Width Difference in the <math display="inline"><mrow><mi>B</mi><mo>-</mo><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> System at Next-to-Next-to-Leading Order of QCD

Gerlach, Marvin; Nierste, Ulrich; Shtabovenko, Vladyslav; Steinhauser, Matthias

doi:10.1103/PhysRevLett.129.102001

Width Difference in the $B - \bar{B}$ System at Next-to-Next-to-Leading Order of QCD

Marvin Gerlach
(
- KIT, Karlsruhe
)
,
Ulrich Nierste
(
- KIT, Karlsruhe
)
,
Vladyslav Shtabovenko
(
- KIT, Karlsruhe
)
,
Matthias Steinhauser
(
- KIT, Karlsruhe
)

May 16, 2022

7 pages

Published in:

Phys.Rev.Lett. 129 (2022) 10, 102001

Published: Aug 31, 2022

e-Print:

2205.07907 [hep-ph]

DOI:

10.1103/PhysRevLett.129.102001 (publication)

Report number:

TTP22-030,
P3H-22-051

View in:

ADS Abstract Service

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Abstract: (APS)

We extend the theoretical prediction for the width difference

Δ Γ_{q}

in the mixing of neutral

B

mesons in the Standard Model to next-to-next-to-leading order in

α_{s}

. To this aim, we calculate three-loop diagrams with two

| Δ B | = 1

current-current operators analytically. In the matching between

| Δ B | = 1

and

| Δ B | = 2

effective theories, we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix

Z_{i j}

for the

| Δ B | = 2

operators and the

O (α_{s}^{2})

corrections to the finite renormalization that ensures the

1 / m_{b}

suppression of the operator

R_{0}

at two-loop order. Our theoretical prediction reads

Δ Γ_{s} / Δ M_{s} = (4.33 \pm 0.93) \times 10^{- 3}

if expressed in terms of the bottom mass in the

\bar{MS}

scheme and

Δ Γ_{s} / Δ M_{s} = (4.20 \pm 0.95) \times 10^{- 3}

for the use of the potential-subtracted mass. While the controversy on

| V_{c b} |

affects both

Δ Γ_{s}

and

Δ M_{s}

, the ratio

Δ Γ_{s} / Δ M_{s}

is not affected by the uncertainty in

| V_{c b} |

.

Note:

7 pages, 4 figures

width: difference
higher-order: 2
infrared problem: regularization
renormalization: finite
operator: suppression
bottom: mass
mixing
B anti-B
quantum chromodynamics

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