KBlueLeaf/taica-nlp-hw1 · Datasets at Hugging Face

text string
in summary , using the sample of @xmath152 tagged @xmath28 decays with the cleo - c detector we obtain the absolute branching fraction of the leptonic decay @xmath153 through @xmath154 @xmath155 where the first uncertainty is statistical and the second is systematic .
this result supersedes our previous measurement @xcite of the same branching fraction , which used a subsample of data used in this work .
the decay constant @xmath33 can be computed using eq .
( [ eq : f ] ) with known values @xcite @xmath156 gev@xmath157 , @xmath158 mev , @xmath159 mev , and @xmath160 s. we assume @xmath161 and use the value @xmath162 given in ref .
we obtain @xmath163 combining with our other determination @xcite of @xmath164 mev with @xmath43 and @xmath0 ( @xmath165 ) decays , we obtain @xmath166 this result is derived from absolute branching fractions only and is the most precise determination of the @xmath91 leptonic decay constant to date . our combined result is larger than the recent lqcd calculation @xmath167 mev @xcite by @xmath168 standard deviations .
the difference between data and lqcd for @xmath33 could be due to physics beyond the sm @xcite , unlikely statistical fluctuations in the experimental measurements or the lqcd calculation , or systematic uncertainties that are not understood in the lqcd calculation or the experimental measurements . combining with our other determination @xcite of @xmath169 , via @xmath44
, we obtain @xmath170 using this with our measurement @xcite of @xmath171 , we obtain the branching fraction ratio @xmath172 this is consistent with @xmath173 , the value predicted by the sm with lepton universality , as given in eq .
( [ eq : f ] ) with known masses @xcite .
we gratefully acknowledge the effort of the cesr staff in providing us with excellent luminosity and running conditions .
d. cronin - hennessy and a. ryd thank the a.p . sloan foundation .
this work was supported by the national science foundation , the u.s .
department of energy , the natural sciences and engineering research council of canada , and the u.k .
science and technology facilities council . c. amsler
_ et al . _
( particle data group ) , phys .
b * 667 * , 1 ( 2008 ) .
k. ikado _ et al . _
( belle collaboration ) , phys .
lett . * 97 * , 251802 ( 2006 ) .
b. aubert _ et al .
_ ( babar collaboration ) , phys . rev .
d * 77 * , 011107 ( 2008 ) .
a. g. akeroyd and c. h. chen , phys .
d * 75 * , 075004 ( 2007 ) ; a. g. akeroyd , prog .
phys . * 111 * , 295 ( 2004 ) .
j. l. hewett , arxiv : hep - ph/9505246 .
w. s. hou , phys .
d * 48 * , 2342 ( 1993 ) .
e. follana , c. t. h. davies , g. p. lepage , and j. shigemitsu ( hpqcd collaboration ) , phys .
lett . *
100 * , 062002 ( 2008 ) .
b. i. eisenstein _ et al .
_ ( cleo collaboration ) , phys . rev .
d * 78 * , 052003 ( 2008 ) .
b. a. dobrescu and a. s. kronfeld , phys .
* 100 * , 241802 ( 2008 ) .
d. cronin - hennessy _ et al .
_ ( cleo collaboration ) , arxiv:0801.3418 .
m. artuso _ et al . _
( cleo collaboration ) , phys .
lett . * 99 * , 071802 ( 2007 ) .
k. m. ecklund _ et al . _
( cleo collaboration ) , phys . rev .
lett . * 100 * , 161801 ( 2008 ) .
j. p. alexander _ et al .
_ ( cleo collaboration ) , phys . rev .
d * 79 * , 052001 ( 2009 ) .
y. kubota _ et al .
_ ( cleo collaboration ) , nucl .
instrum .
a * 320 * , 66 ( 1992 ) .
d. peterson _
et al . _ ,
instrum .
methods phys .
, sec . a * 478 * , 142 ( 2002 ) . m. artuso _ et al . _ ,
nucl . instrum .
methods phys .
a * 502 * , 91 ( 2003 ) .
s. dobbs _ et al .
_ ( cleo collaboration ) , phys . rev .
d * 76 * , 112001 ( 2007 ) .
j. p. alexander _ et al .
_ ( cleo collaboration ) , phys . rev .
lett . * 100 * , 161804 ( 2008 ) .
e. barberio and z. was , comput .
. commun . * 79 * , 291 ( 1994 ) .
the transport properties of nonlinear non - equilibrium dynamical systems are far from well - understood@xcite .
consider in particular so - called ratchet systems which are asymmetric periodic potentials where an ensemble of particles experience directed transport@xcite .
the origins of the interest in this lie in considerations about extracting useful work from unbiased noisy fluctuations as seems to happen in biological systems@xcite .
recently attention has been focused on the behavior of deterministic chaotic ratchets@xcite as well as hamiltonian ratchets@xcite .
chaotic systems are defined as those which are sensitively dependent on initial conditions . whether chaotic or not , the behavior of nonlinear systems including the transition from regular to chaotic behavior is in general sensitively dependent on the parameters of the system .
that is , the phase - space structure is usually relatively complicated , consisting of stability islands embedded in chaotic seas , for examples , or of simultaneously co - existing attractors .
this can change significantly as parameters change .
for example , stability islands can merge into each other , or break apart , and the chaotic sea itself may get pinched off or otherwise changed , or attractors can change symmetry or bifurcate .
this means that the transport properties can change dramatically as well .
a few years ago , mateos@xcite considered a specific ratchet model with a periodically forced underdamped particle .
he looked at an ensemble of particles , specifically the velocity for the particles , averaged over time and the entire ensemble .
he showed that this quantity , which is an intuitively reasonable definition of ` the current ' , could be either positive or negative depending on the amplitude @xmath0 of the periodic forcing for the system . at the same time , there exist ranges in @xmath0 where the trajectory of an individual particle displays chaotic dynamics .
mateos conjectured a connection between these two phenomena , specifically that the reversal of current direction was correlated with a bifurcation from chaotic to periodic behavior in the trajectory dynamics .
even though it is unlikely that such a result would be universally valid across all chaotic deterministic ratchets , it would still be extremely useful to have general heuristic rules such as this .
these organizing principles would allow some handle on characterizing the many different kinds of behavior that are possible in such systems .
a later investigation@xcite of the mateos conjecture by barbi and salerno , however , argued that it was not a valid rule even in the specific system considered by mateos .
they presented results showing that it was possible to have current reversals in the absence of bifurcations from periodic to chaotic behavior .
they proposed an alternative origin for the current reversal , suggesting it was related to the different stability properties of the rotating periodic orbits of the system .
these latter results seem fundamentally sensible . however , this paper based its arguments about currents on the behavior of a _ single _ particle as opposed to an ensemble .
this implicitly assumes that the dynamics of the system are ergodic .
this is not true in general for chaotic systems of the type being considered . in particular , there can be extreme dependence of the result on the statistics of the ensemble being considered .
this has been pointed out in earlier studies @xcite which laid out a detailed methodology for understanding transport properties in such a mixed regular and chaotic system . depending on specific parameter value , the particular system under consideration has multiple coexisting periodic or chaotic attractors or a mixture of both .
it is hence appropriate to understand how a probability ensemble might behave in such a system .
the details of the dependence on the ensemble are particularly relevant to the issue of the possible experimental validation of these results , since experiments are always conducted , by virtue of finite - precision , over finite time and finite ensembles .
it is therefore interesting to probe the results of barbi and salerno with regard to the details of the ensemble used , and more formally , to see how ergodicity alters our considerations about the current , as we do in this paper .
we report here on studies on the properties of the current in a chaotic deterministic ratchet , specifically the same system as considered by mateos@xcite and barbi and salerno@xcite .
we consider the impact of different kinds of ensembles of particles on the current and show that the current depends significantly on the details of the initial ensemble .
we also show that it is important to discard transients in quantifying the current .
this is one of the central messages of this paper : broad heuristics are rare in chaotic systems , and hence it is critical to understand the ensemble - dependence in any study of the transport properties of chaotic ratchets .
having established this , we then proceed to discuss the connection between the bifurcation diagram for individual particles and the behavior of the current .
we find that while we disagree with many of the details of barbi and salerno s results , the broader conclusion still holds .
that is , it is indeed possible to have current reversals in the absence of bifurcations from chaos to periodic behavior as well as bifurcations without any accompanying current reversals .
the result of our investigation is therefore that the transport properties of a chaotic ratchet are not as simple as the initial conjecture .

in summary , using the sample of @xmath152 tagged @xmath28 decays with the cleo - c detector we obtain the absolute branching fraction of the leptonic decay @xmath153 through @xmath154 @xmath155 where the first uncertainty is statistical and the second is systematic .

this result supersedes our previous measurement @xcite of the same branching fraction , which used a subsample of data used in this work .

the decay constant @xmath33 can be computed using eq .

( [ eq : f ] ) with known values @xcite @xmath156 gev@xmath157 , @xmath158 mev , @xmath159 mev , and @xmath160 s. we assume @xmath161 and use the value @xmath162 given in ref .

we obtain @xmath163 combining with our other determination @xcite of @xmath164 mev with @xmath43 and @xmath0 ( @xmath165 ) decays , we obtain @xmath166 this result is derived from absolute branching fractions only and is the most precise determination of the @xmath91 leptonic decay constant to date . our combined result is larger than the recent lqcd calculation @xmath167 mev @xcite by @xmath168 standard deviations .

the difference between data and lqcd for @xmath33 could be due to physics beyond the sm @xcite , unlikely statistical fluctuations in the experimental measurements or the lqcd calculation , or systematic uncertainties that are not understood in the lqcd calculation or the experimental measurements . combining with our other determination @xcite of @xmath169 , via @xmath44

, we obtain @xmath170 using this with our measurement @xcite of @xmath171 , we obtain the branching fraction ratio @xmath172 this is consistent with @xmath173 , the value predicted by the sm with lepton universality , as given in eq .

( [ eq : f ] ) with known masses @xcite .

we gratefully acknowledge the effort of the cesr staff in providing us with excellent luminosity and running conditions .

d. cronin - hennessy and a. ryd thank the a.p . sloan foundation .

this work was supported by the national science foundation , the u.s .

department of energy , the natural sciences and engineering research council of canada , and the u.k .

science and technology facilities council . c. amsler

_ et al . _

( particle data group ) , phys .

b * 667 * , 1 ( 2008 ) .

k. ikado _ et al . _

( belle collaboration ) , phys .

lett . * 97 * , 251802 ( 2006 ) .

b. aubert _ et al .

_ ( babar collaboration ) , phys . rev .

d * 77 * , 011107 ( 2008 ) .

a. g. akeroyd and c. h. chen , phys .

d * 75 * , 075004 ( 2007 ) ; a. g. akeroyd , prog .

phys . * 111 * , 295 ( 2004 ) .

j. l. hewett , arxiv : hep - ph/9505246 .

w. s. hou , phys .

d * 48 * , 2342 ( 1993 ) .

e. follana , c. t. h. davies , g. p. lepage , and j. shigemitsu ( hpqcd collaboration ) , phys .

lett . *

100 * , 062002 ( 2008 ) .

b. i. eisenstein _ et al .

_ ( cleo collaboration ) , phys . rev .

d * 78 * , 052003 ( 2008 ) .

b. a. dobrescu and a. s. kronfeld , phys .

* 100 * , 241802 ( 2008 ) .

d. cronin - hennessy _ et al .

_ ( cleo collaboration ) , arxiv:0801.3418 .

m. artuso _ et al . _

( cleo collaboration ) , phys .

lett . * 99 * , 071802 ( 2007 ) .

k. m. ecklund _ et al . _

( cleo collaboration ) , phys . rev .

lett . * 100 * , 161801 ( 2008 ) .

j. p. alexander _ et al .

_ ( cleo collaboration ) , phys . rev .

d * 79 * , 052001 ( 2009 ) .

y. kubota _ et al .

_ ( cleo collaboration ) , nucl .

instrum .

a * 320 * , 66 ( 1992 ) .

d. peterson _

et al . _ ,

instrum .

methods phys .

, sec . a * 478 * , 142 ( 2002 ) . m. artuso _ et al . _ ,

nucl . instrum .

methods phys .

a * 502 * , 91 ( 2003 ) .

s. dobbs _ et al .

_ ( cleo collaboration ) , phys . rev .

d * 76 * , 112001 ( 2007 ) .

j. p. alexander _ et al .

_ ( cleo collaboration ) , phys . rev .

lett . * 100 * , 161804 ( 2008 ) .

e. barberio and z. was , comput .

. commun . * 79 * , 291 ( 1994 ) .

the transport properties of nonlinear non - equilibrium dynamical systems are far from well - understood@xcite .

consider in particular so - called ratchet systems which are asymmetric periodic potentials where an ensemble of particles experience directed transport@xcite .

the origins of the interest in this lie in considerations about extracting useful work from unbiased noisy fluctuations as seems to happen in biological systems@xcite .

recently attention has been focused on the behavior of deterministic chaotic ratchets@xcite as well as hamiltonian ratchets@xcite .

chaotic systems are defined as those which are sensitively dependent on initial conditions . whether chaotic or not , the behavior of nonlinear systems including the transition from regular to chaotic behavior is in general sensitively dependent on the parameters of the system .

that is , the phase - space structure is usually relatively complicated , consisting of stability islands embedded in chaotic seas , for examples , or of simultaneously co - existing attractors .

this can change significantly as parameters change .

for example , stability islands can merge into each other , or break apart , and the chaotic sea itself may get pinched off or otherwise changed , or attractors can change symmetry or bifurcate .

this means that the transport properties can change dramatically as well .

a few years ago , mateos@xcite considered a specific ratchet model with a periodically forced underdamped particle .

he looked at an ensemble of particles , specifically the velocity for the particles , averaged over time and the entire ensemble .

he showed that this quantity , which is an intuitively reasonable definition of ` the current ' , could be either positive or negative depending on the amplitude @xmath0 of the periodic forcing for the system . at the same time , there exist ranges in @xmath0 where the trajectory of an individual particle displays chaotic dynamics .

mateos conjectured a connection between these two phenomena , specifically that the reversal of current direction was correlated with a bifurcation from chaotic to periodic behavior in the trajectory dynamics .

even though it is unlikely that such a result would be universally valid across all chaotic deterministic ratchets , it would still be extremely useful to have general heuristic rules such as this .

these organizing principles would allow some handle on characterizing the many different kinds of behavior that are possible in such systems .

a later investigation@xcite of the mateos conjecture by barbi and salerno , however , argued that it was not a valid rule even in the specific system considered by mateos .

they presented results showing that it was possible to have current reversals in the absence of bifurcations from periodic to chaotic behavior .

they proposed an alternative origin for the current reversal , suggesting it was related to the different stability properties of the rotating periodic orbits of the system .

these latter results seem fundamentally sensible . however , this paper based its arguments about currents on the behavior of a _ single _ particle as opposed to an ensemble .

this implicitly assumes that the dynamics of the system are ergodic .

this is not true in general for chaotic systems of the type being considered . in particular , there can be extreme dependence of the result on the statistics of the ensemble being considered .

this has been pointed out in earlier studies @xcite which laid out a detailed methodology for understanding transport properties in such a mixed regular and chaotic system . depending on specific parameter value , the particular system under consideration has multiple coexisting periodic or chaotic attractors or a mixture of both .

it is hence appropriate to understand how a probability ensemble might behave in such a system .

the details of the dependence on the ensemble are particularly relevant to the issue of the possible experimental validation of these results , since experiments are always conducted , by virtue of finite - precision , over finite time and finite ensembles .

it is therefore interesting to probe the results of barbi and salerno with regard to the details of the ensemble used , and more formally , to see how ergodicity alters our considerations about the current , as we do in this paper .

we report here on studies on the properties of the current in a chaotic deterministic ratchet , specifically the same system as considered by mateos@xcite and barbi and salerno@xcite .

we consider the impact of different kinds of ensembles of particles on the current and show that the current depends significantly on the details of the initial ensemble .

we also show that it is important to discard transients in quantifying the current .

this is one of the central messages of this paper : broad heuristics are rare in chaotic systems , and hence it is critical to understand the ensemble - dependence in any study of the transport properties of chaotic ratchets .

having established this , we then proceed to discuss the connection between the bifurcation diagram for individual particles and the behavior of the current .

we find that while we disagree with many of the details of barbi and salerno s results , the broader conclusion still holds .

that is , it is indeed possible to have current reversals in the absence of bifurcations from chaos to periodic behavior as well as bifurcations without any accompanying current reversals .

the result of our investigation is therefore that the transport properties of a chaotic ratchet are not as simple as the initial conjecture .