Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks2015/Chesnokov_QFTHEP%202015.pdf Äàòà èçìåíåíèÿ: Sat Jun 27 15:58:56 2015 Äàòà èíäåêñèðîâàíèÿ: Sat Apr 9 23:29:10 2016 Êîäèðîâêà:

Introduction QCD Sum rules Numerical analysis ÿonclusions

¾LEPTONIC CONSTANTS OF TENSOR MESONS IN QCD¿
P. CHESNOKOV
Physics Faculty of LOMONOSOV MOSCOW STATE UNIVERSITY General Nuclear Physics Department

june 27, 2015

Lomonosov Moscow State University

QFTHEP 2015


Contents
1

Introduction QCD Sum rules Numerical analysis ÿonclusions

Introduction Problems Report purpose QCD Sum rules Numerical analysis Initial Sum rules method T-depend eective threshold High order corrections Conclusions
Lomonosov Moscow State University QFTHEP 2015

2 3

4


Contents
1

Introduction QCD Sum rules Numerical analysis ÿonclusions

Problems Report purpose

Introduction Problems Report purpose QCD Sum rules Numerical analysis Initial Sum rules method T-depend eective threshold High order corrections Conclusions
Lomonosov Moscow State University QFTHEP 2015

2 3

4


Introduction QCD Sum rules Numerical analysis ÿonclusions

Problems Report purpose

Quantum Chromodynamics is eld theory of strong interactions based on quark and gluon elds. The purpose
L
is hadrons discription using lagrangian of QCD:

QCD

=
f

f (iD - mf )f - Gµ G /

1 4

µ

(1)

The problem is CONFINEMENT:
s

1

The solution is non-perturbative methods:
Lattice QCD QCD Sum rules ...

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Problems Report purpose

Comparison of two basic non-perturbative methods in QCD: Characteristics Lattice QCD QCD Sum rules Precision + - Flexibility - + Visibility - + "Eectiveness" -(+) +(-)

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Problems Report purpose

Report purpose is: Using QCD Sum Rules for tensor mesons on the example of Ds 2 (2573) meson Extraction of the mass and the current coupling constant for leptonic (weak) decay channel Method correction that improves the accuracy Error analysis of the result
Ds 2 (2573) meson characteristics

Mass Quark content El. charge J 2573 MeV cs +1 2
Lomonosov Moscow State University

P +

0 3, 8 · 10

I



-23

sec

QFTHEP 2015


Contents
1

Introduction QCD Sum rules Numerical analysis ÿonclusions

Introduction Problems Report purpose QCD Sum rules Numerical analysis Initial Sum rules method T-depend eective threshold High order corrections Conclusions
Lomonosov Moscow State University QFTHEP 2015

2 3

4


Introduction QCD Sum rules Numerical analysis ÿonclusions

The basic idea of sum rules method is calculation of correlation function
µ (q ) = i d 4x e
iqx 0|T {jµ (x ), j (0)}|0

(2)

in two ways: using hadronic states using quark-gluon elds when q 2 0 and equating of these two expressions when q 2 < 0.

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Hadronic part: We insert into µ (q ) full system of hadronic states functions | n n |= 1 then we extract the ground state contribution and
nally assosiate it with current coupling constant:
2 (q 2 ) = C (q 2 ) · fD
s2

n

(2573)

+ excited states

(3)

QCD part: We use OPE (Wilson Operator Product Expantion) that includes perturbative part and contribution of vacuum condensates (non-perturbative part):
s0

(q ) =
(mc +ms )2

2

ds

pert (s ) + (s - q 2 )

non-p ert

(q 2 )

(4)

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

B

m -q

2

1

2

=e

-m2 T

(5)

Finally we apply Borel transformation (inverse Laplace transformation) to the both parts of Sum rules, which improves convergence of expansions and also suppresses contribution of excited states.
Lomonosov Moscow State University QFTHEP 2015


Contents
1

Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

Introduction Problems Report purpose QCD Sum rules Numerical analysis Initial Sum rules method T-depend eective threshold High order corrections Conclusions
Lomonosov Moscow State University QFTHEP 2015

2 3

4


Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

Input data:

mc = (1.275 ± 0.025) GeV ms = (0.100 ± 0.023) GeV s s (µ = mc ) = -0.8(0.24 ± 0.01)3 GeV

3

We have also two model parameters: T - borel parameter s0 - eective continuum threshold
T
max

Tmin

: non-pert (T )/pert (T ) 30%, : ground state /excited states 10%, 2 s0 E1 ex .st

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

fDs2 (2573) = (21, 2 ± 1, 1) MeV mDs2 (2573) = (2545 ± 105) MeV

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

Current coupling constant results from dierent methods QCD SR (n = QCD SR (n = Lattice QCD Experiment 0) [1] 0) [1] [2,3] [4]
D -meson (181, 3 ± 8, 4) (206, 2 ± 7, 3) (208.3 ± 5, 2) (205.2 ± 8.1)

MeV MeV MeV MeV

Ds -meson (218, 8 ± 16, 1) MeV (245 ± 15, 7) MeV (252, 2 ± 8, 2) MeV (256, 8 ± 10, 1) MeV

[1] W. Lucha, D. Melikhov, S. Simula, 2011 J. Phys. G: Nucl. Part. Phys. 38 105002 [2] Blossier Bet al(ETM Collaboration) 2009J. High Energy Phys.JHEP07(2009)043 [3] Follana E, Davies C T H, Lepage G P and Shigemitsu J (HPQCD Collaboration and UKQCD Collaboration) 2008Phys. Rev. Lett.100062002 [4] Nakamura Ket al(Particle Data Group) 2010J. Phys. G: Nucl. Part. Phys.37075021

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

Consideration of T -depend eective threshold s0 :
n

s 0 (T ) =
j=

(n )

s
0

(n ) j

T j , n = 0, 1, 2, 3.

(6)

Coecients sj(n) can be found by minimizing the following functional: 1 2 N
N

i=

1

2 2 [mDs2 (2573) (Ti ) - mexp ]2 QFTHEP 2015

(7)

Lomonosov Moscow State University


Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

Method errors have dierent origin:

a) Borel parameter dependence T (±5%). b) Uncertainty in value of qurk condensate (±10%).
Essentially this is the only errors that we can consider. However we should remember about unaccounted errors (its contribution for tensor mesons is unknown now):

c) Contribution of high order condensates 2 d) O (s )- and O (s )- corrections in perturbative part

Lomonosov Moscow State University

QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

Initial Sum rules method T-depend eective threshold High order corrections

2 Contribution of O (s ), O (s ) corrections and quark condensate to Ds and Ds meson parameters:

a)
condensate:

b)
0 0 a) Ratio fDs (T )/fDs b) Ratio fD (T )/fDs s
QFTHEP 2015

Graphs shows contribution of p etrurbative corrections and quark

Lomonosov Moscow State University


Contents
1

Introduction QCD Sum rules Numerical analysis ÿonclusions

Introduction Problems Report purpose QCD Sum rules Numerical analysis Initial Sum rules method T-depend eective threshold High order corrections Conclusions
Lomonosov Moscow State University QFTHEP 2015

2 3

4


Introduction QCD Sum rules Numerical analysis ÿonclusions

We've got current coupling constant and mass for Ds2 (2573) meson using QCD Sum rules. We've considered T-depend eective threshold s0 and demonstrated higher relative accuracy (5%) and also higher value of current coupling constant (10%).
QCD SR (n = 0) QCD SR (n = 0) Experiment [5]
( (

Conclusions

21, 2 23, 1

fD (2573) s2 ± 3, 2) MeV ± 2, 2) MeV

?

(2545 ± 105) MeV (2556 ± 87) MeV (2571, 9 ± 0, 8) MeV

mD (2573) s2

2 We've tried to estimate contribution of O (s ), O (s ) corrections and high order condensates to Ds 2 (2573) current coupling constant by analyzing such corrections for pseudoscholar Ds and vector Ds mesons. We expect addition to fDs2 (2573) value about 15 - 25%. [5] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012). Lomonosov Moscow State University QFTHEP 2015


Introduction QCD Sum rules Numerical analysis ÿonclusions

...

Thanks for your attention!

Lomonosov Moscow State University

QFTHEP 2015