Present status of the pion-nucleon sigma term
(and strange content of nucleon)
2018/11/12 QNP 2018 satellite workshop
J-PARC
Nodoka Yamanaka(IPN Orsay)
Introduction
Applications:
Fundamental property of QCD:
Definition:
�⇡N ⌘ mu +md
2hN |uu+ dd|Ni
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�s ⌘ mshN |ss|Ni<latexit sha1_base64="VNKntUmvoRVeeWFx9yDFNhEaW04=">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</latexit><latexit sha1_base64="VNKntUmvoRVeeWFx9yDFNhEaW04=">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</latexit><latexit sha1_base64="VNKntUmvoRVeeWFx9yDFNhEaW04=">AAACmXichVFNSxtBGH5cbbVrW1O9CLkshhRPMhGhpSdrL9KDxKQxgayE2e0YB2c/3NkN2Ng/4B8otCcLpYh/QvCi3nvITxCPCl566LubhdKK7TvMzDPPvM87z8w4oZI6ZmwwYoyOPXg4PvHInHz85OlU4dn0hg6SyBUNN1BB1HK4Fkr6ohHLWIlWGAnuOUo0nZ036X6zJyItA/9dvBeKTY93fbklXR4T1Sks2Vp2Pd7RlmmL3UT2TI+wrbjfVcJas/Yt2+GRpTWhNcuOMr5TKLEFloV1F1RyUEIe1aDwHTbeI4CLBB4EfMSEFTg0tTYqYAiJ20SfuIiQzPYFPsIkbUJZgjI4sTs0dmnVzlmf1mlNnaldOkVRj0hpocx+sCN2zc7YMbtkP++t1c9qpF72aHaGWhF2pg5m67f/VXk0x9j+rfqn5xhbeJl5leQ9zJj0Fu5Q3/vw6br+qlbuP2df2RX5P2QDdko38Hs37rd1UfsCkz6g8vdz3wUbiwsVwutLpeWV/CsmUMQc5um9X2AZq6iiQed+xgnOcWEUjdfGqvF2mGqM5JoZ/BFG/ReFdJyX</latexit><latexit sha1_base64="VNKntUmvoRVeeWFx9yDFNhEaW04=">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</latexit>
Pion-nucleon sigma term Strange content of nucleon
Current quark mass contribution to the nucleon mass (trace anomaly relation)
Quark scalar matrix element :
Gives the variation of chiral condensate in low density nuclear matter
Useful input in BSM search (especially in dark matter direct detection)
Important input in the baryon chiral perturbation theory
⇒ Shift from 3 is contribution from relativistic quarks inside nucleon
⇒ Probe of quark-gluon interaction and confinement in nucleons
mN =�QCD
2gshN |Gµ⌫
a Gµ⌫,a|Ni+X
q
mq hN |qq|Ni<latexit sha1_base64="vJh5uUuG3z5p026Z8RAOeXR+VSA=">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</latexit><latexit sha1_base64="vJh5uUuG3z5p026Z8RAOeXR+VSA=">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</latexit><latexit sha1_base64="vJh5uUuG3z5p026Z8RAOeXR+VSA=">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</latexit><latexit sha1_base64="vJh5uUuG3z5p026Z8RAOeXR+VSA=">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</latexit>
hN |qq|Ni<latexit sha1_base64="g4m/Nj7ymfEBngChEpd9WJj0y38=">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</latexit><latexit sha1_base64="g4m/Nj7ymfEBngChEpd9WJj0y38=">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</latexit><latexit sha1_base64="g4m/Nj7ymfEBngChEpd9WJj0y38=">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</latexit><latexit sha1_base64="g4m/Nj7ymfEBngChEpd9WJj0y38=">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</latexit>
How to calculate?
Lattice QCD:
Chiral perturbation theory (ChPT) based extractions:Start from Cheng-Dashen (CD) low energy theorem (LET), relate σπN and πN scattering by using analyticity
Fit σπN by calculating πN scattering phase shift in ChPT
M. Hoferichter et al., Phys. Rev. Lett. 115, 092301 (2015) J. Ruiz de Elvira et al., J. Phys. G 45, 024001 (2017)
J. M. Alarcon et al., , Phys. Rev. D 85, 051503(R) (2012)
Direct calculation of the nucleon 3-point correlator
Derivative of the nucleon mass (Feynman-Hellmann theorem)
Perturbative QCD and fit from experimental data :
Other model approaches:
Integrate twist-3 parton distribution function eq(x) (uncertainty is large)
QCD sum rules, Dyson-Schwinger, etc.
P. Gubler and K. Ohtani, Phys. Rev. D 90, 094002 (2014)
RQCD, chiQCD, ETMC, JLQCD, …
BMW, Lutz et al., Ling et al., …
Present status of the calculations of πN sigma term
JLQCD(2018)ETM(2016)
chiQCD(2016)RQCD(2016)
Ling et al.(2017)BMW(2016)
Lutz et al.(2014)QCDSF-UKQCD(2012)
Ruiz de Elvira et al.(2017)Yao et al.(2016)
Hoferichter et al.(2015)Alarcon et al.(2012)
0 10 20 30 40 50 60 70σπN (MeV)
⇒ Visible disagreement between lattice QCD results
and phenomenological extractions
Phenomenological extractions based on ChPT
Application of Feynman-Hellmann theorem to lattice
Direct lattice QCD calculations
Phenomenological extractions : σπN ~ 60 MeV
Lattice QCD calculations : σπN ~ 30 MeV
Present status of the calculations of strange content
Phenomenological extractions based on ChPT
Application of Feynman-Hellmann theorem to lattice
Direct lattice QCD calculations
Other approaches have large uncertainties
Lattice QCD calculations : σs ~ 40 MeV
JLQCD(2018)ETM(2016)
chiQCD(2016)RQCD(2016)BMW(2016)
Lutz et al.(2014)Ren et al.(2014)
QCDSF-UKQCD(2012)Yao et al.(Fit-B)(2016)
Alarcon et al.(2014)
0 50 100 150 200σs (MeV)
Scope of this talk
In this talk, I will review the two approaches,
and let the audience consider it in the hope to resolve it one day
The ChPT based phenomenological and lattice QCD predictions of the pion-nucleon sigma term differ significantly
⇒ A puzzle in QCD which has not yet convincing answer
Unfortunately, this is one of the argument used by one community (either ChPT or lattice) to claim that the other approach does not work
(´∀`;)
Chiral perturbation based approaches
7
Chiral perturbation based approaches
Extraction from πN scattering experimental data (Cheng-Dashen low-energy theorem approach)
Full calculation in chiral perturbation theory
Principle of σπN extraction from Cheng-Dashen LET
Low-energy theorem (LET):
Why subtract Born amplitude?
Consider the πN scattering : ⇡a(q) +N(p) ! ⇡b(q0) +N(p0)<latexit sha1_base64="1TTv/bUCK6Dei+zURsAMspi0m0s=">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</latexit><latexit sha1_base64="1TTv/bUCK6Dei+zURsAMspi0m0s=">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</latexit><latexit sha1_base64="1TTv/bUCK6Dei+zURsAMspi0m0s=">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</latexit><latexit sha1_base64="1TTv/bUCK6Dei+zURsAMspi0m0s=">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</latexit>
Isoscalar, momentum-symmetric πN amplitudeD+ :
ΔR : Higher order SU(2) ChPT correction to D+
⇒ Remove the massless QCD contribution hN(p0)|LQCD(mud = 0)|N(p)i<latexit sha1_base64="A0FgwUxwzBDP1Hh9OVV82HmXne0=">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</latexit><latexit sha1_base64="A0FgwUxwzBDP1Hh9OVV82HmXne0=">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</latexit><latexit sha1_base64="A0FgwUxwzBDP1Hh9OVV82HmXne0=">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</latexit><latexit sha1_base64="A0FgwUxwzBDP1Hh9OVV82HmXne0=">AAACoXichVHLShxBFD228ZHR6EQ3QjZFBnXcyJ0gJAQFiS4MBJkZMypMS9PdlpPG6gfdPQPamR/wB7JwpRBCyGe4cWvAhZ8gLhXcZOGdngZRSXKbrjp17j23TlVZgXKimOiiR+t91tc/MPg8NzT8YmQ0/3JsPfKboS1rtq/8cNMyI6kcT9ZiJ1ZyMwil6VpKbli7S538RkuGkeN7n+O9QG65ZsNzdhzbjJky8vO6Mr2GkmK1GEzPiK+JbptKfGobiR66orK03BZF10ia2+0F4rRYFcVgRuhhKjLyBZqlNMRTUMpAAVmU/fwP6NiGDxtNuJDwEDNWMBHxV0cJhIC5LSTMhYycNC/RRo61Ta6SXGEyu8tjg1f1jPV43ekZpWqbd1H8h6wUmKRz+knXdEq/6JL+/LVXkvboeNnj2epqZWCMHkys3f5X5fIc48u96p+eY+zgXerVYe9BynROYXf1rf1v12vvq5PJFB3TFfs/ogs64RN4rRv7e0VWD5HjByg9vu6nYP3NbIlxZa6w+CF7ikG8wmsU+b7fYhErKKPG+x7jFGf4rRW0j1pZq3ZLtZ5MM44HodXvAJA8npY=</latexit>
+
Estimated to be small, O(�⇡Nm2⇡/m
2N )
<latexit sha1_base64="fl/I60phShnGW4a+eRErj2V2xnQ=">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</latexit><latexit sha1_base64="fl/I60phShnGW4a+eRErj2V2xnQ=">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</latexit><latexit sha1_base64="fl/I60phShnGW4a+eRErj2V2xnQ=">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</latexit><latexit sha1_base64="fl/I60phShnGW4a+eRErj2V2xnQ=">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</latexit>
V. Bernard et al., Phys. Lett. B 389, 144 (1996)
Important point :πN sigma term is �(t = 0)
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�(t = 2m2⇡)
<latexit sha1_base64="FsoEuEuG7VsVpjYRc1b/wRE9XJ4=">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</latexit><latexit sha1_base64="FsoEuEuG7VsVpjYRc1b/wRE9XJ4=">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</latexit><latexit sha1_base64="FsoEuEuG7VsVpjYRc1b/wRE9XJ4=">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</latexit><latexit sha1_base64="FsoEuEuG7VsVpjYRc1b/wRE9XJ4=">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</latexit>
, not !!
corresponds to an off-shell, unphysical point!
We must extrapolate the amplitude to t = 0 !
f2⇡D
+(⌫ = 0, t = 2m2⇡)� (Born term)��R = �(t = 2m2
⇡)<latexit sha1_base64="x/rcqOXG/O2RKDU1Vf8Nwf/8Pw0=">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</latexit><latexit sha1_base64="x/rcqOXG/O2RKDU1Vf8Nwf/8Pw0=">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</latexit><latexit sha1_base64="x/rcqOXG/O2RKDU1Vf8Nwf/8Pw0=">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</latexit><latexit sha1_base64="x/rcqOXG/O2RKDU1Vf8Nwf/8Pw0=">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</latexit>
D+(⌫ = 0, t = 0)<latexit sha1_base64="5MyONN2W7OzhSguG9DnftBs9F1Y=">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</latexit><latexit sha1_base64="5MyONN2W7OzhSguG9DnftBs9F1Y=">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</latexit><latexit sha1_base64="5MyONN2W7OzhSguG9DnftBs9F1Y=">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</latexit><latexit sha1_base64="5MyONN2W7OzhSguG9DnftBs9F1Y=">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</latexit>
T. P. Cheng and R. F. Dashen, Phys. Rev. Lett. 26, 594 (1971)
⌫ ⌘ s� u
4mN<latexit sha1_base64="Rh+yt7FFAUF6eqUKZChZEK573Hc=">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</latexit><latexit sha1_base64="Rh+yt7FFAUF6eqUKZChZEK573Hc=">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</latexit><latexit sha1_base64="Rh+yt7FFAUF6eqUKZChZEK573Hc=">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</latexit><latexit sha1_base64="Rh+yt7FFAUF6eqUKZChZEK573Hc=">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</latexit>
�(t) ⌘ hN(p0)|mud(uu+ dd)|N(p)i<latexit sha1_base64="4giqWi2axAE05fEnZuXvd322Ox8=">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</latexit><latexit sha1_base64="4giqWi2axAE05fEnZuXvd322Ox8=">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</latexit><latexit sha1_base64="4giqWi2axAE05fEnZuXvd322Ox8=">AAACtHichVHLThRBFD20KNigDLghYVNxAvbEhNQYIsQVgQ0r5OEACU0m1T3FWKH6YXf1JDjwA/6AC1eYGGJY8wVs/AEXxK0uDEtI2Ljwdk8nRol6K9116tx7bp2q8mKtUsP5eZ91q//2nYHBu/bQ8L37I5XRsY00yhJfNvxIR8mWJ1KpVSgbRhktt+JEisDTctPbW8zzmx2ZpCoKX5j9WO4Eoh2qXeULQ1Sz8txNVTsQzDE125WvMtVhtqtF2NaSLTvxoxo7YEGzm7UOmeN6ImEZjcesgC3WytPLzIlrzE0KUbNS5dO8CHYT1EtQRRkrUeUYLlqI4CNDAIkQhrCGQEpjG3VwxMTtoEtcQkgVeYlD2KTNqEpShSB2j/5tWm2XbEjrvGdaqH3aRdOXkJJhkn/mH/kl/8RP+Hf+46+9ukWP3Ms+zV5PK+PmyJvx9ev/qgKaDV7+Uv3Ts8Eu5gqvirzHBZOfwu/pO6/fXq4/W5vsTvH3/IL8H/FzfkYnCDtX/odVufYONj1A/c/rvgk2nkzXCa/OVOcXyqcYxAQewqH7nsU8lrCCBu17ii/4im/WU8u1fEv2Sq2+UvMAv4UV/gTy1qRY</latexit><latexit sha1_base64="4giqWi2axAE05fEnZuXvd322Ox8=">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</latexit>
Roy-Steiner equation
J. Gasser et al., PLB 253, 252 (1991); M. Hoferichter et al., Phys. Rep. 625, 1 (2016).
We can analytically extrapolate σπN to off-shell region
We consider a system of “subtracted“ dispersion relations (DRs)with channel couplings : πN→πN, ππ→KK, ππ→NN,…
+ …
DRs respects analyticity, unitarity, crossing symmetry,
(e.g. use scattering length for s-wave D+ at t=0)
⇒ To make converge the integral (get rid of the contour),
we set additional polynomial in the denominator (“subtraction”)
⇒ Due to Cauchy’s theorem, additional terms (c(t)) appear
⇒ If we can identify them with known quantities,
we can constrain the analytic form of D+
⇒ The analytic continuation has limits, but the error is quantifiable
by partial wave decomposition, changing subtraction, considering resonances, etc
DD
D
Overall : result of CD LET approach
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Synopsis of the pion-nucleon sigma term:
�D ⌘ D+(0, 2m2⇡)� ⌃d
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�� ⌘ �(2m2⇡)� �⇡N
<latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit><latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit><latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit><latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit>
�R<latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit><latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit><latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit><latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit>
J. Gasser et al., PLB 253, 260 (1991)
Can be determined from DR analysis as well
Determined by DR analysis (Roy-Steiner eq.)
< 2 MeVV. Bernard et al., Phys. Lett. B 389, 144 (1996)
�D ��� = (�1.8± 0.2)MeV<latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit><latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit><latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit><latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit>
(Uncertainty of ChPT)
Small due to the cancellation (both are ~15 MeV):
⌃d ⌘ f2⇡(d
+00 + 2m2
⇡d+01)
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D+(⌫, t) =1X
n,m=0
d+mn⌫2mtn
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Lowest terms the Taylor and partial wave expansion
Determined from Roy-Steiner analysis
Overall : result of CD LET approach
�⇡N ⌘ �(0) = ⌃d +�D ��� ��R<latexit sha1_base64="Q3hCWEtrEh6dNCWP3LhcJtu35MI=">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</latexit><latexit sha1_base64="Q3hCWEtrEh6dNCWP3LhcJtu35MI=">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</latexit><latexit sha1_base64="Q3hCWEtrEh6dNCWP3LhcJtu35MI=">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</latexit><latexit sha1_base64="Q3hCWEtrEh6dNCWP3LhcJtu35MI=">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</latexit>
Synopsis of the pion-nucleon sigma term:
�D ⌘ D+(0, 2m2⇡)� ⌃d
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�� ⌘ �(2m2⇡)� �⇡N
<latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit><latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit><latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">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</latexit><latexit sha1_base64="95hFbqBMyOD8sbtsFDvMdEyI9yE=">AAACm3ichVFNSxtBGH6ytWrXj6TtpVCEYLDowTAJpS09BeNBRMSvqODqsrtO4uB+dXcSiCF/wD/gQS8VRMR/oRfBXnvITyg9KvTSg292F0oV9V125nmfeZ93npkxfVuEkrFOSnnR87K3r/+VOjA4NJzOvH6zGnr1wOIVy7O9YN00Qm4Ll1ekkDZf9wNuOKbN18zdcnd9rcGDUHjuimz6fNMxaq6oCsuQROmZT9o0t6Wha6GoOYaq8W910VDjLDtedHTNF1vFCXUypvQW5dn5tp7JsTyLIvsQFBKQQxILXuYUGrbhwUIdDjhcSMI2DIT0baAABp+4TbSICwiJaJ2jDZW0dariVGEQu0tjjbKNhHUp7/YMI7VFu9j0B6TMYoz9ZGfshl2xc/aL/X20Vyvq0fXSpNmMtdzX0/vvlv88q3Joltj5p3rSs0QVXyKvgrz7EdM9hRXrG3sHN8tfl8ZaH9gx+03+v7MOu6QTuI1b62SRLx1CpQco3L/uh2C1mC8QXvyYK00lT9GP9xjFON33Z5QwgwVUaN8jXOAaP5QRpazMKnNxqZJKNG/xXyiVOwi0na8=</latexit>
�R<latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">AAACa3ichVG7SgNBFD1Z3/GRaBpRi2CIWMlEBMVK1MIyicYEVMLuOuqQye6yOwnE4A9Y2ljERkFE/Awbf8DCTxCxUrCx8O5mQVTUu8zOmTP33Dlzx3Ck8BRjDxGto7Oru6e3L9o/MDgUiw+PbHp2zTV5wbSl7ZYM3eNSWLyghJK85LhcrxqSF43Kir9frHPXE7a1oRoO36nq+5bYE6auiCptr3Kp9HK+HE+xGRZE8ifIhCCFMLJ2/Arb2IUNEzVUwWFBEZbQ4dG3hQwYHOJ20CTOJSSCfY4jRElboyxOGTqxFfrv02orZC1a+zW9QG3SKZKGS8ok0uyeXbMXdsdu2CN7/7VWM6jhe2nQbLS13CnHjkfX3/5VVWlWOPhU/elZYQ8LgVdB3p2A8W9htvX1w9OX9cV8ujnFLtgT+T9nD+yWbmDVX83LHM+3EKUHyHxv90+wOTuTIZybSy0th0/Ri3FMYpr6PY8lrCGLQtDnE7RwFnnWEtqYNtFO1SKhJoEvoaU/AATDjL0=</latexit><latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit><latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit><latexit sha1_base64="SAClqlvM56EUwXvs40EW30bjoEE=">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</latexit>
J. Gasser et al., PLB 253, 260 (1991)
Can be determined from DR analysis as well
Determined by DR analysis (Roy-Steiner eq.)
< 2 MeVV. Bernard et al., Phys. Lett. B 389, 144 (1996)
�D ��� = (�1.8± 0.2)MeV<latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit><latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit><latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit><latexit sha1_base64="R5bAYP7cdSxKBQJ7rP1Dxb69SDE=">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</latexit>
(Uncertainty of ChPT)
Small due to the cancellation (both are ~15 MeV):
⌃d ⌘ f2⇡(d
+00 + 2m2
⇡d+01)
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D+(⌫, t) =1X
n,m=0
d+mn⌫2mtn
<latexit sha1_base64="ufQwWB76LzNjdbDwcc3POPoW2/s=">AAACpXichVFNa9RAGH4atdZU21UvBS/BpbZiKe8WQREKS/XgRejXbgtNNyTpbDs0mYRksrCG/AH/gAdPCiriz/DSQ68V+hPEYwtePPhuNiC2tL7DzDzzzPu888yMFwcy1UTHI8aVq9dGr4/dMMdv3pqYrN2+006jLPFFy4+CKNn03FQEUomWljoQm3Ei3NALxIa3/3ywv9ETSSojta77sdgO3V0lu9J3NVNOrWl7bmK96DyyZi1bZXP6oblo2mkWOrmaC61FKjq5LVVX9wtrx8lDVXAqJ3byhbCwdIdL1GmeyrDOg0YF6qhiOap9ho0dRPCRIYSAgmYcwEXKbQsNEGLmtpEzlzCS5b5AAZO1GWcJznCZ3edxl1dbFat4PaiZlmqfTwm4J6y0ME1H9IVO6IC+0g/6fWGtvKwx8NLn2RtqRexMvpla+/VfVcizxt5f1aWeNbp4WnqV7D0umcEt/KG+9/rtydqz1en8AX2gn+z/PR3TN76B6p36H1fE6juY/AGNs899HrQX5huMVx7Xm0vVV4zhHu5jlt/7CZp4iWW0+NxPOMQRvhszxitj3WgPU42RSnMX/4Th/AGGm6DS</latexit><latexit sha1_base64="ufQwWB76LzNjdbDwcc3POPoW2/s=">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</latexit><latexit sha1_base64="ufQwWB76LzNjdbDwcc3POPoW2/s=">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</latexit><latexit sha1_base64="ufQwWB76LzNjdbDwcc3POPoW2/s=">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</latexit>
Lowest terms the Taylor and partial wave expansion
Determined from Roy-Steiner analysis
Total : �⇡N = (59.1± 3.5)MeV<latexit sha1_base64="Z2Slbx8OJQDMeOGzQk5wzvT+eZw=">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</latexit><latexit sha1_base64="Z2Slbx8OJQDMeOGzQk5wzvT+eZw=">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</latexit><latexit sha1_base64="Z2Slbx8OJQDMeOGzQk5wzvT+eZw=">AAACkXichVFNSxtBGH5cW41rq1EvBS+LQYkQwmyraIRC0EuhKBqbD3BD2N2O6eB+sbsJ2CV/oEcvHjwpSCn9A15bL/4BD/4E8RjBSw++2SyIStt3mJlnnnmfd56ZMTxLBCFjVwPS4IuXQ8OpEXn01eux8fTEZCVwW77Jy6ZruX7N0ANuCYeXQxFavOb5XLcNi1eNvbXefrXN/UC4zqdw3+N1W286YleYekhUI53TAtG09UakeULZ6Mjv5exiIa8qmmcr7/KL84qWUyLNt5V1Xuk00hmWZ3Eoz4GagAyS2HTT36HhM1yYaMEGh4OQsAUdAbUdqGDwiKsjIs4nJOJ9jg5k0rYoi1OGTuwejU1a7SSsQ+tezSBWm3SKRd0npYJZdsl+sC67YD/ZNfvz11pRXKPnZZ9mo6/lXmP825vtu/+qbJpDfHlQ/dNziF0sx14FefdipncLs69vfz3sbq+UZqM5dsJuyP8xu2LndAOnfWuebvHSEWT6APXpcz8Hlbd5lfDWQqa4mnxFCtOYQZbeewlFfMAmynTuAc7wC7+lKakgFaUkVxpINFN4FNLHe+yzl2g=</latexit><latexit sha1_base64="Z2Slbx8OJQDMeOGzQk5wzvT+eZw=">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</latexit>
M. Hoferichter et al., PRL 115, 092301 (2015).
Full calculation in chiral perturbation theory
J. M. Alarcon et al., Phys. Rev. D 85, 051503 (2012)
-14-12-10
-8-6-4-2 0
1.08 1.1 1.12 1.14 1.16 1.18 1.2 2 3 4 5 6 7 8 9
10 11
1.08 1.1 1.12 1.14 1.16 1.18 1.2
-4-3.5
-3-2.5
-2-1.5
-1-0.5
0 0.5
1.08 1.1 1.12 1.14 1.16 1.18 1.2-1.2
-1-0.8-0.6-0.4-0.2
0 0.2
1.08 1.1 1.12 1.14 1.16 1.18 1.2
0 10 20 30 40 50 60
1.08 1.1 1.12 1.14 1.16 1.18 1.2-2
-1.5-1
-0.5 0
0.5
1.08 1.1 1.12 1.14 1.16 1.18 1.2W (GeV)W (GeV)
W (GeV)W (GeV)
W (GeV)W (GeV)
S11
S31
P11
P13
P31
P33
�⇡N = �4c1m2⇡ � 3g2Am
3⇡
16⇡2f2⇡MN
3M2
N �m2⇡p
4M2N �m2
⇡
arccosm⇡
2MN+m⇡ log
m⇡
MN
!
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σπN at O(p3) in covariant ChPT at in extended on-shell mass scheme :
Extract low energy constants (c1, c2, c3, c4) from O(p2) Lorentz covariant ChPT
Fits for several πN scattering data sets :c1 c2 c3 c4
KH �0.80(6) 1.12(13) �2.96(15) 2.00(7)
GW �1.00(4) 1.01(4) �3.04(2) 2.02(1)
EM �1.00(1) 0.58(3) �2.51(4) 1.77(2)<latexit sha1_base64="1aOPbLGE41vI9qqrxQcVCeull6Q=">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</latexit><latexit sha1_base64="1aOPbLGE41vI9qqrxQcVCeull6Q=">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</latexit><latexit sha1_base64="1aOPbLGE41vI9qqrxQcVCeull6Q=">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</latexit><latexit sha1_base64="1aOPbLGE41vI9qqrxQcVCeull6Q=">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</latexit>
Data sets of G. Washington Group :
σπN = 59(7)MeV
(unit: GeV-1)
Consistent with the result of CD LET approach!
G. Washington Group data set and O(p3) ChPT fit of πN scattering phase shift
Lattice QCD approaches
13
Lattice QCD approaches
Direct calculation of πN sigma term
Feynman-Hellmann theorem calculation
Formulation:
|tsnk-tsrc|, |tvtx-tsrc|
N N
Γ
N N
Γ3-point function on lattice:
Connected diagrams Disconnected diagram(Leading contribution of σπN) (strange content)
< N | qq | N > = < 0 | N (y,tsnk) (qq)(x,tvtx) N†(0,tsrc) | 0 >
< 0 | N (y,tsnk) N†(0,tsrc) | 0 >lim 2mN
⇒ Ratio of 3pt and 2pt functions
ZS : nonperturbative renormalization (µ = 2 GeV)
! 1
Lattice QCD : direct calculation
ZS
0
1
2
3
4
5
6
7
0 2 4 6 8 10 12 14 16
gS
s
∆t/a
∆t’=11∆t’=12∆t’=13∆t’=14∆t’=15∆t’=16
fit-0.4
-0.2
0
0.2
0.4
0.6
0 2 4 6 8 10 12 14 16S
s∆t/a
∆t’=11∆t’=12∆t’=13∆t’=14∆t’=15∆t’=16
fit
Mandatory techniques:
Noise method
Truncated solver method
(tvtx — tsrc)/a (tvtx — tsrc)/a
Operator improvement
…
(smearing, etc)
(for Dirac high modes)
(effectively ↑ statistics)
(need careful treatment, see next page)
Renormalization of qq and operator mixing
(qq)phys = Z0(qq)<latexit sha1_base64="XSDcutCuaHc4RIuQ7iwzsQ4YFAA=">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</latexit><latexit sha1_base64="XSDcutCuaHc4RIuQ7iwzsQ4YFAA=">AAACjXichVE7LwRRFP6M93jsopFoJjZkNXJWCBFEKCi9FmFlMzPuMjEvM7ObrI0/oNAqVCQiotXSaPwBhZ8gShKNwtnZSbyCczNzv/ud85373Xs11zT8gOihSqquqa2rb2iUm5pbWmPxtvZl38l7ukjrjul4q5rqC9OwRTowAlOsup5QLc0UK9rOdDm/UhCebzj2UlB0xYalbtlGztDVgKlsPJnMaKqn7PLoy5YynqW420V/Xx6X17KkfE7GE9RPYSg/QSoCCUQx58TPkcEmHOjIw4KAjYCxCRU+j3WkQHCZ20CJOY+REeYF9iGzNs9VgitUZnf4v8Wr9Yi1eV3u6YdqnXcx+fNYqaCH7umCnumOLumR3n7tVQp7lL0UedYqWuFmYwedi6//qiyeA2x/qP70HCCHkdCrwd7dkCmfQq/oC3tHz4ujCz2lXjqlJ/Z/Qg90yyewCy/62bxYOIbMD5D6ft0/wfJAf4rx/GBicip6igZ0oRtJvu9hTGIWc0jzvoe4wjVupJg0JI1JE5VSqSrSdOBLSDPvR7yWUA==</latexit><latexit sha1_base64="XSDcutCuaHc4RIuQ7iwzsQ4YFAA=">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</latexit><latexit sha1_base64="XSDcutCuaHc4RIuQ7iwzsQ4YFAA=">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</latexit>
(uu+ dd� 2ss)phys = Z8(uu+ dd� 2ss)<latexit sha1_base64="A6gPLWIjCJKutU1mLMYSd5XTGs0=">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</latexit><latexit sha1_base64="A6gPLWIjCJKutU1mLMYSd5XTGs0=">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</latexit><latexit sha1_base64="A6gPLWIjCJKutU1mLMYSd5XTGs0=">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</latexit><latexit sha1_base64="A6gPLWIjCJKutU1mLMYSd5XTGs0=">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</latexit>
Renormalizations of flavor singlet and nonsinglet are in general different:
Renormalizations of ss:
Divergence due to quark loop (mixing with identity operator)
(ss)phys =1
3
"(Z0 + 2Z8)(ss) + (Z0 � Z8)(uu+ dd) +
b0a3
+ · · ·#
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Connected diagram (Large)
Disconnected diagram (Small)
ss operator mixes with the large connected diagram and identity operator!
In Wilson-type fermion, Z0—Z8 ≠ 0 :
⇒ (ss)phys affected by the increase of statistical error due to subtraction
In chiral fermion (DW,overlap) with massless renormalization scheme, the trace of quark loop (disconnected diagram) vanishes ⇒ Z0 = Z8
⇒ No need of subtraction for qq operators!
JLQCD Collaboration, PRD 83, 114506 (2011); PRD 98, 054516 (2018)
Renormalizations of uu+dd: (uu+ dd)phys =2
3
"⇣Z0 +
1
2Z8
⌘(uu+ dd) + (Z0 � Z8)(ss) +
b0a3
+ · · ·#
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uu+dd operator is less affected since connected diagram is the largest
Lattice QCD : Feynman-Hellmann theorem approachOn lattice, one can artificially change the current quark mass (mq)
Feynman-Hellmann theorem:@mN
@mq= hN |qq|Ni
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M
[M
eV]
N
m [MeV]RGIud
M (Φ)N
β = 3.31β = 3.5
β = 3.61β = 3.7β = 3.8β = ∞
0 5 10 15 20 25 30 35 40
1200
800
900
1000
1100
N
RGIs
M (Φ)N
β = 3.31β = 3.5
β = 3.61β = 3.7β = 3.8β = ∞
m [MeV]
M
[M
eV]
100 110 120 130 140 150 160 170 180 190
1200
1100
1000
900
800
mud [MeV] ms [MeV]
mN [
MeV
]
mN [
MeV
]
BMW Collaboration, PRL 116, 172001 (2016)
Correct renormalization needed for Wilson-type quark (see next page)
Feynman-Hellmann theorem may be combined with ChPT :
Fit mud dependence of mN in ChPT with lattice data and take derivative
(see Lutz (2014), Ren (2015), Ling (2017))
Issue of renormalization in Feynman-Hellmann approach
C. Michael et al. (UKQCD Collaboration), NPB Proc. Suppl. 106, 293 (2002).
@(amN )
@mbval
= lim|tsnk�tsrc||txyz�tsrc|
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From Feynman-Hellmann theorem, we have
N N
Γ
N N
Γ
@(amN )
@mbsea
= �Nf lim|tsnk�tsrc||txyz�tsrc|
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and
mbsea = mA + amsea
<latexit sha1_base64="U1034GxSA7qkvfxKuCnAr3QA9VY=">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</latexit><latexit sha1_base64="U1034GxSA7qkvfxKuCnAr3QA9VY=">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</latexit><latexit sha1_base64="U1034GxSA7qkvfxKuCnAr3QA9VY=">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</latexit><latexit sha1_base64="U1034GxSA7qkvfxKuCnAr3QA9VY=">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</latexit>
mbval = mA + amval
<latexit sha1_base64="p4Vwe6oDLWv9dK4bgNQlslEFNzM=">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</latexit><latexit sha1_base64="p4Vwe6oDLWv9dK4bgNQlslEFNzM=">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</latexit><latexit sha1_base64="p4Vwe6oDLWv9dK4bgNQlslEFNzM=">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</latexit><latexit sha1_base64="p4Vwe6oDLWv9dK4bgNQlslEFNzM=">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</latexit>
N N N N
@mN
@mval=
@(amN )
@mbval
<latexit sha1_base64="LXAnRwVUjw0Fs/E+3N/6GmXDP5s=">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</latexit><latexit sha1_base64="LXAnRwVUjw0Fs/E+3N/6GmXDP5s=">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</latexit><latexit sha1_base64="LXAnRwVUjw0Fs/E+3N/6GmXDP5s=">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</latexit><latexit sha1_base64="LXAnRwVUjw0Fs/E+3N/6GmXDP5s=">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</latexit>
Connected : simple derivative of valence q mass
Disconnected : derivative of sea q mass have several terms!
Renormalization of quark mass:
@mN
@msea(1� amseaB �X) =
@(amN )
@mbsea
+ (amseaB +X)@(amN )
@mbval
�mNB<latexit sha1_base64="AZRFGJffklY78fyG+Z+pb2zNSMU=">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</latexit><latexit sha1_base64="AZRFGJffklY78fyG+Z+pb2zNSMU=">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</latexit><latexit sha1_base64="AZRFGJffklY78fyG+Z+pb2zNSMU=">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</latexit><latexit sha1_base64="AZRFGJffklY78fyG+Z+pb2zNSMU=">AAADJHicjVFNSxxBEK2ZaKKjiZt4CeQyuKysyC49EkgIBGRzCQTEr9UF1yw9ba829nzQ07tghvkD/gEPngwkIvkROXjJITfx4CX34NFALh6smR3QrPmqYaZfvar3prrbDaWINCFnhnlnYPDuvaFha2T0/oOxwsNHK1HQUYzXWSAD1XBpxKXweV0LLXkjVJx6ruSr7vartL7a5SoSgb+sd0K+7tFNX7QFoxqpVuFzs60oi5shVVpQaXutueRmFjeVZ0ecJolVdir0JmPX7Epjynpp9VmU0665qd/bvHUTa7rc7zONPv/r0qUyc6lg2a61CkVSJVnYt4GTgyLkMR8UDqEJGxAAgw54wMEHjVgChQifNXCAQIjcOsTIKUQiq3NIwEJtB7s4dlBkt/G7idlazvqYp55Rpmb4F4mvQqUNJXJKjsgF+UI+ke/k8o9eceaRzrKDq9vT8rA1tvt46ec/VR6uGrauVX+dWUMbnmezCpw9zJh0F6yn777bu1h6sViKJ8l7co7zH5Azcow78Ls/2IcFvrgPFl6A03/ct8HKTNVBvPC0OFvLr2IInsAElPG8n8EsvIZ5qAMzSsYbY9momx/Nr+aJedprNY1cMw6/hPntCrIazt8=</latexit>
B ⌘ @(ln a)
@mbsea
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X ⌘ @mA
@mbsea
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mA : additive mass renormalization (in Wilson-type fermion) (must be determined for each gauge ensemble)
(Note that lattice spacing depends also on )mbsea
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⇒ Mixing with valence quark contribution
(bare mass)
(consequence of additive mass renormalization)
(connected) (disconnected)
Both approaches seem robust…
Then what to do??
19
Road to the resolution of the puzzleCalculation of πN (ππ, NN, …) scattering phase shift(s) in lattice QCD
Input of Cheng-Dashen LET approach with Roy-Steiner analysis
Check the consistency with the direct calculation
⇒ HAL QCD method (see talks of T. Hatsuda, K. Sasaki)
What if consistent ?If yes :
If no :
Lattice QCD has trouble with exp. data
ChPT based extractions have problems
Road to the resolution of the puzzleCalculation of πN (ππ, NN, …) scattering phase shift(s) in lattice QCD
Input of Cheng-Dashen LET approach with Roy-Steiner analysis
Check the consistency with the direct calculation
⇒ HAL QCD method (see talks of T. Hatsuda, K. Sasaki)
What if consistent ?If yes :
If no :
Lattice QCD has trouble with exp. data
ChPT based extractions have problems
Issue with the convergence of ChPT?σπN has small correction in SU(3) ChPT
⇒ Did we overlook contribution beyond SU(3) ChPT?V. Bernard et al., Phys. Lett. B 389, 144 (1996)
Road to the resolution of the puzzleCalculation of πN (ππ, NN, …) scattering phase shift(s) in lattice QCD
Input of Cheng-Dashen LET approach with Roy-Steiner analysis
Check the consistency with the direct calculation
⇒ HAL QCD method (see talks of T. Hatsuda, K. Sasaki)
Direct measurement in high-energy QCD experiments?
The integration of the twist-3 quark distribution eq(x) gives the sigma term
⇒ Measure eu,d(x) in experiments to determine σπN
⇒ Measurement of es(x) may provide the first experimental <N|ss|N>
(Compete with the QCD sum rules based extraction from J-PARC exp., ask P. Gubler for detail)
What if consistent ?If yes :
If no :
Lattice QCD has trouble with exp. data
ChPT based extractions have problems
Issue with the convergence of ChPT?σπN has small correction in SU(3) ChPT
⇒ Did we overlook contribution beyond SU(3) ChPT?V. Bernard et al., Phys. Lett. B 389, 144 (1996)
• A review of πN sigma term and strange content. • An important puzzle in the calculations of σπN :
ChPT based phenomenological approach vs lattice QCD⇒ Do not agree, but both seem OK…
• The evaluation of <N|ss|N> on lattice requires a careful renormalization : consistent among modern lattice QCD works, with relatively small absolute value.
Summary
Future prospects:• Lattice calculation of ππ, πN, NN, πK, … phase shifts
will give a strong hint whether ChPT approach is OK or not.
• The high-energy experimental measurement of the twist-3 PDF eq(x) will unveil the true value of σπN.
• Could you give any other ideas?