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Register a new userThe quark contents of the nucleon and their implication for dark matter search
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We present results concerning the light and strange quark contents of the nucleon using $N_f=2+1+1$ flavours of maximally twisted mass fermions. The corresponding $sigma$-terms are casting light on the origin of the nucleon mass and their values are important to interpret experimental data from direct dark matter searches. We discuss our strategy to estimate systematic uncertainties arising in our computations. Our preliminary results for the $sigma-$terms read $sigma_{pi N} = 37(2.6)(24.7) mev$ and $sigma_s=28(8)(10) mev$. We present our recent final analysis of the $y_N$ parameter and found $y_N=0.135(46)$ including systematicscite{Alexandrou:2013nda}.
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The strange quark scalar content plays an important role in both the description of nucleon structure and in the determination of dark matter direct detection cross sections. As a measure of the strange-quark contribution to the nucleon mass, the strange-quark sigma term (sigma_s) provides important insight into the nature of mass generation in QCD. The phenomenological determination of sigma_s exhibits a wide range of variation, with values suggesting that the strange quark contributes anywhere between 0 and more than 30% of the nucleon mass. In the context of dark matter searches, coupled with relatively large Higgs coupling to strangeness, this variation dominates the uncertainty in predicted cross sections for a large class of dark matter models. Here we report on the recent results in lattice QCD, which are now giving a far more precise determination of sigma_s than can be inferred from phenomenology. As a consequence, the lattice determinations of sigma_s can now dramatically reduce the uncertainty in dark matter cross sections associated with the hadronic matrix elements.
We present a QCD calculation of the $u$, $d$ and $s$ scalar quark contents of nucleons based on $47$ lattice ensembles with $N_f = 2+1$ dynamical sea quarks, $5$ lattice spacings down to $0.054,text{fm}$, lattice sizes up to $6,text{fm}$ and pion masses down to $120,text{MeV}$. Using the Feynman-Hellmann theorem, we obtain $f^N_{ud} = 0.0405(40)(35)$ and $f^N_s = 0.113(45)(40)$, which translates into $sigma_{pi N}=38(3)(3),text{MeV}$, $sigma_{sN}=105(41)(37),text{MeV}$ and $y_N=0.20(8)(8)$ for the sigma terms and the related ratio, where the first errors are statistical and the second are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).
In the past few years, a lot of evidences have been accumulated, which indicate that the gluon polarization inside the nucleon is likely to be small at least at the low renormalization scales. On the other hand, the recent lattice QCD analyses suggest that the net orbital angular momentum carried by the quarks is nearly zero. There is also some indication noticed by Brodsky and Gardner based on the COMPASS observation of small single-spin asymmetry on the isoscalar deuteron target, that the gluon orbital angular momentum inside the nucleon is likely to be small. Naively combining all these observations, we are led to a rather embarrassing conclusion that the nucleon constituents altogether do not carry enough amount of angular momentum saturating the total nucleon spin. We show that this somewhat confused state of affairs can be cleared up only by paying careful attention to the scale dependencies of the nucleon spin decomposition.
We show that the canonical seesaw mechanism implemented by the $U(1)_{B-L}$ gauge symmetry provides two-component dark matter naturally. The seesaw scale that breaks $B-L$ defines a residual gauge symmetry to be $Z_6=Z_2otimes Z_3$, where $Z_2$ leads to the usual matter parity, while $Z_3$ is newly recognized, transforming quark fields nontrivially. The dark matter components -- that transform nontrivially under the matter parity and $Z_3$, respectively -- can gain arbitrary masses, despite the fact that the $Z_3$ dark matter may be heavier than the light quarks $u,d$. This dark matter setup can address the XENON1T anomaly recently observed and other observables, given that the dark matter masses are nearly degenerate, heavier than the electron and the $B-L$ gauge boson $Z$, as well as the fast-moving $Z_3$ dark matter has a large $B-L$ charge, while the $Z$ is viably below the beam dump experiment sensitive regime.
Quark line disconnected matrix elements of an operator, such as the axial current, are difficult to compute on the lattice. The standard method uses a stochastic estimator of the operator, which is generally very noisy. We discuss and develop further our alternative approach using the Feynman-Hellmann theorem which involves only evaluating two-point correlation functions. This is applied to computing the contribution of the quark spin to the nucleon and in particular for the strange quark. In this process we also pay particular attention to the development of an SU(3) flavour breaking expansion for singlet operators.
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