Anisotropyofthequark-antiquarkpotentialinamagneticgraduate.physics.sunysb.edu/xqcd/posters/mariti-marco.pdf ·...
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Anisotropy of the quark-antiquark potential in a magnetic field C. Bonati¹, M. D’Elia¹, M. Mariti¹ † , M. Mesiti¹, F. Negro¹, F. Sanfilippo² ¹Dipartimento di Fisica dell’Università di Pisa and INFN, Sezione di Pisa, Pisa, Italy ²School of physics and astronomy, University of Southampton, Southampton, United Kindgdom XQCD 2014, Stony Brook, 19 - 21 June 2014 Abstract We study the static quark-antiquark potential in the presence of an external magnetic field, using lattice QCD simulations. The external field breaks the centrality of the potential, which has a different behavior in the directions parallel and perpendicular with respect to the magnetic field. In particular the string tension is larger (smaller) in the perpendicular (parallel) direction. This effect might be relevant for the phenomenology of off-central heavy ion collisions, leading to modifications of the heavy mesons properties, such as the mass spectrum. Phys. Rev. D 89, 114502 (2014) QCD in the presence of strong magnetic fields ◦ Electromagnetic background interacts only with quarks, however loop effects can modify also gluon dynamics. ◦ Magnetic fields at the strong scale (eB ’ m 2 π ) can modify the QCD dynamics, leading to relevant non perturbative effects. ◦ Phenomenological contexts: . Class of neutron stars, the magnetars (eB ’ 10 10 Tesla). ? . Early stage of the Universe (eB ’ 10 16 Tesla). ? . Off-central heavy ion collisions (eB ’ 10 15 Tesla). ? ◦ Useful to probes QCD properties → Help to clarify many open questions in the theory ( chiral and deconfinement transitions, θ -term, etc...). Off-central heavy ion collisions ◦ In off-central collisions strong mag- netic fields are expected to be created: orthogonal to the reaction plane and almost homogeneous. ◦ The nuclei contributions to the mag- netic field can be evaluate in simple models: ? eB ≈ aZα EM e -a 0 ζ f (b, τ ) a, a 0 constants, ζ nucleus rapidity, f (b, τ ) function of the impact parame- ter (b) nucleus proper time (τ ). ◦ RHIC→ Au-Au collisions with √ s = 200 GeV per nucleon pair, expected fields up to eB ’ 0.02 GeV 2 . ? ◦ LHC→ Pb-Pb collisions at center- of-mass energy √ s =4.5 TeV per nucleon pair, can reach fields up to eB ’ 0.3 GeV 2 . ? ◦ Higher √ s gives stronger B fields, b = 12 fm b = 8 fm b = 4 fm τ (fm) eB (MeV 2 ) 3 2.5 2 1.5 1 0.5 0 10 5 10 4 10 3 10 2 10 1 10 0 but shorter life time → Electrical conductivity could play central role to extend fields duration. ? Static q - ¯ q potential ◦ V q ¯ q confining potential: non perturbative property of QCD. For static quarks, well described by the Cornell potential: V (r )= c + α r + σr α Coulomb term,σ String tension ◦ From V (r ) one qualitatively reproduces spectra of heavy quarkonia. ◦ On the lattice, measure V (r ) from Wilson loop, W (R,T ). . Create a q - ¯ q pair at distance R . Propagate it for a time interval T . . Annihilate the pair. hW (R,T )i’ C exp (-TV (R)) ◦ Extract the potential from large time limit: T R τ x i V (ˆ r )= - lim ˆ t→∞ W (ˆ r, ˆ t) W (ˆ r, ˆ t + 1) ◦ Static quark limit: V q ¯ q due only to gauge fields → B fields modify V q ¯ q ? ◦ B field breaks rotational invariance → Measure V q ¯ q separating different directions. ◦ Fix B = B ˆ z . Separate transverse (XY) and longitudinal (Z) directions when calculating Wilson loops → Construct the potential along different directions. Simulation details L a(fm) β 24 0.2173(4) 3.55 32 0.1535(3) 3.67 40 0.1249(3) 3.75 ◦ Lattice QCD simulation, with N f =2+1 flavous, physical quark masses and state of art discretization. ◦ Exploratory study at T =0. ◦ To implement B = B ˆ z : add proper u(1) phases to gauge links: U μ (n) → U μ (n)u μ (n). ◦ Smearing procedure to smooth gauge configurations: . APE-smearing along spatial links. ? . HYP-smearing along tempo- ral links. ? 0 5 10 n t 0.4 0.45 SM=0 XY SM=8 XY SM=24 XY SM=0 Z SM=8 Z SM=24 Z Results ◦ For each B , fit the transverse and longitudi- nal directions using: aV ( r a ; d)=ˆ c d + α d ( r a ) +ˆ σ d r a where d =XY, Z. ◦ Extract the Sommer parameter r 0 using: α d =ˆ r 2 0d ˆ σ d - 1.65 ◦ For each observable O , evaluate the ratios for each direction d: R O d = O d (|e|B ) O (|e|B = 0) ◦ Splitting of these ratios of the order 10 - 20 % ◦ Fit L = 40 data, according to: R O d =1+ A O d (|e|B ) C O d O xy A O xy C O xy χ 2 /dof r 0xy -0.072(2) 0.79(5) 0.59 σ xy 0.29(2) 0.9(1) 1.14 α xy -0.24(3) 0.7(2) 1.53 O z A O z C O z χ 2 /dof r 0z 0.0161(6) 1.9(1) 1.28 σ z -0.34(1) 1.5(1) 0.92 α z 0.24(3) 1.7(4) 0.32 3 4 5 6 7 8 n s 0.3 0.4 0.5 0.6 0.7 0.8 0.9 aV(n s a) eB = 0.0 GeV 2 eB = 0.7 GeV 2 XY eB = 0.7 GeV 2 XYZ eB = 0.7 GeV 2 Z 0 0.2 0.4 0.6 0.8 1 1.2 eB [GeV 2 ] 0.9 1 1.1 1.2 r 0 (B)/r 0 (B=0) L=24 XY L=32 XY L=40 XY L=24 Z L=32 Z L=40 Z 0 0,2 0,4 0,6 0,8 1 1,2 eB [GeV 2 ] 0,6 0,8 1 1,2 1,4 α(B)/α(B=0) L=24 XY L=32 XY L=40 XY L=24 Z L=32 Z L=40 Z 0 0.2 0.4 0.6 0.8 1 1.2 eB [GeV 2 ] 0.6 0.8 1 1.2 1.4 1.6 σ(B)/σ(B=0) L=24 XY L=32 XY L=40 XY L=24 Z L=32 Z L=40 Z Conclusions • External B fields induce relevant anisotropy in the static V q ¯ q , starting from eB ’ 0.2 GeV 2 . • With respect to B orientation, σ increase (decrease) in the transverse (longitudinal) directions, r 0 and α show an opposite behavior. ◦ Investigate V q ¯ q complete angular dependence with respect to B. ◦ Finite temperature case → relevant for off-central heavy ion collisions. ◦ Study of the flux tube profile along different directions. References [1] R. C. Duncan and C. Thompson, Astrophys. J. 392, L9 (1992). [2] T. Vachaspati, Phys. Lett. B 265, 258 (1991). [3] V. Skokov, A. Y. .Illarionov and V. Toneev, Int. J. Mod. Phys. A 24, 5925 (2009) [4] D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A 803, 227 (2008) [5] K. Tuchin, Adv. High Energy Phys. 2013, 490495 (2013). [6] M. Albanese et al. [APE Collaboration], Phys. Lett. B 192 (1987) 163. [7] A. Hasenfratz and F. Knechtli, Phys. Rev. D 64, 034504 (2001) .
Transcript of Anisotropyofthequark-antiquarkpotentialinamagneticgraduate.physics.sunysb.edu/xqcd/posters/mariti-marco.pdf ·...
Anisotropyof thequark-antiquarkpotential inamagneticfield
C. Bonati¹, M. D’Elia¹, M. Mariti¹†, M. Mesiti¹, F. Negro¹, F. Sanfilippo²¹Dipartimento di Fisica dell’Università di Pisa and INFN, Sezione di Pisa, Pisa, Italy
²School of physics and astronomy, University of Southampton, Southampton, United Kindgdom
XQCD 2014, Stony Brook, 19 - 21 June 2014
AbstractWe study the static quark-antiquark potential in the presence of an external magnetic field, using lattice QCD simulations. The external field breaks
the centrality of the potential, which has a different behavior in the directions parallel and perpendicular with respect to the magnetic field. In particularthe string tension is larger (smaller) in the perpendicular (parallel) direction. This effect might be relevant for the phenomenology of off-central heavyion collisions, leading to modifications of the heavy mesons properties, such as the mass spectrum. Phys. Rev. D 89, 114502 (2014)
QCD in the presence of strong magnetic fields◦ Electromagnetic background interacts only with quarks, however loop
effects can modify also gluon dynamics.◦ Magnetic fields at the strong scale (eB ' m2
π) can modify the QCDdynamics, leading to relevant non perturbative effects.
◦ Phenomenological contexts:. Class of neutron stars, the magnetars (eB ' 1010 Tesla).?
. Early stage of the Universe (eB ' 1016 Tesla).?
. Off-central heavy ion collisions (eB ' 1015 Tesla).?
◦ Useful to probes QCD properties→ Help to clarify many open questionsin the theory ( chiral and deconfinement transitions, θ-term, etc...).
Off-central heavy ion collisions◦ In off-central collisions strong mag-
netic fields are expected to be created:orthogonal to the reaction plane andalmost homogeneous.
◦ The nuclei contributions to the mag-netic field can be evaluate in simplemodels:?
eB ≈ aZαEMe−a′ζf(b, τ)
a, a′ constants, ζ nucleus rapidity,f(b, τ) function of the impact parame-ter (b) nucleus proper time (τ).
◦ RHIC→ Au-Au collisions with√s =
200 GeV per nucleon pair, expectedfields up to eB ' 0.02 GeV2.?
◦ LHC→ Pb-Pb collisions at center-of-mass energy
√s = 4.5 TeV per
nucleon pair, can reach fields up toeB ' 0.3 GeV2.?
◦ Higher√s gives stronger B fields,
b = 12 fmb = 8 fmb = 4 fm
τ(fm)
eB(M
eV2)
32.521.510.50
105
104
103
102
101
100
but shorter life time→ Electrical conductivity could play central roleto extend fields duration.?
Static q − q potential◦ Vqq confining potential: non perturbative property of QCD. For static
quarks, well described by the Cornell potential:
V (r) = c+α
r+ σr α Coulomb term, σ String tension
◦ From V (r) one qualitatively reproduces spectra of heavy quarkonia.◦ On the lattice, measure V (r) from Wilson loop, W (R, T ).
. Create a q − q pair at distance R
. Propagate it for a time interval T .
. Annihilate the pair.
〈W (R, T )〉 ' C exp (−TV (R))
◦ Extract the potential from large time limit:
T
R
τ
xi
V (r) = − limt→∞
W (r, t)
W (r, t+ 1)
◦ Static quark limit: Vqq due only to gauge fields → B fields modify Vqq?◦ B field breaks rotational invariance → Measure Vqq separating different
directions.◦ Fix B = Bz. Separate transverse (XY) and longitudinal (Z) directions
when calculating Wilson loops→ Construct the potential along differentdirections.
Simulation detailsL a(fm) β24 0.2173(4) 3.5532 0.1535(3) 3.6740 0.1249(3) 3.75
◦ Lattice QCD simulation, with Nf = 2 + 1flavous, physical quark masses and state ofart discretization.
◦ Exploratory study at T = 0.
◦ To implement B = Bz: addproper u(1) phases to gauge links:Uµ(n)→ Uµ(n)uµ(n).
◦ Smearing procedure to smoothgauge configurations:
. APE-smearing along spatiallinks.?
. HYP-smearing along tempo-ral links.?
0 5 10
n t
0.4
0.45
SM=0 XY
SM=8 XY
SM=24 XY
SM=0 Z
SM=8 Z
SM=24 Z
Results◦ For each B, fit the transverse and longitudi-
nal directions using:aV (
r
a; d) = cd +
αd( ra )
+ σdr
a
where d =XY, Z.◦ Extract the Sommer parameter r0 using:
αd = r20dσd − 1.65
◦ For each observable O, evaluate the ratiosfor each direction d:
ROd =Od(|e|B)
O(|e|B = 0)◦ Splitting of these ratios of the order 10 - 20 %◦ Fit L = 40 data, according to:
ROd = 1 +AOd(|e|B)COd
Oxy AOxy COxy χ2/dofr0xy -0.072(2) 0.79(5) 0.59σxy 0.29(2) 0.9(1) 1.14αxy -0.24(3) 0.7(2) 1.53
Oz AOz COz χ2/dofr0z 0.0161(6) 1.9(1) 1.28σz -0.34(1) 1.5(1) 0.92αz 0.24(3) 1.7(4) 0.32
3 4 5 6 7 8ns
0.3
0.4
0.5
0.6
0.7
0.8
0.9
aV
(nsa
)
eB = 0.0 GeV2
eB = 0.7 GeV2 XY
eB = 0.7 GeV2 XYZ
eB = 0.7 GeV2 Z
0 0.2 0.4 0.6 0.8 1 1.2
eB [GeV2]
0.9
1
1.1
1.2
r 0(B
)/r 0
(B=
0)
L=24 XYL=32 XYL=40 XYL=24 ZL=32 ZL=40 Z
0 0,2 0,4 0,6 0,8 1 1,2
eB [GeV2]
0,6
0,8
1
1,2
1,4
α(B
)/α
(B=
0)
L=24 XYL=32 XYL=40 XYL=24 ZL=32 ZL=40 Z
0 0.2 0.4 0.6 0.8 1 1.2
eB [GeV2
]
0.6
0.8
1
1.2
1.4
1.6
σ(B
)/σ
(B=
0)
L=24 XYL=32 XYL=40 XYL=24 ZL=32 ZL=40 Z
Conclusions• External B fields induce relevant anisotropy in the static Vqq, starting
from eB ' 0.2 GeV2.• With respect to B orientation, σ increase (decrease) in the transverse
(longitudinal) directions, r0 and α show an opposite behavior.◦ Investigate Vqq complete angular dependence with respect to B.◦ Finite temperature case → relevant for off-central heavy ion collisions.◦ Study of the flux tube profile along different directions.
References[1] R. C. Duncan and C. Thompson, Astrophys. J. 392, L9 (1992).[2] T. Vachaspati, Phys. Lett. B 265, 258 (1991).[3] V. Skokov, A. Y. .Illarionov and V. Toneev, Int. J. Mod. Phys. A 24, 5925 (2009)[4] D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A 803, 227 (2008)[5] K. Tuchin, Adv. High Energy Phys. 2013, 490495 (2013).[6] M. Albanese et al. [APE Collaboration], Phys. Lett. B 192 (1987) 163.[7] A. Hasenfratz and F. Knechtli, Phys. Rev. D 64, 034504 (2001) .
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