Observation of a resonant structure near the DsDs- threshold in the B to Ds Ds- K decay

2025-05-02 0 0 1005.39KB 23 页 10玖币

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2022-200

LHCb-PAPER-2022-018

August 22, 2023

Observation of a resonant structure

near the D+

sD−

sthreshold

in the B+→D+

sD−

sK+decay

LHCb collaboration†

Abstract

An amplitude analysis of the

B+→D+

sD−

sK+

decay is carried out to study for the

ﬁrst time its intermediate resonant contributions, using proton-proton collision data

collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13

TeV

. A

near-threshold peaking structure, referred to as

(3960), is observed in the

D+

sD−

invariant-mass spectrum with signiﬁcance greater than 12 standard deviations.

The mass, width and the quantum numbers of the structure are measured to be

3956

MeV

, 43

MeV

and

JP C

= 0

, respectively, where the ﬁrst

uncertainties are statistical and the second systematic. The properties of the new

structure are consistent with recent theoretical predictions for a state composed of

ccss

quarks. Evidence for an additional structure is found around 4140

MeV

in the

D+

sD−

invariant mass, which might be caused either by a new resonance with the

0++ assignment or by a J/ψϕ ↔D+

sD−

scoupled-channel eﬀect.

Published in Phys. Rev. Lett. 131 (2023) 071901.

†Authors are listed at the end of this paper.

arXiv:2210.15153v2 [hep-ex] 18 Aug 2023

Exotic hadrons

play a crucial role in studies of Quantum Chromodynamics (QCD),

and provide a unique window to understand the nature of the strong interaction. Dozens

of charged states with hidden charm or beauty, which imply exotic nature, such as

(4430)

[1, 2],

(10610)

[3],

(3900)

–

6],

(4020)

[7, 8],

(4450)

[9, 10],

Zcs

(3985)

[11],

Zcs

(4000)

[12], have been recently discovered by various experiments.

Over the last two years, the LHCb collaboration reported three new open-charm tetraquark

states,

X0,1

(2900)

[13, 14] and

Tcc

(3875)

[15, 16], composed of

csud

and

ccud

quarks,

respectively. Interestingly, most of these states have masses close to thresholds of hadron

pairs, which may indicate that they are hadronic molecules loosely bound by deuteron-

like meson-exchange forces [17

–

20]. There are a number of other possible explanations,

including that these particles are compact multi-quark states [21

–

23], hadroquarkonia

in which a

c¯c

core is bound to light quarks and/or gluons via chromo-electric dipole

interactions [24,25], or cusps produced by near-threshold kinematics involving open-charm

hadrons, or other dominant processes [26, 27].

The

χc0

(3930) state was observed by the LHCb collaboration in the

D+D−

invariant-

mass spectrum [14]. The mass and width of this state are consistent with those of the

(3915) resonance observed in the

ωJ/ψ

invariant-mass spectrum [28

–

31]. Moreover, the

(3915) has preferred spin (

), parity (

), and charge-parity (

) quantum numbers

JP C

= 0

[31, 32], so the two states are treated as a single hadron in the following

discussions unless otherwise speciﬁed. However, the

χc0

(3930) state is not considered

to be consistent with being a candidate for either the

χc0

) or

χc0

) state [33

–

37].

Lebed

et al.

[38] propose that it is the lightest

c¯cs¯s

state. Calculations based on QCD

sum rules [39] favour the

χc0

(3930) state as a 0

[

][

] (where

u, d

) or [

][

]

tetraquark. Recent lattice QCD results also indicate that this state is dominated by the

c¯cs¯s

constituents [40]. The

D+

sD−

molecular interpretation is also possible, as suggested by the

quark delocalization color-screening model [41] and other phenomenological studies [42,43].

All these developments point to a potential resonant structure in the vicinity of the

threshold in the D+

sD−

sinvariant-mass spectrum.

Previously, only the Belle experiment studied the D+

sD−

sinvariant-mass spectrum in

processes involving initial-state radiation, where only 1

−−

charmonium(-like) states can

contribute [44]. The

B+→D+

sD−

sK+

process, given its large branching fraction measured

in the accompanying paper [45], provides a good opportunity to study resonances in the

D+

sD−

ﬁnal states, both scalars and those of higher spin, such as the 0

++ charmonium(-like)

states

χc0

(4500) and

χc0

(4700) possibly having an intrinsic

ccss

component [12], the

well-known 1

−−

charmonium states, such as

(4040),

(4160),

(4260),

(4415) and

ψ(4660) [32, 46, 47].

In this Letter, an amplitude analysis of about 360 reconstructed

B+→D+

sD−

sK+

signal decays is presented, leading to the ﬁrst observation of a near-threshold peaking

structure in the

D+

sD−

system, denoted by

(3960). The analysis is based on proton-

proton (

) collision data collected by the LHCb experiment at centre-of-mass energies

of 7, 8 and 13

TeV

between 2011 and 2018, corresponding to an integrated luminosity of

fb−1

. The

D+

candidates are reconstructed via the

D+

s→K−K+π+

decay. The details

of the detector, data and simulation, selection criteria, background composition and

B+

Hadrons that are not composed either of a quark-antiquark pair or of three quarks or three antiquarks

are collectively called exotic hadrons.

The inclusion of charge-conjugate processes is always implied and natural units with

ℏ

= 1 are used

throughout the Letter.

]

0.12 GeV×Yield / [0.15

16 18 20 22 ]

[GeV

)

−

D(m

]

[GeV

)

−

D(m

LHCb

-1

9 fb

Figure 1: Dalitz-plot distribution for the

B+→D+

sD−

sK+

decay after background subtraction.

invariant-mass ﬁt can be found in the accompanying paper [45].

To improve the resolution on the masses of the two-body combinations that are used in

the amplitude analysis, the four momentum of each ﬁnal-state particle is determined from

a kinematic ﬁt [48] where the

B+

mass is constrained to its known value [32]. Figure 1

shows the resulting Dalitz-plot distribution for the

B+→D+

sD−

sK+

signal decays, where

the non-

B+

background is subtracted by the

sPlot

technique [49] with the reconstructed

B+

mass as the discriminating variable. The most evident feature is the band near the

D+

sD−

threshold. To validate that this peaking structure is not due to the combinatorial

background, the

D+

sD−

invariant-mass distribution of candidates in the

B+

mass region

from 5360 to 5600 MeV is investigated and no peak is observed.

Employing an unbinned maximum-likelihood method, an amplitude ﬁt with the

sFit

technique [50] is performed to investigate the intermediate states and determine the

quantum numbers

JP C

of any new particle. Two known 1

−−

charmonium states,

(4260)

and

(4660) [32, 46, 47], and two new 0

++ X

states are needed to ﬁt the structures in

the

D+

sD−

spectrum. One of these scalars,

(3960), describes the

D+

sD−

threshold

enhancement and the other, designated

(4140), is necessary to model the dip around

4140

MeV

, as shown in Fig. 2. The subscript 0 is used to distinguish the latter from the

++ X

(4140) state seen in the

J/ψϕ

ﬁnal state [32]. Additionally, an

-wave three-body

phase-space function [32] is employed to model the nonresonant (NR)

B+→D+

sD−

sK+

component. Since no signiﬁcant contribution of any state is observed in either the

D−

sK+

or D+

sK+systems, these ﬁve contributions constitute the baseline model.

The helicity formalism [51] is used to construct the amplitude model of the

B+→D+

sD−

sK+

decay, with a similar approach applied to previous LHCb analyses

B+

and

decays to three pseudoscalar particles [14, 52

–

54]. The resonant structure

near the

D+

sD−

mass threshold is parameterised by a Flatt´e-like function [19, 32, 55]

depending on the invariant mass m

R(m|M0, gj) = 1

0−m2−iM0Pjgjρj(m),(1)

where

is the mass of the resonance,

denotes the coupling of this resonance to the

-th channel,

ρj

(

) is the phase-space factor [32] for the

-th two-body decay. When the

Figure 2: Background-subtracted invariant-mass distributions (top left)

m(D+

sD−

, (top right)

(

D+

sK+

) and (bottom)

m(D−

sK+)

for the

B+→D+

sD−

sK+

signal. The projections of the ﬁt

with the baseline amplitude model are also shown.

value of

is below the threshold of the channel

i.e. q2

0, an analytic continuation

is applied for

iq−q2

[55, 56]. The total width of the resonance is calculated as

Pjgjρj

(

). In the baseline model, only the

D+

sD−

channel (

= 1) is included in

the Flatt´e-like parameterisation.

Other resonances are modelled by a relativistic Breit–Wigner function

BW(m|M0,Γ0)

with a mass-dependent width [32]. The radius of each resonance entering the Blatt–

Weisskopf barrier factor [57–59] is set to 3 GeV−1, corresponding to about 0.6 fm.

The total probability density function is the squared modulus of the total decay

amplitude multiplied by the eﬃciency, normalised to ensure that the integral over the

Dalitz plot is unity. The ﬁt fraction

expresses the fraction of the total rate due to

the component

, and the interference fraction

Iij

describes the interference between

components

and

. They are deﬁned in Eqs. (18) and (19) of Ref. [53], such that

PiFi+Pi<j Iij = 1.

As shown in Fig. 2, the two-body mass distributions are well modelled by the baseline

amplitude ﬁt. The corresponding numerical results are summarised in Table 1, including

the mass, width, ﬁt fraction, and signiﬁcance (

) of each component. The signiﬁcance

of a given component is evaluated by assuming that the change of twice the negative

log-likelihood (

−

ln L

) between the baseline ﬁt and the ﬁt without that component

obeys a

χ2

distribution, where the number of degrees of freedom (n.d.f.) is given by the

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EUROPEANORGANIZATIONFORNUCLEARRESEARCH(CERN)CERN-EP-2022-200LHCb-PAPER-2022-018August22,2023ObservationofaresonantstructureneartheD+sD−sthresholdintheB+→D+sD−sK+decayLHCbcollaboration†AbstractAnamplitudeanalysisoftheB+→D+sD−sK+decayiscarriedouttostudyforthefirsttimeitsintermediateresonantcontributio...

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Observation of a resonant structure near the DsDs- threshold in the B to Ds Ds- K decay

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