Bs0和Bs0中的共振和CP违反→J/ψK+K−$${\overline{B}}_s^0\toJ/\psi{K}^{+}{K}^{-}$$在above上方的质量区域中衰减（1020）资源-CSDN文库

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JHEP08(2017)037

Published for SISSA by Springer

Received: April 27, 2017

Revised: June 29, 2017

Accepted: July 25, 2017

Published: August 9, 2017

Resonances and CP violation in B

and

→ J/ψK

−

decays in the mass region above

the φ(1020)

The LHCb collaboration

E-mail: liming.zhang@cern.ch

Abstract: The decays of B

and B

mesons into the J/ψK

−

ﬁnal state are studied

in the K

−

mass region above the φ(1020) meson in order to determine the resonant

substructure and measure the CP -violating phase, φ

, the decay width, Γ

, and the width

diﬀerence between light and heavy mass eigenstates, ∆Γ

. A decay-time dependent am-

plitude analysis is employed. The data sample corresponds to an integrated luminosity

of 3 fb

−1

produced in 7 and 8 TeV pp collisions at the LHC, collected by the LHCb ex-

periment. The measurement determines φ

= 119 ± 107 ± 34 mrad. A combination with

previous LHCb measurements using similar decays into the J/ψπ

−

and J/ψφ(1020) ﬁnal

states gives φ

= 1 ±37 mrad, consistent with the Standard Model prediction.

Keywords: B physics, CP violation, Spectroscopy, Hadron-Hadron scattering (experi-

ments)

ArXiv ePrint: 1704.08217

Open Access, Copyright CERN,

for the beneﬁt of the LHCb Collaboration.

Article funded by SCOAP

https://doi.org/10.1007/JHEP08(2017)037

JHEP08(2017)037

ATLAS [10] collaborations using J/ψ φ(1020) ﬁnal states.

The average of all of the above

mentioned measurements is φ

= −30 ± 33 mrad [13].

Previously, using a data sample corresponding to 1 fb

−1

integrated luminosity, the

LHCb collaboration studied the resonant structures in the B

→ J/ψ K

−

decay [14]

revealing a rich resonance spectrum in the K

−

mass distribution. In addition to the

φ(1020) meson, there are signiﬁcant contributions from the f

(1525) resonance [15] and

nonresonant S-wave, which are large enough to allow further studies of CP violation. This

paper presents the ﬁrst measurement of φ

using B

→ J/ψ K

−

decays, where J/ψ →

−

with m

above the φ(1020) region, using data corresponding to an integrated

luminosity of 3 fb

−1

, obtained from pp collisions at the LHC. One third of the data was

collected at a centre-of-mass energy of 7 TeV, and the remainder at 8 TeV. An amplitude

analysis as a function of the B

proper decay time [16] is performed to determine the CP -

violating phase φ

, by measuring simultaneously the CP -even and CP -odd decay amplitudes

for each contributing resonance (and nonresonant S-wave), allowing the improvement of

the φ

accuracy and, in addition, further studies of the resonance composition in the decay.

These B

→ J/ψ K

−

decays are separated into two K

−

mass intervals. Those

with m

< 1.05 GeV are called low-mass and correspond to the region of the φ(1020)

resonance, while those with m

> 1.05 GeV are called high-mass. The high-mass region

has not been analyzed for CP violation before, allowing the measurement of CP violation

in several decay modes, including a vector-tensor ﬁnal state, J/ψ f

(1525). In the SM the

phase φ

is expected to be the same in all such modes. One important diﬀerence from

the previous low-mass analysis [7] is that modelling of the m

distribution is included to

distinguish diﬀerent resonance and nonresonance contributions. In the previous low mass

CP-violation analysis only the φ(1020) resonance and an S-wave amplitude were considered.

This analysis follows very closely the analyses of CP violation in B

→ J/ψ π

−

decays [8]

and in B

→ J/ψ π

−

decays [3], and only signiﬁcant changes with respect to those

measurements are described in this paper. The analysis strategy is to ﬁt the CP -even

and CP -odd components in the decay width probability density functions that describe

the interfering amplitudes in the particle and antiparticle decays. These ﬁts are done as

functions of the B

proper decay time and in a four-dimensional phase space including the

three helicity angles characterizing the decay and m

. Flavour tagging, described below,

allows us to distinguish between initial B

and

states.

This paper is organized as follows. Section 2 describes the B

proper-time dependent

decay widths. Section 3 gives a description of the detector and the associated simulations.

Section 4 contains the event selection procedure and the extracted signal yields. Section 5

shows the measurement of the proper-time resolution and eﬃciencies for the ﬁnal state in

the four-dimensional phase space. Section 6 summarizes the identiﬁcation of the initial

ﬂavour of the state, a process called ﬂavour tagging. Section 7 gives the masses and widths

of resonant states that decay into K

−

, and the description of a model-independent

S-wave parameterization. Section 8 describes the unbinned likelihood ﬁt procedure used

The ﬁnal states D

−

[11] and ψ(2S)φ(1020) [12] are also used by LHCb, but the precisions are not

comparable due to lower statistics.

See also updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/.

– 2 –

JHEP08(2017)037

to determine the physics parameters, and presents the results of the ﬁt, while section 9

discusses the systematic uncertainties. Finally, the results are summarized and combined

with other measurements in section 10.

2 Decay rates for B

and B

→ J/ψ K

−

The total decay amplitude for a B

) meson at decay time equal to zero is taken to be

the sum over individual K

−

resonant transversity amplitudes [17], and one nonresonant

amplitude, with each component labelled as A

). Because of the spin-1 J/ψ in the ﬁnal

state, the three possible polarizations of the J/ψ generate longitudinal (0), parallel (k)

and perpendicular (⊥) transversity amplitudes. When the K

−

forms a spin-0 state

the ﬁnal system only has a longitudinal component. Each of these amplitudes is a pure

CP eigenstate. By introducing the parameter λ

≡

, relating CP violation in the

interference between mixing and decay associated with the state i, the total amplitudes A

and A can be expressed as the sums of the individual B

amplitudes, A =

and A =

|λ

−iφ

. The quantities q and p relate the mass to the ﬂavour

eigenstates [18]. For each transversity state i the CP -violating phase φ

≡ −arg(η

) [19],

with η

being the CP eigenvalue of the state. Assuming that any possible CP violation in

the decay is the same for all amplitudes, then λ ≡ η

and φ

≡ −arg(λ) are common.

The decay rates into the J/ψ K

−

ﬁnal state are

Γ(t) ∝ e

−Γ



|A|

+ |

cosh

∆Γ

|A|

− |A|

cos(∆m

− Re(A

∗

A) sinh

∆Γ

− Im(A

∗

A) sin(∆m



, (2.1)

Γ(t) ∝ e

−Γ



|A|

+ |A|

cosh

∆Γ

−

|A|

− |A|

cos(∆m

− Re(A

∗

A) sinh

∆Γ

+ Im(A

∗

A) sin(∆m



, (2.2)

where ∆Γ

≡ Γ

−Γ

is the decay width diﬀerence between the light and the heavy mass

eigenstates, ∆m

≡ m

− m

is the mass diﬀerence, and Γ

≡ (Γ

+ Γ

)/2 is the average

width. The sensitivity to the phase φ

is driven by the terms containing A

∗

For J/ψ decays to µ

−

ﬁnal states, these amplitudes are themselves functions

of four variables: the K

−

invariant mass m

, and three angular variables Ω ≡

(cos θ

, cos θ

J/ψ

, χ), deﬁned in the helicity basis. These consist of the angle θ

be-

tween the K

direction in the K

−

rest frame with respect to the K

−

direction in

the B

rest frame, the angle θ

J/ψ

between the µ

direction in the J/ψ rest frame with

respect to the J/ψ direction in the B

rest frame, and the angle χ between the J/ψ and

−

decay planes in the B

rest frame [16, 19]. These angles are shown pictorially in

ﬁgure 1. These deﬁnitions are the same for B

and B

, namely, using µ

and K

to deﬁne

the angles for both B

and B

decays. The explicit forms of |A(m

, Ω)|

, |A(m

, Ω)|

and A

∗

, Ω)A(m

, Ω) in eqs. (2.1) and (2.2) are given in ref. [16].

|p/q| = 1 is used. The latest LHCb measurement determined |p/q|

= 1.0039 ± 0.0033 [20].

– 3 –

JHEP08(2017)037

J/ψ

−

Figure 1. Deﬁnition of the helicity angles.

3 Detector and simulation

The LHCb detector [21, 22] is a single-arm forward spectrometer covering the

pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c

quarks. The detector includes a high-precision tracking system consisting of a silicon-strip

vertex detector surrounding the pp interaction region, a large-area silicon-strip detector

located upstream of a dipole magnet with a bending power of about 4 Tm, and three sta-

tions of silicon-strip detectors and straw drift tubes placed downstream of the magnet.

The tracking system provides a measurement of momentum, p, of charged particles with

a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV. The

primary vertex (PV) is constructed from reconstructed tracks that arise from a common

origin [23]. The minimum distance of a track to a PV, the impact parameter (IP), is mea-

sured with a resolution of (15 + 29/p

) µm, where p

is the component of the momentum

transverse to the beam, in GeV. Diﬀerent types of charged hadrons are distinguished using

information from two ring-imaging Cherenkov (RICH) detectors. Photons, electrons and

hadrons are identiﬁed by a calorimeter system consisting of scintillating-pad and preshower

detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identiﬁed

by a system composed of alternating layers of iron and multiwire proportional chambers.

The online event selection is performed by a trigger, which consists of a hardware

stage, based on information from the calorimeter and muon systems, followed by a software

stage, which applies a full event reconstruction. The software trigger is composed of two

stages, the ﬁrst of which performs a partial reconstruction and requires either a pair of

well-reconstructed, oppositely charged muons having an invariant mass above 2.7 GeV, or

a single well-reconstructed muon with high p

and large IP. The second stage applies a

full event reconstruction and for this analysis requires two opposite-sign muons to form a

good-quality vertex that is well separated from all of the PVs, and to have an invariant

mass within ±120 MeV of the known J/ψ mass [24].

In the simulation, pp collisions are generated using Pythia 8 [25, 26]. Decays of

hadronic particles are described by EvtGen [27], in which ﬁnal-state radiation is generated

using Photos [28]. The interaction of the generated particles with the detector, and its

response, are implemented using the Geant4 toolkit [29, 30] as described in ref. [31]. The

simulation covers the full K

−

mass range.

– 4 –

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