Searching for hidden-charm baryonium signals in QCD sum rules

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

We give an explicit QCD sum rule investigation for hidden-charm baryonium states with the quark content ......, spin ......, and of both positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, which can actually couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion, etc. We do not know which structure these currents couple to at the beginning, but after sum rule analyses we can obtain some information. We find some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states with quantum numbers ...... to be around 5.0 GeV. We suggest to search for hidden-charm baryonium states, especially the one of ......, in the D-wave ...... and P-wave ...... and ...... channels in this energy region.

Eur. Phys. J. C (2016) 76:602DOI 10.1140/epjc/s10052-016-4459-0

Regular Article - Theoretical Physics

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Web End = Searching for hidden-charm baryonium signals in QCD sum rules

Hua-Xing Chen1, Dan Zhou1, Wei Chen2,a, Xiang Liu3,4,b, Shi-Lin Zhu5,6,7,c

1 School of Physics, Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China

2 Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK S7N 5E2, Canada

3 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

4 Research Center for Hadron and CSR Physics, Institute of Modern Physics of CAS, Lanzhou University, Lanzhou 730000, China

5 School of Physics, State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China

6 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

7 Center of High Energy Physics, Peking University, Beijing 100871, China

Received: 27 September 2016 / Accepted: 24 October 2016 / Published online: 4 November 2016 The Author(s) 2016. This article is published with open access at Springerlink.com

Abstract We give an explicit QCD sum rule investigation for hidden-charm baryonium states with the quark content ud dc c, spin J = 0/1/2/3, and of both positive and nega

tive parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, which can actually couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion, etc. We do not know which structure these currents couple to at the beginning, but after sum rule analyses we can obtain some information. We nd some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states with quantum numbers J P = 2/3/0+/1+/2+ to be around 5.0 GeV.

We suggest to search for hidden-charm baryonium states, especially the one of J = 3, in the D-wave J/ and

P-wave J/ and J/ channels in this energy region.

1 Introduction

Exploring exotic matter beyond conventional quark model is one of the most intriguing current research topics of hadronic physics. With signicant experimental progress on this issue over the past decade, dozens of charmonium/bottomonium-like XY Z states were reported [1], which are hidden-charm/bottom tetraquark candidates. Besides them, the Pc(4380) and Pc(4450) were observed in the LHCb experiment in 2015 [2], which are hidden-charm pentaquark candidates. They are new blocks of QCD matter, providing impor

a e-mail: mailto:[email protected]

Web End [email protected]

b e-mail: mailto:[email protected]

Web End [email protected]

c e-mail: mailto:[email protected]

Web End [email protected]

tant hints to deepen our understanding of the non-perturbative QCD [35]. Facing their observations, we naturally conjecture that there should exist hidden-charm hexaquark states, and now is the time to hunt for them [6,7].

In this letter we study one kind of hidden-charm hexaquark states, that is the hidden-charm baryonium states consisting of color-singlet heavy baryons and antibaryons. There have been several references on this issue, where the Y (4260), Y (4360), Y (4630), etc. were interpreted as hidden-charm baryonium states [814]. However, these states can also be interpreted as hidden-charm tetraquark states [1,5], so better hidden-charm hexaquark candidates are still waiting to be found.

In this letter we perform an explicit QCD sum rule investigation to hidden-charm baryonium states with the quark content ud dc c, spin J = 0/1/2/3, and of both positive

and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents in Sect. 2. We nd these currents can couple to various structures, including hidden-charm baryonium states [cc qq qq],

charmonium states plus two pions [cc + ], and hidden-

charm tetraquark states plus one pion [cc qq+], etc., which

fact can be helpful to relevant studies, such as lattice QCD. We do not know which structure these currents couple to at the beginning, but we try to perform sum rule analyses using them in Sect. 3 to obtain some information. We nd some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states to be around 5.0 GeV, signicantly larger than the masses of hidden-charm tetraquark states. Accordingly, we suggest to search for hidden-charm baryonium states, especially the one of J = 3, in the D-

wave J/ and P-wave J/ and J/ channels in this energy region. The results are discussed and summarized in

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602 Page 2 of 7 Eur. Phys. J. C (2016) 76 :602

Sect. 4. This paper has a supplementary le OPE.nb containing all the spectral densities.

2 Hidden-charm baryonium currents

To start our study, we rst systematically construct local hidden-charm baryonium interpolating currents with the quark content ud dc c, spin J = 0/1/2/3, and of both posi

tive and negative parities. We use 1j to denote the cur

rent of spin J, and assume it couples to the physical state X j

of spin J through

0|1j |X j = fX 1j , (1) where fX is the decay constant, and 1j is the traceless

and symmetric polarization tensor.

There are two possible color congurations. One has a baryonium structure [ abcuadbcc][ defd de c f ], where

a f are color indices; the other has a three-meson struc

ture, such as [caca][bub][ dcdc], etc. The former congura

tion can be transformed to the latter through the color rearrangement:

abc def = adbecf aebdcf + a f cebd

adbf ce + aebf cd a f cdbe. (2)

We note that the latter cannot be transformed back, suggesting that the three-meson structure is more complicated than the baryonium structure. Equation (2) implies that the hidden-charm baryonium currents can also couple to char-monium states plus two pions, such as c and J/, through

0|1j |[cc + ] = f3M ,where denotes relevant polarization tensors. Moreover,

the hidden-charm baryonium currents may also couple to the XY Z charmonium-like states (taken as hidden-charm tetraquark states) plus one pion through

0|1j |[cc qq + ] = f2M .

We shall nd that both of these two cases are possible.

Besides them, the diquarkanti-diquarkmeson structure is also possible. At the beginning we do not know which structure the current J couples to, but after sum rule analyses we can obtain some information.

To construct local baryonium interpolating currents, we rst systematically construct local heavy baryon elds with the quark content udc. We only investigate the elds of the following type:

[ abc(uTa C idb) j cc], (3)

where i,j are various Dirac matrices. The elds of the other types [ abc(uTa C icb) j dc] and [ abc(dTa C icb) j uc], etc.

can be related to these elds through the Fierz transformation.

The u and d quarks can be either avor symmetric or antisymmetric, and we use the SU(3) avor representations 6F and

3F to denote them, respectively. We can easily construct them based on the results of Ref. [15]:

1. We use B to denote the Dirac baryon elds without free

Lorentz indices. There are three elds of the avor

3F:

1 = abc(uTa Cdb)5cc, 2 = abc(uTa C5db)cc, 3 = abc(uTa C 5db)cc, (4)

and two elds of the avor 6F:

1 = abc(uTa C db)5cc, 2 = abc(uTa Cdb)5cc. (5)

All these elds B have the spin-parity J P = 1/2+, while

5B have 1/2.

2. We use B to denote the baryon elds with one free

Lorentz index. There is one eld of the avor

3F:

4 = abc(uTa C5db)5cc, (6)

and two elds of the avor 6F:

3 = abc(uaT Cdb)cc , 4 = abc(uaT Cdb) cc. (7)

All these elds contain the spin-parity J P = 3/2+ com

ponents, while 5B have 3/2.

3. We use B to denote the baryon elds with two free

antisymmetric Lorentz indices. There is only one eld of the avor 6F:

5 = abc(uaT Cdb)5cc. (8)

This eld also contains the spin J = 3/2 component,

but it contains both positive parity and negative parity

components.

Based on these heavy baryon elds, the local hidden-charm baryonium interpolating currents with the color conguration [ abcuadbcc][ defd de c f ] can be systematically

constructed:

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Eur. Phys. J. C (2016) 76 :602 Page 3 of 7 602

1. We nd altogether 44 baryonium currents of spin J = 0.

Half of these currents have the positive parity:

BB, BB, BB, (9)

and the other half have the negative parity:

B5B, B5B, B5B. (10)

Other currents, such as B B, BB, etc. can be

related to these currents.2. We nd altogether 80 baryonium currents of spin J = 1.

Half of these currents have the positive parity:

B5B, B5B, B5B,

BB, BB, (11)

and the other half have the negative parity:

BB, BB, BB,

B5B, B5B. (12)

Other currents, such as BB, B B, etc. can be

related to these currents.3. We nd altogether 50 baryonium currents of spin J = 2.

Half of these currents have the positive parity:

S2

[bracketleftbig]B1B2[bracketrightbig], S2[bracketleftbig]B1B2[bracketrightbig],

S2

[bracketleftbig]B15B2[bracketrightbig], S2[bracketleftbig]B15B2[bracketrightbig], (13)

where Sj denotes symmetrization in the sets (1 j ).

The other half have the negative parity:

S2

s0s< es/M2

B (s)sds

[integraltext]

[bracketleftbig]B15B2[bracketrightbig], S2[bracketleftbig]B15B2[bracketrightbig],

S2

[bracketleftbig]B1B2[bracketrightbig], S2[bracketleftbig]B1B2[bracketrightbig]. (14)

Other currents, such as S2[bracketleftbig]B B[bracketrightbig], etc. can be related

to these currents.4. We nd altogether 14 baryonium currents of spin J = 3.

Half of these currents have the positive parity:

S3

s0s< es/M2

B (s)ds

[bracketleftbig]B125B3[bracketrightbig], S3[bracketleftbig]B125B3[bracketrightbig], (15)

and the other half have the negative parity:

S3

, (18)

where (s) is the QCD spectral density which we evaluate up to dimension 12, including the perturbative term, the quark condensate qq , the gluon condensate g2sGG , the

quark-gluon mixed condensate gs q Gq , and their combi

nations qq 2, qq gs q Gq , gs q Gq 2 and qq 4. The

full expressions are lengthy and listed in the supplementary le OPE.nb. We use the values listed in Ref. [20] for these condensates and the charm quark mass (see also Refs. [1,21 29]).

There are two free parameters in Eq. (18): the Borel mass MB and the threshold value s0. As the rst step, we x M2B =

4.0 GeV2, and investigate the s0 dependence. We nd that all the currents can be classied into six types, except two currents whose OPE cannot be easily calculated (they are

2 2 and 25 2 of J P = 1 and 1+ respectively):

[bracketleftbig]B125B3[bracketrightbig], S3[bracketleftbig]B12B3[bracketrightbig]. (16)

Other currents, such as S3[bracketleftbig]B12B3[bracketrightbig], etc. can be

related to these currents.

We can also construct some other baryonium currents which contain two free antisymmetric Lorentz indices, such as

BB, BB, BB , etc. However, these currents con

tain both positive parity and negative parity components, which we shall not investigate in the present study for simplicity.

3 QCD sum rule analyses

In the following, we use the method of QCD sum rules [16 19] to investigate these hidden-charm baryonium currents, and try to nd which structure these currents couple to. The two-point correlation function can be written as:

1j,1j (q2)

= i

[integraldisplay] d4xeiqx 0|T [1j (x)1j (0)]|0

= (1)jS j[g11 gjj ] j (q2) + , (17)

where S j denotes symmetrization and subtracting the trace

terms in the sets (1 j ) and (1 j ). Although the cur

rent 1j contains all spin 0 j components, the leading

term j (q2) has been totally symmetrized and only contains the spin j component, while contains other spin compo

nents. Hence, we shall only calculate j (q2) and use it to perform sum rule analyses.

We can calculate the two-point correlation function Eq. (17) in the QCD operator product expansion (OPE) up to certain order in the expansion, which is then matched with a hadronic parametrization to extract information about hadron properties. Following Ref. [19], we obtain the mass of X j to be

M2X(s0, MB) =

[integraltext]

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602 Page 4 of 7 Eur. Phys. J. C (2016) 76 :602

6.0

6.0

6.0

6.0

5.5

5.5

5.5

5.5

5.0

5.0

5.0

5.0

M [GeV]

X

4.5

4.5

4.5

4.5

4.0

4.0

4.0

4.0

3.5

3.5

3.5

3.5

3.0 15 20 25 30

3.0 15 20 25 30

3.0 15 20 25 30

3.0

s [GeV ]

0 2

Fig. 1 Type A [non-structure]: variations of MX with respect to the threshold value s0, when the Borel mass MB is xed to be M2B = 4.0 GeV2.

The currents

15 2 (left),

25 3 (middle), and

5 5 (right) are used as examples

s [GeV ]

0 2

s [GeV ]

0 2

6.0

6.0

6.0

5.5

5.5

5.5

5.0

M [GeV]

X

5.0

5.0

4.5

4.5

4.5

4.0

4.0

4.0

3.5

3.5

3.5

3.0 15 20 25 30

3.0 15 20 25 30

3.0

s [GeV ]

0 2

Fig. 2 Type B [cc+]: variations of MX with respect to the threshold value s0, when the Borel mass MB is xed to be M2B = 4.0 GeV2. The

currents

15 1 (left) and

25 1 (right) are used as examples

A. [Non-structure] Many currents seemingly do not couple to any structure, in other words, these currents seem to well couple to the continuum. Take the current

s [GeV ]

0 2

15 2

of J P = 0 as an example. We use it to perform a QCD

sum rule analysis, and show the obtained mass MX as a function of s0 in the left panel of Fig. 1. We nd that

MX quickly and monotonically increases with s0, suggesting that this current does not couple to any structure. Sometimes the mass curves behave differently, as shown in the middle and right panels of Fig. 1, where the currents

25 3 and

5 5 both of J P = 1 are used

as examples. However, still no structure can be clearly veried.B. [cc + ] Many currents seem to well couple to char-

monium states plus two pions. Take the current

c bound state in Ref. [10].

However, because hidden-charm baryonium states in this region can not be well differentiated from hidden-charm tetraquark states, we shall not pay attention to this case in this paper, but try to nd more signicant hidden-charm baryonium signals. It is just for simplicity that we use [cc qq+] to denote this type.

D. [cc qq qq] Many currents seem to well couple to hidden-

charm baryonium states. Take the current

15 1

of J P = 0 as an example. Its obtained mass MX is

shown as a function of s0 in the left panel of Fig. 2. There is a mass plateau around 3.5 GeV in a wide region of15 GeV2 < s0 < 25 GeV2, suggesting that this current well couple to charmonium states plus two pions. Take the current

25 1 of J P = 0 as another example.

Its obtained mass MX is shown as a function of s0 in the right panel of Fig. 2. MX is around 3.5 GeV in a narrower region of 15 GeV2 < s0 < 20 GeV2, still suggesting that this current couple to charmonium states plus two pions.

C. [cc qq+] Several currents seem to couple to hidden-

charm tetraquark states plus one pion. Take the current

S2

[bracketleftbig]

41 42[bracketrightbig] of J P = 2+ as an example. Its obtained

mass MX is shown as a function of s0 in the left panel of Fig. 3. There is a mass plateau around 4.2 GeV in a very wide region of 16 GeV2 < s0 < 25 GeV2, suggesting that this current well couple to hidden-charm tetraquark states plus one pion.

We note that there may exist hidden-charm baryonium states in this energy region, for example, the Y (4630) was suggested to be a c

3 4 of

J P = 1+ as an example. Its obtained mass MX is shown

as a function of s0 in the right panel of Fig. 3. There is a mass plateau around 4.9 GeV in a wide region of 20 GeV2 < s0 < 30 GeV2. We shall use this type to detailly perform numerical analyses.

123

Eur. Phys. J. C (2016) 76 :602 Page 5 of 7 602

6.0

6.0

6.0

5.5

5.5

5.5

M [GeV]

X

5.0

5.0

5.0

4.5

4.5

4.5

4.0

4.0

4.0

3.5

3.5

3.5

3.0 15 20 25 30

3.0 15 20 25 30

3.0

s [GeV ]

0 2

Fig. 3 Variations of MX with respect to the threshold value s0, when the Borel mass MB is xed to be M2B = 4.0 GeV2. Left Type C [cc qq+],

where the current S2[

41 42] is used as an example; right Type D [cc qq qq], where the current

3 4 is used as an example

s [GeV ]

0 2

6.0

6.0

6.0

5.5

5.5

5.5

5.0

5.0

M [GeV]

X

5.0

4.5

4.5

4.5

4.0

4.0

4.0

3.5

3.5

3.5

3.0 15 20 25 30 35

3.0 15 20 25 30

3.0

s [GeV ]

0 2

Fig. 4 Variations of MX with respect to the threshold value s0, when the Borel mass MB is xed to be M2B = 4.0 GeV2. Left Type E [mixture of

B and D], where the current

45 3 is used as an example; right Type F [mixture of C and D], where the current S3[

412 33] is used as

an example

E. [Mixture of B and D] Many currents seem to couple to both charmonium states plus two pions and hidden-charm baryonium states. Take the current

s [GeV ]

0 2

45 3 of J P = 1+ as an example. Its obtained mass MX is shown

as a function of s0 in the middle panel of Fig. 4. We nd two mass plateaus, one near 3.2 GeV and the other near 5.6 GeV, suggesting that this current may couple to both charmonium states plus two pions and hidden-charm baryonium states. We note that the plateau in the lower-left corner is actually non-physical (the spectral density is negative in this region), but anyway we shall not pay attention to this case in this paper.F. [Mixture of C and D] A few currents seem to couple to both hidden-charm tetraquark states plus one pion and hidden-charm baryonium states. Take the current

S3

[bracketleftbig]

412 33[bracketrightbig] of J P = 3 as an example. Its

obtained mass MX is shown as a function of s0 in the right panel of Fig. 4. Again we nd two mass plateaus (the left plateau is still non-physical), one near 4.5 GeV and the other near 5.0 GeV, suggesting that this current may couple to both hidden-charm tetraquark states plus one pion and hidden-charm baryonium states. We shall

also use this type to perform detailed numerical analyses. It is because of this type that we classied Type C to be hidden-charm tetraquark states plus one pion, i.e., it is less possible that this current couples to two different hidden-charm baryonium states, but it more possible that it couples to two different structures, because it leads to two separated mass plateaus.

We show the numbers of currents belonging to these six types in Table 1, but note that sometimes the currents cannot be well classied, for examples, some currents can be classied to both Type A and Type B (compare the right panel of Fig. 1 and the left panel of Fig. 2). However, we need not solve this problem, because the currents of Type D are probably the best choices to study hidden-charm baryonium states.

Following Ref. [19,30], we use the currents of Type D to perform numerical analyses and evaluate the masses of hidden-charm baryonium states. We list the results in Fig. 5 using blue lines, but leave the detailed analyses for our future studies. We note that the uncertainties of these results are about 0.20 GeV. We nd that all the currents of Type D

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602 Page 6 of 7 Eur. Phys. J. C (2016) 76 :602

Table 1 Classication of hidden-charm baryonium currents. There are altogether six types: Type A [Non-Structure], Type B [cc + ], Type

C [cc qq+], Type D [cc qq qq], Type E [Mixture of B and D], and Type

F [Mixture of C and D]. The numbers of currents belonging to these types are shown below. There are two currents whose OPE cannot be easily calculated. They are

2 2 of J P = 1 and

25 2 of

J P = 1+

J P A B C D E F Total

0 14 8 0 0 0 0 22

1 23 16 0 0 0 0 39

2 10 11 0 1 0 3 25

3 2 3 0 0 0 2 7

0+ 0 0 2 8 12 0 22

1+ 0 2 2 14 21 0 39

2+ 0 3 2 9 11 0 25

3+ 0 2 1 1 3 0 7

6.0

6.0

MassGeV

MassGeV

5.5

5.5

5.0

5.0

4.5

4.5

0

1

2

3

0

1

2

3

Fig. 5 Spectrum

of

hidden-charm

baryonium

states

obtained using the

method of QCD

sum

rules.

The

blue lines

are

obtained

using the currents

of Type F

with the positive parity lead to reasonable sum rules. However, the only current of Type D with the negative parity does not lead to a reasonable sum rule. Hence, we also use the currents of Type F with the negative parity to perform numerical analyses. These currents also lead to reasonable sum rules, whose results are listed in Fig. 5 using red lines.

We nd that the masses of the lowest-lying hidden-charm baryonium states with quantum numbers J P =

2/3/0+/1+/2+ are around 5.0 GeV. Especially, the one of J P = 3 cannot be accessed by the S-wave [cc+] and

[cc qq+] structures, so it is a very good hidden-charm bary

onium candidate for experimental observations. We evaluate its mass to be around 5.04 GeV (see the right panel of Fig. 4), and suggest to search for it in the LHCb and forthcoming BelleII experiments.

4 Summary

To summarize the current letter, we use the method of QCD sum rule to investigate hidden-charm baryonium states with

the quark content ud dc c, spin J = 0/1/2/3, and of both

positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents. We nd they can couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion, etc. At the beginning we do not know which structure these currents couple to, but after sum rule analyses we can obtain some information. We nd some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states with quantum numbers J P = 2/3/0+/1+/2+ to

be around 5.0 GeV. Our results suggest the following.

1. The hidden-charm baryonium currents can probably couple to both charmonium states plus two pions [cc + ]

and hidden-charm baryonium states [cc qq qq], and may

couple to hidden-charm tetraquark states plus one pion [cc qq+]. Actually, the mass signal around 3.5 GeV in

the left panel of Fig. 2 is quite clear, probably related to the c and J/ thresholds.

2. All the currents of Type D with the positive parity and all the currents of Type F with the negative parity lead to reasonable sum rules. The masses of the lowest-lying hidden-charm baryonium states are evaluated to be: 4.83 GeV (J P = 2), 5.04 GeV (J P =

3), 5.00 GeV (J P = 0+), 4.89 GeV (J P = 1+),

5.15 GeV (J P = 2+), and 5.68 GeV (J P = 3+). Accord

ing to their spin-parity quantum numbers and Eq. (2), the hidden-charm baryonium states of J P = 2/3 may

be observed in the D-wave c and J/ channels, and those of J P = 0+/1+/2+ may be observed in the

S-wave J/ and J/ channels. More information on their isospin, etc. will be discussed in our future studies.3. All the currents of J P = 0 and 1 seem not to cou

ple to hidden-charm baryonium states, possibly because these currents can be signicantly affected by the S-wave c and J/ thresholds. However, we do not want to conclude that there do not exist hidden-charm baryonium states of J P = 0 and 1, but note that these states

might not be easily observed if their coupling to c and J/ channels cannot be well constrained.

To end this paper, we note that in the present study we have constructed many interpolating currents, some of which have the same quantum numbers and can mix with each other. Moreover, the physical states are not one-to-one related to these currents, and are probably a mixture of various components coupled by relevant currents. Based on this partial coupling, in this paper we have studied the hidden-charm baryonium states using the method of QCD sum rule, but to study them in a more exact way, one needs to calculate

of Type D, and

the

red lines

are

obtained

using the

currents

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Eur. Phys. J. C (2016) 76 :602 Page 7 of 7 602

both the diagonal elements (the two-point correlation function using the same current) and the off-diagonal elements (the two-point correlation function using two different currents). However, we have only done the former calculations in the present study, because the latter still seem difcult in the current stage and wait to be solved.

Based on the results of this letter, we suggest to search for the hidden-charm baryonium states, especially the one of J = 3, in the D-wave J/ and P-wave J/ and

J/ channels in the energy region around 5.0 GeV, and we hope they can be discovered with the running of LHC at 13 TeV and forthcoming BelleII in the near future. We would also like to see other theoretical studies which can give more accurate predictions on their masses, productions and decay properties, etc.

Acknowledgements This project is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the National Natural Science Foundation of China under Grants No. 11475015, No. 11375024, No. 11222547, No. 11175073, and No. 11575008; the Ministry of Education of China (SRFDP under Grant No. 20120211110002 and the Fundamental Research Funds for the Central Universities); the National Program for Support of Top-notch Youth Professionals.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http://creativecomm http://creativecommons.org/licenses/by/4.0/

Web End =ons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Funded by SCOAP3.

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Web End =arXiv:1602.02433 [hep-ph]

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