Weak matrix elements on the lattice - circa 1995

are discussed and the overall situation with respect to the lattice effort and some of its phenomenological implications are summarized. For \epspeps the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g.\

O_6

), even bounds on their matrix elements would be very helpful. On \bkastg, a constant behavior of

T_2

appears disfavored although dependence of

T_2

could, of course, be milder than a simple pole. Improved data is badly needed to settle this important issue firmly, especially in view of its ramification for extractions of

V_{td}

from

B\to\rho\gamma

. On

B_K

, the preliminary result from JLQCD appears to contradict Sharpe \etal\ JLQCD data seems to fit very well to linear

a

dependence and leads to an appreciably lower value of

B_K

. Four studies of

B_K

in the ``full'' (

n_f=2

) theory indicate very little quenching effects on

B_K

; the full theory value seems to be just a little less than the quenched result. Based on expectations from HQET, analysis of the

B

-parameter (

B_{h\ell}

) for the heavy-light mesons via

B_{h\ell}={}

constant

{}+{}

constants

^\prime/m_{h\ell}

is suggested. A summary of an illustrative sample of hadron matrix elements is given and constraints on CKM parameters (e.g.\

V_{td}/V_{ts}

), on the unitarity triangle and on

x_s/x_d

, emerging from the lattice calculations along with experimental results are briefly discussed. In quite a few cases, for the first time, some indication of quenching errors on weak matrix elements are now becoming available.

review
fermion: lattice field theory
B: radiative decay
radiative decay: B
K0 anti-K0: mixing
K0: nonleptonic decay
nonleptonic decay: K0
K: B-parameter
B: B-parameter
CP: violation

References(96)

Figures(0)

[1]

Weak interactions from lattice QCD

G. Martinelli
(
- CERN
)

- Nucl.Phys.B Proc.Suppl. 42 (1995) 127-139,
- Nucl. Phys. B, Proc. Suppl. 42 (1995) 127-139. In *Bielefeld 1994, Lattice 94* 127-139
•
DOI:
- 10.1016/0920-5632(95)00195-F

[2]

Heavy - light and light-light weak matrix elements on the lattice

Claude W. Bernard
(
- Washington U., St. Louis
)

- Nucl.Phys.B Proc.Suppl. 34 (1994) 47-62,
- Dallas Lattice 1993:0047-62
•
e-Print:
- hep-lat/9312086
•
DOI:
- 10.1016/0920-5632(94)90319-0

[3]

$\epsilon' / \epsilon$ at the Next-to-leading order in QCD and QED

Marco Ciuchini
(
- Rome, ISS and
- Rome U.
)
,
E. Franco
(
- Rome U. and
- INFN, Rome
)
,
G. Martinelli
(
- Rome U. and
- INFN, Rome
)
,
L. Reina
(
- SISSA, Trieste and
- INFN, Trieste
)

- Phys.Lett.B 301 (1993) 263-271
•
e-Print:
- hep-ph/9212203
•
DOI:
- 10.1016/0370-2693(93)90699-I

[3]

Estimates of epsilon-prime / epsilon

Marco Ciuchini
(
- Rome, ISS
)
,
E. Franco
(
- Rome U. and
- INFN, Rome
)
,
G. Martinelli
(
- CERN
)
,
L. Reina
(
- Brookhaven
)

- 2nd DAPHNE Physics Handbook:27-50
•
e-Print:
- hep-ph/9503277

[4]

A Lattice study of the exclusive B ---> K* gamma decay amplitude, using the Clover action at Beta = 6.0

APE

Collaboration

•

A. Abada
(
- Orsay, LPT
)

et al.

- Phys.Lett.B 365 (1996) 275-284
•
e-Print:
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•
DOI:
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[5]

Form-factors for B ---> pi lepton anti-lepton-neutrino and B ---> K* gamma decays on the lattice

UKQCD

Collaboration

•

D.R. Burford
(
- Southampton U.
)

et al.

- Nucl.Phys.B 447 (1995) 425-440
•
e-Print:
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•
DOI:
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[6]

B ---> K* gamma: Penguins on the lattice

UKQCD

Collaboration

•

K.C. Bowler
(
- Edinburgh U.
)

et al.

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•
e-Print:
- hep-lat/9311004
•
DOI:
- 10.1103/PhysRevLett.72.1398

[7]

Phenomenology from 100 large lattices

Tanmoy Bhattacharya
(
- Los Alamos
)
,
Rajan Gupta
(
- Los Alamos
)

- Nucl.Phys.B Proc.Suppl. 42 (1995) 935-941
•
e-Print:
- hep-lat/9501016
•
DOI:
- 10.1016/0920-5632(95)00427-B

[8]

B ---> K* + gamma and B(s) ---> phi + gamma on the lattice

Claude W. Bernard
(
- Washington U., St. Louis
)
,
P. Hsieh
(
- Harvard-Smithsonian Ctr. Astrophys.
)
,
A. Soni
(
- Brookhaven
)

- Phys.Rev.Lett. 72 (1994) 1402-1405
•
e-Print:
- hep-lat/9311010
•
DOI:
- 10.1103/PhysRevLett.72.1402

[9]

Lattice study of the decay anti-B0 ---> rho+ lepton- anti-lepton-neutrino: Model independent determination of |V(ub)|

UKQCD

Collaboration

•

J.M. Flynn
(
- Southampton U.
)

et al.

- Nucl.Phys.B 461 (1996) 327-349
•
e-Print:
- hep-ph/9506398
•
DOI:
- 10.1016/0550-3213(95)00595-1

[10]

(private communications)

J. Flynn
,
J. Nieves

[11]

Relationship Between Form-factors in Semileptonic $\bar{B}$ and $D$ Decays and Exclusive Rare $\bar{B}$ Meson Decays

Nathan Isgur
(
- Toronto U.
)
,
Mark B. Wise
(
- Caltech
)

- Phys.Rev.D 42 (1990) 2388-2391
•
DOI:
- 10.1103/PhysRevD.42.2388

[11]

in: Perspectives of the Standard Model, R.K. Ellis, C. T. Hill and J. D. Lykken (eds.) 94) p.589

H. Georgi

[11]

Heavy quark symmetry

Matthias Neubert
(
- SLAC
)

- Phys.Rept. 245 (1994) 259-396
•
e-Print:
- hep-ph/9306320
•
DOI:
- 10.1016/0370-1573(94)90091-4

[11]

An Introduction to the theory of heavy mesons and baryons

Benjamin Grinstein
(
- UC, San Diego
)

- Boulder TASI 1994:0307-376,
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•
e-Print:
- hep-ph/9411275

[12]

Determination of |V(ts)| from D ---> K* lepton neutrino and B ---> K+ gamma data via heavy quark symmetry and perturbative QCD

- Phys.Rev.D 50 (1994) 5751-5761
•
e-Print:
- hep-ph/9312262
•
DOI:
- 10.1103/PhysRevD.50.5751

[13]

(JLQCD), see Aoki's talk

S. Aoki

[14]

(see Lee's talk )

W. Lee
,
M. Klomfass

[15]

See the talks by

T. Bhattacharya
,
R. Gupta

[16]

Nonperturbative renormalization of the lattice Delta s = 2 four fermion operator

A. Donini
(
- Rome U. and
- INFN, Rome
)
,
G. Martinelli
(
- CERN
)
,
Christopher T. Sachrajda
(
- Southampton U.
)
,
M. Talevi
(
- Rome U. and
- INFN, Rome
)
,
A. Vladikas
(
- Rome U., Tor Vergata
)

- Phys.Lett.B 360 (1995) 83-92
•
e-Print:
- hep-lat/9508020
•
DOI:
- 10.1016/0370-2693(95)01124-9

[16]

A New measurement of direct CP violation in the neutral kaon system

NA31

Collaboration

•

G.D. Barr
(
- CERN
)

et al.

- Phys.Lett.B 317 (1993) 233-242
•
DOI:
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[19]

Measurement of the CP violation parameter Re( $\epsilon^{\prime} / \epsilon$ )

E731

Collaboration

•

L.K. Gibbons
(
- Chicago U., EFI and
- Chicago U.
)

et al.

- Phys.Rev.Lett. 70 (1993) 1203-1206
•
DOI:
- 10.1103/PhysRevLett.70.1203

[20]

Violation of CP Invariance and the Possibility of Very Weak Interactions

L. Wolfenstein
(
- Carnegie Mellon U.
)

- Phys.Rev.Lett. 13 (1964) 562-564,
- In *Lichtenberg, D. B. ( Ed.), Rosen, S. P. ( Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 227-229. ( Phys. Rev. Lett. 13 ( 1964) 562-564)
•
DOI:
- 10.1103/PhysRevLett.13.562

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