2
γP = |ψD∗(0)|
2
|ψD∗s (0)|2
γV ,
where γP = Ds/D and γV = D?s /D? are the suppression fac-
tors measured in the pseudoscalar and vector channels, respec-
tively. Using the βS parameters listed in Table 1, it is clear that
γSI = 0.52γP = 0.64γV .
Final remarks
The naive spin counting prediction for the ratio PV does not
fit the experimental data, in particular in the case of charmed
D mesons. We propose that the fragmentation functions should
be proportional to the square of the produced meson hyperfine-
corrected wave function at the origin. This amounts to change
the normalization factors of the available non-perturbative frag-
mentation functions keeping their dependence on the heavy-
meson energy fraction unchanged. We have analyzed the effects
of this proposal on the values of PV for charmed and bottom
mesons and found very good agreement with the experimental
data using values for the wave functions at the origin fixed from
meson decays. As a way to check our proposal we estimate the
values of PV for charmed-strange and bottom-strange mesons
for which no experimental data are yet available. Further checks
can be performed measuring our proposed spin dependence of
the strange suppression factor.Acknowledgements
We thank F. del Aguila, L. Labarga and M. Zambrana for
useful discussions. F.C. acknowledges financial support from
Junta de Andalucia (FQM-330) and Ministerio Español de
Educación y Ciencia (FPA2006-05294). C.A.G.C. warmly ac-
knowledges the hospitality of Departamento de Física Teórica
y del Cosmos of the Universidad de Granada that made possi-
ble this collaboration and to the Junta de Andalucia for financial
support during his visit to Granada.
References
[1] L.K. Gladilin, in: M. Kuze, K. Nagano, K. Tokushuku (Eds.), Proceed-
ings of the 14th International Workshop on Deep Inelastic Scattering, DIS
2006, Tsukuba, Japan, 20–24 April 2006, World Scientific, 2007, p. 569,
hep-ex/0607036.
[2] The Review of Particle Physics, W.-M. Yao, et al., J. Phys. G 33 (2006) 1.
[3] V.G. Kartvelishvili, A.K. Likhoded, V.A. Petrov, Phys. Lett. B 78 (1978)
615.
[4] M.G. Bowler, Z. Phys. C 11 (1981) 169.
[5] C. Peterson, D. Schlatter, I. Schmitt, P.M. Zerwas, Phys. Rev. D 27 (1983)
105.
[6] P.D.B. Collins, T.P. Spiller, J. Phys. G 11 (1985) 1289.
[7] G. Colangelo, P. Nason, Phys. Lett. B 285 (1992) 167.
[8] E. Braaten, K. Cheung, S. Fleming, T.C. Yuan, Phys. Rev. D 51 (1995)
4819.
[9] J.D. Bjorken, Phys. Rev. D 17 (1978) 171.
[10] M. Suzuki, Phys. Lett. B 71 (1977) 139.
[11] ZEUS Collaboration, S. Chekanov, et al., Eur. Phys. J. C 44 (2005) 351.
[12] ZEUS Collaboration, Contributed paper to the XXXIII International Con-
ference on High Energy Physics, August 2006, preprint number ZEUS-
prel-05-007-plus.
[13] H1 Collaboration, A. Aktas, et al., Eur. Phys. J. C 38 (2005) 447.
[14] L. Gladilin, hep-ex/9912064.
[15] D. Scora, N. Isgur, Phys. Rev. D 52 (1995) 2783.
[16] N. Isgur, D. Scora, B. Grinstein, M.B. Wise, Phys. Rev. D 39 (1989) 799.
[17] K. Hagiwara, W. Qi, C.F. Qiao, J.X. Wang, arXiv: 0705.0803 [hep-ph].


http://sedici.unlp.edu.ar/bitstream/handle/10915/84251/Documento_completo.1016_j.physletb.2008.03.021.pdf?sequence=1&isAllowed=y

Spin dependence of heavy quark fragmentation

Abstract

Similar works

Full text

Available Versions

Servicio de Difusión de la Creación Intelectual

SEDICI - Repositorio de la UNLP