Scaling results for charged sectors of near conformal QCD Article Swipe

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Jahmall Bersini , Alessandra D’Alise , Clelia Gambardella , Francesco Sannino ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1103/physrevd.109.125015

We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge Q operators defined at the lower boundary of the quantum chromodynamics conformal window, Δ˜Q=Δ˜Q*+(mσ4πν)2QΔ3B1+(mπ(θ)4πν)4Q23(1−γ)B2+O(mσ4,mπ8,mσ2mπ4). Here, Δ˜Q/r is the classical ground state energy of the theory on R×Sr3 at fixed isospin charge while Δ˜Q* is the scaling dimension at the leading order in the large charge expansion. In the conformal limit mσ=mπ=0, the state-operator correspondence implies Δ˜Q=Δ˜Q*. The near-conformal corrections are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale 4πν with the θ-angle dependence encoded directly in the pion mass. The characteristic Q-scaling is dictated by the quark mass operator anomalous dimension γ and the one characterizing the dilaton potential Δ. The coefficients Bi with i=1,2 depend on the geometry of the cylinder and properties of the nearby conformal field theory. Published by the American Physical Society 2024

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Landing Page: https://doi.org/10.1103/physrevd.109.125015
PDF: http://link.aps.org/pdf/10.1103/PhysRevD.109.125015
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DOI: https://doi.org/10.1103/physrevd.109.125015

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Title: Scaling results for charged sectors of near conformal QCD

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Publication year: 2024

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Authors: Jahmall Bersini, Alessandra D’Alise, Clelia Gambardella, Francesco Sannino

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Landing page: https://doi.org/10.1103/physrevd.109.125015

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referenced_works	https://openalex.org/W2033445325, https://openalex.org/W3045327001, https://openalex.org/W2120964426, https://openalex.org/W2104501509, https://openalex.org/W2998973487, https://openalex.org/W2074526943, https://openalex.org/W2221094875, https://openalex.org/W2162472030, https://openalex.org/W2336899705, https://openalex.org/W2972374927, https://openalex.org/W2029860608, https://openalex.org/W2078604177, https://openalex.org/W2094572932, https://openalex.org/W2121800248, https://openalex.org/W2899340678, https://openalex.org/W1602275375, https://openalex.org/W4387528323, https://openalex.org/W2086860422, https://openalex.org/W2067520844, https://openalex.org/W2107781918, https://openalex.org/W1985762301, https://openalex.org/W1860651947, https://openalex.org/W2076033034, https://openalex.org/W2063850176, https://openalex.org/W3037433786, https://openalex.org/W2072873009, https://openalex.org/W2045094723, https://openalex.org/W2032606288, https://openalex.org/W3012138205, https://openalex.org/W3088170253, https://openalex.org/W2076154021, https://openalex.org/W2152648241, https://openalex.org/W2088532829, https://openalex.org/W2034523121, https://openalex.org/W4255392117, https://openalex.org/W2076362657, https://openalex.org/W1994692129, https://openalex.org/W1998194137, https://openalex.org/W2067241654, https://openalex.org/W2595927293, https://openalex.org/W2531542185, https://openalex.org/W2301645952, https://openalex.org/W2948431268, https://openalex.org/W3008822502, https://openalex.org/W3161672353, https://openalex.org/W4313244561, https://openalex.org/W2795486177, https://openalex.org/W2964623447, https://openalex.org/W3010666640, https://openalex.org/W4382140302, https://openalex.org/W2050858571, https://openalex.org/W4365509574, https://openalex.org/W4396660147, https://openalex.org/W2884206602, https://openalex.org/W2766066354, https://openalex.org/W4391567419, https://openalex.org/W3091418921, https://openalex.org/W4387528347, https://openalex.org/W3081755631, https://openalex.org/W2798760105, https://openalex.org/W2050780933, https://openalex.org/W1918969639, https://openalex.org/W2732125382, https://openalex.org/W2973529003, https://openalex.org/W3196957190, https://openalex.org/W3013168661, https://openalex.org/W4307818878, https://openalex.org/W4315874592, https://openalex.org/W4392040596, https://openalex.org/W2565731919, https://openalex.org/W2971925891, https://openalex.org/W3090609753, https://openalex.org/W2970425191, https://openalex.org/W2965770164, https://openalex.org/W3210261847, https://openalex.org/W4396885226, https://openalex.org/W2001065717, https://openalex.org/W2041226112, https://openalex.org/W2745650081, https://openalex.org/W196925666, https://openalex.org/W1740296105, https://openalex.org/W2084392413, https://openalex.org/W1963727858, https://openalex.org/W4309490789, https://openalex.org/W2047911152, https://openalex.org/W2051249865, https://openalex.org/W2128409174, https://openalex.org/W1995058291, https://openalex.org/W2951290804, https://openalex.org/W2528053079, https://openalex.org/W3133524934, https://openalex.org/W2031778484, https://openalex.org/W1994101208, https://openalex.org/W2035928167, https://openalex.org/W3023899863, https://openalex.org/W3173615659, https://openalex.org/W3106261105, https://openalex.org/W3100205920, https://openalex.org/W3101219360, https://openalex.org/W3123602109, https://openalex.org/W3103871794, https://openalex.org/W3099195819
referenced_works_count	102
abstract_inverted_index.a	8
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abstract_inverted_index.by	164, 210
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abstract_inverted_index.and	131, 174, 201
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abstract_inverted_index.one	176
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abstract_inverted_index.chiral	138
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abstract_inverted_index.encoded	151
abstract_inverted_index.implies	111
abstract_inverted_index.isospin	18, 79
abstract_inverted_index.leading	3, 94
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abstract_inverted_index.quantum	31
abstract_inverted_index.scaling	12, 90
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abstract_inverted_index.<jb:math	105
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abstract_inverted_index.directly	152
abstract_inverted_index.geometry	197
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abstract_inverted_index.anomalous	169
abstract_inverted_index.classical	65
abstract_inverted_index.conformal	5, 33, 103, 206
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abstract_inverted_index.potential	180
abstract_inverted_index.dependence	150
abstract_inverted_index.expansion.	100
abstract_inverted_index.properties	202
abstract_inverted_index.corrections	6, 123
abstract_inverted_index.coefficients	186
abstract_inverted_index.lowest-lying	16
abstract_inverted_index.characteristic	158
abstract_inverted_index.characterizing	177
abstract_inverted_index.chromodynamics	32
abstract_inverted_index.correspondence	110
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abstract_inverted_index.state-operator	109
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abstract_inverted_index.mathvariant="normal">Δ</bc:mi></bc:math>.	184
abstract_inverted_index.mathvariant="script">O</c:mi><c:mrow><c:mo	53
abstract_inverted_index.display="inline"><zb:mi>γ</zb:mi></zb:math>	173
abstract_inverted_index.xmlns:a="http://www.w3.org/1998/Math/MathML"	21
abstract_inverted_index.xmlns:c="http://www.w3.org/1998/Math/MathML"	36
abstract_inverted_index.xmlns:w="http://www.w3.org/1998/Math/MathML"	58
abstract_inverted_index.stretchy="false">(</c:mo><c:mi>θ</c:mi><c:mo	48
abstract_inverted_index.xmlns:bb="http://www.w3.org/1998/Math/MathML"	74
abstract_inverted_index.xmlns:bc="http://www.w3.org/1998/Math/MathML"	182
abstract_inverted_index.xmlns:eb="http://www.w3.org/1998/Math/MathML"	83
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abstract_inverted_index.xmlns:gc="http://www.w3.org/1998/Math/MathML"	192
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abstract_inverted_index.xmlns:zb="http://www.w3.org/1998/Math/MathML"	172
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abstract_inverted_index.display="inline"><w:mrow><w:msub><w:mrow><w:mover	59
abstract_inverted_index.display="inline"><vb:mi>θ</vb:mi></vb:math>-angle	149
abstract_inverted_index.display="inline"><xb:mi>Q</xb:mi></xb:math>-scaling	161
abstract_inverted_index.mathvariant="normal">Δ</c:mi></c:mrow><c:mrow><c:mo	39, 42
abstract_inverted_index.mathvariant="normal">Δ</w:mi></w:mrow><w:mrow><w:mo	61
abstract_inverted_index.display="inline"><lb:mrow><lb:msub><lb:mrow><lb:mover	114
abstract_inverted_index.display="inline"><eb:mrow><eb:msubsup><eb:mrow><eb:mover	84
abstract_inverted_index.mathvariant="normal">Δ</eb:mi></eb:mrow><eb:mrow><eb:mo	86
abstract_inverted_index.mathvariant="normal">Δ</lb:mi></lb:mrow><lb:mrow><lb:mo	116, 119
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abstract_inverted_index.display="inline"><tb:mn>4</tb:mn><tb:mi>π</tb:mi><tb:mi>ν</tb:mi></tb:math>	144
abstract_inverted_index.display="inline"><ec:msub><ec:mi>B</ec:mi><ec:mi>i</ec:mi></ec:msub></ec:math>	189
abstract_inverted_index.stretchy="false">)</c:mo></c:mrow><c:mrow><c:mn>4</c:mn><c:mi>π</c:mi><c:mi>ν</c:mi></c:mrow></c:mfrac><c:mo	49
abstract_inverted_index.display="inline"><gc:mrow><gc:mi>i</gc:mi><gc:mo>=</gc:mo><gc:mn>1</gc:mn><gc:mo>,</gc:mo><gc:mn>2</gc:mn></gc:mrow></gc:math>	193
abstract_inverted_index.stretchy="false">(</c:mo><c:mfrac><c:mrow><c:msub><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>π</c:mi></c:mrow></c:msub><c:mo	47
abstract_inverted_index.stretchy="false">˜</c:mo></c:mrow></c:mover></c:mrow><c:mrow><c:mi>Q</c:mi></c:mrow></c:msub><c:mo>=</c:mo><c:msubsup><c:mrow><c:mover	40
abstract_inverted_index.mathvariant="double-struck">R</bb:mi><bb:mo>×</bb:mo><bb:msubsup><bb:mi>S</bb:mi><bb:mi>r</bb:mi><bb:mn>3</bb:mn></bb:msubsup></bb:math>	76
abstract_inverted_index.stretchy="false">˜</w:mo></w:mrow></w:mover></w:mrow><w:mrow><w:mi>Q</w:mi></w:mrow></w:msub><w:mo>/</w:mo><w:mi>r</w:mi></w:mrow></w:math>	62
abstract_inverted_index.stretchy="false">)</c:mo></c:mrow></c:msup><c:msub><c:mrow><c:mi>B</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msub><c:mo>+</c:mo><c:mi	52
abstract_inverted_index.stretchy="false">)</c:mo></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msup><c:msup><c:mrow><c:mi>Q</c:mi></c:mrow><c:mrow><c:mfrac><c:mrow><c:mi	45
abstract_inverted_index.stretchy="false">˜</lb:mo></lb:mrow></lb:mover></lb:mrow><lb:mrow><lb:mi>Q</lb:mi></lb:mrow></lb:msub><lb:mo>=</lb:mo><lb:msubsup><lb:mrow><lb:mover	117
abstract_inverted_index.stretchy="false">˜</eb:mo></eb:mrow></eb:mover></eb:mrow><eb:mrow><eb:mi>Q</eb:mi></eb:mrow><eb:mrow><eb:mo>*</eb:mo></eb:mrow></eb:msubsup></eb:mrow></eb:math>	87
abstract_inverted_index.stretchy="false">˜</lb:mo></lb:mrow></lb:mover></lb:mrow><lb:mrow><lb:mi>Q</lb:mi></lb:mrow><lb:mrow><lb:mo>*</lb:mo></lb:mrow></lb:msubsup></lb:mrow></lb:math>.	120
abstract_inverted_index.stretchy="false">˜</c:mo></c:mrow></c:mover></c:mrow><c:mrow><c:mi>Q</c:mi></c:mrow><c:mrow><c:mo>*</c:mo></c:mrow></c:msubsup><c:mo>+</c:mo><c:msup><c:mrow><c:mo	43
abstract_inverted_index.display="inline"><jb:msub><jb:mi>m</jb:mi><jb:mi>σ</jb:mi></jb:msub><jb:mo>=</jb:mo><jb:msub><jb:mi>m</jb:mi><jb:mi>π</jb:mi></jb:msub><jb:mo>=</jb:mo><jb:mn>0</jb:mn></jb:math>,	107
abstract_inverted_index.stretchy="false">(</c:mo><c:mfrac><c:mrow><c:msub><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>σ</c:mi></c:mrow></c:msub></c:mrow><c:mrow><c:mn>4</c:mn><c:mi>π</c:mi><c:mi>ν</c:mi></c:mrow></c:mfrac><c:mo	44
abstract_inverted_index.stretchy="false">)</c:mo></c:mrow><c:mrow><c:mn>4</c:mn></c:mrow></c:msup><c:msup><c:mrow><c:mi>Q</c:mi></c:mrow><c:mrow><c:mfrac><c:mrow><c:mn>2</c:mn></c:mrow><c:mrow><c:mn>3</c:mn></c:mrow></c:mfrac><c:mo	50
abstract_inverted_index.mathvariant="normal">Δ</c:mi></c:mrow><c:mrow><c:mn>3</c:mn></c:mrow></c:mfrac></c:mrow></c:msup><c:msub><c:mrow><c:mi>B</c:mi></c:mrow><c:mrow><c:mn>1</c:mn></c:mrow></c:msub><c:mo>+</c:mo><c:msup><c:mrow><c:mo	46
abstract_inverted_index.stretchy="false">(</c:mo><c:msubsup><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>σ</c:mi></c:mrow><c:mrow><c:mn>4</c:mn></c:mrow></c:msubsup><c:mo>,</c:mo><c:msubsup><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>π</c:mi></c:mrow><c:mrow><c:mn>8</c:mn></c:mrow></c:msubsup><c:mo>,</c:mo><c:msubsup><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>σ</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msubsup><c:msubsup><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>π</c:mi></c:mrow><c:mrow><c:mn>4</c:mn></c:mrow></c:msubsup><c:mo	54
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