research article corrections to the jet quenching...

Research Article1198772 Corrections to the Jet Quenching Parameter

Zi-qiang Zhang1 De-fu Hou2 Yan Wu1 and Gang Chen1

1School of Mathematics and Physics China University of Geosciences Wuhan 430074 China2Key Laboratory of Quark and Lepton Physics (MOE) Central China Normal University Wuhan 430079 China

Correspondence should be addressed to Zi-qiang Zhang zhangzqcugeducn

Received 20 November 2015 Revised 25 March 2016 Accepted 11 April 2016

Academic Editor Enrico Lunghi

Copyright copy 2016 Zi-qiang Zhang et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited Thepublication of this article was funded by SCOAP3

A calculation of 1198772 corrections to the jet quenching parameter from AdSCFT correspondence is presented It is shown that thesecorrections will increase or decrease the jet quenching parameter depending on the coefficients of the high curvature terms

1 Introduction

The experiments of ultrarelativistic nucleus-nucleus colli-sions at RHIC and LHC have produced a strongly coupledquark-gluon plasma (sQGP) One of the interesting prop-erties of sQGP is jet quenching phenomenon due to theinteraction with the medium high energy partons traversingthemedium are strongly quenchedThis phenomenon is usu-ally characterized by the jet quenching parameter (or trans-port coefficient) which describes the average transversemomentum square transferred from the traversing partonper unit mean free path [1 2]

AdSCFT duality can explore the strongly coupledN = 4

supersymmetric Yang-Mills (SYM) plasma through the cor-respondence between type IIB superstring theory formulatedon AdS

5times 1198785 and N = 4 SYM in four dimensions [3ndash5]

Therefore some quantities for instance the jet quenchingparameter can be studied

By using the AdSCFT correspondences Liu et al [6]have calculated the jet quenching parameter for 119873 = 4

SYM theory firstly Interestingly the magnitude of SYM turnsout to be closer to the value extracted from RHIC data[7 8] than pQCD result for the typical value of the rsquot Hooftcoupling 120582 ≃ 6120587 of QCDThis proposal has attracted lots ofinterestThus after [6] there are many attempts to addressingjet quenching parameter [9ndash12] However in [6] the jetquenching parameter was studied only in infinite-couplingcase Therefore it is very interesting to investigate the effectof finite-coupling corrections The purpose of the present

work is to study 1198772 corrections to the jet quenching parame-ter

The organization of this paper is as follows In the nextsection the result of jet quenching parameter fromdual gaugetheory is briefly reviewed [6] In Section 3 we consider 1198772corrections to the jet quenching parameter The last part isdevoted to conclusion and discussion

2 from Dual Gauge Theory

The eikonal approximation relates the jet quenching param-eter with the expectation value of an adjoint Wilson loop119882119860[C] with C a rectangular contour of size 119871 times 119871

minus where

the sides with length 119871minusrun along the light-cone and the

limit 119871minus

rarr infin is taken in the end Under the dipoleapproximation which is valid for small transverse separation119871 the jet quenching parameter defined in [1] is extractedfrom the asymptotic expression for 119879119871 ≪ 1

⟨119882119860[C]⟩ asymp exp [minus 1

4radic2

119871minus1198712] (1)

where ⟨119882119860[C]⟩ asymp ⟨119882119865[C]⟩2 with ⟨119882

119865[C]⟩ the thermal

expectation value in the fundamental representationUsing AdSCFT correspondence we can calculate

⟨119882119865[C]⟩ according to

⟨119882119865[C]⟩ asymp exp [minus119878

119868] (2)

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2016 Article ID 9503491 4 pageshttpdxdoiorg10115520169503491

2 Advances in High Energy Physics

where 119878119868is the regulated finite on-shell string worldsheet

action whose boundary corresponds to the null-like rectan-gular loopC

By using such a strategy they find that [6]

SYM =12058732Γ (34)

Γ (54)

radic1205821198793asymp 753radic120582119879

3 (3)

where 119879 is the temperature ofN = 4 SYM plasma

3 1198772 Corrections to SYM

We now consider the 1198772 corrections to SYM Restricting tothe gravity sector in AdS

5 the leading order higher derivative

corrections can be written as [13]

119878 =1

16120587119866119873

int1198895119909radicminus119892 [119877 minus 2Λ

+ 1198972(12057211198772+ 1205722119877120583]119877120583]+ 1205723119877120583]120588120590119877120583]120588120590

)]

(4)

where 120572119894are arbitrary small coefficients and the negative

cosmological constant Λ is related to the AdS space radius 119897by

Λ = minus6

1198972 (5)

The black brane solution of AdS5space with curvature-

squared corrections is given by

1198891199042= minus119891 (119903) 119889119905

2+1199032

11989721198892+

1

119891 (119903)1198891199032 (6)

where

119891 (119903) =1199032

1198972(1 minus

1199034

0

1199034+ 120572 + 120573

1199038

0

1199038) (7)

with

120572 =2

3(101205721+ 21205722+ 1205723)

120573 = 21205723

(8)

where 119903 denotes the radial coordinate of the black branegeometry 119903 = 119903

0is the horizon and 119897 relates the string tension

121205871205721015840 to the rsquot Hooft coupling constant by 11989721205721015840 = radic120582

The temperature of N = 4 SYM plasma with 1198772

corrections is given by

1198791=

1199030

1205871198972(1 +

1

4120572 minus

5

4120573) = 119879(1 +

1

4120572 minus

5

4120573) (9)

In terms of the light-cone coordinate 119909120583 = (119903 119909plusmn 1199092 1199093)

metric (6) becomes

1198891199042= minus[

1199032

1198972+ 119891 (119903)] 119889119909

+119889119909minus+1199032

1198972(1198891199092

2+ 1198891199092

3)

+1

2[1199032

1198972minus 119891 (119903)] [(119889119909

+)2

+ (119889119909minus)2

] +1198891199032

119891 (119903)

(10)

Theworldsheet in the bulk can be parameterized by 120591 and120590 then the Nambu-Goto action for the worldsheet becomes

119878 =1

21205871205721015840int119889120591 119889120590radicdet119892

120572120573 (11)

We set the pair of quarks at 1199092

= plusmn1198712 and choose119909minus= 120591 119909

2= 120590 In this setup we can ignore the effect of

119909minus dependence of the worldsheet implying 119909

3= const 119909+ =

const then the string action is given by

119878 =

radic21199032

0119871minus

212058712057210158401198972int

1198712

0

119889120590radic1 +11990310158402

1198972

1198911199032 (12)

with 1199031015840 = 120597120590119903

The equation of motion for 119903(120590) reads

11990310158402

= 1205742 1199032119891

1198972 (13)

where 120574 is an integration constant From (13) it is clear thatthe turning point occurs at 119891 = 0 implying 1199031015840 = 0 at thehorizon 119903 = 119903

0 Knowing that 119903 = 119903

0at 120590 = 0 then (13) can be

integrated as

119871

2= int

infin

1199030

119897119889119903

120574radic119891119903

=1198972

1205741199030

int

infin

1

119889119905

radic1199054minus 1 + 120572119905

4+ 1205731199054

=1198861198972

1205741199030

(14)

where

119886 = int

infin

1

119889119905

radic1199054minus 1 + 120572119905

4+ 1205731199054

(15)

Then we can find the action for the heavy quark pair

119878 =120587radic120582119871

minus1198711198792

1

2radic2

radic1 +41198862

12058721198792

11198712 (16)

where we have used the relations 1199030= 1205871198972119879 and 11989721205721015840 = radic120582

This action needs to be subtracted by the self-energy ofthe two quarks given by the parallel flat string worldsheetsthat is

1198780=

2119871minus

21205871205721015840int

infin

1199030

119889119903radic119892minusminus119892119903119903 =119886radic120582119871

minus1198791

radic2

(17)

Therefore the net on-shell action is given by

119878119868= 119878 minus 119878

0asymp

1205872

8radic2119886

radic1205821198793

1119871minus1198712 (18)

where we have used 1198791119871 ≪ 1

Note that is related to ⟨119882119860[C]⟩ according to

⟨119882119860[C]⟩ asymp exp [minus 1

4radic2

119871minus1198712] asymp exp [minus2119878

119868] (19)

Advances in High Energy Physics 3

120573 = 0001

120573 = 0003

120573 = 0006

qR2q

SYM

102

103

104

105

0006 0008 00100004120572

(a)

120572 = 0005

120572 = 0001

qR2q

SYM

100

101

102

0006 0008 00100004120573

120572 = minus0001

(b)

Figure 1 (a) 1198772SYM versus 120572 From top to down 120573 = 0001 0003 0006 (b)

1198772SYM versus 120573 From top to down 120572 = 0005 0001 minus0001

Plugging (18) into (19) we end up with jet quenchingparameter under 1198772 corrections

1198772 =

1205872

119886

radic1205821198793

1

=(1 + (14) 120572 minus (54) 120573)

3

1205872

intinfin

1(119889119905radic119905

4minus 1 + 120572119905

4+ 1205731199054)

radic1205821198793

(20)

Wenowdiscuss our result It is clear that the jet quenchingparameter in (3) can be derived from (20) if we neglectthe effect of curvature-squared corrections by plugging 120572 =

120573 = 0 in (20) Furthermore we compare the jet quenchingparameter under 1198772 corrections with its counterpart in thecase of the dual gauge theory as follows

1198772

SYM=Γ (54)radic120587

Γ (34)

(1 + (14) 120572 minus (54) 120573)3

intinfin

1(119889119905radic119905

4minus 1 + 120572119905

4+ 1205731199054)

(21)

Notice that the result of (21) is related to 120572 and 120573 orin other words it is dependent on 120572

119894 However the exact

interval of 120572119894has not been determined we only know that

120572119894sim 12057210158401198972≪ 1 [14] In order to choose the values of 120572 and 120573

properly we employ the Gauss-Bonnet gravity [15] which hasnice properties that are absent for theories with more generalratios of the 120572

119894rsquos The Gauss-Bonnet gravity is defined by the

following action [16]

119878 =1

16120587119866119873

int1198895119909radicminus119892[119877 minus 2Λ

+120582GB2

1198972(1198772minus 4119877120583]119877120583]+ 119877120583]120588120590119877120583]120588120590

)]

(22)

Comparing (4) with (22) we find

1205721=120582GB2

1205722= minus2120582GB

1205723=120582GB2

(23)

Plugging (23) into (8) we have

120572 = 120582GB

120573 = 120582GB(24)

where 120582GB can be constrained by causality and positive-definiteness of the boundary energy density [11]

minus7

36lt 120582GB le

9

100 (25)

Moreover there is an obstacle to the calculation of (21)we must require that the square root in the denominatorbe everywhere positive and the temperature in (9) be alsopositive Under the above conditions we find

minus7

36lt 120572 le

9

100

0 le 120573 le9

100

120572 + 120573 ge 0

(26)

and then we can discuss the results of (21) for different valuesof 120572 and 120573 in such a range

As a concrete example we plot 1198772SYM versus 120572 with

different 120573 and 1198772SYM versus 120573with different 120572 in Figure 1

In (a) from top to down 120573 = 0001 0003 0006 1198772SYM

increases at each 120573 as 120572 increases While in (b) from top to


down 120572 = 0005 0001 minus0001 at each 120572 1198772SYM is a

decreasing function of 120573From the figure it is clear that 1198772 corrections can affect

the jet quenching parameter With some chosen values of 120572and 120573 in this paper the jet quenching parameter can be largerthan or smaller than its counterpart in infinite-coupling case

4 Conclusion and Discussion

In this paper we have investigated 1198772 corrections to the

jet quenching parameter These corrections are related tocurvature-squared corrections in the corresponding gravitydual It is shown that the corrections will increase or decreasethe jet quenching parameter depending on the coefficients ofthe high curvature terms Interestingly under 1198772 correctionsthe drag force is also larger than or smaller than that in theinfinite-coupling case [17] However we should admit that wecannot predict a result forN = 4 SYMbecause the first higherderivative correction in weakly curved type II B backgroundsenters at order 1198774 and not 1198772

Actually there are some other important finite-couplingcorrections to the jet quenching parameter For example thesubleading order corrections to the jet quenching parameter(3) due to worldsheet fluctuations can be found in [10]

1015840

SYM = SYM (1 minus 197120582minus12

) (27)

Other corrections of 119874(1119873119888) and higher orders in 1radic120582

are also discussed in [11 12] However 1120582 corrections on jetquenching parameter are as yet undetermined we hope toreport our progress in this regard in future

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors would like to thank Professor Hai-cang Ren foruseful discussions This research is partly supported by theMinistry of Science and Technology of China (MSTC) underthe ldquo973rdquo Project no 2015CB856904(4) Zi-qiang Zhang issupported by the NSFC under Grant no 11547204 GangChen is supported by the NSFC under Grant no 11475149De-fu Hou is partly supported by NSFC under Grant nos11375070 and 11221504

References

[1] R Baier Y L Dokshitzer A HMueller S Peigne andD SchiffldquoRadiative energy loss and 119901

perp- broadening of high energy

partons in nucleirdquo Nuclear Physics B vol 484 no 1-2 pp 265ndash282 1997

[2] M Gyulassy I Vitev X-N Wang and B-W Zhang ldquoJetquenching and radiative energy loss in dense nuclear matterrdquo inQuark-Gluon Plasma R C Hwa and X-N Wang Eds p 123World Scientific Singapore 2004

[3] J M Maldacena ldquoThe large N limit of superconformal fieldtheories and supergravityrdquo Advances in Theoretical and Math-ematical Physics vol 2 pp 231ndash252 1998 International Journalof Theoretical Physics vol 38 no 4 pp 1113ndash1133 1999

[4] S S Gubser I R Klebanov and A M Polyakov ldquoGauge theorycorrelators from non-critical string theoryrdquo Physics Letters Bvol 428 no 1-2 pp 105ndash114 1998

[5] O Aharony S S Gubser J Maldacena H Ooguri and YOz ldquoLarge 119873 field theories string theory and gravityrdquo PhysicsReports vol 323 no 3-4 pp 183ndash386 2000

[6] H Liu K Rajagopal andU AWiedemann ldquoCalculating the jetquenching parameter from AdSCFTrdquo Physical Review Lettersvol 97 Article ID 182301 2006

[7] K J EskolaHHonkanenCA Salgado andUAWiedemannldquoThe fragility of high-pT hadron spectra as a hard proberdquoNuclear Physics A vol 747 no 2ndash4 pp 511ndash529 2005

[8] A Dainese C Loizides and G Paic ldquoLeading-particle sup-pression in high energy nucleus-nucleus collisionsrdquo EuropeanPhysical Journal C vol 38 no 4 pp 461ndash474 2005

[9] K B Fadafan ldquoCharge effect and finite rsquot Hooft coupling correc-tion on drag force and jet quenching parameterrdquoThe EuropeanPhysical Journal C vol 68 no 3 pp 505ndash511 2010

[10] Z-Q Zhang D-F Hou and H-C Ren ldquoThe finite 1015840t Hooftcoupling correction on the jet quenching parameter in aN = 4

super Yang-Mills plasmardquo Journal of High Energy Physics vol2013 article 32 2013

[11] A Ficnar S S Gubser andMGyulassy ldquoShooting string holog-raphy of jet quenching at RHIC and LHCrdquo Physics Letters B vol738 pp 464ndash471 2014

[12] N Armesto J D Edelstein and JMas ldquoJet quenching at finite lsquotHooft coupling and chemical potential from AdSCFTrdquo Journalof High Energy Physics no 9 p 39 2006

[13] S M Carroll Spacetime and Geometry An Introduction toGeneral Relativity Addison-Wesley San Francisco Calif USA2004

[14] M Brigante H Liu R C Myers S Shenker and S YaidaldquoViscosity bound violation in higher derivative gravityrdquoPhysicalReview D vol 77 no 12 Article ID 126006 2008

[15] R-G Cai ldquoGauss-Bonnet black holes in AdS spacesrdquo PhysicalReview D vol 65 Article ID 084014 2002

[16] B Zwiebach ldquoCurvature squared terms and string theoriesrdquoPhysics Letters B vol 156 no 5-6 pp 315ndash317 1985

[17] K B Fadafan ldquoR 2 curvature-squared corrections on dragforcerdquo Journal of High Energy Physics vol 2008 no 12 article051 2008

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


where 119878119868is the regulated finite on-shell string worldsheet

action whose boundary corresponds to the null-like rectan-gular loopC

By using such a strategy they find that [6]

SYM =12058732Γ (34)

Γ (54)

radic1205821198793asymp 753radic120582119879

3 (3)

where 119879 is the temperature ofN = 4 SYM plasma

3 1198772 Corrections to SYM

We now consider the 1198772 corrections to SYM Restricting tothe gravity sector in AdS

5 the leading order higher derivative

corrections can be written as [13]

119878 =1

16120587119866119873

int1198895119909radicminus119892 [119877 minus 2Λ

+ 1198972(12057211198772+ 1205722119877120583]119877120583]+ 1205723119877120583]120588120590119877120583]120588120590

)]

(4)

where 120572119894are arbitrary small coefficients and the negative

cosmological constant Λ is related to the AdS space radius 119897by

Λ = minus6

1198972 (5)

The black brane solution of AdS5space with curvature-

squared corrections is given by

1198891199042= minus119891 (119903) 119889119905

2+1199032

11989721198892+

1

119891 (119903)1198891199032 (6)

where

119891 (119903) =1199032

1198972(1 minus

1199034

0

1199034+ 120572 + 120573

1199038

0

1199038) (7)

with

120572 =2

3(101205721+ 21205722+ 1205723)

120573 = 21205723

(8)

where 119903 denotes the radial coordinate of the black branegeometry 119903 = 119903

0is the horizon and 119897 relates the string tension

121205871205721015840 to the rsquot Hooft coupling constant by 11989721205721015840 = radic120582

The temperature of N = 4 SYM plasma with 1198772

corrections is given by

1198791=

1199030

1205871198972(1 +

1

4120572 minus

5

4120573) = 119879(1 +

1

4120572 minus

5

4120573) (9)

In terms of the light-cone coordinate 119909120583 = (119903 119909plusmn 1199092 1199093)

metric (6) becomes

1198891199042= minus[

1199032

1198972+ 119891 (119903)] 119889119909

+119889119909minus+1199032

1198972(1198891199092

2+ 1198891199092

3)

+1

2[1199032

1198972minus 119891 (119903)] [(119889119909

+)2

+ (119889119909minus)2

] +1198891199032

119891 (119903)

(10)

Theworldsheet in the bulk can be parameterized by 120591 and120590 then the Nambu-Goto action for the worldsheet becomes

119878 =1

21205871205721015840int119889120591 119889120590radicdet119892

120572120573 (11)

We set the pair of quarks at 1199092

= plusmn1198712 and choose119909minus= 120591 119909

2= 120590 In this setup we can ignore the effect of

119909minus dependence of the worldsheet implying 119909

3= const 119909+ =

const then the string action is given by

119878 =

radic21199032

0119871minus

212058712057210158401198972int

1198712

0

119889120590radic1 +11990310158402

1198972

1198911199032 (12)

with 1199031015840 = 120597120590119903

The equation of motion for 119903(120590) reads

11990310158402

= 1205742 1199032119891

1198972 (13)

where 120574 is an integration constant From (13) it is clear thatthe turning point occurs at 119891 = 0 implying 1199031015840 = 0 at thehorizon 119903 = 119903

0 Knowing that 119903 = 119903

0at 120590 = 0 then (13) can be

integrated as

119871

2= int

infin

1199030

119897119889119903

120574radic119891119903

=1198972

1205741199030

int

infin

1

119889119905

radic1199054minus 1 + 120572119905

4+ 1205731199054

=1198861198972

1205741199030

(14)

where

119886 = int

infin

1

119889119905

radic1199054minus 1 + 120572119905

4+ 1205731199054

(15)

Then we can find the action for the heavy quark pair

119878 =120587radic120582119871

minus1198711198792

1

2radic2

radic1 +41198862

12058721198792

11198712 (16)

where we have used the relations 1199030= 1205871198972119879 and 11989721205721015840 = radic120582

This action needs to be subtracted by the self-energy ofthe two quarks given by the parallel flat string worldsheetsthat is

1198780=

2119871minus

21205871205721015840int

infin

1199030

119889119903radic119892minusminus119892119903119903 =119886radic120582119871

minus1198791

radic2

(17)

Therefore the net on-shell action is given by

119878119868= 119878 minus 119878

0asymp

1205872

8radic2119886

radic1205821198793

1119871minus1198712 (18)

where we have used 1198791119871 ≪ 1

Note that is related to ⟨119882119860[C]⟩ according to

⟨119882119860[C]⟩ asymp exp [minus 1

4radic2

119871minus1198712] asymp exp [minus2119878

119868] (19)


120573 = 0001

120573 = 0003

120573 = 0006

qR2q

SYM

102

103

104

105

0006 0008 00100004120572

(a)

120572 = 0005

120572 = 0001

qR2q

SYM

100

101

102

0006 0008 00100004120573

120572 = minus0001

(b)




1198772 =

1205872

119886

radic1205821198793

1

=(1 + (14) 120572 minus (54) 120573)

3

1205872

intinfin

1(119889119905radic119905

4minus 1 + 120572119905

4+ 1205731199054)

radic1205821198793

(20)



1198772


Γ (34)

(1 + (14) 120572 minus (54) 120573)3

intinfin

1(119889119905radic119905

4minus 1 + 120572119905

4+ 1205731199054)

(21)








119878 =1

16120587119866119873


+120582GB2

1198972(1198772minus 4119877120583]119877120583]+ 119877120583]120588120590119877120583]120588120590

)]

(22)


1205721=120582GB2

1205722= minus2120582GB

1205723=120582GB2

(23)


120572 = 120582GB

120573 = 120582GB(24)


minus7

36lt 120582GB le

9

100 (25)


minus7

36lt 120572 le

9

100

0 le 120573 le9

100

120572 + 120573 ge 0

(26)














1015840


) (27)



Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




120573 = 0001

120573 = 0003

120573 = 0006

qR2q

SYM

102

103

104

105

0006 0008 00100004120572

(a)

120572 = 0005

120572 = 0001

qR2q

SYM

100

101

102

0006 0008 00100004120573

120572 = minus0001

(b)




1198772 =

1205872

119886

radic1205821198793

1

=(1 + (14) 120572 minus (54) 120573)

3

1205872

intinfin

1(119889119905radic119905

4minus 1 + 120572119905

4+ 1205731199054)

radic1205821198793

(20)



1198772


Γ (34)

(1 + (14) 120572 minus (54) 120573)3

intinfin

1(119889119905radic119905

4minus 1 + 120572119905

4+ 1205731199054)

(21)








119878 =1

16120587119866119873


+120582GB2

1198972(1198772minus 4119877120583]119877120583]+ 119877120583]120588120590119877120583]120588120590

)]

(22)


1205721=120582GB2

1205722= minus2120582GB

1205723=120582GB2

(23)


120572 = 120582GB

120573 = 120582GB(24)


minus7

36lt 120582GB le

9

100 (25)


minus7

36lt 120572 le

9

100

0 le 120573 le9

100

120572 + 120573 ge 0

(26)














1015840


) (27)



Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics











1015840


) (27)



Competing Interests


Acknowledgments


References


























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



research article corrections to the jet quenching...

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